constants.js

var keyMapping = {
    81: {
        index: 0,
        pressed: false
    },
    65: {
        index: 1,
        pressed: false
    },
    90: {
        index: 2,
        pressed: false
    },
    87: {
        index: 3,
        pressed: false
    },
    83: {
        index: 4,
        pressed: false
    },
    88: {
        index: 5,
        pressed: false
    },
    69: {
        index: 6,
        pressed: false
    },
    68: {
        index: 7,
        pressed: false
    },
    67: {
        index: 8,
        pressed: false
    },
    82: {
        index: 9,
        pressed: false
    },
    70: {
        index: 10,
        pressed: false
    },
    86: {
        index: 11,
        pressed: false
    },
    84: {
        index: 12,
        pressed: false
    },
    71: {
        index: 13,
        pressed: false
    },
    66: {
        index: 14,
        pressed: false
    },
    89: {
        index: 15,
        pressed: false
    },
    72: {
        index: 16,
        pressed: false
    },
    78: {
        index: 17,
        pressed: false
    },
    85: {
        index: 18,
        pressed: false
    },
    74: {
        index: 19,
        pressed: false
    },
    77: {
        index: 20,
        pressed: false
    },
    73: {
        index: 21,
        pressed: false
    },
    75: {
        index: 22,
        pressed: false
    },
    188: {
        index: 23,
        pressed: false
    },
    79: {
        index: 24,
        pressed: false
    },
    76: {
        index: 25,
        pressed: false
    },
    190: {
        index: 26,
        pressed: false
    },
    80: {
        index: 27,
        pressed: false
    },
    186: {
        index: 28,
        pressed: false
    },
    191: {
        index: 29,
        pressed: false
    },
    32: {
        index: 30,
        pressed: false
    },
    8: {
        index: 31,
        pressed: false
    }
}
var all_text = 'compares pairs of languages from world atlas of language structures. statistical modeling of experimental physical laws is based on the probability density function of measured variables. it is expressed by experimental data via a kernel estimator. the kernel is determined objectively by the scattering of data during calibration of experimental setup. a physical law, which relates measured variables, is optimally extracted from experimental data by the conditional average estimator. it is derived directly from the kernel estimator and corresponds to a general nonparametric regression. the proposed method is demonstrated by the modeling of a return map of noisy chaotic data. in this example, the nonparametric regression is used to predict a future value of chaotic time series from the present one. the mean predictor error is used in the definition of predictor quality, while the redundancy is expressed by the mean square distance between data points. both statistics are used in a new definition of predictor cost function. from the minimum of the predictor cost function, a proper number of data in the model is estimated. we study a recently proposed formulation of overlap fermions at finite density. in particular we compute the energy density as a function of the chemical potential and the temperature. it is shown that overlap fermions with chemical potential reproduce the correct continuum behavior. we review recent progress in operator algebraic approach to conformal quantum field theory. our emphasis is on use of representation theory in classification theory. this is based on a series of joint works with r. longo. we prove a duality theorem for certain graded algebras and show by various examples different kinds of failure of tameness of local cohomology. this paper has been withdrawn by the authors. the investigation on the production of particles in slowly varying but extremely intense magnetic field in extended to the case of axions. the motivation is, as for some previously considered cases, the possibility that such kind of magnetic field may exist around very compact astrophysical objects. we investigate the bonding of h in o vacancies of zno using density functional calculations. we find that h is anionic and does not form multicenter bonds with zn in this compound. we develop rigorous, analytic techniques to study the behaviour of biased random walks on combs. this enables us to calculate exactly the spectral dimension of random comb ensembles for any bias scenario in the teeth or spine. two specific examples of random comb ensembles are discussed; the random comb with nonzero probability of an infinitely long tooth at each vertex on the spine and the random comb with a power law distribution of tooth lengths. we also analyze transport properties along the spine for these probability measures. a number of recently discovered protein structures incorporate a rather unexpected structural feature: a knot in the polypeptide backbone. these knots are extremely rare, but their occurrence is likely connected to protein function in as yet unexplored fashion. our analysis of the complete protein data bank reveals several new knots which, along with previously discovered ones, can shed light on such connections. in particular, we identify the most complex knot discovered to date in human ubiquitin hydrolase, and suggest that its entangled topology protects it against unfolding and degradation by the proteasome. knots in proteins are typically preserved across species and sometimes even across kingdoms. however, we also identify a knot which only appears in some transcarbamylases while being absent in homologous proteins of similar structure. the emergence of the knot is accompanied by a shift in the enzymatic function of the protein. we suggest that the simple insertion of a short dna fragment into the gene may suffice to turn an unknotted into a knotted structure in this protein. some of the means through which the possible presence of nearly deconfined quarks in neutron stars can be detected by astrophysical observations of neutron stars from their birth to old age are highlighted. we provide a description of the interpolating and sampling sequences on a space of holomorphic functions with a uniform growth restriction defined on finite riemann surfaces. we prove that the limit hypersurfaces of converging curvature flows are stable, if the initial velocity has a weak sign, and give a survey of the existence and regularity results. recent observational and theoretical advances concerning astronomical masers in star forming regions are reviewed. major masing species are considered individually and in combination. key results are summarized with emphasis on present science and future prospects. establishing that a signal of new physics is undoubtly supersymmetric requires not only the discovery of the supersymmetric partners but also probing their spins and couplings. we show that the sbottom spin can be probed at the cern large hadron collider using only angular correlations in sbottom pair production with subsequent decay of sbottoms into bottom quark plus the lightest neutralino, which allow us to distinguish a universal extra dimensional interpretation with a fermionic heavy bottom quark from supersymmetry with a bosonic bottom squark. we demonstrate that this channel provides a clear indication of the sbottom spin provided the sbottom production rate and branching ratio into bottom quark plus the lightest neutralino are sufficiently large to have a clear signal above standard model backgrounds. in trigonometric series terms all polyharmonic functions inside the unit disk are described. for such functions it is proved the existence of their boundary values on the unit circle in the space of hyperfunctions. the necessary and sufficient conditions are presented for the boundary value to belong to certain subspaces of the space of hyperfunctions. the density of states and energy spectrum of the gluon radiation are calculated for the color current of an expanding hydrodynamic skyrmion in the quark gluon plasma with a semiclassical method. results are compared with those in literatures. we present some numerical results obtained from a simple individual based model that describes clustering of organisms caused by competition. our aim is to show how, even when a deterministic description developed for continuum models predicts no pattern formation, an individual based model displays well defined patterns, as a consequence of fluctuations effects caused by the discrete nature of the interacting agents. in a previous paper, we showed how certain orientations of the edges of a graph g embedded in a closed oriented surface s can be understood as discrete spin structures on s. we then used this correspondence to give a geometric proof of the pfaffian formula for the partition function of the dimer model on g. in the present article, we generalize these results to the case of compact oriented surfaces with boundary. we also show how the operations of cutting and gluing act on discrete spin structures and how they change the partition function. these operations allow to reformulate the dimer model as a quantum field theory on surface graphs. an critical overview of the current state of research in turbulence in astrophysical disks. we analytically calculate to second order the correction to the asymptotic form of quasinormal frequencies of four dimensional schwarzschild black holes based on the monodromy analysis proposed by motl and neitzke. our results are in good agreement with those obtained from numerical calculation. the paper presents a survey of mathematical problems, techniques, and challenges arising in the thermoacoustic and photoacoustic tomography. this paper discusses the benefits of describing the world as information, especially in the study of the evolution of life and cognition. traditional studies encounter problems because it is difficult to describe life and cognition in terms of matter and energy, since their laws are valid only at the physical scale. however, if matter and energy, as well as life and cognition, are described in terms of information, evolution can be described consistently as information becoming more complex.   the paper presents eight tentative laws of information, valid at multiple scales, which are generalizations of darwinian, cybernetic, thermodynamic, psychological, philosophical, and complexity principles. these are further used to discuss the notions of life, cognition and their evolution. we explore the effect of an inhomogeneous mass density field on frequencies and wave profiles of torsional alfven oscillations in solar coronal loops. dispersion relations for torsional oscillations are derived analytically in limits of weak and strong inhomogeneities. these analytical results are verified by numerical solutions, which are valid for a wide range of inhomogeneity strength. it is shown that the inhomogeneous mass density field leads to the reduction of a wave frequency of torsional oscillations, in comparison to that of estimated from mass density at the loop apex. this frequency reduction results from the decrease of an average alfven speed as far as the inhomogeneous loop is denser at its footpoints. the derived dispersion relations and wave profiles are important for potential observations of torsional oscillations which result in periodic variations of spectral line widths. torsional oscillations offer an additional powerful tool for a development of coronal seismology. this paper has been withdrawn due to copyright reasons. this paper visualizes a knot reduction algorithm we study the notion of fagnano orbits for dual polygonal billiards. we used them to characterize regular polygons and we study the iteration of the developing map. we construct a simple thermodynamic model to describe the melting of a supported metal nanoparticle with a spherically curved free surface both with and without surface melting. we use the model to investigate the results of recent molecular dynamics simulations, which suggest the melting temperature of a supported metal particle is the same as that of a free spherical particle with the same surface curvature. our model shows that this is only the case when the contact angles of the supported solid and liquid particles are similar. this is also the case for the temperature at which surface melting begins. hourglass is the name given here to a formal isolated quantum system that can radiate. starting from a time when it defines the system it represents clearly and no radiation is present, it is given straightforward hamiltonian evolution. the question of what significance hourglasses have is raised, and this question is proposed to be more consequential than the measurement problem. how to effectively solve the eigen solutions of the nonlinear spinor field equation coupling with some other interaction fields is important to understand the behavior of the elementary particles. in this paper, we derive a simplified form of the eigen equation of the nonlinear spinor, and then propose a scheme to solve their numerical solutions. this simplified equation has elegant and neat structure, which is more convenient for both theoretical analysis and numerical computation. simple examples are constructed that show the entanglement of two qubits being both increased and decreased by interactions on just one of them. one of the two qubits interacts with a third qubit, a control, that is never entangled or correlated with either of the two entangled qubits and is never entangled, but becomes correlated, with the system of those two qubits. the two entangled qubits do not interact, but their state can change from maximally entangled to separable or from separable to maximally entangled. similar changes for the two qubits are made with a swap operation between one of the qubits and a control; then there are compensating changes of entanglement that involve the control. when the entanglement increases, the map that describes the change of the state of the two entangled qubits is not completely positive. combination of two independent interactions that individually give exponential decay of the entanglement can cause the entanglement to not decay exponentially but, instead, go to zero at a finite time. we describe the maximal torus and maximal unipotent subgroup of the picard variety of a proper scheme over a perfect field. paper withdrawn due to the possible error in numerical eigenfunction calculation we measured the correlation of the times between successive flaps of a flag for a variety of wind speeds and found no evidence of low dimensional chaotic behavior in the return maps of these times. we instead observed what is best modeled as random times determined by an exponential distribution. this study was done as an undergraduate experiment and illustrates the differences between low dimensional chaotic and possibly higher dimensional chaotic systems. this paper is concerned with a shape sensitivity analysis of a viscous incompressible fluid driven by stokes equations with nonhomogeneous boundary condition. the structure of shape gradient with respect to the shape of the variable domain for a given cost function is established by using the differentiability of a minimax formulation involving a lagrangian functional combining with function space parametrization technique or function space embedding technique. we apply an gradient type algorithm to our problem. numerical examples show that our theory is useful for practical purpose and the proposed algorithm is feasible. in this paper, we describe a new, systematic and explicit way of approximating solutions of mixed hyperbolic systems with constant coefficients satisfying a uniform lopatinski condition via different penalization approaches. in this paper we investigate the optimal control problem for a class of stochastic cauchy evolution problem with non standard boundary dynamic and control. the model is composed by an infinite dimensional dynamical system coupled with a finite dimensional dynamics, which describes the boundary conditions of the internal system. in other terms, we are concerned with non standard boundary conditions, as the value at the boundary is governed by a different stochastic differential equation. we study a loop of josephson junctions that is quenched through its critical temperature. for three or more junctions, symmetry breaking states can be achieved without thermal activation, in spite of the fact that the relaxation time is practically constant when the critical temperature is approached from above. the probability for these states decreases with quenching time, but the dependence is not allometric. for large number of junctions, cooling does not have to be fast. for this case, we evaluate the standard deviation of the induced flux. our results are consistent with the available experimental data. a quantum protocol is described which enables a user to send sealed messages and that allows for the detection of active eavesdroppers. we examine a class of eavesdropping strategies, those that make use of quantum operations, and we determine the information gain versus disturbance caused by these strategies. we demonstrate this tradeoff with an example and we compare this protocol to quantum key distribution, quantum direct communication, and quantum seal protocols. we investigate the formation of collisionless shocks along the spatial profile of a gaussian laser beam propagating in nonlocal nonlinear media. for defocusing nonlinearity the shock survives the smoothing effect of the nonlocal response, though its dynamics is qualitatively affected by the latter, whereas for focusing nonlinearity it dominates over filamentation. the patterns observed in a thermal defocusing medium are interpreted in the framework of our theory. efficient control of a laser welding process requires the reliable prediction of process behavior. a statistical method of field modeling, based on normalized rbfnn, can be successfully used to predict the spatiotemporal dynamics of surface optical activity in the laser welding process. in this article we demonstrate how to optimize rbfnn to maximize prediction quality. special attention is paid to the structure of sample vectors, which represent the bridge between the field distributions in the past and future. the parsimony score of a character on a tree equals the number of state changes required to fit that character onto the tree. we show that for unordered, reversible characters this score equals the number of tree rearrangements required to fit the tree onto the character. we discuss implications of this connection for the debate over the use of consensus trees or total evidence, and show how it provides a link between incongruence of characters and recombination. in this paper i describe a specialized algorithm for anisotropic diffusion determined by a field of transition rates. the algorithm can be used to describe some interesting forms of diffusion that occur in the study of proton motion in a network of hydrogen bonds. the algorithm produces data that require a nonstandard method of spectral analysis which is also developed here. finally, i apply the algorithm to a simple specific example. we propose and analyze a new method to produce single and entangled photons which does not require cavities. it relies on the collective enhancement of light emission as a consequence of the presence of entanglement in atomic ensembles. light emission is triggered by a laser pulse, and therefore our scheme is deterministic. furthermore, it allows one to produce a variety of photonic entangled states by first preparing certain atomic states using simple sequences of quantum gates. we analyze the feasibility of our scheme, and particularize it to: ions in linear traps, atoms in optical lattices, and in cells at room temperature. under some positivity assumptions, extension properties of rationally connected fibrations from a submanifold to its ambient variety are studied. given a family of rational curves on a complex projective manifold x inducing a covering family on a submanifold y with ample normal bundle in x, the main results relate, under suitable conditions, the associated rational connected fiber structures on x and on y. applications of these results include an extension theorem for mori contractions of fiber type and a classification theorem in the case y has a structure of projective bundle or quadric fibration. the purpose of this paper is to assess the statistical characterization of weighted networks in terms of the generalization of the relevant parameters, namely average path length, degree distribution and clustering coefficient. although the degree distribution and the average path length admit straightforward generalizations, for the clustering coefficient several different definitions have been proposed in the literature. we examined the different definitions and identified the similarities and differences between them. in order to elucidate the significance of different definitions of the weighted clustering coefficient, we studied their dependence on the weights of the connections. for this purpose, we introduce the relative perturbation norm of the weights as an index to assess the weight distribution. this study revealed new interesting statistical regularities in terms of the relative perturbation norm useful for the statistical characterization of weighted graphs. we discuss the asymptotic behaviour of models of lattice polygons, mainly on the square lattice. in particular, we focus on limiting area laws in the uniform perimeter ensemble where, for fixed perimeter, each polygon of a given area occurs with the same probability. we relate limit distributions to the scaling behaviour of the associated perimeter and area generating functions, thereby providing a geometric interpretation of scaling functions. to a major extent, this article is a pedagogic review of known results. the measurement of the flavor composition of the neutrino fluxes from astrophysical sources has been proposed as a method to study not only the nature of their emission mechanisms, but also the neutrino fundamental properties. it is however problematic to reconcile these two goals, since a sufficiently accurate understanding of the neutrino fluxes at the source is needed to extract information about the physics of neutrino propagation. in this work we discuss critically the expectations for the flavor composition and energy spectrum from different types of astrophysical sources, and comment on the theoretical uncertainties connected to our limited knowledge of their structure. we present a lohner type algorithm for the computation of rigorous bounds for solutions of ordinary differential equations and its derivatives with respect to initial conditions up to arbitrary order. as an application we prove the existence of multiple invariant tori around some elliptic periodic orbits for the pendulum equation with periodic forcing and for michelson system. we compute the loss of power in likelihood ratio tests when we test the original parameter of a probability density extended by the first lehmann alternative. the entanglement quantified by negativity of pure bipartite superposed states is studied. we show that if the entanglement is quantified by the concurrence two pure states of high fidelity to one another still have nearly the same entanglement. furthermore this conclusion can be guaranteed by our obtained inequality, and the concurrence is shown to be a continuous function even in infinite dimensions. the bounds on the negativity of superposed states in terms of those of the states being superposed are obtained. these bounds can find useful applications in estimating the amount of the entanglement of a given pure state. in this lecture series, i present the recent progress in our understanding of nuclear forces in terms of chiral effective field theory. in the first section of this paper we prove a theorem for the number of columns of a rectangular area that are identical to the given one. in the next section we apply this theorem to derive several combinatorial identities by counting specified subsets of a finite set. influence of hole shape on extraordinary optical transmission was investigated using hole arrays consisting of rectangular holes with different aspect ratio. it was found that the transmission could be tuned continuously by rotating the hole array. further more, a phase was generated in this process, and linear polarization states could be changed to elliptical polarization states. this phase was correlated with the aspect ratio of the holes. an intuitional model was presented to explain these results. this paper presents an experimental study and the lessons learned from the observation of the attackers when logged on a compromised machine. the results are based on a six months period during which a controlled experiment has been run with a high interaction honeypot. we correlate our findings with those obtained with a worldwide distributed system of lowinteraction honeypots. we study the relationship between transfinite diameter, chebyshev constant and wiener energy in the abstract linear potential analytic setting pioneered by choquet, fuglede and ohtsuka. it turns out that, whenever the potential theoretic kernel has the maximum principle, then all these quantities are equal for all compact sets. for continuous kernels even the converse statement is true: if the chebyshev constant of any compact set coincides with its transfinite diameter, the kernel must satisfy the maximum principle. an abundance of examples is provided to show the sharpness of the results. uniform measures are defined as the functionals on the space of bounded uniformly continuous functions that are continuous on bounded uniformly equicontinuous sets. if every cardinal has measure zero then every countably additive measure is a uniform measure. the functionals sequentially continuous on bounded uniformly equicontinuous sets are exactly uniform measures on the separable modification of the underlying uniform space. the fundamental knowledge on neutrinos acquired in the recent years open the possibility of applied neutrino physics. among it the automatic and non intrusive monitoring of nuclear reactor by its antineutrino signal could be very valuable to iaea in charge of the control of nuclear power plants. several efforts worldwide have already started. conditional independence models in the gaussian case are algebraic varieties in the cone of positive definite covariance matrices. we study these varieties in the case of bayesian networks, with a view towards generalizing the recursive factorization theorem to situations with hidden variables. in the case when the underlying graph is a tree, we show that the vanishing ideal of the model is generated by the conditional independence statements implied by graph. we also show that the ideal of any bayesian network is homogeneous with respect to a multigrading induced by a collection of upstream random variables. this has a number of important consequences for hidden variable models. finally, we relate the ideals of bayesian networks to a number of classical constructions in algebraic geometry including toric degenerations of the grassmannian, matrix schubert varieties, and secant varieties. we extend the calculable analytic approach to marginal deformations recently developed in open bosonic string field theory to open superstring field theory formulated by berkovits. we construct analytic solutions to all orders in the deformation parameter when operator products made of the marginal operator and the associated superconformal primary field are regular. we study interacting systems of linear brownian motions whose drift vector at every time point is determined by the relative ranks of the coordinate processes at that time. our main objective has been to study the long range behavior of the spacings between the brownian motions arranged in increasing order. for finitely many brownian motions interacting in this manner, we characterize drifts for which the family of laws of the vector of spacings is tight, and show its convergence to a unique stationary joint distribution given by independent exponential distributions with varying means. we also study one particular countably infinite system, where only the minimum brownian particle gets a constant upward drift, and prove that independent and identically distributed exponential spacings remain stationary under the dynamics of such a process. some related conjectures in this direction have also been discussed. advances in semiconductor technology are contributing to the increasing complexity in the design of embedded systems. architectures with novel techniques such as evolvable nature and autonomous behavior have engrossed lot of attention. this paper demonstrates conceptually evolvable embedded systems can be characterized basing on acausal nature. it is noted that in acausal systems, future input needs to be known, here we make a mechanism such that the system predicts the future inputs and exhibits pseudo acausal nature. an embedded system that uses theoretical framework of acausality is proposed. our method aims at a novel architecture that features the hardware evolability and autonomous behavior alongside pseudo acausality. various aspects of this architecture are discussed in detail along with the limitations. we relate a generic character sheaf on a disconnected reductive group with a character of a representation of the rational points of the group over a finite field extending a result known in the connected case. these notes are meant to provide a rapid introduction to triangulated categories. we start with the definition of an additive category and end with a glimps of tilting theory. some exercises are included. a simple application of the semipositivity. the corsika program, usually used to simulate extensive cosmic ray air showers, has been adapted to work in a water or ice