equivalence of q bosons using the exponential phase operator various forms of the q boson are explained and their hidden symmetry revealed by transformations using the exponential phase operator both the one component and the multicomponent q bosons are discussed as a byproduct we obtain a new boson algebra having a shifted vacuum structure and define a global operator u 1 gauge transformation

entropy solutions for stochastic porous media equations we provide an entropy formulation for porous medium type equations with a stochastic non linear spatially inhomogeneous forcing well posedness and l1 contraction is obtained in the class of entropy solutions our scope allows for porous medium operators u m 1u for all m 1 and holder continuous diffusion nonlinearity with exponent 1 2

raising and lowering operators factorization and differential difference operators of hypergeometric type starting from the rodrigues formula we present a general construction of raising and lowering operators for orthogonal polynomials of continuous and discrete variables on a uniform lattice in order to have these operators mutually adjoint we introduce orthonormal functions with respect to the scalar product of unit weight using the infeld hull factorization method we generate from the raising and lowering operators the second order self adjoint differential difference operator of hypergeometric type

quantum deformation of bose parastatistics a q deformation of the transformation of the chevalley basis to an odd basis of generators of the universal enveloping of the lie superalgebra g n osp 1 2n is presented it is shown that one thus obtains a reasonable quantum deformation of the algebra of n para bose oscillators

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

complementarity of suq 3 and uq 2 and q boson realization of the suq 3 irreducible representations the complementarity relationship also termed duality that arises between the irreps of the su 3 and u 2 lie algebras when their direct sum su 3 u 2 is embedded into a larger u 6 algebra and single row irreps of the latter are considered is extended to the corresponding q algebras suq 3 and uq 2 it is demonstrated by explicitly constructing the unique q boson state that is simultaneously maximal in suq 3 and uq 2 for a given u q 2 weight in addition the relations between the suq 3 and uq 2 casimir operators resulting from their complementarity are explicitly found together with the q bargmann representation of q boson operators the complementarity relationship is then used to construct a gel fand tseitlin basis for arbitrary suq 3 irreps in terms of q boson operators

convergence of approximations to stochastic scalar conservation laws we develop a general framework for the analysis of approximations to stochastic scalar conservation laws our aim is to prove under minimal consistency properties and bounds that such approximations are converging to the solution to a stochastic scalar conservation law the weak probabilistic convergence mode is convergence in law the most natural in this context we use also a kinetic formulation and martingale methods our result is applied to the convergence of the finite volume method in the companion paper 15

stochastic conservation laws weak in time formulation and strong entropy condition abstract this article is an attempt to complement some recent developments on conservation laws with stochastic forcing in a pioneering development feng and nualart 8 have developed the entropy solution theory for such problems and the presence of stochastic forcing necessitates introduction of strong entropy condition however the authors formulation of entropy inequalities are weak in space but strong in time in the absence of a priori path continuity for the solutions we take a critical outlook towards this formulation and offer an entropy formulation which is weak in time and weak in space

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

generalized commutators and deformation of strong coupling superconductivity we consider quantum deformation of a strong coupling superconductivity model based on creation annihilation operators which satisfy generalized commutator relations it is found that the nature of the superconducting phase transition can be changed from the usual second order to a first order transition if the deformation parameter exceeds a certain critical value metastable normal and superconducting states can exist when the transition is of the first order

convergence of a flux splitting finite volume scheme for conservation laws driven by levy noise abstract we explore numerical approximation of multidimensional stochastic balance laws driven by multiplicative levy noise via flux splitting finite volume method the convergence of the approximations is proved towards the unique entropy solution of the underlying problem

invariant measure of scalar first order conservation laws with stochastic forcing under an hypothesis of non degeneracy of the flux we study the long time behaviour of periodic scalar first order conservation laws with stochastic forcing in any space dimension for sub cubic fluxes we show the existence of an invariant measure moreover for sub quadratic fluxes we show uniqueness and ergodicity of the invariant measure also since this invariant measure is supported by l p for some p small we are led to generalize to the stochastic case the theory of l 1 solutions developed by chen and perthame ann inst h poincare anal non lineaire 20 4 645 668 2003

