hochschild cohomology and atiyah classes abstract in this paper we prove that on a smooth algebraic variety the hkr morphism twisted by the square root of the todd genus gives an isomorphism between the sheaf of poly vector fields and the sheaf of poly differential operators both considered as derived gerstenhaber algebras in particular we obtain an isomorphism between hochschild cohomology and the cohomology of poly vector fields which is compatible with the lie bracket and the cupproduct the latter compatibility is an unpublished result by kontsevich our proof is set in the framework of lie algebroids and so applies without modification in much more general settings as well

a scaled difference chi square test statistic for moment structure analysis a family of scaling corrections aimed to improve the chi square approximation of goodness of fit test statistics in small samples large models and nonnormal data was proposed in satorra and bentler 1994 for structural equations models satorra bentler s sb scaling corrections are available in standard computer software often however the interest is not on the overall fit of a model but on a test of the restrictions that a null model saym0 implies on a less restricted onem1 ift0 andt1 denote the goodness of fit test statistics associated tom0 andm1 respectively then typically the differencetd t0 t1 is used as a chi square test statistic with degrees of freedom equal to the difference on the number of independent parameters estimated under the modelsm0 andm1 as in the case of the goodness of fit test it is of interest to scale the statistictd in order to improve its chi square approximation in realistic that is nonasymptotic and nonormal applications in a recent paper satorra 2000 shows that the difference between two sb scaled test statistics for overall model fit does not yield the correct sb scaled difference test statistic satorra developed an expression that permits scaling the difference test statistic but his formula has some practical limitations since it requires heavy computations that are not available in standard computer software the purpose of the present paper is to provide an easy way to compute the scaled difference chi square statistic from the scaled goodness of fit test statistics of modelsm0 andm1 a monte carlo study is provided to illustrate the performance of the competing statistics

r s analysis of reaction time in neuron type test for human activity in civil aviation abstract human factors become the most serious problem leading to accidents of civil aviation which stimulates the design and analysis of neuron type test ntt system to explore the intrinsic properties and patterns behind the behaviors of professionals and students in civil aviation in the experiment normal practitioners reaction time sequences collected from ntt exhibit log normal distribution approximately we apply the 2 test to compute the goodness of fit by transforming the time sequence with box cox transformation to cluster practitioners the long term correlation of different individual practitioner s time sequence is represented by the hurst exponent via rescaled range analysis also named by range standard deviation r s analysis the different hurst exponent suggests the existence of different collective behavior and different intrinsic patterns of human factors in civil aviation

vertex irf correspondence and factorized l operators for an elliptic r operator as for an ellipticr operator which satisfies the yang baxter equation the incoming and outgoing intertwining vectors are constructed and the vertex irf correspondence for the ellipticr operator is obtained the boltzmann weights of the corresponding irf model satisfy the star traingle relation by means of these intertwining vectors the factorizedl operators for the ellipticr operator are also constructed the vertex irf correspondence and the factorizedl operators for belavin sr matrix are reproduced from those of the ellipticr operator

an analysis of real fourier domain based adaptive algorithms implemented with the hartley transform using cosine sine symmetries the least mean squared lms algorithm and its variants have been the most often used algorithms in adaptive signal processing however the lms algorithm suffers from a high computational complexity especially with large filter lengths the fourier transform based block normalized lms fbnlms reduces the computation count by using the discrete fourier transform dft and exploiting the fast algorithms for implementing the dft even though the savings achieved with the fbnlms over the direct lms implementation are significant the computational requirements of fbnlms are still very high rendering many real time applications like audio and video estimation infeasible the hartley transform based bnlms hbnlms is found to have a computational complexity much less than and a memory requirement almost of the same order as that of the fbnlms this paper is based on the cosine and sine symmetric implementation of the discrete hartley transform dht which is the key in reducing the computational complexity of the fbnlms by 33 asymptotically with respect to multiplications the parallel implementation of the discrete cosine transform dct in turn can lead to more efficient implementations of the hbnlms