medium. the adapted corsika code was used to simulate hadronic showers produced by neutrino interactions. the simulated showers have been used to study the spatial distribution of the deposited energy in the showers. this allows a more precise determination of the acoustic signals produced by ultra high energy neutrinos than has been possible previously. the properties of the acoustic signals generated by such showers are described. the effect of bias voltages on the statistical properties of rough surfaces has been studied using atomic force microscopy technique and its stochastic analysis. we have characterized the complexity of the height fluctuation of a rough surface by the stochastic parameters such as roughness exponent, level crossing, and drift and diffusion coefficients as a function of the applied bias voltage. it is shown that these statistical as well as microstructural parameters can also explain the macroscopic property of a surface. furthermore, the tip convolution effect on the stochastic parameters has been examined. the effect of etching time scale of glass surface on its statistical properties has been studied using atomic force microscopy technique. we have characterized the complexity of the height fluctuation of a etched surface by the stochastic parameters such as intermittency exponents, roughness, roughness exponents, drift and diffusion coefficients and find their variations in terms of the etching time. we study asymptotics of various euclidean geometric phenomena as the dimension tend to infinity. in the series of papers by ida, oda and park, the complete description of hawking radiation to the brane localized standard model fields from mini black holes in the low energy gravity scenarios are obtained. here we briefly review what we have learned in those papers. we establish an equivalent condition to the validity of the collatz conjecture, using elementary methods. we derive some conclusions and show several examples of our results. we also offer a variety of exercises, problems and conjectures. we introduce a new type of local and microlocal asymptotic analysis in algebras of generalized functions, based on the presheaf properties of those algebras and on the properties of their elements with respect to a regularizing parameter. contrary to the more classical frequential analysis based on the fourier transform, we can describe a singular asymptotic spectrum which has good properties with respect to nonlinear operations. in this spirit we give several examples of propagation of singularities through nonlinear operators. this paper has been withdrawn by the author due to some mistakes the existence and stability under linear perturbation of closed timelike curves in the spacetime associated to schwarzschild black hole pierced by a spinning string are studied. due to the superposition of the black hole, we find that the spinning string spacetime is deformed in such a way to allow the existence of closed timelike geodesics. the holographic bound in physics constrains the complexity of life. the finite storage capability of information in the observable universe requires the protein linguistics in the evolution of life. we find that the evolution of genetic code determines the variance of amino acid frequencies and genomic gc content among species. the elegant linguistic mechanism is confirmed by the experimental observations based on all known entire proteomes. we present a general strategy that allows a more flexible method for the construction of fully additive multipartite entanglement monotones than the ones so far reported in the literature of axiomatic entanglement measures. within this framework we give a proof of a conjecture of outstanding implications in information theory: the full additivity of the entanglement of formation. we present a genetic algorithm which is distributed in two novel ways: along genotype and temporal axes. our algorithm first distributes, for every member of the population, a subset of the genotype to each network node, rather than a subset of the population to each. this genotype distribution is shown to offer a significant gain in running time. then, for efficient use of the computational resources in the network, our algorithm divides the candidate solutions into pipelined sets and thus the distribution is in the temporal domain, rather that in the spatial domain. this temporal distribution may lead to temporal inconsistency in selection and replacement, however our experiments yield better efficiency in terms of the time to convergence without incurring significant penalties. in this work we study some general classes of pseudodifferential operators whose symbols are defined in terms of phase space estimates. we have observed reproducible fluctuations of the coulomb drag, both as a function of magnetic field and electron concentration, which are a manifestation of quantum interference of electrons in the layers. at low temperatures the fluctuations exceed the average drag, giving rise to random changes of the sign of the drag. the fluctuations are found to be much larger than previously expected, and we propose a model which explains their enhancement by considering fluctuations of local electron properties. we define an invariant of welded virtual knots from each finite crossed module by considering crossed module invariants of ribbon knotted surfaces which are naturally associated with them. we elucidate that the invariants obtained are non trivial by calculating explicit examples. we define welded virtual graphs and consider invariants of them defined in a similar way. systematic error in calculation of z for high redshift type ia supernovae could help explain unexpected luminosity values that indicate an accelerating rate of expansion of the universe. the thesis covers various aspects of quantum state transfer in permanently coupled spin systems. we prove that if a finite order knot invariant does not distinguish mutant knots, then the corresponding weight system depends on the intersection graph of a chord diagram rather than on the diagram itself. the converse statement is easy and well known. we discuss relationship between our results and certain lie algebra weight systems. microfluidic chips have been fabricated to study electrokinetic pumping generated by a low voltage ac signal applied to an asymmetric electrode array. a measurement procedure has been established and followed carefully resulting in a high degree of reproducibility of the measurements. depending on the ionic concentration as well as the amplitude of the applied voltage, the observed direction of the dc flow component is either forward or reverse. the impedance spectrum has been thoroughly measured and analyzed in terms of an equivalent circuit diagram. our observations agree qualitatively, but not quantitatively, with theoretical models published in the literature. a set of analog electronics boards for serial readout of silicon strip sensors was fabricated. a commercially available amplifier is mounted on a homemade hybrid board in order to receive analog signals from silicon strip sensors. also, another homemade circuit board is fabricated in order to translate amplifier control signals into a suitable format and to provide bias voltage to the amplifier as well as to the silicon sensors. we discuss technical details of the fabrication process and performance of the circuit boards we developed. this work is devoted to the strong unique continuation problem for second order parabolic equations with nonsmooth coefficients. introduction and bibliography have been revised. the authors reply to the comment of golub and lamoreaux. the experimental limit on the neutron electric dipole moment remains unchanged from that previously announced. we show that an unification of quantum mechanics and general relativity implies that there is a fundamental length in nature in the sense that no operational procedure would be able to measure distances shorter than the planck length. furthermore we give an explicit realization of an old proposal by anderson and finkelstein who argued that a fundamental length in nature implies unimodular gravity. finally, using hand waving arguments we show that a minimal length might be related to the cosmological constant which, if this scenario is realized, is time dependent. path integrals similar to those describing stiff polymers arise in the helfrich model for membranes. we show how these types of path integrals can be evaluated and apply our results to study the thermodynamics of a minority stripe phase in a bulk membrane. the fluctuation induced contribution to the line tension between the stripe and the bulk phase is computed, as well as the effective interaction between the two phases in the tensionless case where the two phases have differing bending rigidities. in these notes we formally describe the functionality of calculating valid domains from the bdd representing the solution space of valid configurations. the formalization is largely based on the clab configuration framework. we study the fundamental properties of curvature in groupoids within the framework of synthetic differential geometry. as is usual in synthetic differential geometry, its combinatorial nature is emphasized. in particular, the classical bianchi identity is deduced from its combinatorial one. in this paper we prove scalar and sample path large deviation principles for a large class of poisson cluster processes. as a consequence, we provide a large deviation principle for ergodic hawkes point processes. we consider the static maxwell system with an axially symmetric dielectric permittivity and construct complete systems of its solutions which can be used for analytic and numerical solution of corresponding boundary value problems. the special theory of relativity and the theory of the electron have had an interesting history together. originally the electron was studied in a non relativistic context and this opened up the interesting possibility that lead to the conclusion that the mass of the electron could be thought of entirely in electromagnetic terms without introducing inertial considerations. however the application of special relativity lead to several problems, both for an extended electron and the point electron. these inconsistencies have, contrary to popular belief not been resolved satisfactorily today, even within the context of quantum theory. nevertheless these and subsequent studies bring out the interesting result that special relativity breaks down within the compton scale or when the compton scale is not neglected. this again runs contrary to an uncritical notion that special relativity is valid for point particles. we prove a sharp lp estimate for a singular radon transform according to a size condition of its kernel, which is useful for extrapolation. we construct a quantum theory of free fermion field based on the generalized uncertainty principle using supersymmetry as a guiding principle. a supersymmetric field theory with a real scalar field and a majorana fermion field is given explicitly and we also find that the supersymmetry algebra is deformed from an usual one. we show that green function methods can be straightforwardly applied to nonlinear equations appearing as the leading order of a short time expansion. higher order corrections can be then computed giving a satisfactory agreement with numerical results. the relevance of these results relies on the possibility of fully exploiting a gradient expansion in both classical and quantum field theory granting the existence of a strong coupling expansion. having a green function in this regime in quantum field theory amounts to obtain the corresponding spectrum of the theory. we report that resonant response with a very high quality factor can be achieved in a planar metamaterial by introducing symmetry breaking in the shape of its structural elements, which enables excitation of dark modes, i.e. modes that are weakly coupled to free space. in this work we show that is possible to obtain total quantum zeno effect in an unstable systems for times larger than the correlation time of the bath. the effect is observed for some particular systems in which one can chose appropriate observables which frequent measurements freeze the system into the initial state. for a two level system in a squeezed bath one can show that there are two bath dependent observables displaying total zeno effect when the system is initialized in some particular states. we show also that these states are intelligent states of two conjugate observables associated to the electromagnetic fluctuations of the bath. reply to the comment of chao, he, and ma. in this paper, we compare several functors which take simplicial categories or model categories to complete segal spaces, which are particularly nice simplicial spaces which, like simplicial categories, can be considered to be models for homotopy theories. we then give a characterization, up to weak equivalence, of complete segal spaces arising from these functors. we obtain a set of generalized eigenvectors that provides a generalized spectral decomposition for a given unitary representation of a commutative, locally compact topological group. these generalized eigenvectors are functionals belonging to the dual space of a rigging on the space of square integrable functions on the character group. these riggings are obtained through suitable spectral measure spaces. it is shown that fermionic polar molecules or atoms in a bilayer optical lattice can undergo the transition to a state with circulating currents, which spontaneously breaks the time reversal symmetry. estimates of relevant temperature scales are given and experimental signatures of the circulating current phase are identified. related phenomena in bosonic and spin systems with ring exchange are discussed. we propose a new theoretical method for the calculation of the interaction energy between macromolecular systems at large distances. the method provides a linear scaling of the computing time with the system size and is considered as an alternative to the well known fast multipole method. its efficiency, accuracy and applicability to macromolecular systems is analyzed and discussed in detail. the som algorithm is very astonishing. on the one hand, it is very simple to write down and to simulate, its practical properties are clear and easy to observe. but, on the other hand, its theoretical properties still remain without proof in the general case, despite the great efforts of several authors. in this paper, we pass in review the last results and provide some conjectures for the future work. after the justification of the maximum entropy principle for equilibrium mechanical system from the principle of virtual work, i.e., the virtual work of microscopic forces on the elements of a mechanical system vanishes in thermodynamic equilibrium, we present in this paper an application of the same principle to dynamical systems out of equilibrium. the aim of this work is to justify a least action principle and the concurrent maximum path entropy principle for nonequilibrium thermodynamic systems. the paper deals with the study of labor market dynamics, and aims to characterize its equilibriums and possible trajectories. the theoretical background is the theory of the segmented labor market. the main idea is that this theory is well adapted to interpret the observed trajectories, due to the heterogeneity of the work situations. we discuss the recent proposal of implementing doubly special relativity in configuration space by means of finsler geometry. although this formalism leads to a consistent description of the dynamics of a particle, it does not seem to give a complete description of the physics. in particular, the finsler line element is not invariant under the deformed lorentz transformations of doubly special relativity. we study in detail some simple applications of the formalism. we discuss different arguments that have been raised against the viability of the big trip process, reaching the conclusions that this process can actually occur by accretion of phantom energy onto the wormholes and that it is stable and might occur in the global context of a multiverse model. we finally argue that the big trip does not contradict any holographic bounds on entropy and information. as the likely birthplaces of planets and an essential conduit for the buildup of stellar masses, inner disks are of fundamental interest in star and planet formation. studies of the gaseous component of inner disks are of interest because of their ability to probe the dynamics, physical and chemical structure, and gas content of this region. we review the observational and theoretical developments in this field, highlighting the potential of such studies to, e.g., measure inner disk truncation radii, probe the nature of the disk accretion process, and chart the evolution in the gas content of disks. measurements of this kind have the potential to provide unique insights on the physical processes governing star and planet formation. we construct a modification of the standard model which stabilizes the higgs mass against quadratically divergent radiative corrections, using ideas originally discussed by lee and wick in the context of a finite theory of quantum electrodynamics. the lagrangian includes new higher derivative operators. we show that the higher derivative terms can be eliminated by introducing a set of auxiliary fields; this allows for convenient computation and makes the physical interpretation more transparent. although the theory is unitary, it does not satisfy the usual analyticity conditions. students, after they leave our care, are called to solve the diverse problems of the world, so we should teach to increase transfer: the ability to apply fundamental principles to new problems and contexts. this ability is rare. the following pages are from a workshop for faculty on designing courses that promote transfer. i discuss two design principles: to name the transferable ideas and to illustrate them with examples from diverse subjects. the discussion uses dimensional reasoning as the example of a valuable transferable idea, illustrating it with three diverse examples. we define hecke operators on vector valued modular forms transforming with the weil representation associated to a discriminant form. we describe the properties of the corresponding algebra of hecke operators and study the action on modular forms. in this paper, we propose an achievable rate region for discrete memoryless interference channels with conferencing at the transmitter side. we employ superposition block markov encoding, combined with simultaneous superposition coding, dirty paper coding, and random binning to obtain the achievable rate region. we show that, under respective conditions, the proposed achievable region reduces to han and kobayashi achievable region for interference channels, the capacity region for degraded relay channels, and the capacity region for the gaussian vector broadcast channel. numerical examples for the gaussian case are given. we give axioms which characterize the local reidemeister trace for orientable differentiable manifolds. the local reidemeister trace in fixed point theory is already known, and we provide both uniqueness and existence results for the local reidemeister trace in coincidence theory. each of the two moving observers observes the relative velocity of the other. the two velocities should be equal and opposite. we have shown that this relativistic requirement is not fulfilled by lorentz transformation. we have also shown that the reason is that lorentz transformation is not associative. reciprocal symmetric transformation is associative and fulfills relativistic requirements. we study jamming in granular mixtures from the novel point of view of extended hydrodynamics. using a hard sphere binary mixture model we predict that a few large grains are expected to get caged more effectively in a matrix of small grains compared to a few small grains in a matrix of larger ones. a similar effect has been experimentally seen in the context of colloidal mixtures. it is shown that nonlocal interactions determine energy spectrum in isotropic turbulence at small reynolds numbers. it is also shown that for moderate reynolds numbers the bottleneck effect is determined by the same nonlocal interactions. role of the large and small scales covariance at the nonlocal interactions and in energy balance has been investigated. a possible hydrodynamic mechanism of the nonlocal solution instability at large scales has been briefly discussed. a quantitative relationship between effective strain of the nonlocal interactions and viscosity has been found. all results are supported by comparison with the data of experiments and numerical simulations. in view of the usefulness and importance of the kinetic equation in certain physical problems, the authors derive the explicit solution of a fractional kinetic equation of general character, that unifies and extends earlier results. further, an alternative shorter method based on a result developed by the authors is given to derive the solution of a fractional diffusion equation. this set of notes provides some additional explanatory material on the analytic proof of the finite generation of the canonical ring for a compact complex algebraic manifold of general type. in this paper, we discuss the observation of exclusive events using the dijet mass fraction as measured by the cdf collaboration at the tevatron. we compare the data to pomeron exchange inspired models as well as soft color interaction ones. we also provide the prediction on dijet mass fraction at the lhc using both exclusive and inclusive diffractive events. we introduce a new method for estimating the growth of various quantities arising in dynamical systems. we apply our method to polygonal billiards on surfaces of constant curvature. for instance, we obtain power bounds of degree two plus epsilon in length for the number of billiard orbits between almost all pairs of points in a planar polygon. standard game theory assumes that the structure of the game is common knowledge among players. we relax this assumption by considering extensive games where agents may be unaware of the complete structure of the game. in particular, they may not be aware of moves that they and other agents can make. we show how such games can be represented; the key idea is to describe the game from the point of view of every agent at every node of the game tree. we provide a generalization of nash equilibrium and show that every game with awareness has a generalized nash equilibrium. finally, we extend these results to games with awareness of unawareness, where a player i may be aware that a player j can make moves that i is not aware of, and to subjective games, where payers may have no common knowledge regarding the actual game and their beliefs are incompatible with a common prior. we improve a result of bennett concerning certain sequences involving sums of powers of positive integers. the performance of a quantum teleportation algorithm implemented on an ion trap quantum computer is investigated. first the algorithm is analyzed in terms of the teleportation fidelity of six input states evenly distributed over the bloch sphere. furthermore, a quantum process tomography of the teleportation algorithm is carried out which provides almost complete knowledge about the algorithm. an experiment is proposed to test the interference aspect of the quantum interference computer approach many quantization schemes rely on analogs of classical mechanics where the connections with classical mechanics are indirect. in this work i propose a new and direct connection between classical mechanics and quantum mechanics where the quantum mechanical propagator is derived from a variational principle. this principle allows a physical system to have imperfect information, i.e., there is incomplete knowledge of the physical state, and many paths are allowed. we give accurate estimates for the bond percolation critical probabilities on seven archimedean lattices, for which the critical probabilities are unknown, using an algorithm of newman and ziff. we outline a relationship between conformal field theories and spectral problems of ordinary differential equations, and discuss its generalisation to models related to classical lie algebras. the cosmological constant problem represents an evident tension between our present description of gravity and particle physics. many solutions have been proposed, but experimental tests are always difficult or impossible to perform and present phenomenological investigations focus only on possible relations with the dark energy, that is with the accelerating expansion rate of the contemporary universe. here i suggest that strange stars, if they exist, could represent an interesting laboratory to investigate this puzzle, since their equilibrium configuration is partially determined by the qcd vacuum energy density. we obtain explicit expressions for differential operators defining the action of the virasoro algebra on the space of univalent functions. we also obtain an explicit taylor decomposition for schwarzian derivative and a formula for the grunsky coefficients. we introduce the concept of casimir friction, i.e. friction due to quantum fluctuations. in this first article we describe the calculation of a constant torque, arising from the scattering of quantum fluctuations, on a dielectric rotating in an electromagnetic vacuum. we compute the picard group of the moduli stack of elliptic curves and its canonical compactification over general base schemes. we describe a method for obtaining analytic solutions corresponding to exact marginal deformations in open bosonic string field theory. for the photon marginal deformation we have an explicit analytic solution to all orders. our construction is based on a pure gauge solution where the gauge field is not in the hilbert space. we show that the solution itself is nevertheless perfectly regular. we study its gauge transformations and calculate some coefficients explicitly. finally, we discuss how our method can be implemented for other marginal deformations. in a series of recent papers, a new formalism has been developed that explains the inner structure of dark matter halos as collisionless, dissipationless systems assembled through mergers and accretion at the typical cosmological rate. nearby ellipticals are also collisionless, dissipationless systems assembling their mass through mergers, but contrarily to the former structures they do not continuously accrete external matter because they are shielded by their host halos. here we explore the idea that the infall of their own matter ejected within the halo on the occasion of a violent merger can play a role similar to external accretion in halos. the predicted stellar mass density profile fits the observed one, and the empirical total mass density profile is also recovered. in this article we present a pedagogical introduction of the main ideas and recent advances in the area of topological quantum computation. we give an overview of the concept of anyons and their exotic statistics, present various models that exhibit topological behavior, and we establish their relation to quantum computation. possible directions for the physical realization of topological systems and the detection of anyonic behavior are elaborated. we present a protocol for performing entanglement connection between pairs of atomic ensembles in the single excitation regime. two pairs are prepared in an asynchronous fashion and then connected via a bell measurement. the resulting state of the two remaining ensembles is mapped to photonic modes and a reduced density matrix is then reconstructed. our observations confirm for the first time the creation of coherence between atomic systems that never interacted, a first step towards entanglement connection, a critical requirement for quantum networking and long distance quantum communications. the grothendieck rings of finite dimensional representations of the basic classical lie superalgebras are explicitly described in terms of the corresponding generalised root systems. we show that they can be interpreted as the subrings in the weight group rings invariant under the action of certain groupoids called weyl groupoids. as an alternative to commonly used electrical methods, we have investigated the optical pumping of charged exciton complexes addressing impurity related transitions with photons of the appropriate energy. under these conditions, we demonstrate that the pumping fidelity can be very high while still maintaining a switching behavior between the different excitonic species. this mechanism has been investigated for single quantum dots of different size present in the same sample and compared with the direct injection of spectator electrons from nearby donors. we consider a social system of interacting heterogeneous agents with learning abilities, a model close to random field ising models, where the random field corresponds to the idiosyncratic willingness to pay. given a fixed price, agents decide repeatedly whether to buy or not a unit of a good, so as to maximize their expected utilities. we show that the equilibrium reached by the system depends on the nature of the information agents use to estimate their expected utilities. we introduce a new tool to study the spectral type of rank one transformations using the method of central limit theorem for trigonometric sums. we get some new applications. a spectroscopic method for staggered fermions based on thermodynamical considerations is proposed. the canonical partition functions corresponding to the different quark number sectors are expressed in the low temperature limit as polynomials of the eigenvalues of the reduced fermion matrix. taking the zero temperature limit yields the masses of the lowest states. the method is successfully applied to the goldstone pion and both dynamical and quenched results are presented showing good agreement with that of standard spectroscopy. though in principle the method can be used to obtain the baryon and dibaryon masses, due to their high computational costs such calculations are practically unreachable. a beautiful theorem due to j. l. f. bertrand concerning the laws of attraction that admit bounded closed orbits for arbitrarily chosen initial conditions is translated from french into english. some results on the discontinuity properties of the lempert function and the kobayashi pseudometric in the spectral ball are given. diese kurze einfuehrung in theorie und berechnung linearer rekurrenzen versucht, eine luecke in der literatur zu fuellen. zu diesem zweck sind viele ausfuehrliche beispiele angegeben.   