regular maps with almost sylow cyclic automorphism groups and classification of regular maps with euler characteristic p 2 abstract a regular map m is a cellular decomposition of a surface such that its automorphism group aut m acts transitively on the flags of m it can be shown that if a sylow subgroup p aut m has order coprime to the euler characteristic of the supporting surface then p is cyclic or dihedral this observation motivates the topic of the current paper where we study regular maps whose automorphism groups have the property that all their sylow subgroups contain a cyclic subgroup of index at most 2 the main result of the paper is a complete classification of such maps as an application we show that no regular maps of euler characteristic p 2 exist for p a prime greater than 7

inhomogeneous gaussian image models for estimation and restoration two inhomogeneous gaussian image models are presented for estimation and restoration by incorporating the local statistics of an image a homogeneous autoregressive ar random field can be extended to an inhomogeneous ar field this inhomogeneous random field can provide a better description of the image than the homogeneous one as a consequence of this improved modeling a minimum mean square error estimator mmse based on the inhomogeneous gaussian model can produce good results in both subjective and objective criteria two image models are proposed for use in image estimation and restoration a residual image model original image minus the space variant mean and a normalized image model residual image divided by space variant standard variation the novel aspect of these models is the use of an autoregressive dynamical model for residual and normalized images some aspects of parameter estimation are discussed and simulation results are presented

the multivariate krawtchouk polynomials as matrix elements of the rotation group representations on oscillator states an algebraic interpretation of the bivariate krawtchouk polynomials is provided in the framework of the three dimensional isotropic harmonic oscillator model these polynomials in two discrete variables are shown to arise as matrix elements of unitary reducible representations of the rotation group in three dimensions many of their properties are derived by exploiting the group theoretic setting the bivariate tratnik polynomials of krawtchouk type are seen to be special cases of the general polynomials that correspond to particular rotations involving only two parameters it is explained how the approach generalizes naturally to d 1 dimensions and allows us to interpret multivariate krawtchouk polynomials as matrix elements of so d 1 unitary representations indications are given on the connection with other algebraic models for these polynomials

recurrence relations for the connection coefficients of orthogonal polynomials of a discrete variable we give explicitly recurrence relations satisfied by the connection coefficients between two families of the classical orthogonal polynomials of a discrete variable i e associated with the names of charlier meixner krawtchouk and hahn also a recurrence relation is given for the coefficients in the formula expressing the nth associated polynomial in terms of the original polynomials

some multivariable orthogonal polynomials of the askey tableau continuous families a multivariable generalization is presented for all the continuous families of the askey tableaux this significantly extends some previously known multivariable jacobi polynomials the latter are recovered as a limit case from a family of multivariable continuous hahn polynomials which in turn are obtained as a limit of some multivariable wilson polynomials a continuous analog of the single variable charlier polynomials is also introduced

on the set theoretical yang baxter equation we propose a general way of constructing set theoretical solutions of the yangbaxter equation we study the properties of the construction we also show that our construction includes the earlier ones given by weinstein xu and etingof schedlersoloviev

stochastic models for closed boundary analysis representation and reconstruction the analysis of closed boundaries of arbitrary shapes on a plane is discussed specifically the problems of representation and reconstruction are considered a one to one correspondence between the given closed boundary and a univariate or multivariate sequence of real numbers is set up univariate or multivariate circular autoregressive models are suggested for the representation of the sequence of numbers derived from the closed boundary the stochastic model representing the closed boundary is invariant to transformations like sealing translation choice of starting point and rotation over angles that are multiples of 2 pi n where n is the number of observations methods for estimating the unknown parameters of the model are given and a decision rule for choosing the appropriate number of coefficients is included constraints on the estimates are derived so that the estimates are invariant to the transformations of the boundaries the stochastic model enables the reconstruction of a dosed boundary using fft algorithms results of simulations are included and the application to contour coding is discussed

affine structures of decomposable solvable groups abstract bi crossed products of groups are closely related to braces a ring like structure connected with solutions to the yang baxter equation the asymmetric product of braces which has become useful for the construction of regular affine groups and simple braces as well as several other product constructions are unified extended and simplified all bi crossed products of bicyclic braces are classified