image characterization by fractal descriptors in variational mode decomposition domain application to brain magnetic resonance abstract the main purpose of this work is to explore the usefulness of fractal descriptors estimated in multi resolution domains to characterize biomedical digital image texture in this regard three multi resolution techniques are considered the well known discrete wavelet transform dwt and the empirical mode decomposition emd and the newly introduced variational mode decomposition mode vmd the original image is decomposed by the dwt emd and vmd into different scales then fourier spectrum based fractal descriptors is estimated at specific scales and directions to characterize the image the support vector machine svm was used to perform supervised classification the empirical study was applied to the problem of distinguishing between normal and abnormal brain magnetic resonance images mri affected with alzheimer disease ad our results demonstrate that fractal descriptors estimated in vmd domain outperform those estimated in dwt and emd domains and also those directly estimated from the original image

globalization for perturbative quantization of nonlinear split aksz sigma models on manifolds with boundary we describe a covariant framework to construct a globalized version for the perturbative quantization of nonlinear split aksz sigma models on manifolds with and without boundary and show that it captures the change of the quantum state as one changes the constant map around which one perturbs this is done by using concepts of formal geometry moreover we show that the globalized quantum state can be interpreted as a closed section with respect to an operator that squares to zero this condition is a generalization of the modified quantum master equation as in the bv bfv formalism which we call the modified differential quantum master equation

chiral potts model as a descendant of the six vertex model we observe that then state integrable chiral potts model can be considered as a part of some new algebraic structure related to the six vertex model as a result we obtain a functional equation which is supposed to determine all the eigenvalues of the chiral potts model transfer matrix

application of the detrended fluctuation analysis dfa method for describing cloud breaking abstract a method to sort out correlations and decorrelations in stratus cloud formation persistence and breakup is introduced the detrended fluctuation analysis dfa statistical method is applied to microwave radiometer data the existence of long range power law correlations in stratus cloud liquid water content fluctuations is demonstrated over a 2 h period moreover using a finite size time interval window a change from brownian to non brownian fluctuation regimes is clearly shown to define the cloud structure changes such findings are similar to those found in dna and financial data sequences when mosaics of persistent and antipersistent patches are present the occurrence of these statistics in stratus cloud liquid water content suggests the usefulness of similar studies on cloud resolving model output and for better meteorological predictability

triangular dynamical r matrices and quantization abstract we study some general aspects of triangular dynamical r matrices using poisson geometry we show that a triangular dynamical r matrix r h 2 g always gives rise to a regular poisson manifold using the fedosov method we prove that non degenerate triangular dynamical r matrices i e those such that the corresponding poisson manifolds are symplectic are quantizable and that the quantization is classified by the relative lie algebra cohomology h2 g h

involutions and representations for reduced quantum algebras abstract in the context of deformation quantization there exist various procedures to deal with the quantization of a reduced space m red we shall be concerned here mainly with the classical marsden weinstein reduction assuming that we have a proper action of a lie group g on a poisson manifold m with a moment map j for which zero is a regular value for the quantization we follow bordemann et al 2000 6 with a simplified approach and build a star product red on m red from a strongly invariant star product on m the new questions which are addressed in this paper concern the existence of natural involutions on the reduced quantum algebra and the representation theory for such a reduced algebra we assume that is hermitian and we show that the choice of a formal series of smooth densities on the embedded coisotropic submanifold c j 1 0 with some equivariance property defines a involution for red on the reduced space looking into the question whether the corresponding involution is the complex conjugation which is a involution in the marsden weinstein context yields a new notion of quantized modular class we introduce a left c m submodule and a right c m red red submodule c cf c of c c we define on it a c m red valued inner product and we establish that this gives a strong morita equivalence bimodule between c m red and the finite rank operators on c cf c the crucial point is here to show the complete positivity of the inner product we obtain a rieffel induction functor from the strongly non degenerate representations of c m red red on pre hilbert right d modules to those of c m for any auxiliary coefficient algebra d over c

a new delayless subband adaptive filter structure adaptive subband techniques have been developed to reduce complexity and slow convergence problems of the traditional fullband high order adaptive filters some of the disadvantages often encountered in most of the proposed architectures are the effect of aliasing associated with the multirate structure which is a source of error in the modeling of the unknown system and the delay introduced in the signal path we present a new delayless maximally decimated structure where the optimal subband filters are related to the wideband system in a closed form they make use of a special dft analysis filterbank where the polyphase components of the prototype filter represent fractional delays so that there is no need for adaptive cross filters and the unknown system can modeled perfectly in a closed loop scheme we interpret the proposed structure as a special case of a block adaptive filter with lower computational complexity than the conventional fullband lms algorithm some computer simulations are presented in order to verify the good features of the proposed structure