second order q difference equations solvable by factorization method by solving an infinite nonlinear system of q difference equations one constructs a chain of q difference operators the eigenproblems for the chain are solved and some applications including the one related to q hahn orthogonal polynomials are discussed it is shown that in the limit q 1 the present method corresponds to the one developed by infeld and hull

well posedness and large deviations for a class of spdes with levy noise abstract in this paper a class of stochastic partial differential equations spdes with levy noise is concerned firstly the local well posedness is established by the iterative approximation then the large deviation principle ldp for the regularized spdes is obtained by the weak convergence approach to get the ldp for spdes here an exponential equivalence of the probability measures is proved the results can be applied to some types of spdes such as stochastic burgers equation stochastic b family equation stochastic modified novikov equation and stochastic hunter saxton equation

a q deformed oscillator system with quantum group slq l symmetry a q deformed oscillator system with quantum group slq l symmetry is constructed in terms of the q deformed boson operators the energy level degeneracy associated with the irreducible representation of slq l is analysed especially for the case that q is a root of unity

extension of q deformed analysis and q deformed models of classical mechanics the author presents the generalization of the q derivative and investigates its properties the formula of conjugation for scalar products with respect to the lebesgue and discrete measures is obtained this formalism is applied to classical mechanical systems depending on functional derivatives he derives the deformed euler lagrange equations and deformed poisson bracket by an assumption that it determines the functional evolution of the systems it appears that in such models a hamiltonian analogue is no longer conserved in time for a few examples the explicit forms of constants of evolution are given

representations of the quadratic algebra and partially asymmetric diffusion with open boundaries we consider the one dimensional partially asymmetric exclusion model with open boundaries the model describes a system of hard core particles that hop stochastically in both directions with different rates at both boundaries particles are injected and extracted by means of the method of derrida et al the stationary probability measure can be expressed as a matrix product state involving two matrices forming a fock like representation of a general quadratic algebra we obtain the representations of this algebra which were unknown in the mathematical literature and use the two dimensional one to derive exact expressions for the density profile and correlation functions using the correspondence between the stochastic model and a quantum spin chain we obtain exact correlation functions for a spin heisenberg xxz chain with non diagonal boundary terms generalizations to other reaction diffusion models are discussed

one dimensional partially asymmetric simple exclusion process with open boundaries orthogonal polynomials approach the stationary state of the partially asymmetric simple exclusion process with open boundaries is reconsidered the so called matrix product ansatz is employed this enables us to construct the stationary state in the form of the product of the matrices d and e noticing the fact that the matrix c d e for the model is related to certain q orthogonal polynomials the model is analysed for a wide range of parameters the current and the correlation length are evaluated in the thermodynamic limit it turns out that the phase diagram for the correlation length is richer than that for the totally asymmetric case

raising and lowering operators and their factorization for generalized orthogonal polynomials of hypergeometric type on homogeneous and non homogeneous lattices we complete the construction of raising and lowering operators given in a previous work for the orthogonal polynomials of hypergeometric type on a non homogeneous lattice we extend these operators to the generalized orthogonal polynomials namely those difference orthogonal polynomials that satisfy a similar difference equation of hypergeometric type

the dual hahn q polynomials in the lattice and the q algebras and the dual q hahn polynomials in the non uniform lattice are obtained the main data for these polynomials are calculated the square of the norm of the coefficients of the three term recurrence relation etc as well as the lattice representation as a q hypergeometric series the connection with the clebsch gordan coefficients of the quantum algebras and is also given

factorization method for second order functional equations we apply general difference calculus in order to obtain solutions to the functional equations of the second order we show that factorization method can be successfully applied to the functional case this method is equivariant under the change of variables some examples of applications are presented

the factorization method for the general second order q difference equation and the laguerre hahn polynomials on the general q lattice for the general linear second order q difference equation we show the interconnection between the factorization method and the laguerre hahn polynomials on the general q lattice applications are then given in the cases of the hypergeometric and askey wilson second order q difference equations

