the clebsch gordan coefficients for the two parameter quantum algebra sup q 2 in the lowdin shapiro approach the structure of the irreducible representations of the two parameter quantum algebra sup q 2 is studied the projection operators for this algebra are constructed in the lowdin shapiro form the explicit analytical expressions for the sup q 2 clebsch gordan coefficients are obtained with the help of these projection operators there are clear perspectives to elaborate the theory of tensor operators universal r matrix 6j 9j symbols etc for the sup q 2 algebra using the same tools

a dual mixed finite element method for nonlinear incompressible elasticity with mixed boundary conditions abstract in this paper we consider the hu washizu principle and propose a new dual mixed finite element method for nonlinear incompressible plane elasticity with mixed boundary conditions the approach extends a related previous work on the dirichlet problem and imposes the neumann essential boundary condition in a weak sense by means of an additional lagrange multiplier the resulting variational formulation becomes a twofold saddle point operator equation which for convenience of the subsequent analysis is shown to be equivalent to a nonlinear threefold saddle point problem in this way a slight generalization of the classical babuska brezzi theory is applied to show the well posedness of the continuous and discrete formulations and to derive the corresponding a priori error estimates in particular the classical peers space is suitably enriched to define the associated galerkin scheme next we develop a local problems based a posteriori error analysis and derive an implicit reliable and quasi efficient estimate and a fully explicit reliable one finally several numerical results illustrating the good performance of the explicit a posteriori estimate for the adaptive computation of the discrete solutions are provided

a p q oscillator realization of two parameter quantum algebras it is noted that the study of a quantum algebra sup q 2 with two independent deformation parameters p q leads to a p q oscillator realization for it the analysis is extended to the p q analogues of su 1 1 osp 2 1 and the centreless virasoro algebra the standard single parameter q deformations are obtained in the limit p q

a multigrid method for the pseudostress formulation of stokes problems the purpose of this paper is to develop and analyze a multigrid solver for the finite element discretization of the pseudostress system associated with the differential operator mathcal a gamma mathbf grad mathbf div over 2 times 2 matrix valued functions this system is derived from the pseudostress velocity formulation z cai b lee and p wang siam j numer anal 42 2004 pp 843 859 of two dimensional stokes problems through the penalty method or natural time discretization for the respective steady or unsteady state problems here gamma 0 is a constant associated with either the penalty parameter or the time step size and mathcal a is a singular map in this paper we develop a multigrid solver for the discrete problem using both the raviart thomas rt and the brezzi douglas marini bdm finite elements we show that the multigrid convergence rate is o frac 1 gamma 2 1 gamma 2 m where m is the number of smoothings this convergence rate is independent of the mesh size and the number of levels used in multigrid moreover numerical results presented in this paper show that the multigrid convergence rate for the bdm elements does not depend on the parameter gamma

a two parameter deformation of the jaynes cummings model path integral representation a two parameter p q deformation of the jaynes cummings model is obtained using a recently developed p q deformed oscillator in the rotating wave approximation rwa the dynamical symmetry of the model is the quantum superalgebra up q 1 mod 1 the partition function of the model is obtained as a path integral over generalized perelomov coherent states corresponding to the quantum algebra up q 1 mod 1 the complete spectrum of the model is extracted for both the case when the coupling constants are grassman valued and when they are c number valued it is noted that a relaxation of the rwa extends the dynamical symmetry to the quantum superalgebra ospp q 2 mod 2

a state predictor for continuous time stochastic systems abstract this work investigates the state prediction problem for nonlinear stochastic differential systems affected by multiplicative state noise this problem is relevant in many state estimation frameworks such as filtering of continuous discrete systems i e stochastic differential systems with discrete measurements and time delay systems a very common heuristic to achieve the state prediction exploits the numerical integration of the deterministic nonlinear equation associated to the noise free system unfortunately these methods provide the exact solution only for linear systems instead here we provide the exact state prediction for nonlinear system in terms of the series expansion of the expected value of the state conditioned to the value in a previous time instant obtained according to the carleman embedding technique the truncation of the infinite series allows to compute the prediction at future times with an arbitrary approximation simulations support the effectiveness of the proposed state prediction algorithm in comparison to the aforementioned heuristic method