formality and kontsevich duflo type theorems for lie pairs newcommand poly operatorname poly bullet newcommand td operatorname td l a nabla frac 1 2 newcommand cx 1 operatorname tot big gamma lambda bullet a vee otimes r mathcal 1 poly big newcommand cy 1 mathbb h bullet operatorname ce a mathcal 1 poly kontsevich s formality theorem states that there exists an l infty quasi isomorphism from the dgla t poly m of polyvector fields on a smooth manifold m to the dgla d poly m of polydifferential operators on m which extends the classical hochschild kostant rosenberg map in this paper we extend kontsevich s formality theorem to lie pairs a framework which includes a range of diverse geometric contexts such as complex manifolds foliations and mathfrak g manifolds the spaces cx t and cx d associated with a lie pair l a each carry an l infty algebra structure canonical up to l infty isomorphism these two spaces serve as replacements for the spaces of polyvector fields and polydifferential operators respectively their corresponding cohomology groups cy t and cy d admit canonical gerstenhaber algebra structures we establish the following formality theorem for lie pairs there exists an l infty quasi isomorphism from cx t to cx d whose first taylor coefficient is equal to operatorname hkr circ td here td acts on cx t by contraction furthermore we prove a kontsevich duflo type theorem for lie pairs the hochschild kostant rosenberg map twisted by the square root of the todd class of the lie pair l a is an isomorphism of gerstenhaber algebras from cy t to cy d as applications we establish formality theorems and kontsevich duflo type theorems for complex manifolds foliations and mathfrak g manifolds in the case of complex manifolds we recover the kontsevich duflo theorem of complex geometry

formality for lie algebroids using dolgushev s generalization of fedosov s method for deformation quantization we give a positive answer to a question of p xu can one prove a formality theorem for lie algebroids as a direct application of this result we obtain that any triangular lie bialgebroid is quantizable

representations of toeplitz plus hankel matrices using trigonometric transformations with application to fast matrix vector multiplication abstract representations of real toeplitz and toeplitz plus hankel matrices are presented that involve real trigonometric transformations dct dst dht and diagonal matrices these representations can be used for fast matrix vector multiplication in particular it is shown that the multiplication of an n n toeplitz plus hankel matrix by a vector requires only 4 transformations of length n plus o n operations

the lms algorithm with delayed coefficient adaptation the behavior of the delayed least mean square dlms algorithm is studied it is found that the step size in the coefficient update plays a key role in the convergence and stability of the algorithm an upper bound for the step size is derived that ensures the stability of the dlms the relationship between the step size and the convergence speed and the effect of the delay on the convergence speed are also studied the analytical results are supported by computer simulations

zn n 1 generalization of the chiral potts model we show that ther matrix which intertwines twon by nn 1 state cyclicl operators related with a generalization ofuq sl n algebra can be considered as a boltzmann weight of four spin box for a lattice model with two spin interaction just as ther matrix of the checkerboard chiral potts model the rapidity variables lie on the algebraic curve of the genusg n2 n 1 n 1 n n 1 defined by 2n 3 independent moduli this curve is a natural generalization of the curve which appeared in the chiral potts model factorization properties of thel operator and its connection to the sos models are also discussed

quantization of formal classical dynamical r matrices the reductive case abstract in this paper we prove the existence of a formal dynamical twist quantization for any triangular and non modified formal classical dynamical r matrix in the reductive case the dynamical twist is constructed as the image of the dynamical r matrix by a l quasi isomorphism this quasi isomorphism also allows us to classify formal dynamical twist quantizations up to gauge equivalence

long range anticorrelations and non gaussian behavior of the heartbeat we find that the successive increments in the cardiac beat to beat interals of healthy subjects display scale invariant long range anticorrelations up to 10 4 heart beats furthermore we find that the histogram for the heartbeat intervals increments is well described by a l evy stable distribution for a group of subjects with severe heart disease we find that the distribution is unchanged but the long range correlations vanish therefore the different scaling behavior in health and disease must relate to the underlying dynamics of the heartbeat