signal plus noise models in shape classification abstract in this study we show how a signal plus noise formulation can be used to improve the performance of auto regressive shape classifiers in environments with time varying noise characteristics variations of this type may be due to changes in atmospheric conditions or the relative effect of discretization errors this approach is compared to existing methodologies using a number of noisy templates in a cluttered environment typical applications are to aircraft identification and automatic signature validation

interbasis expansions for the isotropic 3d harmonic oscillator and bivariate krawtchouk polynomials an explicit expression for the general bivariate krawtchouk polynomials is obtained in terms of the standard krawtchouk and dual hahn polynomials the bivariate krawtchouk polynomials occur as matrix elements of the unitary reducible representations of so 3 on the energy eigenspaces of the three dimensional isotropic harmonic oscillator and the explicit formula is obtained from the decomposition of these representations into their irreducible components the decomposition entails expanding the cartesian basis states in the spherical bases that span irreducible so 3 representations the overlap coefficients are obtained from the clebsch gordan problem for the lie algebra

a decomposition theorem for square free unitary solutions of the quantum yang baxter equation abstract it is known that every skew polynomial ring with generating set x and binomial relations in the sense of gateva ivanova trans amer math soc 343 1994 203 is an artin schelter regular domain of global dimension x moreover every such ring gives rise to a non degenerate unitary set theoretical solution r x 2 x 2 of the quantum yang baxter equation which fixes the diagonal of x 2 gateva ivanova s conjecture talk at the international algebra conference miskolc hungary 1996 states that conversely every such solution r comes from a skew polynomial ring with binomial relations an equivalent conjecture duke math j 100 1999 169 says that the underlying set x is r decomposable we prove these conjectures and construct an indecomposable solution r with x which shows that an extension to infinite x is false

discrete orthogonal polynomials and difference equations of several variables the goal of this work is to characterize all second order difference operators of several variables that have discrete orthogonal polynomials as eigenfunctions under some mild assumptions we give a complete solution of the problem

9 j symbols of the oscillator algebra and krawtchouk polynomials in two variables a simple generating function for the 9j symbols of the oscillator algebra is found on the basis of this function it is shown that corresponding 9j symbols are expressed in terms of polynomials in two discrete variables which are orthogonal with respect to the trinomial distribution these polynomials depend on four independent parameters and can be considered as a two dimensional analogue of the krawtchouk polynomials difference difference relations the factorization chain the duality property and the rodriguez formula for these polynomials are obtained it is shown that the polynomials are eigenfunctions of two commuting difference operators these polynomials are also covariant with respect to two commuting difference derivation operators in a special symmetric case these polynomials admit a simple factorized expression in terms of two distinct ordinary krawtchouk polynomials in another special case we obtain an explicit expression of 9j symbols in terms of the appell hypergeometric function in two variables

some multivariable orthogonal polynomials of the askey tableau discrete families a multivariable generalization is presented for all the discrete families of the askey tableau this significantly extends the multivariable hahn polynomials introduced by karlin and mcgregor the latter are recovered as a limit case from a family of multivariable racah polynomials

classifying non uniformly sampled vector valued curves we propose a novel means of classifying vector valued curves using functional principal components this uses cross validation to select curve components the degree of smoothing and scores associated with the best classification performance our approach is well suited to data generated by sensors of different modalities and time varying sampling frequencies experimental comparisons show this approach has significant advantages over conventional techniques using non uniformly sampled data our approach also generates novel forms of derivative analysis a widely used technique for classifying spectral functions from contaminated data

multivariable biorthogonal hahn polynomials a multivariable biorthogonal generalization of the discrete hahn polynomials a p 1 complex parameter family where p is the number of variables is presented it is shown that the polynomials are orthogonal with respect to subspaces of lower degree and biorthogonal within a given subspace these properties are over the discrete simplex 0 x1 x2 xp where x1 x2 xp and are non negative integers some further properties of the closely related multivariable continuous hahn polynomials are also discussed

