linear dependence of a function set of m variables with vanishing generalized wronskians abstract necessary and sufficient conditions are established for a set of n functions i em e1 which together with their partial derivatives of order at least n 1 are continuous to be linearly dependent one of these conditions is that all generalized wronskians vanish identically

connection coefficients between boas buck polynomial sets abstract in this paper a general method to express explicitly connection coefficients between two boas buck polynomial sets is presented as application we consider some generalized hypergeometric polynomials from which we derive some well known results including duplication and inversion formulas

the cardinality balanced multi target multi bernoulli filter and its implementations it is shown analytically that the multitarget multibernoulli member recursion proposed by mahler has a significant bias in the number of targets to reduce the cardinality bias a novel multibernoulli approximation to the multi target bayes recursion is derived under the same assumptions as the member recursion the proposed recursion is unbiased in addition a sequential monte carlo smc implementation for generic models and a gaussian mixture gm implementation for linear gaussian models are proposed the latter is also extended to accommodate mildly nonlinear models by linearization and the unscented transform

on askey scheme and d orthogonality i a characterization theorem this is the first in a series of papers dealing with generalized hypergeometric d orthogonal polynomials extending the polynomial families in the askey scheme in this paper we give a characterization theorem to introduce new examples of generalized hypergeometricd orthogonal polynomials to be studied in the forthcoming works for d 1 we obtain an unification of some known characterization theorems in the orthogonal polynomials theory

optimal estimation theory for dynamic systems with set membership uncertainty an overview in many problems such as linear and nonlinear regressions parameter and state estimation of dynamic systems state space and time series prediction interpolation smoothing and functions approximation one has to evaluate some unknown variable using available data the data are always associated with some uncertainty and it is necessary to evaluate how this uncertainty affects the estimated variables typically the problem is approached assuming a probabilistic description of uncertainty and applying statistical estimation theory an interesting alternative approach referred to as set membership or unknown but bounded ubb error description has been investigated since the late 1960s in this approach uncertainty is described by an additive noise which is known only to have given integral typically l2 of l1 or componentwise l bounds in this paper we review the main results of this theory with special attention to the most recent advances obtained in the case of componentwise bounds

d orthogonality of little q laguerre type polynomials abstract in this paper we solve a characterization problem in the context of the d orthogonality that allows us on one hand to provide a q analog for the d orthogonal polynomials of laguerre type introduced by the first author and douak and on the other hand to derive new l q classical d orthogonal polynomials generalizing the little q laguerre polynomials various properties of the resulting basic hypergeometric polynomials are singled out for d 1 we obtain a characterization theorem involving as far as we know new l q classical orthogonal polynomials for which we give the recurrence relation and the difference equation

obstructions to embeddability into hyperquadrics and explicit examples we give series of explicit examples of levi nondegenerate real analytic hypersurfaces in complex spaces that are not transversally holomorphically embeddable into hyperquadrics of any dimension for this we construct invariants attached to a given hypersurface that serve as obstructions to embeddability we further study the embeddability problem for real analytic submanifolds of higher codimension and answer a question by forstneric

an efficient wave based method for 2d acoustic problems containing corner singularities abstract the wave based method is an efficient alternative prediction technique based on a trefftz approach which as compared to element based methods can be applied in a wider frequency range at a reasonable cost this paper discusses the use of this method for the particular case of 2d acoustic problems where singularities are present in the corners of the acoustic domain the conventional set of expansion functions used to approximate the dynamic pressure field is extended with special purpose functions that incorporate the singular behaviour in the region around the singular corners this enrichment comes with a beneficial convergence rate while only a small increase of computational effort is incurred this is illustrated for various problem settings including different combinations of both homogeneous and non homogeneous boundary conditions and bounded as well as unbounded problems are considered