the poisson bracket for q deformed systems it is shown that the quantum system of q deformed oscillators with the uq n group symmetry can be obtained by the canonical quantization of a classical system with a modified poisson bracket the modification of the poisson bracket is connected with a non canonical transformation of phase space variables in this approach the deformation parameter turns out to be a function of the planck constant and some dimensional parameters characterizing the classical system

representations of quantum superalgebra uq gl 2 1 in a coherent state basis and generalization the coherent state method has proved to be useful in quantum physics and mathematics this method more precisely the vector coherent state method has been used by some authors to construct representations of superalgebras but almost to our knowledge it has not yet been extended to quantum superalgebras except uq osp 1 2 one of the smallest quantum superalgebras in this article the method is applied to a bigger quantum superalgebra namely uq gl 2 1 in constructing q boson fermion realizations and finite dimensional representations which when irreducible are classified into typical and nontypical representations this construction leads to a more general class of q boson fermion realizations and finite dimensional representations of uq gl 2 1 and thus at q 1 of gl 2 1 both gl 2 1 and uq gl 2 1 have found different physics applications therefore it is meaningful to construct their representations

generating function for clebsch gordan coefficients of the suq 2 quantum algebra some methods have been developed to calculate the suq 2 clebsch gordan coefficients cgc here the authors develop a method based on the calculation of clebsch gordan generating functions through the use of quantum algebraic coherent states calculating the suq 2 cgc by means of this generating function is an easy and straightforward task

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

completeness of coherent states associated with self similar potentials and ramanujan s integral extension of the beta function a decomposition of identity is given as a complex integral over the coherent states associated with a class of shape invariant self similar potentials there is a remarkable connection between these coherent states and ramanujan s integral extension of the beta function

realizability of a model in infinite statistics following greenberg and others we study a space with a collection of operatorsa k satisfying the q mutator relations a l a k a l k l corresponding forq 1 to classical bose and fermi statistics we show that then n matrixa n q representing the scalar products ofn particle states is positive definite for alln ifq lies between 1 and 1 so that the commutator relations have a hilbert space representation in this case this has also been proved by fivel and by bozejko and speicher we also give an explicit factorization ofa n q as a product of matrices of the form 1 q jt 1 with 1 j n andt a permutation matrix in particular a n q is singular if and only ifq m 1 for some integerm of the formk 2 k 2 k n

real de sitter and conformal algebras in terms of q oscillators we express the cartan weyl basis of all quantum real d 4 de sitter and d 4 conformal algebras in terms of q deformed oscillators

time quantization and q deformations we extend to quantum mechanics the technique of stochastic subordination by means of which one can express any semi martingale as a time changed brownian motion as examples we considered two versions of the q deformed harmonic oscillator in both ordinary and imaginary time and show how these various cases can be understood as different patterns of time quantization rules

nonlinear lie algebra and ladder operators for orbital angular momentum based on the nonlinear lie algebra a new framework is put forward to treat the problem of angular momentum from this framework the ladder operators for the orbital angular momentum can be solved as simultaneous eigenvectors of the lie derivations ad l2 and ad l2 in an operator space the ladder operators for solvable central potentials can also be found in a united way

renormalized entropy solutions of stochastic scalar conservation laws with boundary condition abstract this paper is concerned with the renormalized stochastic entropy solutions of stochastic scalar conservation law forced by a multiplicative noise on a bounded domain with a non homogeneous boundary condition we first introduce a notion of renormalized stochastic entropy solutions and then establish the existence and uniqueness of the renormalized stochastic entropy solutions for a general l 1 data our results allow us to give a positive answer to an open problem posed by bauzet vallet and wittbold in 4

discrete darboux transformation for discrete polynomials of hypergeometric type the darboux transformation well known in second order differential operator theory is applied to the difference equations satisfied by the discrete hypergeometric polynomials charlier meixner kravchuk hahn

q classical polynomials and the q askey and nikiforov uvarov tableaus abstract in this paper we continue the study of the q classical discrete polynomials in the hahn s sense started in medem et al this issue comput appl math 135 2001 157 196 here we will compare our scheme with the well known q askey scheme and the nikiforov uvarov tableau also new families of q polynomials are introduced