polynomial filtering for linear discrete time non gaussian systems in this work we propose a new filtering approach for linear discrete time non gaussian systems that generalizes a previous result concerning quadratic filtering a de santis a germani and m raimondi ieee trans automat control 40 1995 pp 1274 1278 a recursive nu th order polynomial estimate of finite memory delta is achieved by defining a suitable extended state which allows one to solve the filtering problem via the classical kalman linear scheme the resulting estimate will be the mean square optimal one among those estimators that take into account nu polynomials of the last delta observations numerical simulations show the effectiveness of the proposed method

new q deformed coherent states with an explicitly known resolution of unity we construct a new family of q deformed coherent states zq where 0 q 1 these states are normalizable on the whole complex plane and continuous in their label z they allow the resolution of unity in the form of an ordinary integral with a positive weight function obtained through the analytic solution of the associated stieltjes power moment problem and expressed in terms of one of the two jacksons s q exponentials they also permit exact evaluation of matrix elements of physically relevant operators we use this to show that the photon number statistics for the states is sub poissonian and that they exhibit quadrature squeezing as well as an enhanced signal to quantum noise ratio over the conventional coherent state value finally we establish that they are the eigenstates of some deformed boson annihilation operator and study some of their characteristics in deformed quantum optics

q analogues of the parabose and parafermi oscillators and representations of quantum algebras deformations of the one dimensional parabose oscillators are presented they are shown to provide fock representations of the quantum sp q 2 algebra and ospq 1 2 superalgebra the representations of suq 2 are used to define the q analogues of the parafermi oscillators

a note on p q oscillators and bibasic hypergeometric functions the authors examine the relation between the representation theory of a two parameter deformation of the oscillator algebra and certain bibasic laguerre functions and polynomials

on unscented kalman filtering for state estimation of continuous time nonlinear systems this paper considers the application of the unscented kalman filter ukf to continuous time filtering problems where both the state and measurement processes are modeled as stochastic differential equations the mean and covariance differential equations which result in the continuous time limit of the ukf are derived the continuous discrete ukf is derived as a special case of the continuous time filter when the continuous time prediction equations are combined with the update step of the discrete time ukf the filter equations are also transformed into sigma point differential equations which can be interpreted as matrix square root versions of the filter equations

approximation by p q baskakov beta operators in the present paper we consider p q analogue of the baskakov beta operators and using it we estimate some direct results on approximation also we represent the convergence of these operators graphically using matlab

double squeezing in generalized q coherent states using a generalization of the q commutation relations we develop a formalism in which we define generalized q bosonic operators this formalism includes both types of the usual q deformed bosons as special cases the coherent states of these operators show interesting and novel noise reduction properties including simultaneous squeezing in both field components unlike the conventional case in which squeezing is permitted in only one component this also contrasts with the usual quantum group deformation which also only permits one component squeezing

representations of two parameter quantum algebras and p q special functions abstract in this paper the connection between p q analogue of special functions and representations of certain two parameter quantum algebras has been developed the realizations of the representations of these quantum algebras are in terms of p q derivative operators the matrix elements of these representations are computed in terms of the generalized p q hypergeometric series this leads to the developments in the theory of p q special functions

memoryless approach to the lq and lqg problems with variable input delay this note studies the lq and lqg problems for linear time invariant systems with a single time varying input delay and instantaneous memoryless state feedback we extend the memoryless state feedback solution proposed in 1 in two directions we prove that in the deterministic case a memoryless state feedback can be in general optimal only up to a certain delay for which we provide a sufficient and sometimes strict bound moreover we show that this memoryless control is optimal also in the case of time varying delays and that the quadratic cost functional has the same value as in the case without delay for time varying delays the control law requires that the relationship between time points in which the input is generated and applied is known and invertible even if the delay function needs not to be differentiable or even continuous finally we prove that the cost functional is bounded also in the stochastic case for the same delay interval as in the deterministic case but with a larger cost than the delay less lqg solution

filtering of stochastic nonlinear differential systems via a carleman approximation approach this paper deals with the state estimation problem for stochastic nonlinear differential systems driven by standard wiener processes and presents a filter that is a generalization of the classical extended kalman bucy filter ekbf while the ekbf is designed on the basis of a first order approximation of the system around the current estimate the proposed filter exploits a carleman like approximation of a chosen degree v ges 1 the approximation procedure applied to both the state and the measurement equations allows to define an approximate representation of the system by means of a bilinear system for which a filtering algorithm is available from the literature numerical simulations on an example show the improvement in terms of sample error covariance of the filter based on the first order second order and third order system approximations v 1 2 3