factorized representation of felder s elliptic quantum group we constructed a factorized representation of the felder s elliptic quantum group by using the intertwining vectors and further derived its explicit form which is in a special case identical with what bo yu hou et al gave i e a cyclic representation of the sklyanin algebra up to a factor

r matrix quantization of the elliptic ruijsenaars schneider model it is shown that the classical l operator algebra of the elliptic ruijsenaars schneider model can be realized as a subalgebra of the algebra of functions on the cotangent bundle over the centrally extended current group in two dimensions it is governed by two dynamic and bar r matrices satisfying a closed system of equations the corresponding quantum r and bar r matrices are found as solutions to quantum analogues of these equations we present the quantum l operator algebra and show that the system of equations for r and bar r arises as the compatibility condition for this algebra it turns out that the r matrix is twist equivalent to the felder elliptic rf matrix with bar r playing the role of the twist the simplest representation of the quantum l operator algebra corresponding to the elliptic ruijsenaars schneider model is obtained the connection of the quantum l operator algebra to the fundamental relation rb ll llrb with the belavin elliptic r matrix is established as a by product of our construction we find a new n parameter elliptic solution to the classical yang baxter equation

a family of hyperbolic spin calogero moser systems and the spin toda lattices in this paper we continue to develop a general scheme to study a broad class of integrable systems naturally associated with the coboundary dynamical lie algebroids in particular we present a factorization method for solving the hamiltonian flows we also present two important classes of new examples a family of hyperbolic spin calogero moser systems and the spin toda lattices to illustrate our factorization theory we show how to solve these hamiltonian systems explicitly 2004 wiley periodicals inc

an embedding approach to frequency domain and subband adaptive filtering frequency domain and subband implementations improve the computational efficiency and the convergence rate of adaptive schemes the well known multidelay adaptive filter mdf belongs to this class of block adaptive structures and is a dft based algorithm we develop adaptive structures that are based on the trigonometric transforms discrete cosine transform dct and discrete sine transform dst and on the discrete hartley transform dht as a result these structures involve only real arithmetic and are attractive alternatives in cases where the traditional dft based scheme exhibits poor performance the filters are derived by first presenting a derivation for the classical dft based filter that allows us to pursue these extensions immediately the approach used in this paper also provides further insights into subband adaptive filtering

l operator for belavin s r matrix acting on the space of theta functions for the z nz symmetric elliptic r matrix l operators which act on the space of a 1 n 1 integrable characters or the affine weyl group invariants of the fixed level l are constructed for l 1 the matrix elements of the l operator and those of the r matrix are shown to be the same

crossing symmetry in elliptic solutions of the yang baxter equation and a new l operator for belavin s solution some algebraic structures in elliptic solutions of the yang baxter equations are investigated the author proves the crossing symmetry in belavin s model 1981 as well as in the an 1 1 face model and constructs a new family of l operators for belavin s r matrix as an application

solutions of the quantum dynamical yang baxter equation and dynamical quantum groups the quantum dynamical yang baxter qdyb equation is a useful generalization of the quantum yang baxter qyb equation this generalization was introduced by gervais neveu and felder unlike the qyb equation the qdyb equation is not an algebraic but a difference equation with respect to a matrix function rather than a matrix the qdyb equation and its quasiclassical analogue the classical dynamical yang baxter equation arise in several areas of mathematics and mathematical physics conformal field theory integrable systems representation theory the most interesting solution of the qdyb equation is the elliptic solution discovered by felder in this paper we prove the first classification results for solutions of the qdyb equation these results are parallel to the classification of solutions of the classical dynamical yang baxter equation obtained in our previous paper all solutions we found can be obtained from felder s elliptic solution by a limiting process and gauge transformations fifteen years ago the quantum yang baxter equation gave rise to the theory of quantum groups namely it turned out that the language of quantum groups hopf algebras is the adequate algebraic language to talk about solutions of the quantum yang baxter equation in this paper we propose a similar language originating from felder s ideas which we found to be adequate for the dynamical yang baxter equation this is the language of dynamical quantum groups or hopf algebroids which is the quantum counterpart of the language of dynamical poisson groupoids introduced in our previous paper