this short introduction to theory and usage of linear recurrences tries to fill a gap in the literature by giving many extensive examples. we show equivalence of pure point diffraction and pure point dynamical spectrum for measurable dynamical systems build from locally finite measures on locally compact abelian groups. this generalizes all earlier results of this type. our approach is based on a study of almost periodicity in a hilbert space. it allows us to set up a perturbation theory for arbitrary equivariant measurable perturbations. we present a novel notion of stable objects in the derived category of coherent sheaves on a smooth projective variety. as one application we compactify a moduli space of stable bundles using genuine complexes. we study the whitham equations for all the higher order kdv equations. the whitham equations are neither strictly hyperbolic nor genuinely nonlinear. we are interested in the solution of the whitham equations when the initial values are given by a step function. the interaction of charges in nqed is discussed. it is shown that the relativistic correction have the same form as in the commutative case provided the weyl ordering rule is used. the main goal of this project is to research technical advances in order to enhance the possibility to develop narratives within immersive mediated environments. an important part of the research is concerned with the question of how a script can be written, annotated and realized for an immersive context. a first description of the main theoretical framework and the ongoing work and a first script example is provided. this project is part of the program for presence research, and it will exploit physiological feedback and computational intelligence within virtual reality. this article discusses the techniques used to select online promising events at high energy and high luminosity colliders. after a brief introduction, explaining some general aspects of triggering, the more specific implementation options for well established machines like the tevatron and large hadron collider are presented. an outlook on what difficulties need to be met is given when designing trigger systems at the super large hadron collider, or at the international linear collider the puzzle presented by the famous stumps of gilboa, new york, finds a solution in the discovery of two fossil specimens that allow the entire structure of these early trees to be reconstructed. we characterize convex cocompact subgroups of the mapping class group of a surface in terms of uniform convergence actions on the zero locus of the limit set. we also construct subgroups that act as uniform convergence groups on their limit sets, but are not convex cocompact. this paper deals with the problem of increasing the minimum distance of a linear code by adding one or more columns to the generator matrix. several methods to compute extensions of linear codes are presented. many codes improving the previously known lower bounds on the minimum distance have been found. withdrawn due to an incompleteness of the main results. we prove a wegner estimate for a large class of multiparticle anderson hamiltonians on the lattice. these estimates will allow us to prove anderson localization for such systems. a detailed proof of localization will be given in a subsequent paper. in this paper the motion of quantum particles with initial mass m is investigated. the quantum mechanics equation is formulated and solved. it is shown that the wave function contains the component which is depended on the gravitation fine structure constant an unified model of the universe, black holes, particles .... and beyond. we construct new families of spectral triples over quantum spheres, with a particular attention focused on the standard podles quantum sphere and twisted dirac operators. we define the notion of complex stratification by quasifolds and show that such spaces occur as complex quotients by certain nonclosed subgroups of tori associated to convex polytopes. the spaces thus obtained provide a natural generalization to the nonrational case of the notion of toric variety associated with a rational convex polytope. we prove the result stated in the title, which answers the equicharacteristic case of a question of vasconcelos. we consider a circulation system arising in turbulence modelling in fluid dynamics with unbounded eddy viscosities. various notions of weak solutions are considered and compared. we establish existence and regularity results. in particular we study the boundedness of weak solutions. we also establish an existence result for a classical solution a wireless network in which packets are broadcast to a group of receivers through use of a random access protocol is considered in this work. the relation to previous work on networks of interacting queues is discussed and subsequently, the stability and throughput regions of the system are analyzed and presented. a simple network of two source nodes and two destination nodes is considered first. the broadcast service process is analyzed assuming a channel that allows for packet capture and multipacket reception. in this small network, the stability and throughput regions are observed to coincide. the same problem for a network with n sources and m destinations is considered next. the channel model is simplified in that multipacket reception is no longer permitted. bounds on the stability region are developed using the concept of stability rank and the throughput region of the system is compared to the bounds. our results show that as the number of destination nodes increases, the stability and throughput regions diminish. additionally, a previous conjecture that the stability and throughput regions coincide for a network of arbitrarily many sources is supported for a broadcast scenario by the results presented in this work. in this paper we survey the computational time complexity of assorted simple stochastic game problems, and we give an overview of the best known algorithms associated with each problem. we systematically compute the gaussian average of wilson lines inherent in the color glass condensate, which provides useful formulae for evaluation of the scattering amplitude in the collision of a light projectile and a heavy target. this work considers the problem of transmitting multiple compressible sources over a network at minimum cost. the aim is to find the optimal rates at which the sources should be compressed and the network flows using which they should be transmitted so that the cost of the transmission is minimal. we consider networks with capacity constraints and linear cost functions. the problem is complicated by the fact that the description of the feasible rate region of distributed source coding problems typically has a number of constraints that is exponential in the number of sources. this renders general purpose solvers inefficient. we present a framework in which these problems can be solved efficiently by exploiting the structure of the feasible rate regions coupled with dual decomposition and optimization techniques such as the subgradient method and the proximal bundle method. comments on six papers published by s.p. anjali devi and r. kandasamy in heat and mass transfer, zamm, mechanics research communications, international communications in heat and mass transfer, communications in numerical methods in engineering, journal of computational and applied mechanics   in conclusion all the above papers are of very low quality, written without care and are partly or completely wrong. the theory of acoustic wave scattering by many small bodies is developed for bodies with impedance boundary condition. it is shown that if one embeds many small particles in a bounded domain, filled with a known material, then one can create a new material with the properties very different from the properties of the original material. moreover, these very different properties occur although the total volume of the embedded small particles is negligible compared with the volume of the original material. we study the phase diagram of quark matter and nuclear properties based on the strong coupling expansion of lattice qcd. both of baryon and finite coupling correction are found to have effects to extend the hadron phase to a larger mu direction relative to tc. in a chiral rmf model with logarithmic sigma potential derived in the strong coupling limit of lattice qcd, we can avoid the chiral collapse and normal and hypernuclei properties are well described. we show that the characters of all highest weight modules over an affine lie algebra with the highest weight away from the critical hyperplane are meromorphic functions in the positive half of cartan subalgebra, their singularities being at most simple poles at zeros of real roots. we obtain some information about these singularities. we derive explicit expressions for green functions and some related characteristics of the rashba and dresselhaus hamiltonians with a uniform magnetic field. i review discrete and continuum approaches to quantized gravity based on the covariant feynman path integral approach. this is a survey of some problems in geometric group theory which i find interesting. the problems are from different areas of group theory. each section is devoted to problems in one area. it contains an introduction where i give some necessary definitions and motivations, problems and some discussions of them. for each problem, i try to mention the author. if the author is not given, the problem, to the best of my knowledge, was formulated by me first. recently, bagno, garber and mansour studied a kind of excedance number on the complex reflection groups and computed its multidistribution with the number of fixed points on the set of involutions in these groups. in this note, we consider the similar problems in more general cases and make a correction of one result obtained by them. given a closed hyperbolic riemannian surface, the aim of the present paper is to describe an explicit construction of smooth deformations of the hyperbolic metric into finsler metrics that are not riemannian and whose properties are such that the classical riemannian results about entropy rigidity, marked length spectrum rigidity and boundary rigidity all fail to extend to the finsler category. the formation of ultracold molecules via stimulated emission followed by a radiative deexcitation cascade in the presence of a static electric field is investigated. by analyzing the corresponding cross sections, we demonstrate the possibility to populate the lowest rotational excitations via photoassociation. the modification of the radiative cascade due to the electric field leads to narrow rotational state distributions in the vibrational ground state. external fields might therefore represent an additional valuable tool towards the ultimate goal of quantum state preparation of molecules. it is shown that a locally geometrical structure of arbitrarily curved riemannian space is defined by a deformed group of its diffeomorphisms the entanglement fidelity provides a measure of how well the entanglement between two subsystems is preserved in a quantum process. by using a simple model we show that in some cases this quantity in its original definition fails in the measurement of the entanglement preserving. on the contrary, the modified entanglement fidelity, obtained by using a proper local unitary transformation on a subsystem, is shown to exhibit the behavior similar to that of the concurrence in the quantum evolution. we show that finite parallel transports of vectors in riemannian spaces, determined by the multiplication law in the deformed groups of diffeomorphisms, and sequences of infinitesimal parallel transports of vectors along geodesics are equivalent. we study langevin dynamics of a driven charged particle in the presence as well as in the absence of magnetic field. we discuss the validity of various work fluctuation theorems using different model potentials and external drives. we also show that one can generate an orbital magnetic moment in a nonequilibrium state which is absent in equilibrium. along a ricci flow solution on a closed manifold, we show that if ricci curvature is uniformly bounded from below, then a scalar curvature integral bound is enough to extend flow. moreover, this integral bound condition is optimal in some sense. impedance measurements provide a useful probe of the physics of bolometers and calorimeters. we describe a method for measuring the complex impedance of these devices. in previous work, stray impedances and readout electronics of the measurement apparatus have resulted in artifacts in the impedance data. the new technique allows experimenters to find an independent thevenin or norton equivalent circuit for each frequency. this method allows experimenters to easily isolate the device impedance from the effects of parasitic impedances and frequency dependent gains in amplifiers. two virtual link diagrams are homotopic if one may be transformed into the other by a sequence of virtual reidemeister moves, classical reidemeister moves, and self crossing changes. we recall the pure virtual braid group. we then describe the set of pure virtual braids that are homotopic to the identity braid. in the general context of complex data processing, this paper reviews a recent practical approach to the continuous wavelet formalism on the sphere. this formalism notably yields a correspondence principle which relates wavelets on the plane and on the sphere. two fast algorithms are also presented for the analysis of signals on the sphere with steerable wavelets. we show that the cobordism groups of negative codimensional folds maps contain direct sums of stable homotopy groups of thom spaces of vector bundles like the circle and the infinite dimensional projective space. we give geometrical invariants which detect these direct summands. we demonstrate the possibility of controlling the border between the quantum and the classical world by performing nonselective measurements on quantum systems. we consider a quantum harmonic oscillator initially prepared in a schroedinger cat state and interacting with its environment. we show that the environment induced decoherence transforming the cat state into a statistical mixture can be strongly inhibited by means of appropriate sequences of measurements. we report molecular dynamics simulations of the segregation of two overlapping chains in cylindrical confinement. we find that the entropic repulsion between the chains can be sufficiently strong to cause segregation on a time scale that is short compared to the one for diffusion. this result implies that entropic driving forces are sufficiently strong to cause rapid bacterial chromosome segregation. in the present work we investigate one possible variation on the usual static pulsars: the inclusion of rotation. we use a formalism proposed by hartle and thorne to calculate the properties of rotating pulsars with all possible compositions. all calculations were performed for zero temperature and also for fixed entropy equations of state. motivated by applications to quantum field theory we consider gibbs measures for which the reference measure is wiener measure and the interaction is given by a double stochastic integral and a pinning external potential. in order properly to characterize these measures through dlr equations, we are led to lift wiener measure and other objects to a space of configurations where the basic observables are not only the position of the particle at all times but also the work done by test vector fields. we prove existence and basic properties of such gibbs measures in the small coupling regime by means of cluster expansion. n the present work we investigate one possible variation on the usual electrically neutral pulsars: the inclusion of electric charge. we study the effect of electric charge in pulsars assuming that the charge distribution is proportional to the energy density. all calculations were performed for zero temperature and fixed entropy equations of state. a singular foliation on a complete riemannian manifold m is said to be riemannian if each geodesic that is perpendicular at one point to a leaf remains perpendicular to every leaf it meets. we prove that the regular leaves are equifocal, i.e., the end point map of a normal foliated vector field has constant rank. this implies that we can reconstruct the singular foliation by taking all parallel submanifolds of a regular leaf with trivial holonomy. in addition, the end point map of a normal foliated vector field on a leaf with trivial holonomy is a covering map. these results generalize previous results of the authors on singular riemannian foliations with sections. transcription regulation typically involves the binding of proteins over long distances on multiple dna sites that are brought close to each other by the formation of dna loops. the inherent complexity of the assembly of regulatory complexes on looped dna challenges the understanding of even the simplest genetic systems, including the prototypical lac operon. here we implement a scalable quantitative computational approach to analyze systems regulated through multiple dna sites with looping. our approach applied to the lac operon accurately predicts the transcription rate over five orders of magnitude for wild type and seven mutants accounting for all the combinations of deletions of the three operators. a quantitative analysis of the model reveals that the presence of three operators provides a mechanism to combine robust repression with sensitive induction, two seemingly mutually exclusive properties that are required for optimal functioning of metabolic switches. quantum transmissions of a free particle passing through a rectangular potential barrier with dissipation are studied using a path decomposition technique. dissipative processes strongly suppress the transmission probability at resonance just above the barrier resulting in an unexpected reduction of the mean traversal time through the potential barrier. given a finite set of lattice points, we compare its sumsets and lattice points in its dilated convex hulls. both of these are known to grow as polynomials. generally, the former are subsets of the latter. in this paper, we will see that sumsets occupy all the central lattice points in convex hulls, giving us a kind of approximation to lattice points in polytopes. we use a recently proved fluctuation theorem for the currents to develop the response theory of nonequilibrium phenomena. in this framework, expressions for the response coefficients of the currents at arbitrary orders in the thermodynamic forces or affinities are obtained in terms of the fluctuations of the cumulative currents and remarkable relations are obtained which are the consequences of microreversibility beyond onsager reciprocity relations. this paper is an introduction to the jet schemes and the arc space of an algebraic variety. we also introduce the nash problem on arc families. we discuss here the measurement of gravitomagnetism and frame dragging with lunar laser ranging, lageos and lares satellites, and gravity probe b. without abstract. we present a necessary and sufficient condition for a finite dimensional density matrix to be an extreme point of the convex set of density matrices with positive partial transpose with respect to a subsystem. we also give an algorithm for finding such extreme points and illustrate this by some examples. this paper introduces the concept of symbolic sensor as an extension of the smart sensor one. then, the links between the physical world and the symbolic one are introduced. the creation of symbols is proposed within the frame of the pretopology theory. in order to adapt the sensor to the measurement context, a learning process has been used to provide an adaptive interpretation of the measurement. finally, an example is presented in the case of a temperature measurement. we present a description of finite dimensional quantum entanglement, based on a study of the space of all convex decompositions of a given density matrix. on this space we construct a system of real polynomial equations describing separable states. we further study this system using statistical mechanical methods. finally, we apply our techniques to werner states of two qubits and obtain a sufficient criterion for separability. there is evidence for the existence of massive planets at orbital radii of several hundred au from their parent stars where the timescale for planet formation by core accretion is longer than the disc lifetime. these planets could have formed close to their star and then migrated outwards. we consider how the transfer of angular momentum by viscous disc interactions from a massive inner planet could cause significant outward migration of a smaller outer planet. we find that it is in principle possible for planets to migrate to large radii. we note, however, a number of effects which may render the process somewhat problematic. we prove some conditions on the existence of natural boundaries of dirichlet series. we show that generically the presumed boundary is the natural one. we also give an application of natural boundaries in determining asymptotic results. a unified treatment of schwinger parametrised feynman amplitudes is suggested which addresses vertices of arbitrary order on the same footing as propagators. contributions from distinct diagrams are organised collectively. the scheme is based on the continuous graph laplacian. the analogy to a classical statistical diffusion system of vector charges on the graph is explored. we consider a dynamical system of phantom scalar field under exponential potential in background of loop quantum cosmology. in our analysis, there is neither stable node nor repeller unstable node but only two saddle points, hence no big rip singularity. physical solutions always possess potential energy greater than magnitude of the negative kinetic energy. we found that the universe bounces after accelerating even in the domination of the phantom field. after bouncing, the universe finally enters oscillatory regime. in the framework of the lindblad theory for open quantum systems, we determine the degree of quantum decoherence of a harmonic oscillator interacting with a thermal bath. it is found that the system manifests a quantum decoherence which is more and more significant in time. we calculate also the decoherence time scale and analyze the transition from quantum to classical behaviour of the considered system. we present a lattice boltzmann algorithm based on an underlying free energy that allows the simulation of the dynamics of a multicomponent system with an arbitrary number of components. the thermodynamic properties, such as the chemical potential of each component and the pressure of the overall system, are incorporated in the model. we derived a symmetrical convection diffusion equation for each component as well as the navier stokes equation and continuity equation for the overall system. the algorithm was verified through simulations of binary and ternary systems. the equilibrium concentrations of components of binary and ternary systems simulated with our algorithm agree well with theoretical expectations. we prove the uniqueness of solutions of the ricci flow on complete noncompact manifolds with bounded curvatures using the de turck approach. as a consequence we obtain a correct proof of the existence of solution of the ricci harmonic flow on complete noncompact manifolds with bounded curvatures. tropical algebraic geometry offers new tools for elimination theory and implicitization. we determine the tropicalization of the image of a subvariety of an algebraic torus under any homomorphism from that torus to another torus. we prove that the average smooth renyi entropy rate will approach the entropy rate of a stationary, ergodic information source, which is equal to the shannon entropy rate for a classical information source and the von neumann entropy rate for a quantum information source. the paper contains critical comments to the paper mentioned in the title from the mathematical point of view we theoretically discuss how to tune the competition between forster transfer and spontaneous emission in a continuous and nondestructive fashion. the proposed approach is especially suitable for delicate biological systems like light harvesting complexes and fluorescent protein oligomers. we demonstrate that the manipulation of the density of photonic states at the emission frequency of the energy donor results in a change of the quantum efficiencies of the competing energy transfer and spontaneous emission processes. this change will be manifested in a modification of the donor and acceptor emission intensities. thus, by controlling the local density of photonic states forster coupled systems can be manipulated and analyzed without the need to physically separate donor and acceptor chromophores for individual analysis, which is of interest, for example, for oligomeric reef coral fluorescent proteins. higgs algebras are used to construct rotational hamiltonians. the correspondence between the spectrum of a triaxial rotor and the spectrum of a cubic higgs algebra is demonstrated. it is shown that a suitable choice of the parameters of the polynomial algebra allows for a precise identification of rotational properties. the harmonic limit is obtained by a contraction of the algebra, leading to a linear symmetry. a class of generalized complex polynomials of hermite type, suggested by a special magnetic schrodinger operator, is introduced and some related basic properties are discussed. we discuss the current conservation laws in sigma models based on a compact lie groups of the same dimensionality and connected to each other via pseudoduality transformations in two dimensions. we show that pseudoduality transformations induce an infinite number of nonlocal conserved currents on the pseudodual manifold. a closed riemannian manifold is said to have cross blocking if whenever distinct points p and q are at distance less than the diameter, all light rays from p can be shaded away from q with at most two point shades. similarly, a closed riemannian manifold is said to have sphere blocking if for each point p, all the light rays from p are shaded away from p by a single point shade. we prove that riemannian manifolds with cross and sphere blocking are isometric to round spheres. this paper has been withdrawn by the author in this paper we consider a correspondence between the holographic dark energy density and chaplygin gas energy density in frw universe. then we reconstruct the potential and the dynamics of the scalar field which describe the chaplygin cosmology. spherically symmetric transonic accretion of a fractal medium has been studied in both the stationary and the dynamic regimes. the stationary transonic solution is greatly sensitive to infinitesimal deviations in the outer boundary condition, but the flow becomes transonic and stable, when its evolution is followed through time. the evolution towards transonicity is more pronounced for a fractal medium than what is it for a continuum. the dynamic approach also shows that there is a remarkable closeness between an equation of motion for a perturbation in the flow, and the metric of an analogue acoustic black hole. the stationary inflow solutions of a fractal medium are as much stable under the influence of linearised perturbations, as they are for the fluid continuum. we give an especially simple proof of a theorem in graph theory that forms the key part of the solution to a problem in commutative algebra, on how to characterize the integral closure of a polynomial ring generated by quadratic monomials. we discuss two models for describing the behavior of matter at large densities and intermediate temperatures. in both models a softening of the equation of state takes place due to the appearance of new degrees of freedom. the first is a hadronic model in which the softening is due to chiral symmetry restoration. in the second model the softening is associated with the formation of clusters of quarks in the mixed phase. we show that both models allow a significant softening but, in the first case the bulk modulus is mainly dependent on the density, while in the mixed phase model it also strongly depends on the temperature. we also show that the bulk modulus is not vanishing in the mixed phase due to the presence of two conserved charges, the baryon and the isospin one. only in a small region of densities and temperatures the incompressibility becomes extremely small. finally we compare our results with recent analysis of heavy ion collisions at intermediate energies. skew critical problems occur in continuous and discrete nonholonomic lagrangian systems. they are analogues of constrained optimization problems, where the objective is differentiated in directions given by an apriori distribution, instead of tangent directions to the constraint. we show semiglobal