models of q algebra representations matrix elements of the q oscillator algebra this article continues a study of function space models of irreducible representations of q analogs of lie enveloping algebras motivated by recurrence relations satisfied by q hypergeometric functions here a q analog of the oscillator algebra not a quantum algebra is considered it is shown that various q analogs of the exponential function can be used to mimic the exponential mapping from a lie algebra to its lie group and the corresponding matrix elements of the group operators on these representation spaces are computed this local approach applies to more general families of special functions e g with complex arguments and parameters than does the quantum group approach it is shown that the matrix elements themselves transform irreducibly under the action of the algebra q analogs of a formula are found for the product of two hypergeometric functions 1f1 and the product of a 1f1 and a bessel function they are interpreted here as expansions of the matrix elements of a group operator

the classical n body problem within a generalized statistical mechanics the modifications that must be introduced within the framework of standard classical n body statistical mechanics techniques in order to deal with the recently proposed generalized scenario of non extensive statistical mechanics are discussed a generalized version of the equipartition theorem is shown to hold the ideal gas is revisited as a simple application

on the combinatorics of normal ordering bosonic operators and deformations of it recently some combinatorial aspects for the normal ordering of powers of arbitrary monomials of boson operators were discussed in particular it was shown that the resulting formulae lead to generalizations of the usual bell and stirling numbers in this paper these considerations are generalized to the q deformed case in particular it is shown that the simplest example of this generalization leads to q deformed lah numbers the connection between generalized stirling and bell numbers and matrix elements of the above mentioned operators with respect to the usual fock space basis and coherent states is discussed

stirling number identities interconsistency of q analogues q analogues of stirling number identities are formulated and the interconsistency among the q analogues of the stirling numbers and of the binomial coefficients is investigated the close relation with the normal ordering problem for arik coon type q bosons plays a central role in the derivations presented

some approximation results by p q analogue of bernstein stancu operators in this paper we introduce a new analogue of bernstein stancu operators based on p q integers which we call as p q bernstein stancu operators we study approximation properties for these operators based on korovkin s type approximation theorem and also study some direct theorems furthermore we give comparisons and some illustrative graphics for the convergence of operators to some function

accurate numerical implementation of the continuous discrete extended kalman filter this paper addresses an accurate and effective implementation of the continuous discrete extended kalman filtering method the technique under discussion is grounded in numerical solution of the moment differential equations to predict the state mean of the stochastic dynamical system and the corresponding error covariance matrix here we apply an efficient embedded runge kutta pair possessing superior stability and many other attractive features including automatic global error control in order to improve performance of the complex computational procedure consisting of the extended kalman filter and the underlying adaptive ode solver thus we introduce a new continuous discrete adaptive extended kalman filter and show its advantage over the standard variant on two test examples in practice this technique allows for much longer sampling intervals without any loss of accuracy and that improves the applied potential of the extended kalman filtering method significantly

parabosons virasoro type algebras and their deformations two parameter p q deformation of a parabosonic algebra underlying the two particle calogero model is considered the fock space representation bargmann fock representation coherent states spectrum generating algebra and a hidden supersymmetry are discussed the paraboson algebra induces a centreless virasoro type algebra with a doubling of the space of generators a two parameter deformation of this virasoro type algebra is studied

on p q μ ν ϕ1 ϕ2 generalized oscillator algebra and related bibasic hypergeometric functions this paper provides the generalization of the work by floreanini et al 1993 j phys a math gen 26 611 4 who generated bibasic hypergeometric functions from p q oscillators we consider a six parameter deformed oscillator algebra realized from the p q deformed boson oscillators we build the corresponding fock space representation in an infinite dimensional subspace of the hilbert space of a harmonic oscillator we also discuss the properties of a discrete spectrum of the hamiltonian of the deformed harmonic oscillator corresponding to this system we then define a realization of the deformed algebra in terms of a generalized derivative and investigate the relation between this representation and generalized bibasic laguerre functions and polynomials