fedosov dg manifolds associated with lie pairs given any pair l a of lie algebroids we construct a differential graded manifold l 1 oplus l a q which we call fedosov dg manifold we prove that the homological vector field q constructed on l 1 oplus l a by the fedosov iteration method arises as a byproduct of the poincare birkhoff witt map established in 18 finally using the homological perturbation lemma we establish a quasi isomorphism of dolgushev fedosov type the differential graded algebras of functions on the dg manifolds a 1 d a and l 1 oplus l a q are homotopy equivalent

brst quantization of quasisymplectic manifolds and beyond we consider a class of factorizable poisson brackets which includes almost all reasonable poisson structures a particular case of the factorizable brackets are those associated with symplectic lie algebroids the brst theory is applied to describe the geometry underlying these brackets as well as to develop a deformation quantization procedure in this particular case this can be viewed as an extension of the fedosov deformation quantization to a wide class of irregular poisson structures in a more general case the factorizable poisson brackets are shown to be closely connected with the notion of n algebroid a simple description is suggested for the geometry underlying the factorizable poisson brackets based on construction of an odd poisson algebra bundle equipped with an abelian connection it is shown that the zero curvature condition for this connection generates all the structure relations for the n algebroid as well as a generalization of the yang baxter equation for the symplectic structure

ruijsenaars macdonald type difference operators from belavin model with open boundary conditions antisymmetric fusions of the belavin model with integrable open boundary conditions are studied the centre of the corresponding operator algebra the sklyanin determinant is constructed we prove that the transfer matrices of the fusion hierarchies mutually commute utilizing the factorized l operators this commuting family is expressed as mutually commuting difference operators acting on a function space this gives ruijsenaars macdonald type commuting difference operators which describe the conservation laws of an integrable system

kontsevich s graph complex grt and the deformation complex of the sheaf of polyvector fields we generalize kontsevich s construction of l1 derivations of polyvector elds from the ane space to an arbitrary smooth algebraic variety more precisely we construct a map in the homotopy category from kontsevich s graph complex to the deformation complex of the sheaf of polyvector elds on a smooth algebraic variety we show that the action of deligne drinfeld

on the globalization of the poisson sigma model in the bv bfv formalism we construct a formal global quantization of the poisson sigma model in the bv bfv formalism using the perturbative quantization of aksz theories on manifolds with boundary and analyze the properties of the boundary bfv operator moreover we consider mixed boundary conditions and show that they lead to quantum anomalies i e to a failure of the modified differential quantum master equation we show that it can be restored by adding boundary terms to the action at the price of introducing corner terms in the boundary operator we also show that the quantum grothendieck bfv operator on the total space of states is a differential i e squares to zero which is necessary for a well defined bv cohomology

a formality theorem for hochschild chains abstract we prove tsygan s formality conjecture for hochschild chains of the algebra of functions on an arbitrary smooth manifold m using the fedosov resolutions proposed in math qa 0307212 and the formality quasi isomorphism for hochschild chains of r y 1 y d proposed in paper math qa 0010321 by shoikhet this result allows us to describe traces on the quantum algebra of functions on an arbitrary poisson manifold

transform domain adaptive filters an analytical approach transform domain adaptive filters refer to lms filters whose inputs are preprocessed with a unitary data independent transformation followed by a power normalization stage the transformation is typically chosen to be the discrete fourier transform dft although other transformations such as the cosine transform dct the hartley transform dht or the walsh hadamard transform have also been proposed in the literature the resulting algorithms are generally called dft lms dct lms etc this preprocessing improves the eigenvalue distribution of the input autocorrelation matrix of the lms filter and as a consequence ameliorates its convergence speed in this paper we start with a brief intuitive explanation of transform domain algorithms we then analyze the effects of the preprocessing performed in dft lms and dct lms for first order markov inputs in particular we show that for markov 1 inputs of correlation parameter spl rho spl isin 0 1 the eigenvalue spread after dft and power normalization tends to 1 spl rho l 1 spl rho as the size of the filter gets large whereas after dct and power normalization it reduces to 1 spl rho for comparison the eigenvalue spread before transformation is asymptotically equal to 1 spl rho sup 2 1 spl rho sup 2 the analytical method used in the paper provides additional insight into how the algorithms work and is expected to extend to other input signal classes and other transformations