existence and uniqueness for nondegenerate skew critical problems, and show that the solutions of two skew critical problems have the same contact as the problems themselves. also, we develop some infrastructure that is necessary to compute with contact order geometrically, directly on manifolds. this paper has been withdrawn by the author. this paper describes an approach for obtaining direct access to the attacked squares of sliding pieces without resorting to rotated bitboards. the technique involves creating four hash tables using the built in hash arrays from an interpreted, high level language. the rank, file, and diagonal occupancy are first isolated by masking the desired portion of the board. the attacked squares are then directly retrieved from the hash tables. maintaining incrementally updated rotated bitboards becomes unnecessary as does all the updating, mapping and shifting required to access the attacked squares. finally, rotated bitboard move generation speed is compared with that of the direct hash table lookup method. a computer simulation technique, suited to replicate real adsorption experiments, was applied to pure simulated silica in order to gain insight into the fractal regime of its surface. the previously reported experimental fractal dimension was closely approached and the hitherto uncharted lower limit of fractal surface behaviour is reported herein. the notion of a weyl module, previously defined for the untwisted affine algebras, is extended here to the twisted affine algebras. we describe an identification of the weyl modules for the twisted affine algebras with suitably chosen weyl modules for the untwisted affine algebras. this identification allows us to use known results in the untwisted case to compute the dimensions and characters of the weyl modules for the twisted algebras. the idea of graph compositions, which was introduced by a. knopfmacher and m. e. mays, generalizes both ordinary compositions of positive integers and partitions of finite sets. in their original paper they developed formulas, generating functions, and recurrence relations for composition counting functions for several families of graphs. here we show that some of the results involving compositions of bipartite graphs can be derived more easily using exponential generating functions. colouring sparse graphs under various restrictions is a theoretical problem of significant practical relevance. here we consider the problem of maximizing the number of different colours available at the nodes and their neighbourhoods, given a predetermined number of colours. in the analytical framework of a tree approximation, carried out at both zero and finite temperatures, solutions obtained by population dynamics give rise to estimates of the threshold connectivity for the incomplete to complete transition, which are consistent with those of existing algorithms. the nature of the transition as well as the validity of the tree approximation are investigated. for encyclopedia of complexist and system science. we describe methods to evaluate elementary logarithmic integrals. the integrand is the product of a rational function and a linear polynomial in ln x. the paper is devoted to classification problem of finite dimensional complex none lie filiform leibniz algebras. actually, the observations show there are two resources to get classification of filiform leibniz algebras. the first of them is naturally graded none lie filiform leibniz algebras and the another one is naturally graded filiform lie algebras. using the first resource we get two disjoint classes of filiform leibniz algebras. the present paper deals with the second of the above two classes, the first class has been considered in our previous paper. the algebraic classification here means to specify the representatives of the orbits, whereas the geometric classification is the problem of finding generic structural constants in the sense of algebraic geometry. our main effort in this paper is the algebraic classification. we suggest here an algebraic method based on invariants. utilizing this method for any given low dimensional case all filiform leibniz algebras can be classified. moreover, the results can be used for geometric classification of orbits of such algebras. we argue for a compositional semantics grounded in a strongly typed ontology that reflects our commonsense view of the world and the way we talk about it. assuming such a structure we show that the semantics of various natural language phenomena may become nearly trivial. we present a five dimensional global monopole within the framework of lyra geometry. also the gravitational field of the monopole solution has been considered. nonconvex functionals with spherical symmetry are studied. existence of one and radial symmetry of all global minimizers is shown with an approach based on convex relaxation. we present a proof for the gehring lemma in a metric measure space endowed with a doubling measure. as an application we show the self improving property of muckenhoupt weights. we are interested to the multifractal analysis of inhomogeneous bernoulli products which are also known as coin tossing measures. we give conditions ensuring the validity of the multifractal formalism for such measures. on another hand, we show that these measures can have a dense set of phase transitions. interaction between metal surface waves and periodic geometry of subwavelength structures is at the core of the recent but crucial renewal of interest in plasmonics. one of the most intriguing points is the observation of abnormal strong transmission through these periodic structures, which can exceed by orders of magnitude the classical transmission given by the filling factor of the plate. the actual paradigm is that this abnormal transmission arises from the periodicity, and then that such high transmission should disappear in random geometries. here, we show that extra energy can be coupled through the subwavelength structure by adding a controlled quantity of noise to the position of the apertures. this result can be modelled in the statistical framework of stochastic resonance. the evolution of the coupled energy with respect to noise gives access to the extra energy coupled at the surface of the subwavelength array. overlap fermions have an exact chiral symmetry on the lattice and are thus an appropriate tool for investigating the chiral and topological structure of the qcd vacuum. we study various chiral and topological aspects of quenched gauge field configurations. this includes the localization and chiral properties of the eigenmodes, the local structure of the ultraviolet filtered field strength tensor, as well as the structure of topological charge fluctuations. we conclude that the vacuum has a multifractal structure. when will the internet become aware of itself? in this note the problem is approached by asking an alternative question: can the internet cope with stress? by extrapolating the psychological difference between coping and defense mechanisms a distributed software experiment is outlined which could reject the hypothesis that the internet is not a conscious entity. by analyzing the relationships between a socioeconomical system modeled through evolutionary game theory and a physical system modeled through quantum mechanics we show how although both systems are described through two theories apparently different both are analogous and thus exactly equivalents. the extensions of quantum mechanics to statistical physics and information theory let us use some of their definitions for the best understanding of the behavior of economics and biology. the quantum analogue of the replicator dynamics is the von neumann equation. a system in where all its members are in nash equilibrium is equivalent to a system in a maximum entropy state. nature is a game in where its players compete for a common welfare and the equilibrium of the system that they are members. they act as a whole besides individuals like they obey a rule in where they prefer to work for the welfare of the collective besides the individual welfare. green and tao proved that the primes contains arbitrarily long arithmetic progressions. we show that, essentially the same proof leads to the following result: the primes in an short interval contains many arithmetic progressions of any given length. we study semiparametric efficiency bounds and efficient estimation of parameters defined through general moment restrictions with missing data. identification relies on auxiliary data containing information about the distribution of the missing variables conditional on proxy variables that are observed in both the primary and the auxiliary database, when such distribution is common to the two data sets. the auxiliary sample can be independent of the primary sample, or can be a subset of it. for both cases, we derive bounds when the probability of missing data given the proxy variables is unknown, or known, or belongs to a correctly specified parametric family. we find that the conditional probability is not ancillary when the two samples are independent. for all cases, we discuss efficient semiparametric estimators. an estimator based on a conditional expectation projection is shown to require milder regularity conditions than one based on inverse probability weighting. the stock market has been known to form homogeneous stock groups with a higher correlation among different stocks according to common economic factors that influence individual stocks. we investigate the role of common economic factors in the market in the formation of stock networks, using the arbitrage pricing model reflecting essential properties of common economic factors. we find that the degree of consistency between real and model stock networks increases as additional common economic factors are incorporated into our model. furthermore, we find that individual stocks with a large number of links to other stocks in a network are more highly correlated with common economic factors than those with a small number of links. this suggests that common economic factors in the stock market can be understood in terms of deterministic factors. the identification of the limiting factors in the dynamical behavior of complex systems is an important interdisciplinary problem which often can be traced to the spectral properties of an underlying network. by deriving a general relation between the eigenvalues of weighted and unweighted networks, here i show that for a wide class of networks the dynamical behavior is tightly bounded by few network parameters. this result provides rigorous conditions for the design of networks with predefined dynamical properties and for the structural control of physical processes in complex systems. the results are illustrated using synchronization phenomena as a model process. we demonstrate that bistability of the nuclear spin polarization in optically pumped semiconductor quantum dots is a general phenomenon possible in dots with a wide range of parameters. in experiment, this bistability manifests itself via the hysteresis behavior of the electron zeeman splitting as a function of either pump power or external magnetic field. in addition, our theory predicts that the nuclear polarization can strongly influence the charge dynamics in the dot leading to bistability in the average dot charge. this is an essay that considering the knowledge structure and language of a different nature, attempts to build on an explanation of the object of study and characteristics of the mathematical science. we end up with a learning cycle of mathematics and a paradigm for education, namely learn to structure. we consider a cubic nonlinear schroedinger equation with periodic potential. in a semiclassical scaling the nonlinear interaction of modulated pulses concentrated in one or several bloch bands is studied. the notion of closed mode systems is introduced which allows for the rigorous derivation of a finite system of amplitude equations describing the macroscopic dynamics of these pulses. the procedure has been developed for extracting homocharge and heterocharge currents from experimentally measured thermally stimulated depolarization currents of corona poled pvdf. application of different depolarization modes supplemented with the isothermal currents allowed to obtain such parameters of relaxation processes, as activation energies, characteristic frequencies and time constants. the existence of magnetosonic solitons in dusty plasmas is investigated. the nonlinear magnetohydrodynamic equations for a warm dusty magnetoplasma are thus derived. a solution of the nonlinear equations is presented. it is shown that, due to the presence of dust, static structures are allowed. this is in sharp contrast to the formation of the so called shocklets in usual magnetoplasmas. a comparatively small number of dust particles can thus drastically alter the behavior of the nonlinear structures in magnetized plasmas. i give a general review of the history of inflationary cosmology and of its present status. we present a systematic derivation of some definite integrals in the classical table of gradshteyn and ryzhik that can be reduced to the gamma function. this note elaborates the procedures involved in the derivation of breakup densities in nuclear fragmentation. it is stressed that the formalism employed in the analysis served only as a spectral fitting function and does not imply any specific reaction mechanism. we show that a quantum state may be represented as the sum of a joint probability and a complex quantum modification term. the joint probability and the modification term can both be observed in successive projective measurements. the complex modification term is a measure of measurement disturbance. a selective phase rotation is needed to obtain the imaginary part. this leads to a complex quasiprobability, the kirkwood distribution. we show that the kirkwood distribution contains full information about the state if the two observables are maximal and complementary. the kirkwood distribution gives a new picture of state reduction. in a nonselective measurement, the modification term vanishes. a selective measurement leads to a quantum state as a nonnegative conditional probability. we demonstrate the special significance of the schwinger basis. we argue that dark matter can be described by an interacting field theory with a mass parameter of the order of the proton mass and an interaction coupling of the order of the qed coupling. the aim of this work is to perform numerical simulations of the propagation of a laser in a plasma. at each time step, one has to solve a helmholtz equation in a domain which consists in some hundreds of millions of cells. to solve this huge linear system, one uses a iterative krylov method with a preconditioning by a separable matrix. the corresponding linear system is solved with a block cyclic reduction method. some enlightments on the parallel implementation are also given. lastly, numerical results are presented including some features concerning the scalability of the numerical method on a parallel architecture. we study resonances of multidimensional chaotic map dynamics. we use the calculus of variations to determine the additive forcing function that induces the largest response, that is, the greatest deviation from the unperturbed dynamics. we include the additional constraint that only select degrees of freedom be forced, corresponding to a very general class of problems in which not all of the degrees of freedom in an experimental system are accessible to forcing. we find that certain lagrange multipliers take on a fundamental physical role as the efficiency of the forcing function and the effective forcing experienced by the degrees of freedom which are not forced directly. furthermore, we find that the product of the displacement of nearby trajectories and the effective total forcing function is a conserved quantity. we demonstrate the efficacy of this methodology with several examples. there has been a great deal of debate surrounding the issue of whether it is possible for a single photon to exhibit nonlocality. a number of schemes have been proposed that claim to demonstrate this effect, but each has been met with significant opposition. the objections hinge largely on the fact that these schemes use unobservable initial states and so, it is claimed, they do not represent experiments that could actually be performed. here we show how it is possible to overcome these objections by presenting an experimentally feasible scheme that uses realistic initial states. furthermore, all the techniques required for photons are equally applicable to atoms. it should, therefore, also be possible to use this scheme to verify the nonlocality of a single massive particle. a category is described to which the cuntz semigroup belongs and as a functor into which it preserves inductive limits. we demonstrate that an experiment with recoilless resonant emission and absorption of tritium antineutrinos could have an important impact on our understanding of the origin of neutrino oscillations. the large deviations principles are established for a class of multidimensional degenerate stochastic differential equations with reflecting boundary conditions. the results include two cases where the initial conditions are adapted and anticipated. we investigate the electromagnetic field generated by a point charge moving along a helical trajectory inside a circular waveguide with conducting walls filled by homogeneous dielectric. the parts corresponding to the radiation field are separated and the formulae for the radiation intensity are derived for both te and tm waves. it is shown that the main part of the radiated quanta is emitted in the form of the te waves. various limiting cases are considered. the results of the numerical calculations show that the insertion of the waveguide provides an additional mechanism for tuning the characteristics of the emitted radiation by choosing the parameters of the waveguide and filling medium. we explicitly construct two classes of infinitly many commutative operators in terms of the deformed virasoro algebra. we call one of them local integrals and the other nonlocal one, since they can be regarded as elliptic deformations of the local and nonlocal integrals of motion obtained by v.bazhanov, s.lukyanov and al.zamolodchikov. we discuss a mechanism which generates a mass term for a scalar field in an expanding universe. the mass of this field turns out to be generated by the cosmological constant and can be naturally small if protected by a conformal symmetry which is however broken in the gravitational sector. the mass is comparable today to the hubble time. this scalar field could thus impact our universe today and for example be at the origin of a time variation of the couplings and masses of the parameters of the standard model. parallel transport of a connection in a smooth fibre bundle yields a functor from the path groupoid of the base manifold into a category that describes the fibres of the bundle. we characterize functors obtained like this by two notions we introduce: local trivializations and smooth descent data. this provides a way to substitute categories of functors for categories of smooth fibre bundles with connection. we indicate that this concept can be generalized to connections in categorified bundles, and how this generalization improves the understanding of higher dimensional parallel transport. we discuss threshold resummation in radiative and charmless semileptonic b decays. to deal with the large non perturbative effects, we introduce a model for nnll resummed form factors based on the analytic qcd coupling. by means of this model we can reproduce with good accuracy the experimental data. finally we briefly present an improved threshold resummed formula to deal with jets initiated by massive quarks as in the case of semileptonic charmed decays. in a very recent paper, m. rahman introduced a remarkable family of polynomials in two variables as the eigenfunctions of the transition matrix for a nontrivial markov chain due to m. hoare and m. rahman. i indicate here that these polynomials are bispectral. this should be just one of the many remarkable properties enjoyed by these polynomials. for several challenges, including finding a general proof of some of the facts displayed here the reader should look at the last section of this paper. we find actual evidence, relying upon vorticity time series taken in a high reynolds number atmospheric experiment, that to a very good approximation the surface boundary layer flow may be described, in a statistical sense and under certain regimes, as an advected ensemble of homogeneous turbulent systems, characterized by a lognormal distribution of fluctuating intensities. our analysis suggests that usual direct numerical simulations of homogeneous and isotropic turbulence, performed at moderate reynolds numbers, may play an important role in the study of turbulent boundary layer flows, if supplemented with appropriate statistical information concerned with the structure of large scale fluctuations. we propose a pedestrian review of the noncommutative standard model in its present state. monoatomic layers of graphite can be electrically contacted and used as building blocks for new promising devices. these experiment are today possible thanks to the fact that very thin graphite can be identified on a dielectric substrate using a simple optical microscope. we investigate the mechanism behind the strong visibility of graphite and we discuss the importance of the substrate and of the microcope objective used for the imaging. lunar laser ranging analysis, as regularly performed in the solar system barycentric frame, requires the presence of the gravitomagnetic term in the equation of motion at the strength predicted by general relativity. the same term is responsible for the lense thirring effect. any attempt to modify the strength of the gravitomagnetic interaction would have to do so in a way that does not destroy the fit to lunar ranging data and other observations. we prove that the displacement energy of a stable coisotropic submanifold is bounded away from zero if the ambient symplectic manifold is closed, rational and satisfies a mild topological condition. every action on a poisson manifold by poisson diffeomorphisms lifts to a hamiltonian action on its symplectic groupoid which has a canonically defined momentum map. we study various properties of this momentum map as well as its use in reduction. supersolidity of glasses is explained as a property of an unusual state of condensed matter. this state is essentially different from both normal and superfluid solid states. the mechanism of the phenomenon is the transfer of mass by tunneling two level systems. we explore the possibility that a magnetar may owe its strong magnetic field to a magnetized core which, as indicated by certain equations of state, may form due to phase transitions at high density mediated by strong interaction within a sufficiently massive neutron star. we argue that the field derived from such a core could explain several inferred evolutionary behaviors of magnetars. a rule to assign a physical meaning to lagrange multipliers is discussed. examples from mechanics, statistical mechanics and quantum mechanics are given. we study a simple geometric model of transportation facility that consists of two points between which the travel speed is high. this elementary definition can model shuttle services, tunnels, bridges, teleportation devices, escalators or moving walkways. the travel time between a pair of points is defined as a time distance, in such a way that a customer uses the transportation facility only if it is helpful.   we give algorithms for finding the optimal location of such a transportation facility, where optimality is defined with respect to the maximum travel time between two points in a given set. a manifestly covariant expression for the current matrix elements of three quark bound systems is derived in the framework of the point form relativistic hamiltonian dynamics. the relativistic impulse approximation is assumed in the model. a critical comparison is made with other expressions usually given in the literature. the besicovitch pseudodistance measures the relative size of the set of points where two functions take different values; the quotient space modulo the induced equivalence relation is endowed with a natural metric. we study the behavior of cellular automata in the new topology and show that, under suitable additional hypotheses, they retain certain properties possessed in the usual product topology; in particular, that injectivity still implies surjectivity. the act of bluffing confounds game designers to this day. the very nature of bluffing is even open for debate, adding further complication to the process of creating intelligent virtual players that can bluff, and hence play, realistically. through the use of intelligent, learning agents, and carefully designed agent outlooks, an agent can in fact learn to predict its opponents reactions based not only on its own cards, but on the actions of those around it. with this wider scope of understanding, an agent can in learn to bluff its opponents, with the action representing not an illogical action, as bluffing is often viewed, but rather as an act of maximising returns through an effective statistical optimisation. by using a tee dee lambda learning algorithm to continuously adapt neural network agent intelligence, agents have been shown to be able to learn to bluff without outside prompting, and even to learn to call each others bluffs in free, competitive play. the laws of thermodynamics provide a clear concept of the temperature for an equilibrium system in the continuum limit. meanwhile, the equipartition theorem allows one to make a connection between the ensemble average of the kinetic energy and the uniform temperature. when a system or its environment is far from equilibrium, however, such an association does not necessarily apply. in small systems, the regression hypothesis may not even apply. herein, we show that in small nonequilibrium systems, the regression hypothesis still holds though with a generalized definition of the temperature. the latter must now be defined for each such manifestation. a study of gamma rays produced when stars collapse or collide reveals details of the explosion mechanism, particularly the role of magnetic fields. a covariant gauge independent derivation of the generalized dispersion relation of electromagnetic waves in a medium with local and linear constitutive law is presented. a generalized photon propagator is derived. for maxwell constitutive tensor, the standard light cone structure and the standard feynman propagator are reinstated. the electromagnetic field inside a cubic cavity filled up with a linear magnetodielectric medium and in the presence of external charges is quantized by modelling the magnetodielectric medium with two independent quantum fields. electric and magnetic polarization densities of the medium are defined in terms of the ladder operators of the medium and eigenmodes of the cavity. maxwell and constitutive equations of the medium together with the equation of motion of the charged particles have been obtained from the heisenberg equations using a minimal coupling scheme. spontaneous emission of a two level atom embedded in a magnetodielectric medium is calculated in terms of electric and magnetic susceptibilities of the medium and the green function of the cubic cavity as an application of the model. this document describes the qspn, the routing discovery algorithm used by netsukuku. through a deductive analysis the main proprieties of the qspn are shown. moreover, a second version of the algorithm, is presented. we present the abnormal netsukuku domain name anarchy system. andna is the distributed, non hierarchical and decentralised system of hostname management used in the netsukuku network. integrated light in direct excitation and energy transfer luminescence has been investigated. in the investigations reported here, monomolecular centers were taken into account. it was found that the integrated light is equal to the product of generation rate and time of duration of excitation pulse for both direct excitation and energy transfer luminescence. we prove a central limit theorem with aassumptions which are many weak than classical conditions we study the spectrum of the even parity excitations of the nucleon in quenched lattice qcd. we extend our earlier analysis by including an expanded basis of nucleon interpolating fields, increasing the physical size of the lattice, including more configurations to enhance statistics and probing closer to the chiral limit. with a review of world lattice data, we conclude that there is little evidence of the roper resonance in quenched lattice qcd. we show both theoretically and experimentally that the magnetization density accompanying ultrafast excitation of a semiconductor with circular polarized light varies rapidly enough to produce a detectable thz field. one of the basic assumptions of the string model is that as a result of a dis in nucleus a single string arises, which then breaks into hadrons. however the pomeron exchange considered in this work, leads to the production of two strings in the one event. the hadrons produced in these events have smaller formation lengths, than those with the same energy produced in the single string events. as a consequence, they undergo more substantial absorption in the nuclear matter. we compute the lower and upper bounds for which the planar front speed propagation is valid. to take into account delay or memory effects in the front propagation, an hyperbolic differential equation is introduced as an extension of the model. karolyhazy uncertainty relation, which