the quantum group suq 2 and a q analogue of the boson operators a new realisation of the quantum group suq 2 is constructed by means of a q analogue to the jordan schwinger mapping determining thereby both the complete representation structure and q analogues to the wigner and racah operators to achieve this realisation a new elementary object is defined a q analogue to the harmonic oscillator the uncertainty relation for position and momentum in a q harmonic oscillator is quite unusual

various ways to compute the continuous discrete extended kalman filter the extended kalman filter ekf is a very popular tool dealing with state estimation its continuous discrete version cd ekf estimates the state trajectory of continuous time nonlinear models whose internal state is described by a stochastic differential equation and which is observed through a noisy nonlinear form of the sampled state the prediction step of the cd ekf leads to solve a differential equation that cannot be generally solved in a closed form this technical note presents an overview of the numerical methods including recent works usually implemented to approximate this filter comparisons of theses methods on two different nonlinear models are finally presented the first one is the van der pol oscillator which is widely used as a benchmark the second one is a neuronal population model this more original model is used to simulate eeg activity of the cortex experiments showed better stability properties of implementations for which the positivity of the prediction matrix is guaranteed

time dependent algorithms for the simulation of viscoelastic flows with spectral element methods applications and stability this paper presents the development of spectral element methods to simulate unsteady flows of viscoelastic fluids using a closed form differential constitutive equation the generation and decay poiseuille planar flows are considered as benchmark problems to test the abilities of our computational method to deal with truly time dependent flows satisfactory results converging toward steady state regimes have been obtained for the flow through a four to one planar abrupt contraction with unsteady algorithms time dependent simulations of viscoelastic flows are prone to numerical instabilities even for simple geometrical configurations possible methods to improve the numerical stability of the computational algorithms are discussed in view of the results carried out with numerical simulations for the flows through a straight channel and the four to one contraction

on models of certain p q algebra representations the p q oscillator algebra we construct one and two variable models of the p q oscillator algebra in terms of ladder operators by using two p q analogs of the exponential function mapping we show that matrix elements of these operators can be represented in terms of p q special functions further we exhibit that these matrix elements satisfy certain biorthogonality relations

a survey of numerical methods for nonlinear filtering problems the main goal of filtering is to obtain recursively in time good estimates of the state of a stochastic dynamical system based on noisy partial observations of the same in settings where the signal observation dynamics are significantly nonlinear or the noise intensities are high an extended kalman filter ekf which is essentially a first order approximation to an infinite dimensional problem can perform quite poorly it may require very frequent re initializations and in some situations may even diverge the theory of nonlinear filtering addresses these difficulties by considering the evolution of the conditional distribution of the state of the system given all the available observations in the space of probability measures we survey a variety of numerical schemes that have been developed in the literature for approximating the conditional distribution described by such stochastic evolution equations with a special emphasis on an important family of schemes known as the particle filters a numerical study is presented to illustrate that in settings where the signal observation dynamics are non linear a suitably chosen nonlinear scheme can drastically outperform the extended kalman filter

compatible spectral approximations for the velocity pressure stress formulation of the stokes problem the numerical approximation of the mixed velocity pressure stress formulation of the stokes problem using spectral methods is considered in addition to the compatibility condition between the discrete velocity and pressure spaces a second condition between the discrete velocity and stress spaces must also be satisfied in order to have a well posed problem the theory is developed by considering a doubly constrained minimization problem in which the viscous stress tensor is minimized subject to the constraint that the viscous forces are irrotational the discrete problem is analyzed and error estimates are derived a comparison between the mixed approach and the standard velocity pressure formulation is made in terms of the condition number of the resulting systems

cubature kalman filtering for continuous discrete systems theory and simulations in this paper we extend the cubature kalman filter ckf to deal with nonlinear state space models of the continuous discrete kind to be consistent with the literature the resulting nonlinear filter is referred to as the continuous discrete cubature kalman filter cd ckf we use the ito taylor expansion of order 1 5 to transform the process equation modeled in the form of stochastic ordinary differential equations into a set of stochastic difference equations building on this transformation and assuming that all conditional densities are gaussian distributed the solution to the bayesian filter reduces to the problem of how to compute gaussian weighted integrals to numerically compute the integrals we use the third degree cubature rule for a reliable implementation of the cd ckf in a finite word length machine it is structurally modified to propagate the square roots of the covariance matrices the reliability and accuracy of the square root version of the cd ckf are tested in a case study that involves the use of a radar problem of practical significance the problem considered herein is challenging in the context of radar in two respects high dimensionality of the state and increasing degree of nonlinearity the results presented herein indicate that the cd ckf markedly outperforms existing continuous discrete filters