recurrence relations for connection coefficients between two families of orthogonal polynomials we describe a simple approach in order to build recursively the connection coefficients between two families of orthogonal polynomial solutions of second and fourth order differential equations

invariant matching and identification of curves using b splines curve representation there have been many techniques for curve shape representation and analysis ranging from fourier descriptors to moments to implicit polynomials to differential geometry features to time series models to b splines etc the b splines stand as one of the most efficient curve surface representations and possess very attractive properties such as spatial uniqueness boundedness and continuity local shape controllability and invariance to affine transformations these properties made them very attractive for curve representation and consequently they have been extensively used in computer aided design and computer graphics very little work however has been devoted to them for recognition purposes one possible reason might be due to the fact that the b spline curve is not uniquely described by a single set of parameters control points which made the curve matching recognition process difficult when comparing the respective parameters of the curves to be matched this paper is an attempt to find matching solutions despite this limitation and as such it deals the problem of using b splines for shape recognition and identification from curves with an emphasis on the following applications affine invariant matching and classification of 2 d curves with applications in identification of aircraft types based on image silhouettes and writer identification based on handwritten text

cyclic tridiagonal pairs higher order onsager algebras and orthogonal polynomials abstract the concept of cyclic tridiagonal pairs is introduced and explicit examples are given for a fairly general class of cyclic tridiagonal pairs with cyclicity n we associate a pair of divided polynomials the properties of this pair generalize the ones of tridiagonal pairs of racah type the algebra generated by the pair of divided polynomials is identified as a higher order generalization of the onsager algebra it can be viewed as a subalgebra of the q onsager algebra for a proper specialization at q the primitive 2 n th root of unity orthogonal polynomials beyond the leonard duality are revisited in light of this framework in particular certain second order dunkl shift operators provide a realization of the divided polynomials at n 2 or q i

on limit relations between some families of bivariate hypergeometric orthogonal polynomials in this paper we deal with limit relations between bivariate hypergeometric polynomials we analyze the limit relation from trinomial distribution to bivariate gaussian distribution obtaining the limit transition from the second order partial difference equation satisfied by bivariate hypergeometric kravchuk polynomials to the second order partial differential equation verified by bivariate hypergeometric hermite polynomials as a consequence the limit relation between both families of orthogonal polynomials is established a similar analysis between bivariate hahn and bivariate appell orthogonal polynomials is also presented

unbiased parameter estimation of nonstationary signals in noise recent approaches to the modeling of nonstationary signals by means of ar or arma models use a representation with time varying parameters the time varying parameters are assumed to be linear combinations of a set of basis time functions so that the model is specified by constant parameters for stationary signals disturbed by white noise an approach based upon a modified least squares method leads to a good unbiased estimator of the parameters in this correspondence a similar algorithm deriving the unbiased parameters for nonstationary signals in white noise is given the experimental results show the good performance of the proposed estimator

solutions of the yang baxter equation associated with a left brace abstract given a left brace b a method is given to construct explicitly all the non degenerate involutive set theoretic solutions x r of the yang baxter equation such that the associated permutation group g x r is isomorphic as a left brace to b this method depends entirely on the brace structure of b

minimal recurrence relations for connection coefficients between classical orthogonal polynomials discrete case abstract we present a simple approach in order to compute recursively the connection coefficients between two families of classical discrete orthogonal polynomials charlier meixner kravchuk hahn i e the coefficients cm n in the expression p n x n m 0 c m n q m x where pn x and qm x belong to the aforementioned class of polynomials this is scv2 done by adapting a general and systematic algorithm recently developed by the authors to the discrete classical situation moreover extensions of this method allow to give new addition formulae and to estimate cm n asymptotics in limit relations between some families

normalization of discrete planar objects abstract the case is made for normalization of discrete planar objects prior to comparison with test objects and an expression for normalization is derived using a euclidean distance function based on the underlying continuous boundaries of the objects and their prototypes the results are given in both the spatial and the frequency domain an analysis of errors due to the quantization introduced by using a discrete grid is also given