multi parametric deformed heisenberg algebras a route to complexity we introduce a generalization of the heisenberg algebra which is written in terms of a functional of one generator of the algebra f j0 that can be any analytical function when f is linear with slope we show that the algebra in this case corresponds to q oscillators for q2 tan the case where f is a polynomial of order n in j0 corresponds to an n parameter deformed heisenberg algebra the representations of the algebra when f is any analytical function are shown to be obtained through the study of the stability of the fixed points of f and their composed functions the case when f is a quadratic polynomial in j0 the simplest nonlinear scheme which is able to create chaotic behaviour is analysed in detail and special regions in the parameter space give representations that cannot be continuously deformed to representations of heisenberg algebra

generalized q oscillators and their hopf structures we study the relationships among the various forms of the q oscillator algebra and consider the conditions under which it supports a hopf structure we also present a generalization of this algebra together with its corresponding hopf structure its multimode extensions are also considered

three dimensional quantum groups from contractions of su 2 q contractions of lie algebras and of their representations are generalized to define new quantum groups an explicit and complete exposition is made for the one dimensional heisenberg h 1 q and the two dimensional euclidean quantum group e 2 q obtained by contracting su 2 q

factorization method on time scales abstract we present an approach to the factorization method for second order difference equations on time scales we construct hilbert spaces of functions on the time scale and show how to construct a chain of intertwined first order difference operators a k in the sense that a k and a k act as ladder operators generating new solutions of eigenproblem of a k a k

factorization method for difference equations of hypergeometric type on nonuniform lattices we study the factorization of the hypergeometric type difference equation of nikiforov and uvarov on nonuniform lattices an explicit form of the raising and lowering operators is derived and some relevant examples are given

density large deviations for multidimensional stochastic hyperbolic conservation laws we investigate the density large deviation function for a multidimensional conservation law in the vanishing viscosity limit when the probability concentrates on weak solutions of a hyperbolic conservation law conservation law when the conductivity and dif fusivity matrices are proportional i e an einstein like relation is satisfied the problem has been solved in 4 when this proportionality does not hold we compute explicitly the large deviation function for a step like density profile and we show that the associated optimal current has a non trivial structure we also derive a lower bound for the large deviation function valid for a general weak solution and leave the general large deviation function upper bound as a conjecture

laplace equation and poisson integral the resolution of laplace equation in polar coordinates abuts to poisson integral in this paper it is proved that the laplace equation remains invariable by inverse mapping inversion after the poisson integral is calculated for periodic solution of this equation for which some trigonometric integrals are calculated on intervals having email protected for length finally two examples are resolved

on nonlinear stochastic balance laws we are concerned with multidimensional stochastic balance laws we identify a class of nonlinear balance laws for which uniform spatial bv bound for vanishing viscosity approximations can be achieved moreover we establish temporal equicontinuity in l1 of the approximations uniformly in the viscosity coefficient using these estimates we supply a multidimensional existence theory of stochastic entropy solutions in addition we establish an error estimate for the stochastic viscosity method as well as an explicit estimate for the continuous dependence of stochastic entropy solutions on the flux and random source functions various further generalizations of the results are discussed

relations for clebsch gordan and racah coefficients in suq 2 and yang baxter equations relations are exploited among clebsch gordan cg and racah coefficients in the algebra suq 2 known as a deformation of su 2 these are used to show that the yang baxter yb relation for the irf interaction round a face model results from one of the symmetry relations for the 9 j symbol specific to suq 2 and that in an asymptotic limit this yb relation becomes the yb relation for the two dimensional vertex model the racah coefficient which has a particularly simple dependence on q is efficiently used such that an asymptotic limit of the racah coefficient is the cg coefficient and another limit gives the factorized s matrix of the vertex model

the factorization method for the askey wilson polynomials a special infeld hull factorization is given for the askey wilson second order q difference operator it is then shown how to deduce a generalization of the corresponding askey wilson polynomials c 1999 elsevier science b v all rights reserved

on the solution of a partial differential equation arising in stokes flow the partial differential equation e 4 j 0 that arises in the theory of fluids associated with axisymmetric stokes flow in a torus will be investigated in toroidal coordinates the solution j which represents the stream function will be shown to depend on legendre trigonometric and hyperbolic functions