u r s gl 4 symmetry for r s hypergeometric series contiguous operators for a two parameter analogue of hypergeometric series are constructed these represent a two parameter quantum enveloping algebra introduced by takeuchi

least squares spectral elements applied to the stokes problem least squares spectral element methods are based on two important and successful numerical methods spectral hp element methods and least squares finite element methods in this respect least squares spectral element methods seem very powerful since they combine the generality of finite element methods with the accuracy of the spectral methods and also have the theoretical and computational advantages of the least squares methods these features make the proposed method a competitive candidate for the solution of large scale problems arising in scientific computing in order to demonstrate its competitiveness the method has been applied to an analytical problem and the theoretical optimal and suboptimal a priori estimates have been confirmed for various boundary conditions moreover the exponential convergence rates typical for a spectral element discretization have also been confirmed the comparison with the classical galerkin spectral element method revealed that the least squares spectral element method is as accurate as the galerkin method for the smooth model problem

dynamic conditional independence models and markov chain monte carlo methods abstract in dynamic statistical modeling situations observations arise sequentially causing the model to expand by progressive incorporation of new data items and new unknown parameters for example in clinical monitoring patients and data arrive sequentially and new patient specific parameters are introduced with each new patient markov chain monte carlo mcmc might be used for continuous updating of the evolving posterior distribution but would need to be restarted from scratch at each expansion stage thus mcmc methods are often too slow for real time inference in dynamic contexts by combining mcmc with importance resampling we show how real time sequential updating of posterior distributions can be effected the proposed dynamic sampling algorithms use posterior samples from previous updating stages and exploit conditional independence between groups of parameters to allow samples of parameters no longer of interest to be discarded such as when a patient dies or is discharged we apply the

deformation of the askey wilson algebra with three generators a most general algebra with three generators and with ladder and duality properties gaw 3 is considered it is shown that the obtained algebra corresponds to p q deformation of the askey wilson algebra for the new algebra gaw 3 the ladder representation is constructed and the overlap problem is discussed

on models of certain p q algebra representations the quantum euclidean algebra e p q 2 abstract we construct one and two variable models of the p q algebra e p q 2 in terms of ladder operators we define two p q analogues of the exponential function mapping and using these show that matrix elements of these operators can be represented in terms of p q series further we exhibit that these matrix elements satisfy certain biorthogonality relations

three dimensional quadratic algebras some realizations and representations four classes of three dimensional quadratic algebra of the type q0 q q q q aq02 bq0 c where a b c are constants or central elements of the algebra are constructed using a generalization of the well known two mode bosonic realizations of su 2 and su 1 1 the resulting matrix representations and single variable differential operator realizations are obtained some remarks on the mathematical and physical relevance of such algebras are given

on the representations of glp q 2 glp q 1 mod 1 and non commutative spaces explicit realizations of the quantum groups glp q 2 and glp q 1 mod 1 corresponding to unimodular values of the deformation parameters p and q are given in terms of the canonically conjugate x p operators using the heisenberg weyl commutation relations matrix representations are also discussed some observations are made on similar realizations of the non commutative coordinate spaces on which the quantum groups act as endomorphisms

filtering continuous time linear systems with time varying measurement delay we consider the filtering problem of lti continuous time systems with known and bounded measurement delays the aim of the technical note is the design of a finite dimensional sub optimal filter whose performance in terms of the estimation error is comparable to optimal infinite dimensional approaches we show that the proposed approach allows for a precise characterization of the relationship between measurement delay and the covariance of the estimation error in the time varying case no restrictive hypotheses on the delay function are needed the proposed filter can therefore be applied to delay functions for which traditional infinite dimensional approaches cannot be straightforwardly applied

residual a posteriori error estimator for a three field model of a non linear generalized stokes problem in this article we propose and analyze an a posteriori error estimator for a three field model of a generalized stokes problem the components of the a posteriori error estimator are defined via a non linear projection of the residues of the variational equations both upper and lower bounds for the approximation error are derived in terms of the components of the a posteriori error estimator the non linear projections do not need to be explicitly computed to construct the a posteriori error estimates