can be viewed also as a relation between uv and ir scales in the framework of an effective quantum field theory satisfying a black hole entropy bound, strongly favors the existence of dark energy with its observed value. here we estimate the dynamics of dark energy predicted by the karolyhazy relation during the cosmological evolution of the universe. water vapour inside the mass comparator enclosure is a critical parameter. in fact, fluctuations of this parameter during mass weighing can lead to errors in the determination of an unknown mass. to control that, a proposal method is given and tested. preliminary results of our observation of water vapour sorption and desorption processes from walls and mass standard are reported. a simple but general microscopic mechanism to understand the interplay between the electric and magnetic degrees of freedom is developed. within this mechanism, the magnetic structure generates an electric current which induce an counterbalance electric current from the spin orbital coupling. when the magnetic structure is described by a single order parameter, the electric polarization is determined by the single spin orbital coupling parameter, and the material is predicted to be a half insulator. this mechanism provides a simple estimation of the value of ferroelectricity and sets a physical limitation as well. we study infinite tree and ultrametric matrices, and their action on the boundary of the tree. for each tree matrix we show the existence of a symmetric random walk associated to it and we study its green potential. we provide a representation theorem for harmonic functions that includes simple expressions for any increasing harmonic function and the martin kernel. in the boundary, we construct the markov kernel whose green function is the extension of the matrix and we simulate it by using a cascade of killing independent exponential random variables and conditionally independent uniform variables. for ultrametric matrices we supply probabilistic conditions to study its potential properties when immersed in its minimal tree matrix extension. we elaborate a theory for the modeling of concepts using the mathematical structure of quantum mechanics. concepts are represented by vectors in the complex hilbert space of quantum mechanics and membership weights of items are modeled by quantum weights calculated following the quantum rules. we apply this theory to model the disjunction of concepts and show that experimental data of membership weights of items with respect to the disjunction of concepts can be modeled accurately. it is the quantum effects of interference and superposition, combined with an effect of context, that are at the origin of the effects of overextension and underextension observed as deviations from a classical use of the disjunction. we put forward a graphical explanation of the effects of overextension and underextension by interpreting the quantum model applied to the modeling of the disjunction of concepts. we define the alternating sign matrix polytope as the convex hull of nxn alternating sign matrices and prove its equivalent description in terms of inequalities. this is analogous to the well known result of birkhoff and von neumann that the convex hull of the permutation matrices equals the set of all nonnegative doubly stochastic matrices. we count the facets and vertices of the alternating sign matrix polytope and describe its projection to the permutohedron as well as give a complete characterization of its face lattice in terms of modified square ice configurations. furthermore we prove that the dimension of any face can be easily determined from this characterization. we present a definition of time measurement based on high energy photons and the fundamental length scale, and show that, for macroscopic time, it is in accord with the lorentz transformation of special relativity. to do this we define observer in a different way than in special relativity. we have developed a linearization method to investigate the subthreshold oscillatory behaviors in nonlinear autonomous systems. by considering firstly the neuronal system as an example, we show that this theoretical approach can predict quantitatively the subthreshold oscillatory activities, including the damping coefficients and the oscillatory frequencies which are in good agreement with those observed in experiments. then we generalize the linearization method to an arbitrary autonomous nonlinear system. the detailed extension of this theoretical approach is also presented and further discussed. we describe the geometric and dynamical properties of expansive markov systems. complex evolving systems such as the biosphere, ecosystems and societies exhibit sudden collapses, for reasons that are only partially understood. here we study this phenomenon using a mathematical model of a system that evolves under darwinian selection and exhibits the spontaneous growth, stasis and collapse of its structure. we find that the typical lifetime of the system increases sharply with the diversity of its components or species. we also find that the prime reason for crashes is a naturally occurring internal fragility of the system. this fragility is captured in the network organizational character and is related to a reduced multiplicity of pathways between its components. this work suggests new parameters for understanding the robustness of evolving molecular networks, ecosystems, societies, and markets. actual organizations, in particular the ones which operate in evolving and distributed environments, need advanced frameworks for the management of the knowledge life cycle. these systems have to be based on the social relations which constitute the pattern of collaboration ties of the organization. we demonstrate here, with the aid of a model taken from the theory of graphs, that it is possible to provide the conditions for an effective knowledge management. a right way could be to involve the actors with the highest betweeness centrality in the generation of discussion groups. this solution allows the externalization of tacit knowledge, the preservation of knowledge and the raise of innovation processes. we study, in the framework of open systems, the entanglement generation of two independent uniformly accelerated atoms in interaction with the vacuum fluctuations of massless scalar fields subjected to a reflecting plane boundary. we demonstrate that, with the presence of the boundary, the accelerated atoms exhibit distinct features from static ones in a thermal bath at the corresponding unruh temperature in terms of the entanglement creation at the neighborhood of the initial time. in this sense, accelerated atoms in vacuum do not necessarily have to behave as if they were static in a thermal bath at the unruh temperature. a quick overview is provided on the current development of the wp metric geometry. this article provides a formalism making it possible to manage the solutions of the direct and inverse kinematic models of the fully parallel manipulators. we introduce the concept of working modes to separate the solutions from the opposite geometrical model. then, we define, for each working mode, the aspects of these manipulators. to separate the solutions from the direct kinematics model, we introduce the concept of characteristic surfaces. then, we define the uniqueness domains, as being the greatest domains of the workspace in which there is unicity of solutions. the principal applications of this work are the design, the trajectory planning. using only a single tracking satellite capable of only range measurements to an orbiting object in an unknown keplerian orbit, it is theoretically possible to calculate the orbit and a current state vector. in this paper we derive an algorithm that can perform this calculation. we consider simple cusp algebras, that is certain subalgebras of the algebra of holomorphic functions on a disk that are annihilated by some distributions living on a singleton. we determine when these algebras can be holized in two dimensions, and when these holizations are globally biholomorphic. this paper, third in the series on indian tradition of physics, describes conceptions of the cosmos with ideas that are clearly spelt out in texts such as yoga vasishtha.in particular, the conception of multiple universes that occurs often in this text will be examined in the framework of the indian physics. the other surprising concepts that are discussed include flow of time and its variability with respect to different observers, and the possibility of passage across universes. a method based on bayesian neural networks and genetic algorithm is proposed to control the fermentation process. the relationship between input and output variables is modelled using bayesian neural network that is trained using hybrid monte carlo method. a feedback loop based on genetic algorithm is used to change input variables so that the output variables are as close to the desired target as possible without the loss of confidence level on the prediction that the neural network gives. the proposed procedure is found to reduce the distance between the desired target and measured outputs significantly. the purpose of this paper is to study the problem of estimating a compactly supported density of probability from noisy observations of its moments. in fact, we provide a statistical approach to the famous hausdorff classical moment problem. we prove an upper bound and a lower bound on the rate of convergence of the mean squared error showing that the considered estimator attains minimax rate over the corresponding smoothness classes. i exemplify part of my recent work on the upper halfplane. we propose a scheme which implements a controllable change of the state of the target spin qubit in such a way that both the control and the target spin qubits remain in their ground states. the interaction between the two spins is mediated by an auxiliary spin, which can transfer to its excited state. our scheme suggests a possible relationship between the gate and adiabatic quantum computation. we show that in the accelerating universe the generalized second law of thermodynamics holds only in the case where the enveloping surface is the apparent horizon, but not in the case of the event horizon. the present analysis relies on the most recent sne ia events, being model independent. our study might suggest that event horizon is not a physical boundary from the point of view of thermodynamics. this paper has been withdrawn by the author due to essential mistakes in some previous versions. it is about the uniqueness of the iwasawa decomposition. internet worms cause billions of dollars in damage yearly, affecting millions of users worldwide. for countermeasures to be deployed timeously, it is necessary to use an automated system to detect the spread of a worm. this paper discusses a method of determining the presence of a worm, based on routing information currently available from internet routers. an autoencoder, which is a specialized type of neural network, was used to detect anomalies in normal routing behavior. the autoencoder was trained using information from a single router, and was able to detect both global instability caused by worms as well as localized routing instability. we give a new proof of the classical result due to rodney y. sharp and peter vamos on the dimension of tensor product of a finite number of field extensions of a given field. we study the relative motion of nearby free test particles in cosmological spacetimes, such as the flrw and ltb models. in particular, the influence of spatial inhomogeneities on local tidal accelerations is investigated. the implications of our results for the dynamics of the solar system are briefly discussed. that is, on the basis of the models studied in this paper, we estimate the tidal influence of the cosmic gravitational field on the orbit of the earth around the sun and show that the corresponding temporal rate of variation of the astronomical unit is negligibly small. with the knowledge of diffractive parton densities extracted from hera data, we discuss the observation of exclusive events using the dijet mass fraction as measured by the cdf collaboration at the tevatron. in particular the impact of the gluon density uncertainty is analysed. some prospects are given for diffractive physics at the lhc. we measure the fluctuations of the position of a silica bead trapped by an optical tweezers during the aging of a laponite suspension. we find that the effective temperature is equal to the bath temperature. we consider the asymptotic behaviour of the solution of one dimensional stochastic differential equations and langevin equations in periodic backgrounds with zero average. we prove that in several such models, there is generically a non vanishing asymptotic velocity, despite of the fact that the average of the background is zero. this paper has been withdrawn abstract: this paper has been withdrawn by the author due to the publication. in this paper, we propose a way of assigning static type information to unmarshalling functions and we describe a verification technique for unmarshalled data that preserves the execution safety provided by static type checking. this technique, whose correctness is proven, relies on singleton types whose values are transmitted to unmarshalling routines at runtime, and on an efficient checking algorithm able to deal with sharing and cycles. in this paper we present a unifying approach to study the homotopy type of several complexes arising from forests. we show that this method applies uniformly to many complexes that have been extensively studied. we study the horofunction boundary of an artin group of dihedral type with its word metric coming from either the usual artin generators or the dual generators. in both cases, we determine the horoboundary and say which points are busemann points, that is the limits of geodesic rays. in the case of the dual generators, it turns out that all boundary points are busemann points, but this is not true for the artin generators. we also characterise the geodesics with respect to the dual generators, which allows us to calculate the associated geodesic growth series. using the hierarchy picture of the fractional quantum hall effect, we study the the ground state periodicity of a finite size quantum hall droplet in a quantum hall fluid of a different filling factor. the droplet edge charge is periodically modulated with flux through the droplet and will lead to a periodic variation in the conductance of a nearby point contact, such as occurs in some quantum hall interferometers. our model is consistent with experiment and predicts that superperiods can be observed in geometries where no interfering trajectories occur. the model may also provide an experimentally feasible method of detecting elusive neutral modes and otherwise obtaining information about the microscopic edge structure in fractional quantum hall states. in this paper we describe our massively parallel version of enzo, a multiphysics, parallel, amr application for simulating cosmological structure formation developed at ucsd and columbia. we describe its physics, numerical algorithms, implementation, and performance on current terascale platforms. we also discuss our future plans and some of the challenges we face as we move to the petascale. we discuss the problem of designing an unambiguous programmable discriminator for mixed quantum states. we prove that there does not exist such a universal unambiguous programmable discriminator for mixed quantum states that has two program registers and one data register. however, we find that we can use the idea of programmable discriminator to unambiguously discriminate mixed quantum states. the research shows that by using such an idea, when the success probability for discrimination reaches the upper bound, the success probability is better than what we do not use the idea to do, except for some special cases. the ratio of transverse momentum distribution of thermal photons to dilepton has been evaluated. it is observed that this ratio reaches a plateau beyond a certain value of transverse momentum. we argue that this ratio can be used to estimate the initial temperature of the system by selecting the transverse momentum and invariance mass windows judiciously. it is demonstrated that if the radial flow is large then the plateau disappear and hence a deviation from the plateau can be used as an indicator of large radial flow. the sensitivity of the results on various input parameters has been studied. the theory for large amplitude circularly polarized waves propagating along an external magnetic field is extended in order to include also vacuum polarization effects. a general dispersion relation, which unites previous results, is derived. this paper has been withdrawn by the author. we prove that a bers slice is never algebraic, meaning that its zariski closure in the character variety has strictly larger dimension. a corollary is that skinning maps are never constant.   the proof uses grafting and the theory of complex projective structures. we provide here a modest improvement upon a large sieve inequality for quadratic polynomial amplitudes orginally due to liangyi zhao. bayesian neural networks were used to model the relationship between input parameters, democracy, allies, contingency, distance, capability, dependency and major power, and the output parameter which is either peace or conflict. the automatic relevance determination was used to rank the importance of input variables. control theory approach was used to identify input variables that would give a peaceful outcome. it was found that using all four controllable variables democracy, allies, capability and dependency; or using only dependency or only capabilities avoids all the predicted conflicts. we consider estimation procedures which are recursive in the sense that each successive estimator is obtained from the previous one by a simple adjustment. we propose a wide class of recursive estimation procedures for the general statistical model and study convergence. we consider estimation procedures which are recursive in the sense that each successive estimator is obtained from the previous one by a simple adjustment. we study rate of convergence of recursive estimation procedures for the general statistical model. we present the first calculation of saltation transport and dune formation on mars and compare it to real dunes. we find that the rate at which grains are entrained into saltation on mars is one order of magnitude higher than on earth. with this fundamental novel ingredient, we reproduce the size and different shapes of mars dunes, and give an estimate for the wind velocity on mars. the choice of a star product realization for noncommutative field theory can be regarded as a gauge choice in the space of all equivalent star products. with the goal of having a gauge invariant treatment, we develop tools, such as integration measures and covariant derivatives on this space. the covariant derivative can be expressed in terms of connections in the usual way giving rise to new degrees of freedom for noncommutative theories. we study the boundary terms of the spectral action of the noncommutative space, defined by the spectral triple dictated by the physical spectrum of the standard model, unifying gravity with all other fundamental interactions. we prove that the spectral action predicts uniquely the gravitational boundary term required for consistency of quantum gravity with the correct sign and coefficient. this is a remarkable result given the lack of freedom in the spectral action to tune this term. we present a new model for the propagation of polarized light in a random birefringent medium. this model is based on a decomposition of the higher order statistics of the reduced stokes parameters along the irreducible representations of the rotation group. we show how this model allows a detailed description of the propagation, giving analytical expressions for the probability densities of the mueller matrix and the stokes vector throughout the propagation. it also allows an exact description of the evolution of averaged quantities, such as the degree of polarization. we will also discuss how this model allows a generalization of the concepts of reduced stokes parameters and degree of polarization to higher order statistics. we give some notes on how it can be extended to more general random media. we remark on the garnier system in two variables. a vector field splitting approach is discussed for the systematic derivation of numerical propagators for deterministic dynamics. based on the formalism, a class of numerical integrators for langevin dynamics are presented for single and multiple timestep algorithms. the precise determination of the arrival direction of cosmic rays is a fundamental prerequisite for the search for sources or the study of their anisotropies on the sky. one of the most important aspects to achieve an optimal measurement of these directions is to properly take into account the measurement uncertainties in the estimation procedure. in this article we present a model for the uncertainties associated with the time measurements in the auger surface detector array. we show that this model represents well the measurement uncertainties and therefore provides the basis for an optimal determination of the arrival direction. with this model and a description of the shower front geometry it is possible to estimate, on an event by event basis, the uncertainty associated with the determination of the arrival directions of the cosmic rays. one possible feature of quantum gravity may be the violation of lorentz invariance. in this paper we consider one particular manifestation of the violation of lorentz invariance, namely modified dispersion relations for massive neutrinos. we show how such modified dispersion relations may affect atmospheric neutrino oscillations. we then consider how neutrino telescopes, such as antares, may be able to place bounds on the magnitude of this type of lorentz invariance violation. grids include heterogeneous resources, which are based on different hardware and software architectures or components. in correspondence with this diversity of the infrastructure, the execution time of any single job, as well as the total grid performance can both be affected substantially, which can be demonstrated by measurements. running a simple benchmarking suite can show this heterogeneity and give us results about the differences over the grid sites. an exact cubic open string field theory rolling tachyon solution was recently found by kiermaier et. al. and schnabl. this oscillatory solution has been argued to be related by a field redefinition to the simple exponential rolling tachyon deformation of boundary conformal theory. in the latter approach, the disk partition function takes a simple form. out of curiosity, we compute the disk partition function for an oscillatory tachyon profile, and find that the result is nevertheless almost the same. we show that genuine multiparty quantum correlations can exist on its own, without a supporting background of genuine multiparty classical correlations, even in macroscopic systems. such possibilities can have important implications in the physics of quantum information and phase transitions. selection of an ensemble of equally prepared quantum systems, based on measurements on it, is a basic step in quantum state purification. for an ensemble of single qubits, iterative application of selective dynamics has been shown to lead to complex chaos, which is a novel form of quantum chaos with true sensitivity to the initial conditions. the julia set of initial valuse with no convergence shows a complicated structre on the complex plane. the shape of the julia set varies with the parameter of the dynamics. we present here results for the two qubit case demonstrating how a purification process can be destroyed with chaotic oscillations. we reduce complex stripped patterns to a basic topological network of edges and vertices to define defects and measure their influence on the pattern. we present statistics on the spatial and temporal distribution of defects within the state of spiral defect chaos state in experiments on rayleigh benard convection. these measure the role of boundary influence on the dynamics, and suggest an exponential distribution for the length of edges in the pattern. we also indicate a systematic method to study hierarchies of defect interactions based on the network structure. this paper has been withdrawn by the authors due to the violation of atlas experiment publication policy. the switching process of the vortex core in a permalloy nanodisk affected by a rotating magnetic field is studied theoretically. a detailed description of magnetization dynamics is obtained by micromagnetic simulations. the creation of spacetimes with horizons is discussed, focussing on baby universes and black holes as examples. there is a complex interplay of quantum theory and general relativity in both cases, leading to consequences for the future of the universe and the information loss paradox, and to a deeper understanding of quantum gravity. in this paper, we consider the necessary and sufficient conditions for the tensor product of the fundamental representations for the restricted quantum loop algebras of type a at roots of unity to be irreducible. we determine the abelianization of the symmetric mapping class group of a double unbranched cover using the riemann theta constant, schottky theta constant, and the theta multiplier. we also give lower bounds of the abelianizations of some finite index subgroups of the mapping class group. quantum transport properties in quantum hall wires in the presence of spatially correlated random potential are investigated numerically. it is found that the potential correlation reduces the localization length associated with the edge state, in contrast to the naive expectation that the potential correlation increases it. the effect appears as the sizable shift of quantized conductance plateaus in long wires, where the plateau transitions occur at energies much higher than the landau band centers. the scale of the shift is of the order of the strength of the random potential and is insensitive to the strength of magnetic fields. experimental implications are also discussed. the new property of minimal surfaces is obtained in this article. we calculate the free energy of the disordered urn model using the law of large numbers. it is revealed that the saddle point equation obtained by the usage of the law of large numbers is the same as that obtained by the replica method. hence, we conclude that the replica symmetric solution is adequate for the disordered urn model. furthermore, we point out the mathematical similarity of free energies between the urn models and the random field ising model; this similarity gives an evidence that the replica symmetric solution of the urn models is exact. we parallelize several previously proposed algorithms for the minimum routing cost spanning tree problem and some related problems. writing the boundary integral equation for an exterior problem of elasticity is subordinate so far to hypotheses on the asymptotical behaviour at infinity of solutions. the sufficient conditions met in the literature are too restrictive and do not notably cover the case when the loading has a non zero resultant force. this difficulty can be removed by considering the problem in displacements relatively to one point located at a finite distance from the loading. finally, this auxiliary problem allows widening the conditions of validity of the usual formulation of the direct integral method. we present a new semiclassical method that yields an approximation to the quantum mechanical wavefunction at a fixed, predetermined position. in the approach, a hierarchy of odes are solved along a trajectory with zero velocity. the new approximation is local, both literally and from a quantum mechanical point of view, in the sense that neighboring trajectories do not communicate with each other. the approach is readily extended to imaginary time propagation and is particularly useful for the calculation of quantities where only local information is required. we present two applications: the calculation of tunneling probabilities and the calculation of low energy eigenvalues. in both applications we obtain excellent agrement with the exact quantum mechanics, with a single trajectory propagation. alice is the experiment at the lhc collider at cern dedicated to heavy ion physics. in this report, the alice detector will be presented, together with its expected performance as far as some selected physics topics are concerned. we show that the monogamy of entanglement is a sufficient phenomenon in every physical theory, if the quantum key distribution is to be safe on the grounds of such theory. to do so we present the qkd protocol that is safe in any physical theory under the assumption of the monogamous entanglement only. the necessity of this condition is also discussed. we show that an arbitrary probability distribution can be represented in exponential form. in physical contexts, this implies that the equilibrium distribution of any classical or quantum dynamical system is expressible in grand canonical form. we study the integral and measure theory of the ultraproduct of finite sets. as a main application we construct limit objects for hypergraph sequences. we give a new proof for the hypergraph removal lemma and the hypergraph regularity lemma. in this paper, we make the notion of approximating an artinian local ring by a gorenstein artin local ring precise using the concept of gorenstein colength. we also answer the question as to when the gorenstein colength is at most two. we present a calculation of pi, d and b mesons