coarse to fine planar object identification using invariant curve features and b spline modeling abstract this paper presents a hybrid algorithm for coarse to fine matching of affine invariant object features and b spline object curves and simultaneous estimation of transformation parameters for coarse matching two dissimilar measures are exploited by using the significant corners of object boundaries to remove candidate objects with large dissimilarity to a target object for fine matching a robust point interpolation approach and a simple gradient based algorithm are applied to b spline object curves under mmse criterion the combination of coarse and fine matching steps reduces the computational cost without degrading the matching accuracy the proposed algorithm is evaluated using affine transformed objects

bivariate krawtchouk polynomials in this paper we present a recurrent procedure to solve an inversion problem for monic bivariate krawtchouk polynomials written in vector column form giving its solution explicitly as a by product a general connection problem between two vector column of monic bivariate krawtchouk families is also explicitly solved moreover in the non monic case and also for krawtchouk families several expansion formulas are given but for polynomials written in scalar form

shape description by time series time series modeling techniques are adapted to represent or describe two dimensional closed contours both linear and nonlinear models are fitted it is found that to detect small changes in shape nonlinear modeling is necessary even though linear models may be sufficient to differentiate between shapes which differ widely a nonlinear model called the noncausal quadratic volterra model is developed for the purpose implementation is illustrated with shapes of aircraft

new connection formulae for some q orthogonal polynomials in q askey scheme new nonlinear connection formulae of the q orthogonal polynomials such as continuous q laguerre continuous big q hermite q meixner pollaczek and q gegenbauer polynomials in terms of their respective classical analogues are obtained using a special realization of the q exponential function as infinite multiplicative series of ordinary exponential function

a bivariate autoregressive technique for analysis and classification of planar shapes a bivariate autoregressive model is introduced for the analysis and classification of closed planar shapes the boundary coordinate sequence of a digitized binary image is sampled to produce a polygonal approximation to an object s shape this circular sample sequence is then represented by a vector autoregressive difference equation which models the individual cartesian coordinate sequences as well as coordinate interdependencies several classification features which are functions or transformations of the estimated coefficient matrices and the associated residual error covariance matrices are developed these features are shown to be invariant to object transformations such as translation rotation and scaling laboratory experiments involving object sets representative of industrial shapes are presented superior classification results are demonstrated

classification of partial 2 d shapes using fourier descriptors we present a method for the classification of 2 d partial shapes using fourier descriptors we formulate the problem as one of estimating the fourier descriptors of the unknown complete shape from the observations derived from an arbitrarily rotated and scaled shape with missing segments the method used for obtaining the estimates of the fourier descriptors minimizes a sum of two terms the first term of which is a least square fit to the given data subject to the condition that the number of missing boundary points is not known and the second term is the perimeter2 area of the unknown shape experiments with synthetic and real boundaries show that estimates closer to the true values of fourier descriptors of complete boundaries are obtained also classification experiments performed using real boundaries indicate that reasonable classification accuracies are obtained even when 20 30 percent of the data is missing

contour sequence moments for the classification of closed planar shapes abstract a technique for classifying closed planar shapes is described in which a shape is characterized by a one dimensional sequence that represents the euclidean distance between the centroid and all contour pixels of the shape contour sequences obtained from shapes belonging to the same class are similar and are considered to be different realizations of a stochastic process statistical moment functions derived from contour sequences are used to characterize the process and hence the shapes it is shown that these moment functions are invariant to shape translation rotation and scale transformations examples are presented to illustrate the performance of these moment functions in the classification of noisy shapes

affine invariant b spline moments for curve matching the article deals with the problem of matching and recognizing planar curves that are modeled by b splines independently of possible affine transformations to which the original curve has been subjected for example rotation translation scaling orthographic and semiperspective projections and possible occlusion it presents a fast algorithm for estimating the b spline control points that is robust to nonuniform sampling noise and local deformations curve matching is achieved by using a similarity measure based on the b spline knot points introduced by cohen et al 1991 this method however can neither handle the affine transformation between the curves nor the occlusion solutions to these two problems are presented through the use of a new class of weighted b spline curve moments that are well defined for both open and closed curves the method has been applied to classifying affine transformed aircraft silhouettes and appears to perform well