brief paper box particle filtering for nonlinear state estimation using interval analysis in recent years particle filters have been applied to a variety of state estimation problems a particle filter is a sequential monte carlo bayesian estimator of the posterior density of the state using weighted particles the efficiency and accuracy of the filter depend mostly on the number of particles used in the estimation and on the propagation function used to re allocate weights to these particles at each iteration if the imprecision i e bias and noise in the available information is high the number of particles needs to be very large in order to obtain good performances this may give rise to complexity problems for a real time implementation this kind of imprecision can easily be represented by interval data if the maximum error is known handling interval data is a new approach successfully applied to different real applications in this paper we propose an extension of the particle filter algorithm able to handle interval data and using interval analysis and constraint satisfaction techniques in standard particle filtering particles are punctual states associated with weights whose likelihoods are defined by a statistical model of the observation error in the box particle filter particles are boxes associated with weights whose likelihood is defined by a bounded model of the observation error experiments using actual data for global localization of a vehicle show the usefulness and the efficiency of the proposed approach

bernoulli particle box particle filters for detection and tracking in the presence of triple measurement uncertainty this work presents sequential bayesian detection and estimation methods for nonlinear dynamic stochastic systems using measurements affected by three sources of uncertainty stochastic set theoretic and data association uncertainty following mahler s framework for information fusion the paper develops the optimal bayes filter for this problem in the form of the bernoulli filter for interval measurements two numerical implementations of the optimal filter are developed the first is the bernoulli particle filter pf which turns out to require a large number of particles in order to achieve a satisfactory performance for the sake of reduction in the number of particles the paper also develops an implementation based on box particles referred to as the bernoulli box pf a box particle is a random sample that occupies a small and controllable rectangular region of nonzero volume in the target state space manipulation of boxes utilizes the methods of interval analysis the two implementations are compared numerically and found to perform remarkably well the target is reliably detected and the posterior probability density function of the target state is estimated accurately the bernoulli box pf however when designed carefully is computationally more efficient

the equivalence problem and rigidity for hypersurfaces embedded into hyperquadrics we consider the class of levi nondegenerate hypersurfaces m in inline graphic xmlns xlink http www w3 org 1999 xlink xlink href 01i that admit a local cr transversal embedding near a point p e m into a standard nondegenerate hyperquadric in inline graphic xmlns xlink http www w3 org 1999 xlink xlink href 02i with codimension k n n small compared to the cr dimension n of m we show that for hypersurfaces in this class there is a normal form which is closely related to the embedding such that any local equivalence between two hypersurfaces in normal form must be an automorphism of the associated tangent hyperquadric we also show that if the signature of m and that of the standard hyperquadric in inline graphic xmlns xlink http www w3 org 1999 xlink xlink href 03i are the same then the embedding is rigid in the sense that any other embedding must be the original embedding composed with an automorphism of the quadric

on d symmetric classical d orthogonal polynomials abstract the d symmetric classical d orthogonal polynomials are an extension of the standard symmetric classical polynomials according to the hahn property in this work we give some characteristic properties for these polynomials related to generating functions and recurrence differential equations as applications we characterize the d symmetric classical d orthogonal polynomials of boas buck type we construct a d 1 order linear differential equation with polynomial coefficients satisfied by each polynomial of a d symmetric classical d orthogonal set and we show that the d symmetric classical d orthogonal property is preserved by the derivative operator some of the obtained properties appear to be new even for the case d 1

d orthogonality of hermite type polynomials abstract in this paper we state a characterization theorem for d orthogonal polynomials of hermite type as application we solve two characterization problems related to gould hopper polynomials and charlier type polynomials various properties of the resulting generalized hypergeometric polynomials are singled out in particularly we derive the d dimensional functional vectors ensuring the d orthogonality of these polynomials the obtained weight functions are reduced to the well known weight functions of charlier and hermite polynomials for d 1 we also explicitly express the d dimensional functional vector associated with polynomials of laguerre type which are related to the obtained hermite type polynomials