production at rhic and lhc energies based upon the kkt model of gluon saturation. we discuss dependence of the nuclear modification factor on rapidity and transverse momentum. we determine constraints on the form of axisymmetric toroidal magnetic fields dictated by hydrostatic balance in a type ii superconducting neutron star with a barotropic equation of state. using lagrangian perturbation theory, we find the quadrupolar distortions due to such fields for various models of neutron stars with type ii superconducting and normal regions. we find that the star becomes prolate and can be sufficiently distorted to display precession with a period of the order of years. we also study the stability of such fields using an energy principle, which allows us to extend the stability criteria established by r. j. tayler for normal conductors to more general media with magnetic free energy that depends on density and magnetic induction, such as type ii superconductors. we also derive the growth rate and instability conditions for a specific instability of type ii superconductors, first discussed by p. muzikar, c. j. pethick and p. h. roberts, using a local analysis based on perturbations around a uniform background. in the framework of the lindblad theory for open quantum systems we determine the degree of quantum decoherence and classical correlations of a harmonic oscillator interacting with a thermal bath. the transition from quantum to classical behaviour of the considered system is analyzed and it is shown that the classicality takes place during a finite interval of time. we calculate also the decoherence time and show that it has the same scale as the time after which statistical fluctuations become comparable with quantum fluctuations. methods and techniques of the theory of nonlinear dynamical systems and patterns can be useful in astrophysical applications. some works on the subjects of dynamical astronomy, stellar pulsation and variability, as well as spatial complexity in extended systems, in which such approaches have already been utilized, are reviewed. prospects for future directions in applications of this kind are outlined. in the present work, torsion energy is defined. its law of conservation is given. it is shown that this type of energy gives rise to a repulsive force which can be used to interpret supernovae type ia observations, and consequently the accelerating expansion of the universe. this interpretation is a pure geometric one and is a direct application of the geometrization philosophy. torsion energy can also be used to solve other problems of general relativity especially the singularity problem. this paper has been withdrawn by the authors due to some fatal errors in the analysis. a general result on the method of randomized stopping is proved. it is applied to optimal stopping of controlled diffusion processes with unbounded coefficients to reduce it to an optimal control problem without stopping. this is motivated by recent results of krylov on numerical solutions to the bellman equation. we discuss the notion of the orbifold transform, and illustrate it on simple examples. the basic properties of the transform are presented, including transitivity and the exponential formula for symmetric products. the connection with the theory of permutation orbifolds is addressed, and the general results illustrated on the example of torus partition functions. this paper has been withdrawn by the author for further modification. we compute de chow motive of certain subvarieties of the flags manifold and show that it is an artin motive. we consider the problem of binary classification where one can, for a particular cost, choose not to classify an observation. we present a simple proof for the oracle inequality for the excess risk of structural risk minimizers using a lasso type penalty. we define a grid presentation for singular links i.e. links with a finite number of rigid transverse double points. then we use it to generalize link floer homology to singular links. besides the consistency of its definition, we prove that this homology is acyclic under some conditions which naturally make its euler characteristic vanish. this article deals with the problem of gathering information on the time evolution of a single metastable quantum system whose evolution is impeded by the quantum zeno effect. it has been found it is in principle possible to obtain some information on the time evolution and, depending on the specific system, even to measure its average decay rate, even if the system does not undergo any evolution at all. we provide supplementary appendices to the paper misere quotients for impartial games. these include detailed solutions to many of the octal games discussed in the paper, and descriptions of the algorithms used to compute most of our solutions. initiated by gromov, the study of holomorphic curves in symplectic manifolds has been a powerfull tool in symplectic topology, however the moduli space of holomorphic curves is often very difficult to find. a common technique is to study the limiting behavior of holomorphic curves in a degenerating family of complex structures which corresponds to a kind of adiabatic limit. the category of exploded fibrations is an extension of the smooth category in which some of these degenerations can be described as smooth families.   the first part of this paper is devoted to defining exploded fibrations and a slightly more specialized category of exploded torus fibrations. later sections contain the transverse interesction theory for exploded fibrations and some examples of holomorphic curves in exploded torus fibrations, including a brief discussion of the relationship between tropical geometry and exploded torus fibrations. in the final section, the perturbation theory of holomorphic curves in exploded torus fibrations is sketched. we study the phenomenology of gauge singlet extensions of the standard model scalar sector and their implications for the electroweak phase transition. we determine the conditions on the scalar potential parameters that lead to a strong first order phase transition as needed to produce the observed baryon asymmetry of the universe. we analyze the constraints on the potential parameters derived from higgs boson searches at lep and electroweak precision observables. for models that satisfy these constraints and that produce a strong first order phase transition, we discuss the prospective signatures in future higgs studies at the large hadron collider and a linear collider. we argue that such studies will provide powerful probes of phase transition dynamics in models with an extended scalar sector. hyperspectral images can be represented either as a set of images or as a set of spectra. spectral classification and segmentation and data reduction are the main problems in hyperspectral image analysis. in this paper we propose a bayesian estimation approach with an appropriate hiearchical model with hidden markovian variables which gives the possibility to jointly do data reduction, spectral classification and image segmentation. in the proposed model, the desired independent components are piecewise homogeneous images which share the same common hidden segmentation variable. thus, the joint bayesian estimation of this hidden variable as well as the sources and the mixing matrix of the source separation problem gives a solution for all the three problems of dimensionality reduction, spectra classification and segmentation of hyperspectral images. a few simulation results illustrate the performances of the proposed method compared to other classical methods usually used in hyperspectral image processing. this paper we consider the problem of separating noisy instantaneous linear mixtures of document images in the bayesian framework. the source image is modeled hierarchically by a latent labeling process representing the common classifications of document objects among different color channels and the intensity process of pixels given the class labels. a potts markov random field is used to model regional regularity of the classification labels inside object regions. local dependency between neighboring pixels can also be accounted by smoothness constraint on their intensities. within the bayesian approach, all unknowns including the source, the classification, the mixing coefficients and the distribution parameters of these variables are estimated from their posterior laws. the corresponding bayesian computations are done by mcmc sampling algorithm. results from experiments on synthetic and real image mixtures are presented to illustrate the performance of the proposed method. in this paper we give an algorithmic characterization of rank two locally nilpotent derivations in dimension three. together with an algorithm for computing the plinth ideal, this gives a method for computing the rank of a locally nilpotent derivation in dimension three. in this paper we give an algorithm to recognize triangulable locally nilpotent derivations in dimension three. in case the given derivation is triangulable, our method produces a coordinate system in which it exhibits a triangular form. it is shown that schroedinger operators, with potentials along the shift embedding of lebesgue almost every interval exchange transformations, have cantor spectrum of measure zero and pure singular continuous for lebesgue almost all points of the interval. an adjoint pair of contravariant functors between abelian categories can be extended to the adjoint pair of their derived functors in the associated derived categories. we describe the reflexive complexes and interpret the achieved results in terms of objects of the initial abelian categories. in particular we prove that, for functors of any finite cohomological dimension, the objects of the initial abelian categories which are reflexive as stalk complexes form the largest class where a cotilting theorem in the sense of colby and fuller works. this paper has been withdrawn by the author. we address the role of community structure of an interaction network in ordering dynamics, as well as associated forms of metastability. we consider the voter and ab model dynamics in a network model which mimics social interactions. the ab model includes an intermediate state between the two excluding options of the voter model. for the voter model we find dynamical metastable disordered states with a characteristic mean lifetime. however, for the ab dynamics we find a power law distribution of the lifetime of metastable states, so that the mean lifetime is not representative of the dynamics. these trapped metastable states, which can order at all time scales, originate in the mesoscopic network structure. we discuss memory effects in the conductance of hopping insulators due to slow rearrangements of structural defects leading to formation of polarons close to the electron hopping states. an abrupt change in the gate voltage and corresponding shift of the chemical potential change populations of the hopping sites, which then slowly relax due to rearrangements of structural defects. as a result, the density of hopping states becomes time dependent on a scale relevant to rearrangement of the structural defects leading to the excess time dependent conductivity. we study boundary regularity for conformally compact einstein metrics in even dimensions by generalizing the ideas of michael anderson. our method of approach is to view the vanishing of the ambient obstruction tensor as an nth order system of equations for the components of a compactification of the given metric. this, together with boundary conditions that the compactification is shown to satisfy provide enough information to apply classical boundary regularity results. these results then provide local and global versions of finite boundary regularity for the components of the compactification. we study the confinement of fermionic magnetic monopoles by a thin flux tube of the abelian higgs model. parity demands that the monopole currents be axial. this implies that the model is consistent only if there are at least two species of fermions being confined. we define generalized vector fields, and contraction and lie derivatives with respect to them. generalized commutators are also defined. the models of star formation function and of dissipation of turbulent energy of interstellar medium are proposed. in star formation model the feedback of supernovae is taken into account. it is shown that hierarchical scenario of galaxy formation with proposed models is able to explain the observable star formation pause in the galaxy. we discuss the concept of energy packets in respect to the energy transported by electromagnetic waves and we demonstrate that this physical quantity can be used in physical problems involving relativistic effects. this refined concept provides results compatible to those obtained by simpler definition of energy density when relativistic effects apply to the free electromagnetic waves. we found this concept further compatible to quantum theory perceptions and we show how it could be used to conciliate between different physical approaches including the classical electromagnetic wave theory, the special relativity and the quantum theories. we introduce a feasible method of constructing the entanglement witness that detects the genuine entanglement of a given pure multiqubit state. we illustrate our method in the scenario of constructing the witnesses for the multiqubit states that are broadly theoretically and experimentally investigated. it is shown that our method can construct the effective witnesses for experiments. we also investigate the entanglement detection of symmetric states and mixed states. it is well known that the cp violating theta term of qcd can be converted to a phase in the quark mass term. however, a theory with a complex mass term for quarks can be regularized so as not to violate cp, for example through a zeta function. the contradiction is resolved through the recognition of a dependence on the regularization or measure. the appropriate choice of regularization is discussed and implications for the strong cp problem are pointed out. we classify finite dimensional simple spherical representations of rational double affine hecke algebras, and we study a remarkable family of finite dimensional simple spherical representations of double affine hecke algebras. we give a simple, explicit, sufficient condition for the existence of a sector of minimal growth for second order regular singular differential operators on graphs. we specifically consider operators with a singular potential of coulomb type and base our analysis on the theory of elliptic cone operators. consider a smooth log fano variety over the function field of a curve. suppose that the boundary has positive normal bundle. choose an integral model over the curve. then integral points are zariski dense, after removing an explicit finite set of points on the base curve. in this paper, first a great number of inverse problems which arise in instrumentation, in computer imaging systems and in computer vision are presented. then a common general forward modeling for them is given and the corresponding inversion problem is presented. then, after showing the inadequacy of the classical analytical and least square methods for these ill posed inverse problems, a bayesian estimation framework is presented which can handle, in a coherent way, all these problems. one of the main steps, in bayesian inversion framework is the prior modeling of the unknowns. for this reason, a great number of such models and in particular the compound hidden markov models are presented. then, the main computational tools of the bayesian estimation are briefly presented. finally, some particular cases are studied in detail and new results are presented. we consider simple models of tunneling of an object with intrinsic degrees of freedom. this important problem was not extensively studied until now, in spite of numerous applications in various areas of physics and astrophysics. we show possibilities of enhancement for the probability of tunneling due to the presence of intrinsic degrees of freedom split by weak external fields or by polarizability of the slow composite object. we review our recent formulation of colombeau type algebras as hausdorff sequence spaces with ultranorms, defined by sequences of exponential weights. we extend previous results and give new perspectives related to echelon type spaces, possible generalisations, asymptotic algebras, concepts of association, and applications thereof. virtualization became recently a hot topic once again, after being dormant for more than twenty years. in the meantime, it has been almost forgotten, that virtual machines are not so perfect isolating environments as it seems, when looking at the principles. these lessons were already learnt earlier when the first virtualized systems have been exposed to real life usage.   contemporary virtualization software enables instant creation and destruction of virtual machines on a host, live migration from one host to another, execution history manipulation, etc. these features are very useful in practice, but also causing headaches among security specialists, especially in current hostile network environments.   in the present contribution we discuss the principles, potential benefits and risks of virtualization in a deja vu perspective, related to previous experiences with virtualization in the mainframe era. an analogy between wigner resonant tunneling and tunneling across a static potential barrier in a static magnetic field is found. whereas in the process of wigner tunneling an electron encounters a classically allowed regions, where a discrete energy level coincides with its energy, in the magnetic field a potential barrier is a constant in the direction of tunneling. along the tunneling path the certain regions are formed, where, in the classical language, the kinetic energy of the motion perpendicular to tunneling is negative. these regions play a role of potential wells, where a discrete energy level can coincide with the electron energy. such phenomenon, which occurs at the certain magnetic field, is called euclidean resonance and substantially depends on a shape of potential forces in the direction perpendicular to tunneling. under conditions of euclidean resonance a long distance underbarrier motion is possible. we define and study a class of codes obtained from scrolls over curves of any genus over finite fields. these codes generalize goppa codes in a natural way, and the orthogonal complements of these codes belong to the same class. we show how syndromes of error vectors correspond to certain vector bundle extensions, and how decoding is associated to finding destabilizing subbundles. we have presented first an axiomatic derivation of boltzmann entropy on the basis of two axioms consistent with two basic properties of thermodynamic entropy. we have then studied the relationship between boltzmann entropy and information along with its physical significance. we investigate cosmological constraints on primordial isocurvature and tensor perturbations, using recent observations of the cosmic microwave background and the large scale structure. we find that present observations are consistent with purely adiabatic initial conditions for the structure formation under any priors on correlations of isocurvature modes, and upper limits on the contribution of isocurvature and tensor perturbations are presented. we also apply the obtained constraints to some specific theoretical models, axion isocurvature perturbation models and curvaton models, and give some implications for theoretical models. we introduce the notion of weak commensurabilty of arithmetic subgroups and relate it to the length equivalence and isospectrality of locally symmetric spaces. we prove many strong consequences of weak commensurabilty and derive from these many interesting results about isolength and isospectral locally symmetric spaces. the mutual relation between quantum micro and classical macro is clarified by a unified formulation of instruments describing measurement processes and the associated amplification processes, from which some perspective towards a description of emergence processes of spacetime structure is suggested. the new axiomatic system for the quantum field theory is proposed. the new axioms are the description of the distributions. for the finite series these distributions satisfy the linear wightman axioms. in quantum field theory it is generally assumed that there is a lower bound to the energy of a quantum state. here, it will be shown that there is no lower bound to the energy of physical states in qed in a manifestly covariant gauge. we examine the maximum negative energy density which can be attained in various quantum states of a massless scalar field. we consider states in which either one or two modes are excited, and show that the energy density can be given in terms of a small number of parameters. we calculate these parameters for several examples of superposition states for one mode, and entangled states for two modes, and find the maximum magnitude of the negative energy density in these states. we consider several states which have been, or potentially will be, generated in quantum optics experiments. in this paper the motion of ultrahigh energy particles produced in sasefel is investigated. the critical field which opose the acceleration of the ultra high energy particles is calculated we show that the enhancement of the saturation scale in large nuclei relative to the proton is significantly influenced by the effects of quantum evolution and the impact parameter dependence of dipole cross sections in high energy qcd. we demonstrate that there is a strong a dependence in diffractive deeply inelastic scattering and discuss its sensitivity to the measurement of the recoil nucleus. the paper considers the halting scheme for quantum turing machines. the scheme originally proposed by deutsch appears to be correct, but not exactly as originally intended. we discuss the result of ozawa as well as the objections raised by myers, kieu and danos and others. finally, the relationship of the halting scheme to the quest for a universal quantum turing machine is considered. we study supersymmetric qcd in the conformal window as a laboratory for unparticle physics, and analyze couplings between the unparticle sector and the higgs sector. these couplings can lead to the unparticle sector being pushed away from its scale invariant fixed point. we show that this implies that low energy experiments will not be able to see unparticle physics, and the best hope of seeing unparticles is in high energy collider experiments such as the tevatron and the lhc. we also demonstrate how the breaking of scale invariance could be observed at these experiments. we derive exact analytical solutions of the goy shell model of turbulence. in the absence of forcing and viscosity we obtain closed form solutions in terms of jacobi elliptic functions. with three shells the model is integrable. in the case of many shells, we derive exact recursion relations for the amplitudes of the jacobi functions relating the different shells and we obtain a kolmogorov solution in the limit of infinitely many shells. for the special case of six and nine shells, these recursions relations are solved giving specific analytic solutions. some of these solutions are stable whereas others are unstable. all our predictions are substantiated by numerical simulations of the goy shell model. from these simulations we also identify cases where the models exhibits transitions to chaotic states lying on strange attractors or ergodic energy surfaces. the quantum oscillations of population in an asymmetric double quantum dots system coupled to a phonon bath are investigated theoretically. it is shown how the environmental temperature has effect on the system. we consider triangular arrays of markov chains that converge weakly to a diffusion process. second order edgeworth type expansions for transition densities are proved. the paper differs from recent results in two respects. we allow nonhomogeneous diffusion limits and we treat transition densities with time lag converging to zero. small time asymptotics are motivated by statistical applications and by resulting approximations for the joint density of diffusion values at an increasing grid of points. for infinitely large sparse networks of spiking neurons mean field theory shows that a balanced state of highly irregular activity arises under various conditions. here we analytically investigate the microscopic irregular dynamics in finite networks of arbitrary connectivity, keeping track of all individual spike times. for delayed, purely inhibitory interactions we demonstrate that the irregular dynamics is not chaotic but rather stable and convergent towards periodic orbits. moreover, every generic periodic orbit of these dynamical systems is stable. these results highlight that chaotic and stable dynamics are equally capable of generating irregular activity. dynamical properties of complex networks are related to the spectral properties of the laplacian matrix that describes the pattern of connectivity of the network. in particular we compute the synchronization time for different types of networks and different dynamics. we show that the main dependence of the synchronization time is on the smallest nonzero eigenvalue of the laplacian matrix, in contrast to other proposals in terms of the spectrum of the adjacency matrix. then, this topological property becomes the most relevant for the dynamics. an approximation of the real line shape of a scintillation detector with a generalized gamma distribution is proposed. the approximation describes the ideal scintillation line shape better than the conventional normal distribution. two parameters of the proposed function are uniquely defined by the first two moments of the detector response. a cohomology theory of the adjoint of hopf algebras, via deformations, is presented by means of diagrammatic techniques. explicit calculations are provided in the cases of group algebras, function algebras on groups, and the bosonization of the super line. as applications, solutions to the ybe are given and quandle cocycles are constructed from groupoid cocycles. in this work we show that the ordering ambiguity on quantization depends on the representation choice. this property is then used to solve unambiguously some particular systems. finally, we speculate on the consequences for more involved cases. the diagnostics of stellar flaring coronal loops have been so far largely based on the analysis of the decay phase. we derive new diagnostics from the analysis of the rise and peak phase of stellar flares. we release the assumption of full equilibrium of the flaring loop at the flare peak, according to the frequently observed delay between the temperature and the density maximum. from scaling laws and hydrodynamic simulations we derive diagnostic formulas as a function of observable quantities and times. we obtain a diagnostic toolset related to the rise phase, including the loop length, density and aspect ratio. we discuss the limitations of this approach and find that the assumption of loop equilibrium in the analysis of the decay leads to a moderate overestimate of the loop length. a few relevant applications to previously analyzed stellar flares are shown. the analysis of the flare rise and peak phase complements and completes the analysis of the decay phase. we present a quantitative analysis of throwing ability for major league outfielders and catchers. we use detailed game event data to tabulate success and failure events in outfielder and catcher throwing opportunities. we attribute a run contribution to each success or failure which are tabulated for each player in each season. we use four seasons of data to estimate the overall throwing ability of each player using a bayesian hierarchical model. this model allows us to shrink individual player estimates towards an overall population mean depending on the number of opportunities for each player. we use the posterior distribution of player abilities from this model to identify players with significant positive and negative throwing contributions. the chiral anomaly in the context of an extended standard model with minimal lorentz invariance violation is studied. taking into account bounds from measurements of the speed of light, we argue that the chiral anomaly and its consequences are general results valid even beyond the relativistic symmetry. we evaluate the predictive power of the neutrino mass matrices arising from seesaw mechanism subjected to texture zero and satisfying a cyclic permutation invariant. we found that only two from eight possible patterns of the neutrino mass matrices are invariant under a cyclic permutation. the two resulted neutrino mass matrices which are invariant under a cyclic permutation can be used qualitatively to explain the neutrino mixing phenomena for solar neutrino and to derive the mixing angle that agress with the experimental data. we find an exact classical solution in euclidean gravity coupled to a scalar field with a particular form of potential commonly used in tachyon cosmology. this solution represents a tunneling between two vacua. in this paper we present three simple applications of probability and highlight and discuss their paradoxical flavour. this study examines the simulation of quantum algorithms on a classical computer. the program code implemented on a classical computer will be a straight connection between the mathematical formulation of quantum mechanics and computational methods. the computational language will include formulations such as quantum state, superposition and quantum operator. we introduce a new numerical invariant of knots and links from the descending diagrams. it is considered to live between the unknotting number and the bridge number. we construct all planar semimodular lattices in three simple steps from the direct product of two chains. we consider the stability of a compressible shear flow separating two streams of different speeds and temperatures. the velocity and temperature profiles in this mixing layer are hyperbolic tangents.   