brst cohomology for uq sl 2 representations a nilpotent brst operator qq is constructed for the q deformation of the universal enveloping algebra of sl 2 an associated operator rq such that qq rq cq is introduced where cq is the q deformed casimir invariant cq fe 1 2h q 1 2h 1 q the related operator qq conjugate to qq is also considered the resulting brst cohomology of uq sl 2 representations is discussed

well posedness for stochastic scalar conservation laws with the initial boundary condition abstract in this paper we are interested in the initial non homogeneous dirichlet boundary value problem for a multi dimensional scalar non linear conservation law with a multiplicative stochastic forcing we introduce a notion of renormalized kinetic formulations in which the kinetic defect measures on the boundary of a domain are truncated in such a kinetic formulation we establish a result of well posedness of the initial boundary value problem under only the assumptions h 1 h 2 and h 3 stated below which are very similar ones in 6

the distribution of zeros of general q polynomials a general system of q orthogonal polynomials is defined by means of its three term recurrence relation this system encompasses many of the known families of q polynomials among them the q analogue of the classical orthogonal polynomials the asymptotic density of zeros of the system is shown to be a simple and compact expression of the parameters which characterize the asymptotic behaviour of the coefficients of the recurrence relation this result is applied to specific classes of polynomials known by the names q hahn q kravchuk q racah q askey and wilson al salam carlitz and the celebrated little and big q jacobi

approach of spherical harmonics to the representation of the deformed su 1 1 algebra the m shifting generators of su 2 algebra together with a pair of l shifting ladder symmetry operators have been used in the space of all spherical harmonics ylm in order to introduce a new set of operators expressing the transitions between them it is shown that the space of spherical harmonics whose l 2m or l 2m is given presents negative and positive irreducible representations of a deformed su 1 1 algebra respectively these internal symmetries also suggest new algebraic methods to construct the spherical harmonics in the framework of the spectrum generating algebras

stochastic scalar conservation laws we introduce a notion of stochastic entropic solution a la kruzkov but with ito s calculus replacing deterministic calculus this results in a rich family of stochastic inequalities defining what we mean by a solution a uniqueness theory is then developed following a stochastic generalization of l1 contraction estimate an existence theory is also developed by adapting compensated compactness arguments to stochastic setting we use approximating models of vanishing viscosity solution type for the construction while the uniqueness result applies to any spatial dimensions the existence result in the absence of special structural assumptions is restricted to one spatial dimension only

a study of representations of the algebra of functions on the quantum group glq n a q analogue of the root system is constructed for this algebra which is similar to the root system of classical lie algebras it is then used to construct in detail a class of representations of the algebra of functions on the quantum group glq n and a q boson realization of the generators of glq n is given i also construct infinite dimensional hilbert space representations of this algebra the main result of this paper is stated in proposition 8

a simple difference realization of the heisenberg q algebra a realization of the heisenberg q algebra whose generators are first order difference operators on the full real line is discussed herein the eigenfunctions of the corresponding q oscillator hamiltonian are given explicitly in terms of the q 1 hermite polynomials the nonuniqueness of the measure for these q oscillator states is also studied

suq h cross to 0 2 and suq h cross 2 the classical and quantum q deformations of the su 2 algebra ii the hopf algebra the yang baxter equation and multi deformed algebraic structures for pt i see ibid vol 23 p 4185 1990 the suq 2 algebra is realized by means of both the poisson brackets in classical mechanics and commutators in quantum mechanics in a system with q deformed oscillators of two different types the structures of the hopf algebra and the quantum yang baxter equation are also discussed on a quantum level a set of j representations of the quantum algebra suq 2 is constructed based on the type ii q oscillators multi deformations of the oscillators of the two types and multi deformed algebras expressed in poisson brackets as well as in lie brackets are proposed

verma module of the quantum group gl n q and its q boson and heisenberg weyl relation realizations the structure and verma module of the quantum matrix element algebra a n q of the quantum group gl n q are studied the method used here is similar to that for studying the structure and verma module of semisimple lie algebras the concept of the cartan subalgebra raising and lowering operators and their pairs is defined the q boson and the corresponding heisenberg weyl relation realizations are generally studied and the cyclic representations of a n q are obtained the explicit examples a 2 q and a 3 q are discussed in detail