relative formality theorem and quantisation of coisotropic submanifolds we prove a relative version of kontsevich s formality theorem this theorem involves a manifold m and a submanifold c and reduces to kontsevich s theorem if c m it states that the dgla of multivector fields on an infinitesimal neighbourhood of c is l quasiisomorphic to the dgla of multidifferential operators acting on sections of the exterior algebra of the conormal bundle applications to the deformation quantisation of coisotropic submanifolds are given the proof uses a duality transformation to reduce the theorem to a version of kontsevich s theorem for supermanifolds which we also discuss in physical language the result states that there is a duality between the poisson sigma model on a manifold with a d brane and the poisson sigma model on a supermanifold without branes or more properly with a brane which extends over the whole supermanifold

the non commutative weil algebra for any compact lie group g together with an invariant inner product on its lie algebra g we define the non commutative well algebra w g as a tensor product of the universal enveloping algebra u g and the clifford algebra cl 8 just like the usual we

formality of cyclic cochains abstract we prove m kontsevich s cyclic formality conjecture this conjecture is the cyclic analog of the formality theorem for hochschild chains concretely it states that the differential graded lie algebra of polydifferential cyclic cochains of the algebra of smooth functions on a manifold m is l quasi isomorphic to the second term in the spectral sequence computing its cohomology as an application we can classify all closed star products on m

covariant and equivariant formality theorems abstract we give a proof of kontsevich s formality theorem for a general manifold using fedosov resolutions of algebras of polydifferential operators and polyvector fields the main advantage of our construction of the formality quasi isomorphism is that it is based on the use of covariant tensors unlike kontsevich s original proof which is based on jets of polydifferential operators and polyvector fields using our construction we prove that if a group g acts smoothly on a manifold m and m admits a g invariant affine connection then there exists a g equivariant quasi isomorphism of formality this result implies that if a manifold m is equipped with a smooth action of a finite or compact group g or equipped with a free action of a lie group g then m admits a g equivariant formality quasi isomorphism in particular this gives a solution of the deformation quantization problem for an arbitrary poisson orbifold

a nonlinear time frequency analysis method an alternative method of time frequency signal analysis is introduced and is compared with the conventional discrete fourier transfer dft based methods the structure of the proposed algorithm and its mathematical properties are presented the proposed algorithm has a nonlinear structure that provides a frequency adaptivity feature it can be implemented both in analog and in digital form and is particularly suitable for real time applications where computational efficiency is important a comparison is made with the dft in terms of algorithm efficiency sensitivity and complexity it is shown that compared with the dft the algorithm is more efficient for real time applications and is less sensitive to noise and variations in the frequency and sampling rate while maintaining simplicity of the structure and computational efficiency slower convergence rate of the algorithm compared with the dft constitutes its main shortcoming

from local to global deformation quantization of poisson manifolds we give an explicit construction of a deformation quantization of the algebra of functions on a poisson manifold based on m kontsevich s local formula the deformed algebra of functions is realized as the algebra of horizontal sections of a vector bundle with flat connection

formality theorems for hochschild chains in the lie algebroid setting in this paper we prove lie algebroid versions of tsygan s formality conjecture for hochschild chains both in the smooth and holomorphic settings in the holomorphic setting our result implies a version of tsygan s formality conjecture for hochschild chains of the structure sheaf of any complex manifold and in the smooth setting this result allows us to describe quantum traces for an arbitrary poisson lie algebroid the proofs are based on the use of kontsevich s quasi isomorphism for hochschild cochains of r y 1 y d shoikhet s quasi isomorphism for hochschild chains of r y 1 y d and fedosov s resolutions of the natural analogues of hochschild co chain complexes associated with a lie algebroid

commuting difference operators arising from the elliptic c2 1 face model we study a pair of commuting difference operators arising from the elliptic c2 1 face model the operators whose coefficients are expressed in terms of the jacobi s elliptic theta function act on the space of meromorphic functions on the weight space of the c2 type simple lie algebra we show that the space of functions spanned by the level one characters of the affine lie algebra sp 4 c is invariant under the action of the difference operators