the normal mode analysis of the flow stability reduces to an eigenvalue problem for the pressure perturbation. we briefly describe the numerical method that we used to solve this problem. then, we introduce the notions of the absolute and convective instabilities and examine the effects of mach number, and the velocity and temperature ratios of each stream on the transition between convective and absolute instabilities. finally, we discuss the implication of the results presented in this paper for the heliopause stability. some years ago, cho and vilenkin, introduced a model which presents topological solutions, despite not having degenerate vacua as is usually expected. here we present a new model with topological defects, connecting degenerate vacua but which in a certain limit recovers precisely the one proposed originally by cho and vilenkin. in other words, we found a kind of parent model for the so called vacuumless model. then the idea is extended to a model recently introduced by bazeia et al. finally, we trace some comments the case of the liouville model. the method for solving the kdv are considered. this paper presents a model of the dynamics of the wage income distribution. we illustrate the concept of mathematical proof. the notions of mass and center of mass are extended to laminae of the hyperbolic plane. the resulting formulae contain many surprises. we give a bound on the spectral radius of subgraphs of regular graphs with given order and diameter. we give a lower bound on the smallest eigenvalue of a nonbipartite regular graph of given order and diameter. we show that direct feedback based on quantum jump detection can be used to generate entangled steady states. we present a strategy that is insensitive to detection inefficiencies and robust against errors in the control hamiltonian. this feedback procedure is also shown to overcome spontaneous emission effects by stabilising states with high degree of entanglement. sturm oscillation theorem for second order differential equations was generalized to systems and higher order equations with positive leading coefficient by several authors. what we propose here is a sturm oscillation theorem for systems of even order having strongly indefinite leading coefficient. in this paper we consider a correspondence between the holographic dark energy density and tachyon energy density in frw universe. then we reconstruct the potential and the dynamics of the tachyon field which describe tachyon cosmology. the heavy ion program of the cms experiment will examine the qcd matter under extreme conditions, through the study of global observables and specific probes. generalizations of ostrowski type inequality for functions of lipschitzian type are established. applications in numerical integration and cumulative distribution functions are also given. this paper is painfully withdrawn. we define and study symmetrized and antisymmetrized multivariate exponential functions. they are defined as determinants and antideterminants of matrices whose entries are exponential functions of one variable. these functions are eigenfunctions of the laplace operator on corresponding fundamental domains satisfying certain boundary conditions. to symmetric and antisymmetric multivariate exponential functions there correspond fourier transforms. there are three types of such fourier transforms: expansions into corresponding fourier series, integral fourier transforms, and multivariate finite fourier transforms. eigenfunctions of the integral fourier transforms are found. we calculate the spin susceptibility of a superconductor without inversion symmetry, both in the clean and disordered cases. the susceptibility has a large residual value at zero temperature, which is further enhanced in the presence of scalar impurities. the spin can be described in the star product formalism by extending the bosonic moyal product in the fermionic sector. the fermionic star product is then the clifford product of geometric algebra and it is possible to formulate the fermionic star product formalism in analogy to the bosonic star product formalism. for the fermionic star product description of spin, one can then establish the relation to other approaches that describe spin with fermionic variables, i.e. the operator formalism and the path integral formalism. it is shown that the fermionic star product formalism and the fermionic path integral formalism are related in analogy to their bosonic counterparts. the star product formalism has proved to be an alternative formulation for nonrelativistic quantum mechanics. we want introduce here a covariant star product in order to extend the star product formalism to relativistic quantum mechanics in the proper time formulation. incoherent noise is manifest in measurements of expectation values when the underlying ensemble evolves under a classical distribution of unitary processes. while many incoherent processes appear decoherent, there are important differences. the distribution functions underlying incoherent processes are either static or slowly varying with respect to control operations and so the errors introduced by these distributions are refocusable. the observation and control of incoherence in small hilbert spaces is well known. here we explore incoherence during an entangling operation, such as is relevant in quantum information processing. as expected, it is more difficult to separate incoherence and decoherence over such processes. however, by studying the fidelity decay under a cyclic entangling map we are able to identify distinctive experimental signatures of incoherence. this result is demonstrated both through numerical simulations and experimentally in a three qubit nuclear magnetic resonance implementation. we construct knot invariants from the radical part of projective modules of restricted quantum groups. we also show a relation between these invariants and the colored alexander invariants. it is conjectured that a hyperbolic knot admits at most three dehn surgeries which yield closed three manifolds containing incompressible tori. we show that there exist infinitely many hyperbolic knots which attain the conjectural maximum number. interestingly, those surgeries correspond to consecutive integers. we present a short review on the recent progresses that have been made in meson spectroscopy. we discuss the experimental discoveries made at the babar and belle experiments, as well as the possible interpretations of the new resonances. counting of microscopic states of black holes is discussed within the framework of loop quantum gravity. there are two different ways, one allowing for all spin states and the other involving only pure horizon states. the number of states with a definite value of the total spin is also found. radial tidal forces can be compressive instead of disruptive, a possibility that is frequently overlooked in high level physics courses. for example, radial tidal compression can emerge in extended stellar systems containing a smaller stellar cluster. for particular conditions the tidal field produced by this extended mass distribution can exert on the cluster it contains compressive effects instead of the common disruptive forces. this interesting aspect of gravity can be derived from standard relations given in many textbooks and introductory courses in astronomy and can serve as an opportunity to look closer at some aspects of gravitational physics, stellar dynamics, and differential geometry. the existence of compressive tides at the center of huge stellar systems might suggest new evolutionary scenarios for the formation of stars and primordial galactic formation processes. we study stability conditions induced by functors between triangulated categories. given a finite group acting on a smooth projective variety we prove that the subset of invariant stability conditions embeds as a closed submanifold into the stability manifold of the equivariant derived category. as an application we examine stability conditions on kummer and enriques surfaces and we improve the derived version of the torelli theorem for the latter surfaces already present in the litterature. we also study the relationship between stability conditions on projective spaces and those on their canonical bundles. we consider insurance derivatives depending on an external physical risk process, for example a temperature in a low dimensional climate model. we assume that this process is correlated with a tradable financial asset. we derive optimal strategies for exponential utility from terminal wealth, determine the indifference prices of the derivatives, and interpret them in terms of diversification pressure. moreover we check the optimal investment strategies for standard admissibility criteria. finally we compare the static risk connected with an insurance derivative to the reduced risk due to a dynamic investment into the correlated asset. we show that dynamic hedging reduces the risk aversion in terms of entropic risk measures by a factor related to the correlation. we propose that recent transport experiments revealing the existence of an energy gap in graphene nanoribbons may be understood in terms of coulomb blockade. electron interactions play a decisive role at the quantum dots which form due to the presence of necks arising from the roughness of the graphene edge. with the average transmission as the only fitting parameter, our theory shows good agreement with the experimental data. a review of the superstatistics concept is provided, including various recent applications to complex systems. niels bohr introduced the concept of complementarity in order to give a general account of quantum mechanics, however he stressed that the idea of complementarity is related to the general dificulty in the formation of human ideas, inherent in the distinction between subject and object. earlier, we have introduced a development of the concept of complementarity which constitutes a new approach to the interpretation of quantum mechanics. we argue that this development allows a better understanding of some of the paradigmatic interpretational problems of quantum theory.   within the scheme proposed by modal interpretations we analyze the relation between holism and reductionism as well as the problems proposed by arntzenius and clifton. we discuss the problem of presupposing the concept of entity within the quantum formalism and bring into stage the concept of faculty as a way to recover the objective character of quantum mechanics. the joint cumulative distribution function for order statistics arising from several different populations is given in terms of the distribution function of the populations. the computational cost of the formula in the case of two populations is still exponential in the worst case, but it is a dramatic improvement compared to the general formula by bapat and beg. in the case when only the joint distribution function of a subset of the order statistics of fixed size is needed, the complexity is polynomial, for the case of two populations. we develop a skein exact sequence for knot floer homology, involving singular knots. this leads to an explicit, algebraic description of knot floer homology in terms of a braid projection of the knot. the dissipative quantum system is studied using the thirring model with a boundary mass. at the critical point where the thirring coupling vanishes, the theory reduces to a free fermion theory with a boundary mass. we construct boundary states for the dissipative quantum systems in one dimension, which describes the system off the critical points as well as at the critical points. we study the fibers of a projective morphism and some related algebraic problems. we characterize the analytic spread of a homogeneous ideal through properties of its syzygy matrix. powers of linearly presented ideals need not be linearly presented, but we identify a weaker linearity property that is preserved under taking powers. the electromagnetic field in an anisotropic and inhomogeneous magnetodielectric is quantized by modelling the medium with two independent quantum fields. some coupling tensors coupling the electromagnetic field with the medium are introduced. electric and magnetic polarizations are obtained in terms of the ladder operators of the medium and the coupling tensors explicitly. using a minimal coupling scheme for electric and magnetic interactions, the maxwell equations and the constitutive equations of the medium are obtained. the electric and magnetic susceptibility tensors of the medium are calculated in terms of the coupling tensors. finally the efficiency of the approach is elucidated by some examples. collisions are a major modification process over the history of the kuiper belt. recent work illuminates the complex array of possible outcomes of individual collisions onto porous, volatile bodies. the cumulative effects of such collisions on the surface features, composition, and internal structure of kuiper belt objects are not yet known. in this chapter, we present the current state of knowledge of the physics of cratering and disruptive collisions in kbo analog materials. we summarize the evidence for a rich collisional history in the kuiper belt and present the range possible physical modifications on individual objects. the question of how well present day bodies represent primordial planetesimals can be addressed through future studies of the coupled physical and collisional evolution of kuiper belt objects. this paper is about kripke structures that are inside a relational database and queried with a modal language. at first the modal language that is used is introduced, followed by a definition of the database and relational algebra. based on these definitions two things are presented: a mapping from components of the modal structure to a relational database schema and instance, and a translation from queries in the modal language to relational algebra queries. a small tabletop experiment for a direct measurement of the speed of light to an accuracy of few percent is described. the experiment is accessible to a wide spectrum of undergraduate students, in particular to students not majoring in science or engineering. the experiment may further include a measurement of the index of refraction of a sample. details of the setup and equipment are given. results and limitations of the experiment are analyzed, partly based on our experience in employing the experiment in our student laboratories. safety considerations are also discussed. we study the mathematical evolution of a liquid fuel droplet inside a vessel. in particular, we analyze the evolution of the droplet radius on a finite time interval. the model problem involves an hyperbolic system coupled with the pressure and velocity of the surrounding gas. existence of bounded solutions for the mass fraction of the liquid, submitted to nonlinear constraints, is shown. numerical simulations are given, in agreement with known physical experiments. for thermoelectric, galvanomagnetic and some other effects there may simultaneously exist two percolation thresholds, close to which the effective kinetic coefficients of macroscopically disordered media are critically dependent on the proximity to percolation thresholds, their behavior being described by universal critical indexes. we consider dynamics of the frw universe with a scalar field. using maupertuis principle we find a curvature of geodesics flow and show that zones of positive curvature exist for all considered types of scalar field potential. usually, phase space of systems with the positive curvature contains islands of regular motion. we find these islands numerically for shallow scalar field potentials. it is shown also that beyond the physical domain the islands of regularity exist for quadratic potentials as well. we consider a multidimensional random walk in a product random environment with bounded steps, transience in some spatial direction, and high enough moments on the regeneration time. we prove an invariance principle, or functional central limit theorem, under almost every environment for the diffusively scaled centered walk. the main point behind the invariance principle is that the quenched mean of the walk behaves subdiffusively. the gravitational instability of a fully ionized gas is analyzed within the framework of linear irreversible thermodynamics. in particular, the presence of a heat flux corresponding to generalized thermodynamic forces is shown to affect the properties of the dispersion relation governing the stability of this kind of system in certain problems of interest. a few remarks on how mathematics quests for freedom. this is an overview of merging the techniques of riesz space theory and convex geometry. we present a general theoretical method to generate maximally entangled mixed states of a pair of photons initially prepared in the singlet polarization state. this method requires only local operations upon a single photon of the pair and exploits spatial degrees of freedom to induce decoherence. we report also experimental confirmation of these theoretical results. we give a review on entanglement purification for bipartite and multipartite quantum states, with the main focus on theoretical work carried out by our group in the last couple of years. we discuss entanglement purification in the context of quantum communication, where we emphasize its close relation to quantum error correction. various bipartite and multipartite entanglement purification protocols are discussed, and their performance under idealized and realistic conditions is studied. several applications of entanglement purification in quantum communication and computation are presented, which highlights the fact that entanglement purification is a fundamental tool in quantum information processing. we discuss the consistency of the axioms which the definition of quantum lie algebras is usually based on. we derive a new class of exact time dependent solutions in a warped six dimensional supergravity model. under the assumptions we make for the form of the underlying moduli fields, we show that the only consistent time dependent solutions lead to all six dimensions evolving in time, implying the eventual decompactification or collapse of the extra dimensions. we also show how the dynamics affects the quantization of the deficit angle. we consider singularly perturbed second order elliptic system in the whole space with fast oscillating coefficients. we construct the complete asymptotic expansions for the eigenvalues converging to the isolated ones of the homogenized system, as well as the complete asymptotic expansions for the associated eigenfunctions. it is shown that multiple volume reflections from different planes of one bent crystal becomes possible when particles move at a small angle with respect to a crystal axis. such a multiple volume reflection makes it possible to increase the particle deflection angle inside one crystal by more than four times and can be used to increase the efficiency of beam extraction and collimation at the lhc and many other accelerators. hypertoric varieties are quaternionic analogues of toric varieties, important for their interaction with the combinatorics of matroids as well as for their prominent place in the rapidly expanding field of algebraic symplectic and hyperkahler geometry. the aim of this survey is to give clear definitions and statements of known results, serving both as a reference and as a point of entry to this beautiful subject. this paper offers an alternative approach to discussing both the principle of relativity and the derivation of the lorentz transformations. this approach uses the idea that there may not be a preferred inertial frame through a privileged access to information about events. in classroom discussions, it has been my experience that this approach produces some lively arguments. gauge invariance is a powerful tool to determine the dynamics of the electroweak and strong forces. the particle content, structure and symmetries of the standard model lagrangian are discussed. special emphasis is given to the many phenomenological tests which have established this theoretical framework as the standard theory of electroweak interactions. simulations are used to examine the microscopic origins of strain hardening in polymer glasses. while traditional entropic network models can be fit to the total stress, their underlying assumptions are inconsistent with simulation results. there is a substantial energetic contribution to the stress that rises rapidly as segments between entanglements are pulled taut. the thermal component of stress is less sensitive to entanglements, mostly irreversible, and directly related to the rate of local plastic arrangements. entangled and unentangled chains show the same strain hardening when plotted against the microscopic chain orientation rather than the macroscopic strain. we introduce a new numerical invariant of knots and links made from the partitioned diagrams. it measures the complexity of knots and links. when a droplet is gently laid onto the surface of the same liquid, it stays at rest for a moment before coalescence. the coalescence can be delayed and sometimes inhibited by injecting fresh air under the droplet. this can happen when the surface of the bath oscillates vertically, in this case the droplet basically bounces on the interface. the lifetime of the droplet has been studied with respect to the amplitude and the frequency of the excitation. the lifetime decreases when the acceleration increases. the thickness of the air film between the droplet and the bath has been investigated using interference fringes obtained when the system is illuminated by low pressure sodium lamps. moreover, both the shape evolution and the motion of the droplet center of mass have been recorded in order to evidence the phase offset between the deformation and the trajectory. a short lifetime is correlated to a small air film thickness and to a large phase offset between the maximum of deformation and the minimum of the vertical position of the centre of mass. in the context of synthetic differential geometry, we describe a notion of higher connection with values in a cubical groupoid. we do this by exploiting a certain structure of cubical complex derived from the first neighbourhood of the diagonal of a manifold. this cubical complex consists of infinitesimal parallelelpipeda. with his general theory of relativity, albert einstein produced a revolution in our conception of reality and of the knowledge we can obtain from it. this revolution can be viewed from philosophy as leading to one of the great paradigms in the history of thought which, together with the aristotelian and the newtonian paradigms, embodied the different ways of conceiving the universe and our access to it. the comparison among these three paradigms allows us to understand how the human being has progressively lost his central place in the cosmos, not only in physical terms, but also in an epistemic sense, regarding his power of knowledge about reality. we find an exact solution for the stability limit of relativistic charged spheres for the case of constant gravitational mass density and constant charge density. we argue that this provides an absolute stability limit for any relativistic charged sphere in which the gravitational mass density decreases with radius and the charge density increases with radius. we then provide a cruder absolute stability limit that applies to any charged sphere with a spherically symmetric mass and charge distribution. we give numerical results for all cases. in addition, we discuss the example of a neutral sphere surrounded by a thin, charged shell. the volume capture in classical relativistic mechanics is considered as a scattering process for the high energy charged particles in a field with no central or mirror symmetry. the parameters of volume capture for potentials with smooth variable curvature are received and analyzed. in a recent note ellis criticizes varying speed of light theories on the grounds of a number of foundational issues. his reflections provide us with an opportunity to clarify some fundamental matters pertaining to these theories. let x be a geometrically connected smooth projective curve of genus one, defined over the field of real numbers, such that x does not have any real points. we classify the isomorphism classes of all stable real algebraic vector bundles over x. we have found that a novel type of entrainment occurs in two nonidentical limit cycle oscillators subjected to a common external white gaussian noise. this entrainment is anomalous in the sense that the two oscillators have different mean frequencies, where the difference is constant as the noise intensity increases, but their phases come to be locked for almost all the time. we present a theory and numerical evidence for this phenomenon. we investigate the dynamics of a relativistic electron in a strongly nonlinear plasma wave in terms of classical mechanics by taking into account the action of the radiative reaction force. the two limiting cases are considered. in the first case where the energy of the accelerated electrons is low, the electron makes many betatron oscillations during the acceleration. in the second case where the energy of the accelerated electrons is high, the betatron oscillation period is longer than the electron residence time in the accelerating phase. we show that the force of radiative friction can severely limit the rate of electron acceleration in a plasma accelerator. we study an action of the skew divided difference operators on the schubert polynomials and give an explicit formula for structural constants for the schubert polynomials in terms of certain weighted paths in the bruhat order on the symmetric group. we also prove that, under certain assumptions, the skew divided difference operators transform the schubert polynomials into polynomials with positive integer coefficients. the present paper seeks to construct a quantum theory of the cosmological constant in which its presently observed very small value emerges naturally. we consider a classical interacting dimer model which interpolates between the square lattice case and the triangular lattice case by tuning a chemical potential in the diagonal bonds. the interaction energy simply corresponds to the number of plaquettes with parallel dimers. using transfer matrix calculations, we find in the anisotropic triangular case a succession of different physical phases as the interaction strength is increased: a short range disordered liquid dimer phase at low interactions, then a critical phase similar to the one found for the square lattice, and finally a transition to an ordered columnar phase for large interactions. the existence of the critical phase is in contrast with the belief that criticality for dimer models is ascribed to bipartiteness. for the isotropic triangular case, we have indications that the system undergoes a first order phase transition to an ordered phase, without appearance of an intermediate critical phase. we discuss two separate techniques for kalman filtering in the presence of state space equality constraints. we then prove that despite the lack of similarity in their formulations, under certain conditions, the two methods result in mathematically equivalent constrained estimate structures. we conclude that the potential benefits of using equality constraints in kalman filtering often outweigh the computational costs, and as such, equality constraints, when present, should be enforced by way of one of these two methods. in this paper we derive the equations for loop corrected belief propagation on a continuous variable gaussian model. using the exactness of the averages for belief propagation for gaussian models, a different way of obtaining the covariances is found, based on belief propagation on cavity graphs. we discuss the relation of this loop correction algorithm to expectation propagation algorithms for the case in which the model is no longer gaussian, but slightly perturbed by nonlinear terms. we show that there is significant cancellation in certain exponential sums over small multiplicative subgroups of finite fields, giving an exposition of the arguments by bourgain and chang. low energy experiments with photons can provide deep insights into fundamental physics. in this note we concentrate on minicharged particles. we discuss how they can arise in extensions of the standard model and how we can search for them using a variety of laboratory experiments. the concept of time as used in various applications and interpretations of quantum theory is briefly reviewed. this paper extends the construction of invariants for virtual knots to virtual long knots and introduces two new invariant modules of virtual long knots. several interesting features are described that distinguish virtual long knots from their classical counterparts with respect to their symmetries and the concatenation product. this paper suffers from conceptual difficulties and unjustified approximations that render its conclusions dubious. one of the less known facets of ludwig boltzmann was that of an advocate of aviation, one of the most challenging technological problems of his times. boltzmann followed closely the studies of pioneers like otto lilienthal in berlin, and during a lecture on a prestigious conference he vehemently defended further investments in the area. in this article i discuss his involvement with aviation, his