path integral formalism for suq 2 coherent states a path integral formulation in the representation of coherent states for the quantum group suq 2 is introduced an expression for the transition amplitude connecting two suq 2 coherent states is constructed and the corresponding canonical equations of motion are also derived

a new completeness relation in the q deformed two mode fock space in two mode fock space a new completeness relation for the q analogue of the single complex variable state is proved by virtue of some q deformed combinatorial identities which are also derived here for the first time

the dirichlet problem for a conservation law with a multiplicative stochastic perturbation abstract in this paper we are interested in the dirichlet boundary value problem for a multi dimensional nonlinear conservation law with a multiplicative stochastic perturbation using the concept of measure valued solutions and kruzhkov s semi entropy formulations a result of existence and uniqueness of the entropy solution is proved

on position and momentum operators in the q oscillator algebra the aim of this paper is to study the position and momentum operators in q deformed oscillator algebras the natural form of the position operator is xp qpn a a qpn where p is a real number this operator is an operator representable by a jacobi matrix using the theory of jacobi matrices the theory of classical moment problem and the theory of basic hypergeometric functions it is shown that depending on values of q and p xp can be unbounded symmetric operator which has the deficiency indices 1 1 and hence is not self adjoint but has self adjoint extensions bounded self adjoint operator with continuous simple spectrum or self adjoint operator of trace class therefore with discrete spectrum with zero as the point of accumulation of eigenvalues the connection of the q deformed heisenberg relation px qxp 1 for the position and momentum operators with a q deformation of the quantum harmonic oscillator is also considered

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

degenerate parabolic stochastic partial differential equations quasilinear case we study the cauchy problem for a quasilinear degenerate parabolic stochastic partial differential equation driven by a cylindrical wiener process in particular we adapt the notion of kinetic formulation and kinetic solution and develop a well posedness theory that includes also an l 1 contraction property in comparison to the first order case debussche and vovelle 2010 and to the semilinear degenerate parabolic case hofmanova 2013 the present result contains two new ingredients a generalized ito formula that permits a rigorous derivation of the kinetic formulation even in the case of weak solutions of certain nondegenerate approximations and a direct proof of strong convergence of these approximations to the desired kinetic solution of the degenerate problem

a priori estimates for rough pdes with application to rough conservation laws we introduce a general framework to study pdes driven by rough paths we develop new a priori estimates based on a rough gronwall lemma argument for weak solutions to rough pdes this will allow us to follow standard pde strategies to obtain existence and uniqueness results in particular our approach does not rely on any sort of transformation formula flow transformation feynman kac representation formula etc and is therefore rather flexible as an application we study conservation laws driven by rough paths establishing well posedness for the corresponding kinetic formulation

biorthogonality condition for axisymmetric stokes flow in a toroidal region in the present paper the biorthogonality condition for axisymmetric stokes flow in a toroidal geometry is derived this condition is needed to compute the coefficients of the eigenfunction expansion solution of the corresponding stokes flow problem

resolution d equations d evolution quasilineaires en dimension n d espace a l aide d equations lineaires en dimension n 1 on montre que l on peut calculer les solutions de l equation d evolution quasi lineaire dans r n d t u div b u a u 0 u x t r x r n t 0 et en particulier de l equation d ordre 1 d t u div b u 0 u x t r x r n t 0 a l aide d une equation d evolution lineaire dans r n r

path dependent convex conservation laws abstract for convex scalar conservation laws in 1 d driven by a rough path z t in the sense of lions perthame and souganidis in 32 we show that it is possible to replace z t by a piecewise linear path and still obtain the same solution at a given time this result is connected to the spatial regularity of solutions we show that solutions are spatially lipschitz continuous for an a priori set of times depending on the path and the initial data fine properties of the map z u for a prescribed time are studied we provide a detailed description of the properties of the rough path z t that influence the solution this description is extracted by a factorization of the solution operator at time in a companion paper 24 we make use of the observations herein to construct computationally efficient numerical methods