results for some inversion problems for classical continuous and discrete orthogonal polynomials explicit expressions for the coefficients in the expansion of classical discrete orthogonal polynomials charlier meixner krawtchouck hahn hahn eberlein into the falling factorial basis are given the corresponding inversion problems are solved explicitly this is done by using a general algorithm recently developed by the authors which is also applied to this kind of inversion problem but relating the basis and the classical continuous orthogonal polynomials of jacobi laguerre hermite and bessel

auto regressive shape classifiers in time varying noise abstract good results have been reported in a number of recent studies where auto regressive shape classifiers have been used to allocate objects to a pre determined number of classes it is shown that this approach may give unsatisfactory results when applied to imaging systems whose noise characteristics vary substantially over time such variation may be due to changes in atmospheric conditions or the relative effect of discretization errors observations are based on the reconstruction of a number of noisy synthetic templates

registering coronal histological 2 d sections of a rat brain with coronal sections of a 3 d brain atlas using geometric curve invariants and b spline representation a new approach is proposed for registering a set of histological coronal two dimensional images of a rat brain sectional material with coronal sections of a three dimensional brain atlas an intrinsic step and a significant challenge to current efforts in brain mapping and multimodal fusion of experimental data the alignment problem is based on matching external contours of the brain sections and operates in the presence of tissue distortion and tears which are routinely encountered and possible scale rotation and shear changes the affine and weak perspective groups it is based on a novel set of local absolute affine invariants derived from the set of ordered inflection points on the external contour represented by a cubic b spline curve the inflection points are local intrinsic geometric features which are preserved under both the affine and the weak perspective transformations the invariants are constructed from the sequence of area patches bounded by the contour and the line connecting two consecutive inflection points and hence do make direct use of the area volume invariance property associated with the affine transformation these local absolute invariants are very well suited to handle the tissue distortion and tears occlusion problem

nonstationary autoregressive modeling of object contours a spatially variant circular autoregressive svcar model is introduced for the analysis and classification of closed shape boundaries the model represents a closed shape boundary sequence as the output of a nonstationary all pole linear system driven by white noise whose coefficient s spatial evolution can be expressed as a truncated function expansion features derived from the svcar model are shown to be invariant to shape scaling rotation and translation a shape matching algorithm is developed to optimally adjust the svcar model coefficients for changes in contour sequence starting point laboratory experiments involving object sets representative of industrial military and geographic shapes are presented superior classification results are demonstrated

representations of orthogonal polynomials abstract zeilberger s algorithm provides a method to compute recurrence and differential equations from given hypergeometric series representations and an adaption of almquist and zeilberger computers recurrence and differential equations for hyperexponential integrals further versions of this algorithm allow the computation of recurrence and differential equations from rodrigues type formulas and from generating functions in particular these algorithms can be used to compute the differential difference and recurrence equations for the classical continuous and discrete orthogonal polynomials from their hypergeometric representations and from their rodrigues representations and generating functions in recent work we used an explicit formula for the recurrence equation of families of classical continuous and discrete orthogonal polynomials in terms of the coefficients of their differential difference equations to give an algorithm to identify the polynomial system from a given recurrence equation in this article we extend these results by presenting a collection of algorithms with which any of the conversions between the differential difference equation the hypergeometric representation and the recurrence equation is possible the main technique is again to use explicit formulas for structural identities of the given polynomial systems

multivariable meixner krawtchouk and meixner pollaczek polynomials a multivariable biorthogonal generalization of the meixner krawtchouk and meixner pollaczek polynomials is presented it is shown that these are orthogonal with respect to subspaces of lower degree and biorthogonal within a given subspace the weight function associated with the krawtchouk polynomials is the multivariate binomial distribution