characterization of mathcal r p q deformed rogers szego polynomials associated quantum algebras deformed hermite polynomials and relevant properties this paper addresses a new characterization of deformed rogers szego polynomials by providing their three term recurrence relation and the associated quantum algebra built with corresponding creation and annihilation operators the whole construction is performed in a unified way generalizing all known relevant results which are straightforwardly derived as particular cases continuous deformed hermite polynomials and their recurrence relation are also deduced novel relations are provided and discussed

boson para boson and boson fermion representations of some graded lie algebras some graded lie algebras with the lie algebras so 3 so 2 1 so 4 so 3 1 and so 2 2 as their bose sectors are realized in terms of bosons para bosons and certain bilinear combinations of bosons and fermions

on p q analogue of bernstein operators in this paper we introduce a new analogue of bernstein operators and we call it as p q bernstein operators which is a generalization of q bernstein operators we also study approximation properties based on korovkin s type approximation theorem of p q bernstein operators and establish some direct theorems furthermore we show comparisons and some illustrative graphics for the convergence of operators to a function

consistent multiparameter quantisation of gl n the author describes a manifold of quantum group structures on the vector space of the universal enveloping algebra of gl n and on its dual the space of polynomials in n2 variables the dimension of the manifold is n2 n 2 2

spectral element methods for axisymmetric stokes problems abstract the approximation of the stokes problem in axisymmetric geometries using the spectral element method is considered the presence of the volume element r dr dz in the weak formulation of the problem is shown to be a potential source of difficulty the discrete equations associated with nodes on the axis of symmetry can lead to a degeneracy in the global system of equations this difficulty is resolved by incorporating the factor r into the weight function for spectral elements adjacent to the axis of symmetry and using appropriate basis functions in these elements in the radial direction properties of the jacobi polynomials are used to construct the elements of the modified method numerical results are presented demonstrating some of the features of the proposed approach

new p q μ ν f deformed states we construct a new family of deformed states these states are normalizable on the whole complex plane and continuous in their label z under fixed values of parameters they allow the resolution of unity in the form of an ordinary integral with a positive weight function obtained through the analytic solution of the associated stieltjes power moment problem in addition to the mathematical characteristics the quantum statistical properties of these states are analytically and numerically discussed in detail in the context of conventional as well as deformed quantum optics we find that for non deformed photons the states exhibit quadrature squeezing and their photon number statistics is sub poissonian on the other hand for deformed photons the states are super poissonian and no quadrature squeezing occurs

a new spectral element method for the reliable computation of viscoelastic flow abstract a new stabilised spectral element method has been developed by the authors for the accurate integration of the mixed elliptic hyperbolic system of partial differential equations governing certain viscoelastic flows the method is illustrated by solving the benchmark problem of the flow of an oldroyd b and a ptt fluid past a cylinder in a channel results are presented to demonstrate the advantages of the proposed method over traditional galerkin type procedures in terms of accuracy and stability

q μ and p q ζ exponential functions rogers szegő polynomials and fourier gauss transform from the realization of q oscillator algebra in terms of generalized derivative we compute the matrix elements from deformed exponential functions and deduce generating functions associated with rogers szeg polynomials as well as their relevant properties we also compute the matrix elements associated with the p q oscillator algebra a generalization of the q one and perform the fourier gauss transform of a generalization of the deformed exponential functions

brief paper a quadrature based method of moments for nonlinear filtering according to the nonlinear filtering theory optimal estimates of a general continuous discrete nonlinear filtering problem can be obtained by solving the fokker planck equation coupled with a bayesian update rule this procedure does not rely on linearizations of the dynamical and or measurement models however the lack of fast and efficient methods for solving the fokker planck equation presents challenges in real time nonlinear filtering problems in this paper a direct quadrature method of moments is introduced to solve the fokker planck equation efficiently and accurately this approach involves representation of the state conditional probability density function in terms of a finite collection of dirac delta functions the weights and locations abscissas in this representation are determined by moment constraints and modified using the bayes rule according to measurement updates as demonstrated by numerical examples this approach appears to be promising in the field of nonlinear filtering