geometry and classificatin of solutions of the classical dynamical yang baxter equation the classical yang baxter equation cybe is an algebraic equation central in the theory of integrable systems its nondegenerate solutions were classified by belavin and drinfeld quantization of cybe led to the theory of quantum groups a geometric interpretation of cybe was given by drinfeld and gave rise to the theory of poisson lie groups

deformation quantization in algebraic geometry abstract we study deformation quantizations of the structure sheaf o x of a smooth algebraic variety x in characteristic 0 our main result is that when x is d affine any formal poisson structure on x determines a deformation quantization of o x canonically up to gauge equivalence this is an algebro geometric analogue of kontsevich s celebrated result

displacement structure theory and applications in this survey paper we describe how strands of work that are important in two different fields matrix theory and complex function theory have come together in some work on fast computational algorithms for matrices with what we call displacement structure in particular a fast triangularization procedure can be developed for such matrices generalizing in a striking way an algorithm presented by schur 1917 j reine angew math 147 1917 pp 205 232 in a paper on checking when a power series is bounded in the unit disc this factorization algorithm has a surprisingly wide range of significant applications going far beyond numerical linear algebra we mention among others inverse scattering analytic and unconstrained rational interpolation theory digital filter design adaptive filtering and state space least squares estimation

ruijsenaars commuting difference operators as commuting transfer matrices for belavin s elliptic quantum r matrix we construct an l operator as a set of difference operators acting on functions on the type a weight space according to the fundamental relation rll llr taking the trace of the l operator gives a set of commuting difference operators we show that for the above mentioned l operator this approach gives macdonald type operators with elliptic theta function coefficient actually equivalent to ruijsenaars operators the relationship between the difference l operator and krichever s lax matrix is given and an explicit formula for elliptic commuting differential operators is derived we also study the invariant subspace for the system which is spanned by symmetric theta functions on the weight space

clustering of casablanca stock market based on hurst exponent estimates abstract this paper deals with the problem of casablanca stock exchange cse topology modeling as a complex network during three different market regimes general trend characterized by ups and downs increasing trend and decreasing trend in particular a set of seven different hurst exponent estimates are used to characterize long range dependence in each industrial sector generating process they are employed in conjunction with hierarchical clustering approach to examine the co movements of the casablanca stock exchange industrial sectors the purpose is to investigate whether cluster structures are similar across variable increasing and decreasing regimes it is observed that the general structure of the cse topology has been considerably changed over 2009 variable regime 2010 increasing regime and 2011 decreasing regime time periods the most important findings follow first in general a high value of hurst exponent is associated to a variable regime and a small one to a decreasing regime in addition hurst estimates during increasing regime are higher than those of a decreasing regime second correlations between estimated hurst exponent vectors of industrial sectors increase when casablanca stock exchange follows an upward regime whilst they decrease when the overall market follows a downward regime

the dynamical twisting and nondynamical r matrix structure of the elliptic ruijsenaars schneider model from the dynamical twisting of the classical r matrix we obtain a new lax operator for the elliptic ruijsenaars schneider model cf ruijsenaars the corresponding r matrix is shown to be the classical zn symmetric elliptic r matrix which is the same as that obtained in the study of the nonrelativistic version the an 1 calogero moser model

correlations in economic time series a financial index of the new york stock exchange the sp here f is called the crossover frequency iii we confirm these results using the dfa detrended fluctuation analysis method see fig 2b which allows accurate estimates of exponents independent of local trends

conformal blocks on elliptic curves and the knizhnik zamolodchikov bernard equations we give an explicit description of the vector bundle of wzw conformal blocks on elliptic curves with marked points as a subbundle of a vector bundle of weyl group invariant vector valued theta functions on a cartan subalgebra we give a partly conjectural characterization of this subbundle in terms of certain vanishing conditions on affine hyperplanes in some cases explicit calculations are possible and confirm the conjecture the friedan shenker flat connection is calculated and it is shown that horizontal sections are solutions of bernard s generalization of the knizhnik zamolodchikov equation

the non dynamical r matrix structure for the elliptic calogero moser model in this paper we construct a new lax operator for the elliptic calogero moser model with general from the classical dynamical twisting in which the corresponding r matrix is purely numerical non dynamic the non dynamical r matrix structure of this lax operator is obtained which is the elliptic symmetric r matrix