role in its development and his correspondence with two flight pioneers, otto lilienthal e wilhelm kress. semantic network research has seen a resurgence from its early history in the cognitive sciences with the inception of the semantic web initiative. the semantic web effort has brought forth an array of technologies that support the encoding, storage, and querying of the semantic network data structure at the world stage. currently, the popular conception of the semantic web is that of a data modeling medium where real and conceptual entities are related in semantically meaningful ways. however, new models have emerged that explicitly encode procedural information within the semantic network substrate. with these new technologies, the semantic web has evolved from a data modeling medium to a computational medium. this article provides a classification of existing computational modeling efforts and the requirements of supporting technologies that will aid in the further growth of this burgeoning domain. resolution of the cosmological constant problem based on causal set theory is discussed. it is argued that one should not observe any spacetime variations in cosmological constant if causal set approach is correct. we propose a method for quantum state transfer from one atom laser beam to another via an intermediate optical field, using raman incoupling and outcoupling techniques. our proposal utilises existing experimental technologies to teleport macroscopic matter waves over potentially large distances without shared entanglement. in this note we compute some enumerative invariants of real and complex projective spaces by means of some enriched graphs called floor diagrams. in these lectures i will review some theoretical results that have been obtained for spin glasses. i will concentrate my attention on the formulation of the mean field approach and on its numerical and experimental verifications. i will present the various hypothesis at the basis of the theory and i will discuss their mathematical and physical status. this article consists of a brief discussion of the energy density over time or frequency that is obtained with the wavelet transform. also an efficient algorithm is suggested to calculate the continuous transform with the morlet wavelet. the energy values of the wavelet transform are compared with the power spectrum of the fourier transform. useful definitions for power spectra are given. the focus of the work is on simple measures to evaluate the transform with the morlet wavelet in an efficient way. the use of the transform and the defined values is shown in some examples. it is common to use reciprocal best hits, also known as a boomerang criterion, for determining orthology between sequences. the best hits may be found by blast, or by other more recently developed algorithms. previous work seems to have assumed that reciprocal best hits is a sufficient but not necessary condition for orthology. in this article, i explain why reciprocal best hits cannot logically be a sufficient condition for orthology. if reciprocal best hits is neither sufficient nor necessary for orthology, it would seem worthwhile to examine further the logical foundations of some unsupervised algorithms that are used to identify orthologs. in his treatise on floating bodies archimedes determines the equilibrium positions of a floating paraboloid segment, but only in the case when the basis of the segment is either completely outside of the fluid or completely submerged. here we give a mathematical model for the remaining case, i.e., two simple conditions which describe the equilibria in closed form. we provide tools for finding all equilibria in a reliable way and for the classification of these equilibria. this paper can be considered as a continuation of a recent article of rorres. we establish some upper and lower bounds for the number of rational points of prym varieties over finite fields. a new kind of aperiodic tiling is introduced. it is shown to underlie a structure obtained as a superposition of waves with incommensurate periods. its connections to other other tilings and quasicrystals are discussed. we find a protocol transmitting two quantum states crossly in the butterfly network only with prior entanglement between two senders. this protocol requires only one qubit transmission or two classical bits transmission in each channel in the butterfly network. it is also proved that it is impossible without prior entanglement. more precisely, an upper bound of average fidelity is given in the butterfly network when prior entanglement is not allowed. we consider the question of deriving initial conditions for scalar fields in driving both an early and late quintessence phase. the dark energy field presents an unresolved uniformity problem. further difficulties with initial conditions for assisted, kinetic and phantom inflation are presented. we review the use of the canonical measure and find the negative conclusions of gibbons and hawking can be allayed by means of a reasonable quantum cosmological input. we remark upon some attempts at incorporating inflationary schemes into cyclic and bouncing models. we compare the behavior of a wave packet in the presence of a complex and a pure quaternionic potential step. this analysis, done for a gaussian convolution function, sheds new light on the possibility to recognize quaternionic deviations from standard quantum mechanics. in this paper we determine the number of the meaningful compositions of higher order of the differential operations and gateaux directional derivative. game theory has many limitations implicit in its application. by utilizing multiagent modeling, it is possible to solve a number of problems that are unsolvable using traditional game theory. in this paper reinforcement learning is applied to neural networks to create intelligent agents this brief article discusses some aspects of quantum theory and their impact on popular culture. the basic features of quantum entanglement between two or more parties are introduced in a language suitable for a general audience, and metaphorically connected to love and faithfulness in human relationships. reformulation of the generalized electromagnetic fields of dyons has been dicussed in inhomogenous media and corresponding quaternionic equations are derived in compact, simple and unique manner. we have also discussed the monochromatic fields of generalized electromagnetic fields of dyons in slowly changing media in a consistent manner. using gch, we force the following: there are continuum many simple cardinal characteristics with pairwise different values. in this paper, we propose a probabilistic approach to the study of the characteristic polynomial of a random unitary matrix. we recover the mellin fourier transform of such a random polynomial, first obtained by keating and snaith, using a simple recursion formula, and from there we are able to obtain the joint law of its radial and angular parts in the complex plane. in particular, we show that the real and imaginary parts of the logarithm of the characteristic polynomial of a random unitary matrix can be represented in law as the sum of independent random variables. from such representations, the celebrated limit theorem obtained by keating and snaith is now obtained from the classical central limit theorems of probability theory, as well as some new estimates for the rate of convergence and law of the iterated logarithm type results. this lecture addresses the concept of form factor in magnetic scattering of thermal neutrons, analyzing its meaning, discussing its measurement by polarized neutrons and detailing its computation for the ions by the spherical tensor operator formalism. conformally invariant massless field systems involving only dimensionless parameters are known to describe particle physics at very high energy. in the presence of an external gravitational field, the conformal symmetry may generalize to weyl invariance. however, the latter symmetry no longer survives after quantization: a weyl anomaly appears. in this letter, a purely algebraic understanding of the universal structure of the weyl anomalies is presented. the results hold in arbitrary dimensions and independently of any regularization scheme. simple recursion relations for zero energy states of supersymmetric matrix models are derived by using an unconventional reducible representation for the fermionic degrees of freedom. it has hitherto been known that in a transitive unimodular graph, each tree in the wired spanning forest has only one end a.s. we dispense with the assumptions of transitivity and unimodularity, replacing them with a much broader condition on the isoperimetric profile that requires just slightly more than uniform transience. this paper has been withdrawn by the authors. we present the very simple model of a particle detector and the proposal for the calculation of the average value of the time of arrival. although conservation of energy is fundamental in physics, its principles seem to be violated in the field of wave propagation in turbid media by the energy enhancement of the coherent backscattering cone. in this letter we present experimental data which show that the energy enhancement of the cone is balanced by an energy cutback at all scattering angles. moreover, we give a complete theoretical description, which is in good agreement with these data. the additional terms needed to enforce energy conservation in this description result from an interference effect between incident and multiply scattered waves, which is reminiscent of the optical theorem in single scattering. the stability problem of the rotation induced electrostatic wave in extragalactic jets is presented. solving a set of equations describing dynamics of a relativistic plasma flow of agn jets, an expression of the instability rate has been derived and analyzed for typical values of agns. the growth rate was studied versus the wave length and the inclination angle and it has been found that the instability process is much efficient with respect to the accretion disk evolution, indicating high efficiency of the instability. we compute the hilbert coefficients of a graded module with pure resolution and discuss lower and upper bounds for these coefficients for arbitrary graded modules. we present a preliminary set of updated nlo parton distributions. for the first time we have a quantitative extraction of the strange quark and antiquark distributions and their uncertainties determined from ccfr and nutev dimuon cross sections. additional jet data from hera and the tevatron improve our gluon extraction. lepton asymmetry data and neutrino structure functions improve the flavour separation, particularly constraining the down quark valence distribution. we prove that jordan triple elementary surjective maps on unital rings containing a nontrivial idempotent are automatically additive. we include in statistical model calculations the facts that in the nuclear multifragmentation process the fragments are produced within a given volume and have a finite size. the corrections associated with these constraints affect the partition modes and, as a consequence, other observables in the process. in particular, we find that the favored fragmenting modes strongly suppress the collective flow energy, leading to much lower values compared to what is obtained from unconstrained calculations. this leads, for a given total excitation energy, to a nontrivial correlation between the breakup temperature and the collective expansion velocity. in particular we find that, under some conditions, the temperature of the fragmenting system may increase as a function of this expansion velocity, contrary to what it might be expected. we prove that jordan elementary surjective maps on rings are automatically additive. we describe the results of the first tests made on lisa, a simulator of planetary environments designed and built in padua, dedicated to the study of the limit of bacterial life on the planet mars. tests on the cryogenic circuit, on the uv illumination and on bacterial coltures at room temperature that shall be used as references are described. a magnetic detector such as minos which is measuring the sign of muons has to deal with issues of bending, which depend on the magnetic field configuration, and multiple scattering, which depends on the amount of material which is traversed. above some momentum which depends on these factors, the momentum cannot be resolved. issues related to measurement of the muon charge ratio in minos are discussed. we describe a sensor for the measurement of thin dielectric layers capable of operation in a variety of environments. the sensor is obtained by microfabricating a capacitor with interleaved aluminum fingers, exposed to the dielectric to be measured. in particular, the device can measure thin layers of solid frozen from a liquid or gaseous medium. sensitivity to single atomic layers is achievable in many configurations and, by utilizing fast, high sensitivity capacitance read out in a feedback system onto environmental parameters, coatings of few layers can be dynamically maintained. we discuss the design, read out and calibration of several versions of the device optimized in different ways. we specifically dwell on the case in which atomically thin solid xenon layers are grown and stabilized, in cryogenic conditions, from a liquid xenon bath. we give some new bounds for the clique and independence numbers of a graph in terms of its eigenvalues. the software trim offers implementations of tropical implicitization and tropical elimination, as developed by tevelev and the authors. given a polynomial map with generic coefficients, trim computes the tropical variety of the image. when the image is a hypersurface, the output is the newton polytope of the defining polynomial. trim can thus be used to compute mixed fiber polytopes, including secondary polytopes. we define the concept of weighted lattice polynomial functions as lattice polynomial functions constructed from both variables and parameters. we provide equivalent forms of these functions in an arbitrary bounded distributive lattice. we also show that these functions include the class of discrete sugeno integrals and that they are characterized by a median based decomposition formula. based on the concept of curved spacetime in einsteinian general relativity, the field theories and their quantum theories in the curved octonion spaces etc are discussed. the research results discover the close relationships of the curved spacetimes with the field theories and quantum theories. in the field theories of curved spacetimes, the curvatures have direct effect on field strength and field source etc. while the curvatures have direct impact on wave functions and quantum equations etc in the quantum theories of curved spacetimes. the research results discover that some abnormal phenomena of field source particles could be explained by the field theories or quantum theories in the curved spacetimes. in this paper we will first introduce the notion of affine structures on a ringed space and then obtain several properties. affine structures on a ringed space, arising mainly from complex analytical spaces of algebraic schemes over number fields, behave like differential structures on a smooth manifold.   as one does for differential manifolds, we will use pseudogroups of affine transformations to define affine atlases on a ringed space. an atlas on a space is said to be an affine structure if it is maximal. an affine structure is admissible if there is a sheaf on the underlying space such that they are coincide on all affine charts, which are in deed affine open sets of a scheme. in a rigour manner, a scheme is defined to be a ringed space with a specified affine structure if the affine structures are in action in some special cases such as analytical spaces of algebraic schemes. particularly, by the whole of affine structures on a space, we will obtain respectively necessary and sufficient conditions that two spaces are homeomorphic and that two schemes are isomorphic, which are the two main theorems of the paper. it follows that the whole of affine structures on a space and a scheme, as local data, encode and reflect the global properties of the space and the scheme, respectively. resources in a distributed system can be identified using identifiers based on random numbers. when using a distributed hash table to resolve such identifiers to network locations, the straightforward approach is to store the network location directly in the hash table entry associated with an identifier. when a mobile host contains a large number of resources, this requires that all of the associated hash table entries must be updated when its network address changes.   we propose an alternative approach where we store a host identifier in the entry associated with a resource identifier and the actual network address of the host in a separate host entry. this can drastically reduce the time required for updating the distributed hash table when a mobile host changes its network address. we also investigate under which circumstances our approach should or should not be used. we evaluate and confirm the usefulness of our approach with experiments run on top of opendht. we use a variational method to construct soliton solutions for systems characterized by opposing dispersion and competing nonlinearities at fundamental and second harmonics. we show that both ordinary and embedded solitons tend to gain energy when the second harmonic field becomes weaker than the first harmonic field. this paper has been withdrawn. the authors realized that the obtained results were not new. it is explained how the time evolution of the operadic variables may be introduced. as an example, an operadic lax representation of the harmonic oscillator is considered. this paper aims to give a probabilistic construction of interactions which may be relevant for building physical theories such as interacting quantum field theories. we start with the path integral definition of partition function in quantum field theory which recall us the probabilistic nature of this physical theory. from a gaussian law considered as free theory, an interacting theory is constructed by nontrivial convolution product between the free theory and an interacting term which is also a probability law. the resulting theory, again a probability law, exhibits two proprieties already present in nowadays theories of interactions such as gauge theory : the interaction term does not depend on the free term, and two different free theories can be implemented with the same interaction. the direct use of gaussian measures allows to generalize the present construction for infinite dimensional spaces equipped with gaussian measures. we consider the static and dynamic models of cournot duopoly with tax evasion. in the dynamic model we introduce the time delay and we analyze the local stability of the stationary state. there is a critical value of the delay when the hopf bifurcation occurs. we enumerate rooted triangulations of a sphere with multiple holes by the total number of edges and the length of each boundary component. the proof relies on a combinatorial identity due to w.t. tutte. elementary particle physics is the quadrant of nature whose laws can be written in a few lines with absolute precision and the greatest empirical adequacy. if this is the case, as i believe it is, it must be possible and is probably useful to introduce the students and the interested readers to the entire subject in a compact way. this is the main aim of these lectures. we find solutions of supersymmetric string field theory that correspond to the photon marginal deformation in the boundary conformal field theory. we revisit the bosonic string marginal deformation and generate a real solution for it. we find a map between the solutions of bosonic and supersymmetric string field theories and suggest a universal solution to superstring field theory. the jacobian algebras are introduced and their various properties are studied. a method for constructing lagrangians for the lie transformation groups is explained. as examples, the lagrangians for real plane rotations and affine transformations of the real line are constructed. we put a new conjecture on primes from the point of view of its binary expansions and make a step towards justification. a general reconstruction and calibration procedure for tracking and wire position determination of the opera drift tubes is presented. the mathematics of the pattern recognition and the track fit are explained. we discuss energy current correlations in thermal equilibrium and point out the linkage to the fluctuating peierls equation. the commonly used west and yennie integral formula for the relative phase between the coulomb and elastic hadronic amplitudes might be consistently applied to only if the hadronic amplitude had the constant ratio of the real to the imaginary parts al all kinematically allowed values of four momentum transfer squared. for investigation of electron transport on the nanoscale, a system possessing a simple to interpret electronic structure is composed of alkane chains bridging two electrodes via end groups; to date the majority of experiments and theoretical investigations on such structures have considered thiols bonding to gold electrodes. recently experiments show that well defined molecular conductances may be resolved if the thiol end groups are replaced by amines. in this theoretical study, we investigate the bonding of amine groups to gold clusters and calculate electron transport across the resulting tunnel junctions. we find very good agreement with recent experiments for alkane diamines and discuss differences with respect to the alkane dithiol system. we study the almost sure convergence of randomly truncated stochastic algorithms. we present a new convergence theorem which extends the already known results by making vanish the classical condition on the noise terms. the aim of this work is to prove an almost sure convergence result of randomly truncated stochastic algorithms under easily verifiable conditions we explain how the kinetic theory of l. boltzmann is applied to weakly nonlinear wave equations. we give a survey of results relating the restricted holonomy of a riemannian spin manifold with lower bounds on the spectrum of its dirac operator, giving a new proof of a result originally due to kirchberg. the exact relativistic form for the beta decay endpoint spectrum is derived and presented in a simple factorized form. we show that our exact formula can be well approximated to yield the endpoint form used in the fit method of the katrin collaboration. we also discuss the three neutrino case and how information from neutrino oscillation experiments may be useful in analyzing future beta decay endpoint experiments. in quantum mechanics textbooks the momentum operator is defined in the cartesian coordinates and rarely the form of the momentum operator in spherical polar coordinates is discussed. consequently one always generalizes the cartesian prescription to other coordinates and falls in a trap. in this work we introduce the difficulties one faces when the question of the momentum operator in general curvilinear coordinates arises. we have tried to elucidate the points related to the definition of the momentum operator taking spherical polar coordinates as our specimen coordinate system and proposed an elementary method in which we can ascertain the form of the momentum operator in general coordinate systems. we construct real analytic flat moebius strips of arbitrary isotopy types, whose centerlines are geodesics or lines of curvature. we present numerical simulations of a model of cellulose consisting of long stiff rods, representing cellulose microfibrils, connected by stretchable crosslinks, representing xyloglucan molecules, hydrogen bonded to the microfibrils. within a broad range of temperature the competing interactions in the resulting network give rise to a slow glassy dynamics. in particular, the structural relaxation described by orientational correlation functions shows a logarithmic time dependence. the glassy dynamics is found to be due to the frustration introduced by the network of xyloglucan molecules. weakening of interactions between rod and xyloglucan molecules results in a more marked reorientation of cellulose microfibrils, suggesting a possible mechanism to modify the dynamics of the plant cell wall. we discuss a recent result by c. culter: every polygonal outer billiard has a periodic trajectory. the discovery of many objects with unprecedented, amazing observational characteristics caused the last decade to be the most prolific period for the supernova research. many of these new supernovae are transitional objects between existing classes, others well enter within the defined classes, but still show unique properties. this makes the traditional classification scheme inadequate to take into account the overall sn variety and, consequently, requires the introduction of new subclasses. we present two new continuous time quantum search algorithms similar to the adiabatic search algorithm, but now without an adiabatic evolution. we find that both algorithms work for a wide range of values of the parameters of the hamiltonian, and one of them has, as an additional feature that, for values of time larger than a characteristic one, it will converge to a state which can be close to the searched state. we present an account of negative differential forms within a natural algebraic framework of differential graded algebras, and explain their relationship with forms on path spaces. we review extended theories of gravity in metric and palatini formalism pointing out their cosmological and astrophysical application. the aim is to propose an alternative approach to solve the puzzles connected to dark components. in the setting of additive regression model for continuous time process, we establish the optimal uniform convergence rates and optimal asymptotic quadratic error of additive regression. to build our estimate, we use the marginal integration method. the effect of an intense external linear polarized radiation field on the angular distributions and polarization states of the photons emitted during the radiative recombination is investigated. it is predicted, on symmetry grounds, and corroborated by numerical calculations of approximate recombination rates, that emission of elliptically polarized photons occurs when the momentum of the electron beam is not aligned to the direction of the oscillating field. moreover, strong modifications to the angular distributions of the emitted photons are induced by the external radiation field. inertial effects in fluctuations of the work to sustain a system in a nonequilibrium steady state are discussed for a dragged massive brownian particle model using a path integral approach. we calculate the work distribution function in the laboratory and comoving frames and prove the asymptotic fluctuation theorem for these works for any initial condition. important and observable differences between the work fluctuations in the two frames appear for finite times and are discussed concretely for a nonequilibrium steady state initial condition. we also show that for finite times a time oscillatory behavior appears in the work distribution function for masses larger than a nonzero critical value. the question of whether charged leptons oscillate is discussed in detail, with a special emphasis on the coherence properties of the charged lepton states created via weak interactions. this analysis allows one to clarify also an important issue of the theory of neutrino oscillations. here we present a system of coupled phase oscillators with nearest neighbors coupling, which we study for different boundary conditions. we concentrate at the transition to total synchronization. we are able to develop exact solutions for the value of the coupling parameter when the system becomes completely synchronized, for the case of periodic boundary conditions as well as for an open chain with fixed ends. we compare the results with those calculated numerically. a covariant functor on the elliptic curves with complex multiplication is constructed. the functor takes values in the noncommutative tori with real multiplication. a conjecture on the rank of an elliptic curve is formulated. a bayesian approach is used to estimate the covariance matrix of gaussian data. ideas from gaussian graphical models and model selection are used to construct a prior for the covariance matrix that is a mixture over all decomposable graphs. for this prior the probability of each graph size is specified by the user and graphs of equal size are assigned equal probability. most previous approaches assume that all graphs are equally probable. we show empirically that the prior that assigns equal probability over graph sizes outperforms the prior that assigns equal probability over all graphs, both in identifying the correct decomposable graph and in more efficiently estimating the covariance matrix. we briefly review the contribution of sn rate measurements to the debate on sn progenitor scenarios. we find that core collapse rates confirms the rapid evolution of the star formation rate with redshift. after accounting for the dispersion of sn ia measurements and uncertainty of the star formation history, the standard scenarios for sn ia progenitors appear consistent with all observational constraints. the paper surveys recent progress in establishing uniqueness and developing inversion formulas and algorithms for the thermoacoustic tomography. in mathematical terms, one deals with a rather special inverse problem for the wave equation. in the case of constant sound speed, it can also be interpreted as a problem concerning the spherical mean transform.'