a deformed oscillator with coulomb energy spectrum a deformed oscillator with eigenvalues equal to the eigenvalues of the schrodinger equation with the coulomb potential is constructed the deformed oscillator algebra has a polynomial realization and the associate deformed operations of integration and differentiation are studied

a new suboptimal approach to the filtering problem for bilinear stochastic differential systems the aim of this paper is to present a new approach to the filtering problem for the class of bilinear stochastic multivariable systems consisting in searching for suboptimal state estimates instead of the conditional statistics as a first result a finite dimensional optimal linear filter for the considered class of systems is defined then the more general problem of designing polynomial finite dimensional filters is considered the equations of a finite dimensional filter are given producing a state estimate which is optimal in a class of polynomial transformations of the measurements with arbitrarily fixed degree numerical simulations show the effectiveness of the proposed filter

a twofold spline approximation for finite horizon lqg control of hereditary systems in this paper an approximation scheme is developed for the solution of the linear quadratic gaussian lqg control on a finite time interval for hereditary systems with multiple noncommensurate delays and distributed delay the solution here proposed is achieved by means of two approximating subspaces the first one to approximate the riccati equation for control and the second one to approximate the filtering equations since the approximating subspaces have finite dimension the resulting equations can be implemented the convergence of the approximated control law to the optimal one is proved simulation results are reported on a wind tunnel model showing the high performance of the method

the q t gaussian process the q t fock space fq t h introduced in this paper is a deformation of the q fock space of bozejko and speicher the corresponding creation and annihilation operators now satisfy the commutation relation aq t f aq t g qaq t g aq t f f g htn turn mathjax off a defining relation of the chakrabarti jagannathan deformed quantum oscillator algebra the moments of the deformed gaussian element sq t h aq t h aq t h are encoded by the joint statistics of crossings and nestings in pair partitions the q 0 t specialization yields a natural single parameter deformation of the full boltzmann fock space of free probability with the corresponding semicircular measure variously encoded via the rogers ramanujan continued fraction the t airy function the t catalan numbers of carlitz riordan and the first order statistics of the reduced wigner process

a quantum algebra approach to basic multivariable special functions generalizations to a base q of the appell and lauricella hypergeometric functions are studied within the framework of the representation theory of quantum algebras of type an this allows deriving various identities and formulae involving these q functions

on the q oscillator and the quantum algebra suq 1 1 the authors discuss some problems of the q deformed harmonic oscillator different q bosonisations of the quantum suq 1 1 algebra are given and the corresponding infinite dimensional representations of discrete series are analysed

representations of the quantum algebra uq su1 1 all irreducible representations of the quantum group uq su1 1 are given they are determined by two complex numbers infinitesimally unitary representations are separated from the set of irreducible representations it is shown that the symmetric operators of irreducible infinitesimally unitary representations corresponding to generators of the lie algebra su1 1 admit self adjoint extensions

linear estimation of continuous discrete linear state space models with multiplicative noise this paper deals with the estimation of the state variable of continuous discrete linear state space models with multiplicative noise specifically the optimal minimum variance linear filter for that class of models is constructed moreover the solutions of the differential equations that describe the evolution of the two first conditional moments between observations are obtained and an algorithm for their numerical computation is also given the performance of the linear filter is illustrated by means of numerical experiments

optimal filtering for a class of linear ito stochastic systems the dichotomic case this paper focuses on the problem of optimal h2 filtering for a class of continuous time stochastic systems without assuming their exponential stability in the mean square sense indeed the stability assumption is relaxed and we assume instead that the lyapunov operator associated to the dynamical stochastic system is exponentially dichotomic the optimal solution of the considered optimization problem is expressed in terms of the unique solution of a suitable algebraic lyapunov equation and the stabilizing solution of a certain algebraic riccati equation

finite dimensional representations of the quantum group glp q 2 using the exponential map from up q gl 2 using the fronsdal galindo formula for the exponential mapping from the quantum algebra up q gl 2 to the quantum group glp q 2 we show how the 2j 1 dimensional representations of glp q 2 can be obtained by exponentiating the well known 2j 1 dimensional representations of up q gl 2 for j 1 3 2 j 1 2 corresponds to the defining two dimensional t matrix the earlier results on the finite dimensional representations of glq 2 and slq 2 or suq 2 are obtained when p q representations of uq q 2 q in c mod r and uq 2 q in r mod 0 are also considered the structure of the clebsch gordan matrix for up q gl 2 is studied the same clebsch gordan coefficients are applicable in the reduction of the direct product representations of the quantum group glp q 2