involutive yang baxter groups in 1992 drinfeld posed the question of finding the set theoretic solutions of the yang baxter equation recently gateva ivanova and van den bergh and etingof schedler and soloviev have shown a group theoretical interpretation of involutive non degenerate solutions namely there is a one to one correspondence between involutive non degenerate solutions on finite sets and groups of i type a group g of i type is a group isomorphic to a subgroup of fa n sym n so that the projection onto the first component is a bijective map where fa n is the free abelian group of rank n and sym n is the symmetric group of degree n the projection of g onto the second component sym n we call an involutive yang baxter group iyb group this suggests the following strategy to attack drinfeld s problem for involutive non degenerate set theoretic solutions first classify the iyb groups and second for a given iyb group g classify the groups of i type with g as associated iyb group it is known that every iyb group is solvable in this paper some results supporting the converse of this property are obtained more precisely we show that some classes of groups are iyb groups we also give a non obvious method to construct infinitely many groups of i type and hence infinitely many involutive non degenerate set theoretic solutions of the yang baxter equation with a prescribed associated iyb group

counterexample to a conjecture about braces abstract we find an example of a finite solvable group in fact a finite p group in which is not possible to define a left brace structure or equivalently which is not an iyb group this answers a question posed by cedo jespers and del rio related to the yang baxter equation our argument is an improvement of an argument of rump using results about hopf galois extensions and lsa structures we explain explicitly the relation between these two areas of mathematics and brace theory hoping that it will be useful in the future

linear partial difference equations of hypergeometric type orthogonal polynomial solutions in two discrete variables in this paper a systematic study of the orthogonal polynomial solutions of a second order partial difference equation of hypergeometric type of two variables is done the pearson s systems for the orthogonality weight of the solutions and also for the difference derivatives of the solutions are presented the orthogonality property in subspaces is treated in detail which leads to an analog of the rodrigues type formula for orthogonal polynomials of two discrete variables a classification of the admissible equations as well as some examples related with bivariate hahn kravchuk meixner and charlier families and their algebraic and difference properties are explicitly given

multivariable biorthogonal continuous discrete wilson and racah polynomials several families of multivariable biorthogonal partly continuous and partly discrete wilson polynomials are presented these yield limit cases that are purely continuous in some of the variables and purely discrete in the others or purely discrete in all the variables the latter are referred to as the multivariable biorthogonal racah polynomials interesting further limit cases include the multivariable biorthogonal hahn and dual hahn polynomials

solving connection and linearization problems within the askey scheme and its q analogue via inversion formulas for the polynomial families pn x n belonging to the askey scheme or to its q analogue the hypergeometric represen tation provides a natural expansion of the form pn x n 0 dm n m x where the expanding basism x is in general a product of pochhammer symbols or q shifted factorials in this paper we solve the corresponding inversion problem i e we compute the coe6cients im n in the expansionn x n m 0 im n pm x which are then used as a tool for solving any connection and linearization problem within the askey scheme and its q analogue extensions of this approach for polynomials outside these two schemes are also given c

uniform resampling of digitized contours this paper addresses the problem of the nonuniform intersample distance of digital curves obtained as a result of quantization of continuous contours on a square lattice a resampling algorithm based on variable factor interpolation and decimation is presented and its performance is evaluated analytically and by computer simulations assuming the grid intersect quantization it is shown that the output of the resampling algorithm outperforms the original digital curve in terms of the average and maximum error in the measurement of length by 50 and 73 percent respectively the resampling algorithm can be used as a preprocessing stage in shape analysis systems to enhance their performance by increasing the accuracy and consistency of both local and global features such as curvature and the fourier shape descriptors

structure relations for monic orthogonal polynomials in two discrete variables in this paper extensions of several relations linking differences of bivariate discrete orthogonal polynomials and polynomials themselves are given by using an appropriate vector matrix notation three term recurrence relations are presented for the partial differences of the monic polynomial solutions of admissible second order partial difference equation of hypergeometric type structure relations difference representations as well as lowering and raising operators are obtained finally expressions for all matrix coefficients appearing in these finite type relations are explicitly presented for a finite set of hahn and kravchuk orthogonal polynomials

braces radical rings and the quantum yang baxter equation abstract non degenerate cycle sets are equivalent to non degenerate unitary set theoretical solutions of the quantum yang baxter equation we embed such cycle sets into generalized radical rings braces and study their interaction in this context we establish a galois theory between ideals of braces and quotient cycle sets our main result determines the relationship between two square free cycle sets operating transitively on each other