q oscillators realization of fq 4 and gq 3 a realization of the quantum superalgebras corresponding to f 4 and g 3 is given in terms of q deformed bosonic and fermionic oscillators

stochastic nonlocal conservation laws on whole space abstract after introducing an entropy formulation for stochastic nonlocal conservation laws via an integral formula we develop a uniqueness theory by using a doubling variables technique and an existence theory by using a vanishing viscosity method we further consider the continuous dependence of the entropy solution on initial data

uniqueness of renormalized solutions of degenerate elliptic parabolic problems we consider a general class of degenerate elliptic paraboic problems associated with the equation b v t div a v dv f using kruzhkov s method of doubling variables both in space and time we prove uniqueness and a comparison principle in l 1 for renormalized solutions

factorization of the hypergeometric type difference equation on non uniform lattices dynamical algebra we argue that one can factorize the difference equation of hypergeometric type on non uniform lattices in the general case it is shown that in the most cases of q linear spectrum of the eigenvalues this directly leads to the dynamical symmetry algebra suq 1 1 whose generators are explicitly constructed in terms of the difference operators obtained in the process of factorization thus all models with the q linear spectrum some of them but not all previously considered in a number of publications can be treated in a unified form

entropy solutions for nonlinear degenerate problems we consider a class of elliptic hyperbolic degenerate equations g u delta b u divg phi u f with dirichlet homogeneous boundary conditions and a class of elliptic parabolic hyperbolic degenerate equations g u t delta b u divg phi u f with homogeneous dirichlet conditions and initial conditions existence of entropy solutions for both problems is proved for nondecreasing continuous functions g and b vanishing at zero and for a continuous vectorial function satisfying rather general conditions comparison and uniqueness of entropy solutions are proved for g and b continuous and nondecreasing and for continuous

the q boson realizations of the quantum group uq sl n 1 c the authors give an explicit expression of the recurrency formulae of canonical realization for quantum enveloping algebras uq sl n 1 c in these formulae the generators of the algebra uq sl n 1 c are expressed by means of n canonical q boson pairs one auxiliary representation of the algebra uq gl n c

continuous dependence estimate for conservation laws with levy noise abstract we are concerned with multidimensional stochastic balance laws driven by levy processes using bounded variation bv estimates for vanishing viscosity approximations we derive an explicit continuous dependence estimate on the nonlinearities of the entropy solutions under the assumption that levy noise only depends on the solution this result is used to show the error estimate for the stochastic vanishing viscosity method in addition we establish fractional bv estimate for vanishing viscosity approximations in case the noise coefficient depends on both the solution and spatial variable

scalar conservation laws with stochastic forcing we show that the cauchy problem for a randomly forced periodic multi dimensional scalar first order conservation law with additive or multiplicative noise is well posed it admits a unique solution characterized by a kinetic formulation of the problem which is the limit of the solution of the stochastic parabolic approximation

on stochastic conservation laws and malliavin calculus abstract for stochastic conservation laws driven by a semilinear noise term we propose a generalization of the kru kov entropy condition by allowing the kru kov constants to be malliavin differentiable random variables existence and uniqueness results are provided our approach sheds some new light on the stochastic entropy conditions put forth by feng and nualart 17 and bauzet vallet and wittbold 2 and in our view simplifies some of the proofs

an algebraic q deformed form for shape invariant systems a quantum deformed theory applicable to all shape invariant bound state systems is introduced by defining q deformed ladder operators we show that these new ladder operators satisfy new q deformed commutation relations in this context we construct an alternative q deformed model that preserves the shape invariance property presented by the primary system q deformed generalizations of morse scarf and coulomb potentials are given as examples

a discontinuous galerkin method for stochastic conservation laws in this paper we present a discontinuous galerkin dg method to approximate stochastic conservation laws which is an efficient high order scheme we study the stability for the semidiscrete dg me

alternative hamiltonian quantization the authors take a standard hamiltonian quadratic in a set of creation and annihilation operators and demonstrate an alternative quantization by quommutators i e a set of rules for transposition of these operators different from the those of the usual canonical commutation relations which yields a new spectrum of a type reminiscent of logarithmic trajectories