a posteriori error estimates for spectral element solutions to viscoelastic flow problems abstract in this paper we develop an a posteriori error estimate for viscoelastic flow calculations using spectral elements the error estimate is compared with the exact error obtained by computing the difference between the numerical solution and a reference calculation for the benchmark problem of viscoelastic flow past a rigid sphere in a tube

spectral element methods for transient viscoelastic flow problems spectral element methods are developed for solving transient flows of viscoelastic fluids the fluids are modeled using the upper convected maxwell and oldroyd b constitutive relationships several temporal schemes for dealing with the time dependent nature of the problems are considered the computation associated with each time step comprises an explicit treatment of the convection and deformation terms and an implicit treatment of the linear terms the generalized three field stokes problem generated in the latter is solved using a nested preconditioned conjugate gradient method the performance of a number of preconditioners is investigated a modified formulation of the stokes problem is presented that ensures a unique pressure approximation with zero mean is obtained at each time step the performance of the schemes and models when applied to the benchmark problem of start up of plane poiseuille flow is investigated

on p q analogue of kantorovich type bernstein stancu schurer operators in this paper we introduce a new kind of kantorovich type bernstein stancu schurer operators based on the concept of p q integers we investigate statistical approximation properties and establish a local approximation theorem we also give a convergence theorem for the lipschitz continuous functions finally we give some graphics and numerical examples to illustrate the convergence properties of operators to some functions

example of infinite statistics i give a second quantized example of infinite statistics in which any representation of the symmetric group can occur for identical particles and discuss the properties of the example

the choice of spectral element basis functions in domains with an axis of symmetry new spectral element basis functions are constructed for problems possessing an axis of symmetry in problems defined in domains with an axis of symmetry there is a potential problem of degeneracy of the system of discrete equations corresponding to nodes located on the axis of symmetry the standard spectral element basis functions are modified so that the axial conditions are satisfied identically the modified basis is employed only in spectral elements that are adjacent to the axis of symmetry this modification of the spectral element method ensures that the nodes are the same in each element which is not the case in other methods that have been proposed to tackle the problem along the axis of symmetry and that there are no nodes along the axis of symmetry the problems of stokes flow past a confined cylinder and sphere are considered and the performance of the original and modified basis functions are compared

the quantum mechanical schrodinger picture of a q oscillator a q deformed version of standard quantum mechanics in the coordinate schrodinger picture is obtained by replacing the ordinary coordinate derivative by the so called q discrete derivative as the representative of the momentum operator the chosen q discrete derivative is symmetric with respect to the exchange of q and q 1 under the usually adopted assumptions a q deformed schrodinger equation is derived for a harmonic oscillator the complete set of eigenfunctions can be explicitly constructed as special q functions and the corresponding energy eigenvalues are identical to those obtained by biedenharn in his pioneering work 1989 this q deformed oscillator exhibits a rich novel structure including dynamical symmetry and in the limit q to 1 it reveals some hitherto unknown features of the harmonic oscillator eigenfunctions

on irreducible p q representations of gl 2 the theory of irreducible p q representations of the complex lie algebra gl 2 is developed we construct a one variable model of irreducible p q representations of the gl 2 in terms of p q derivative operator and derive a generating function based on it

quasi fibonacci oscillators we study the properties of the sequences of the energy eigenvalues for some generalizations of q deformed oscillators including the p q oscillator and the three four and five parameter deformed oscillators given in the literature it is shown that most of the considered models belong to the class of so called fibonacci oscillators for which any three consecutive energy levels satisfy the relation en 1 en en 1 with real constants on the other hand for a certain oscillator known since 1993 we prove its non fibonacci nature possible generalizations of the three term fibonacci relation are discussed among which for the oscillator we choose as the most adequate the so called quasi fibonacci or local fibonacci property of the energy levels the property is encoded in the three term quasi fibonacci qf relation with the non constant n dependent coefficients and various aspects of the qf relation are elaborated for the oscillator and some of its extensions