the quantum heisenberg group h 1 q the structure of the quantum heisenberg group is studied in the two different frameworks of the lie algebra deformations and of the quantum matrix pseudogroups the r matrix connecting the two approaches together with its classical limit r are explicitly calculated by using the contraction technique and the problems connected with the limiting procedure discussed some unusual properties of the quantum enveloping heisenberg algebra are shown

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

nonstandard quantum groups and superization we obtain the universal r matrix of the nonstandard quantum group associated to the alexander conway knot polynomial we show further that this nonstandard quantum group is related to the super quantum group uq gl 1 1 by a general process of superization which we describe we also study a twisted variant of this nonstandard quantum group and obtain as a result a twisted version of uq gl 1 1 as a q supersymmetry of the exterior differential calculus of any quantum plane of hecke type acting by mixing the bosonic xi coordinates and the forms dxi

multiparametric quantum gl 2 lie bialgebras quantum r matrices and non relativistic limits multiparametric quantum deformations of gl 2 are studied through a complete classification of gl 2 lie bialgebra structures from these the non relativistic limit leading to harmonic oscillator lie bialgebras is implemented by means of a contraction procedure new quantum deformations of gl 2 together with their associated quantum r matrices are obtained and other known quantizations are recovered and classified several connections with integrable models are outlined

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

scalar curvature and warped products of riemann manifolds we establish the relationship between the scalar curvature of a warped product m xf n of riemann manifolds and those ones of m and n then we search for weights f to obtain constant scalar curvature on m xf n when m is compact

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

bivariate splines on hexagonal lattice for digital image processing in this paper the applications of multi variable spline functions in the digital signal processing was investigated further several two dimensional spline functions were constructed for hexagonal lattice they are actually variation of bivariate cardinal splines on regular triangular partition that were constructed earlier those bivariate cardinal splines have a number of desirable features which make it applicable for image processing and other areas one feature lies in the fact that the coefficients of the interpolation representations with bivariate cardinal splines are basically the sample data at the interpolation points the interpolations converge uniformly to the function being interpolated as the sampling increment approaches zero compare to the popular tensor product with the same degree of smoothness our bivariate cardinal splines has the same degree of accuracy with smaller local support lower degree of the polynomials therefore it should lead to the reduction of computation time and storage space

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

le nombre de solutions de certains problemes semi lineaires elliptiques abstract in this paper we compute the exact number of solutions for certain semi linear elliptic problems in the first part we derive some complementary results to a theorem of ambrosetti and prodi the global behaviour of bifurcating branches is then studied for some classes of problems in the context of a concave or a convex nonlinearity in the second part we consider the branch of positive solutions lastly in the third part in dimension one for an autonomous equation we obtain a precise description of all the solutions to these problems the proofs rely on simple eigenvalue comparison arguments

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

two dimensional spline interpolation for image reconstruction a scheme of two dimensional 2 d spline interpolation for image reconstruction is presented it is aimed to be applied in image data compression an impulse response derived from 2 d quadratic spline functions is theoretically analysed then it is approximated to be a finite duration one fir for practical implementation with this scheme compression rate of greater than 12 is achieved for x ray left ventricular cineangiogram image data compression

special standard static space times abstract essentially some conditions for the riemannian factor and the warping function of a standard static space time are obtained in order to guarantee that no nontrivial warping function on the riemannian factor can make the standard static space time einstein

random operator approach for word enumeration in braid groups we investigate analytically the problem of enumeration of nonequivalent primitive words in the locally free and braid groups for by analysing the random word statistics and target spaces on these groups we develop a symbolic dynamics method for exact word enumeration in locally free groups and give arguments in support of the conjecture that the number of very long primitive words in the braid group is not sensitive to the precise local commutation relations we touch briefly the connection of these problems with conventional random operator theory localization phenomena and statistics of systems with quenched disorder we also discuss the relation of particular problems of random operator theory to the theory of modular functions

abstract splines in krein spaces abstract we present generalizations to krein spaces of the abstract interpolation and smoothing problems proposed by atteia in hilbert spaces given a krein space k and hilbert spaces h and e bounded surjective operators t h k and v h e 0 and a fixed z 0 e we study the existence of solutions of the problems argmin t x t x k v x z 0 and argmin t x t x k v x z 0 e 2 x h