multiple orthogonal polynomials for classical weights a new set of special functions which has a wide range of applications from number theory to integrability of nonlinear dynamical systems is described we study multiple orthogonal polynomials with respect to p 1 weights satisfying pearson s equation in particular we give a classification of multiple orthogonal polynomials with respect to classical weights which is based on properties of the corresponding rodrigues operators we show that the multiple orthogonal polynomials in our classification satisfy a linear differential equation of order p 1 we also obtain explicit formulas and recurrence relations for these polynomials

on the embeddability of real hypersurfaces into hyperquadrics abstract a well known result of forstneric 15 states that most real analytic strictly pseudoconvex hypersurfaces in complex space are not holomorphically embeddable into spheres of higher dimension a more recent result by forstneric 16 states even more most real analytic hypersurfaces do not admit a holomorphic embedding even into a merely algebraic hypersurface of higher dimension in particular a hyperquadric we emphasize that both cited theorems are proved by showing that the set of embeddable hypersurfaces is a set of first baire category at the same time the classical theorem of webster 30 asserts that every real algebraic levi nondegenerate hypersurface admits a transverse holomorphic embedding into a nondegenerate real hyperquadric in complex space in this paper we provide effective results on the non embeddability of real analytic hypersurfaces into a hyperquadric we show that under the codimension restriction n 2 n the defining functions z z u of all real analytic hypersurfaces m v z z u c n 1 containing levi nondegenerate points and locally transversally holomorphically embeddable into some hyperquadric q c n 1 satisfy an universal algebraic partial differential equation d 0 where the algebraic differential operator d d n n depends on n 1 n n 2 n only to the best of our knowledge this is the first effective result characterizing real analytic hypersurfaces embeddable into a hyperquadric of higher dimension as an application we show that for every n n as above there exists n n such that a zariski generic real analytic hypersurface m c n 1 of degree is not transversally holomorphically embeddable into any hyperquadric q c n 1 we also provide an explicit upper bound for in terms of n n to the best of our knowledge this gives the first effective lower bound for the cr complexity of a zariski generic real algebraic hypersurface in complex space of a fixed degree

d orthogonality of humbert and jacobi type polynomials in this paper we treat three questions related to the d orthogonality of the humbert polynomials the first one consists to determinate the explicit expression of the d dimensional functional vector for which the d orthogonality holds the second one is the investigation of the components of humbert polynomial sequence that allows us to introduce as far as we know new d orthogonal polynomials generalizing the classical jacobi ones the third one consists to solve a characterization problem related to a generalized hypergeometric representation of the humbert polynomials

segre varieties and lie symmetries we show that biholomorphic automorphisms of a real analytic hypersurface in mathbb c n 1 can be considered as pointwise lie symmetries of a holomorphic completely overdetermined involutive second order pde system defining its segre family using the classical s lie method we obtain a complete description of infinitesimal symmetries of such a system and give a new proof of some well known results of cr geometry

higher order darboux transformations and wronskian representations for schrodinger equations with quadratically energy dependent potentials we construct higher order darboux transformations for schrodinger equations with quadratically energy dependent potentials similar to the case of conventional darboux also known as supersymmetric transformations both the solutions and the potentials of transformed equations are expressed through wronskians we discuss properties of our darboux transformations and provide an application

a condition equivalent to linear dependence for functions with vanishing wronskian abstract it is well known that though the vanishing of the wronskian w of a set of functions on an interval i is a necessary condition for it to be linearly dependent it is not a sufficient one since peano in 1989 expressed an interest in finding classes of functions for which w 0 is sufficient for dependence and offered one such example himself others m b cher d r curtiss w hurewicz and g h meisters have provided related results here the author gives a final answer to the question by first generalizing peano s result using the order of a critical point thereby obtaining a dense set of intervals of dependence he then shows that w 0 together with a condition that the intersection of certain subspaces of en is nontrivial is equivalent to the linear dependence of on i the above results are used to establish the dynamical theorem that motion of a particle under the action of a central force field is planar so long as the particle is restricted from the origin the author provides a counterexample for the case in which the particle passes through the origin

a survey of convergence results on particle filtering methods for practitioners optimal filtering problems are ubiquitous in signal processing and related fields except for a restricted class of models the optimal filter does not admit a closed form expression particle filtering methods are a set of flexible and powerful sequential monte carlo methods designed to solve the optimal filtering problem numerically the posterior distribution of the state is approximated by a large set of dirac delta masses samples particles that evolve randomly in time according to the dynamics of the model and the observations the particles are interacting thus classical limit theorems relying on statistically independent samples do not apply in this paper our aim is to present a survey of convergence results on this class of methods to make them accessible to practitioners

vector orthogonal relations vector qd algorithm vector pade approximants to a function f f 1 f d from to d have been defined uniquely without any auxiliary choice than the degrees of the numerator and the denominator the same for all the components f i as in the scalar case 1 5 the denominators are associated to polynomials p r s which are given by vector orthogonal properties r and which satisfy for each s recurrence relations of order d 1 i e with d 2 terms called relations d we study here consequences of r and d first we prove an algorithm similar to the generalized mna al gorithm then we define a vector qd algorithm which links two diagonals p r s r and p r s 1 r conversely if a family p r s r 0 verifying d is given it is possible to build p r s r 0 s 0 and d linear functionals c a a 1 d such that p r 0 p r and p r s verify the orthogonal relations r with respect to the c a

intrinsic diophantine approximation on manifolds general theory we investigate the question of how well points on a nondegenerate k dimensional submanifold m subseteq mathbb r d can be approximated by rationals also lying on m establishing an upper bound on the intrinsic dirichlet exponent for m we show that relative to this exponent the set of badly intrinsically approximable points is of full dimension and the set of very well intrinsically approximable points is of zero measure our bound on the intrinsic dirichlet exponent is phrased in terms of an explicit function of k and d which does not seem to have appeared in the literature previously it is shown to be optimal for several particular cases the requirement that the rationals lie on m distinguishes this question from the more common context of ambient diophantine approximation on manifolds and necessitates the development of new techniques our main tool is an analogue of the simplex lemma for rationals lying on m which provides new insights on the local distribution of rational points on nondegenerate manifolds

fundamentals of statistical signal processing estimation theory minimum variance unbiased estimation cramer rao lower bound linear models general minimum variance unbiased estimation best linear unbiased estimators maximum likelihood estimation least squares method of moments the bayesian philosophy general bayesian estimators linear bayesian estimators kalman filters summary of estimators extension for complex data and parameters

linear dependence of quotients of analytic functions of several variables with the least subcollection of generalized wronskians abstract we study linear dependence in the case of quotients of analytic functions in several variables real or complex we identify the least subcollection of generalized wronskians whose identical vanishing is sufficient for linear dependence our proof admits a straight forward algebraic generalization and also constitutes an alternative proof of the previously known result that the identical vanishing of the whole collection of generalized wronskians implies linear dependence motivated by the structure of this proof we introduce a method for calculating the space of linear relations we conclude with some reflections about this method that may be promising from a computational point of view

regarding an adaptive algorithm for testing multivariate linear dependence for a finite collection of functions within some differential field of several variables there exists an adaptive algorithm for calculating a basis of their linear relations we study the complexity of this algorithm noting how it compares to some other existing techniques also we demonstrate some modifications for improving implementation in the course of our analysis we define the marginal set of a young like set and show how the size of the former can be bounded in terms of the size of the latter

d orthogonality via generating functions in this paper starting from a suitable generating function of a polynomial set we show how to decide whether the considered polynomial set is d orthogonal and if it is so how to determine the corresponding d dimensional functional vector then we apply the obtained results to some known and new d orthogonal polynomial sets for the known ones we give new proofs for some already obtained results

some discrete d orthogonal polynomial sets in this paper we characterize all polynomial sets which are at the same time d orthogonal and appell the resulting polynomials reduce to charlier polynomials for d 1 1 various properties of the obtained polynomials are singled out generating function recurrence relation of order d 1 and a difference equation of order d 1 we also explicitly express the d dimensional functional for which the d orthogonality holds