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

b spline signal processing ii efficiency design and applications for pt i see ibid vol 41 no 2 p 821 33 1993 a class of recursive filtering algorithms for the efficient implementation of b spline interpolation and approximation techniques is described in terms of simplicity of realization and reduction of computational complexity these algorithms compare favorably with conventional matrix approaches a filtering interpretation low pass filter followed by an exact polynomial spline interpolator of smoothing spline and least squares approximation methods is proposed these techniques are applied to the design of digital filters for cubic spline signal processing an efficient implementation of a smoothing spline edge detector is proposed it is also shown how to construct a cubic spline image pyramid that minimizes the loss of information in passage from one resolution level to the next in terms of common measures of fidelity this data structure appears to be superior to the gaussian laplacian pyramid

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

colored quantum universal enveloping algebras we define some new algebraic structures termed colored hopf algebras by combining the coalgebra structures and antipodes of a standard hopf algebra set h corresponding to some parameter set q with the transformations of an algebra isomorphism group g herein called color group such transformations are labeled by some color parameters taking values in a color set c we show that various classes of hopf algebras such as almost cocommutative coboundary quasitriangular and triangular ones can be extended into corresponding colored algebraic structures and that colored quasitriangular hopf algebras in particular are characterized by the existence of a colored universal r matrix satisfying the colored yang baxter equation the present definitions extend those previously introduced by ohtsuki which correspond to some substructures in those cases where the color group is abelian we apply the new concepts to construct colored quantum universal enveloping algebras of both semisimple and nonsemisimple lie algebras considering several examples with fixed or varying parameters as a by product some of the matrix representations of colored universal r matrices derived in the present paper provide new solutions of the colored yang baxter equation which might be of interest in the context of integrable models

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

a non standard quantum double as the l state boson algebra and its r matrices for the quantum yang baxter equation in this paper we construct a new quantum double by endowing the l state boson algebra with a non trivial hopf algebra structure which is not a q deformation of the lie algebra or superalgebra the universal r matrix for the yang baxter equation associated with this new quantum group structure is obtained explicitly by building the representations of this quantum double we obtain some r matrices which can result in new representations of the braid group

new hierarchy of colored braid group representations novel solutions of the yang baxter relation for a series of multistate vertex models are presented in the braid group limit the obtained family of solutions gives a sequence of colored braid group representations possible generalizations of the multivariable alexander polynomial are discussed

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

quantum structure of the motion groups of the two dimensional cayley klein geometries a simultaneous and global scheme of quantum deformation is defined for the set of algebras corresponding to the groups of motions of the two dimensional cayley klein geometries their central extensions are also considered under this unified pattern in both cases some fundamental properties characterizing the classical ck geometries as the existence of a set of commuting involutions contractions and dualities relationships remain in the quantum version

braid group representations from a deformation of the harmonic oscillator algebra we describe a new technique to obtain representations of the braid group bn from the matrix of a quantum deformed algebra of the one dimensional harmonic oscillator we consider the action of the matrix not on the tensor product of representations of the algebra that in the harmonic oscillator case are infinite dimensional but on the subspace of the tensor product corresponding to the lowest weight vectors

fast b spline transforms for continuous image representation and interpolation efficient algorithms for the continuous representation of a discrete signal in terms of b splines direct b spline transform and for interpolative signal reconstruction indirect b spline transform with an expansion factor m are described expressions for the z transforms of the sampled b spline functions are determined and a convolution property of these kernels is established it is shown that both the direct and indirect spline transforms involve linear operators that are space invariant and are implemented efficiently by linear filtering fast computational algorithms based on the recursive implementations of these filters are proposed a b spline interpolator can also be characterized in terms of its transfer function and its global impulse response cardinal spline of order n the case of the cubic spline is treated in greater detail the present approach is compared with previous methods that are reexamined from a critical point of view it is concluded that b spline interpolation correctly applied does not result in a loss of image resolution and that this type of interpolation can be performed in a very efficient manner

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

b spline signal processing i theory the use of continuous b spline representations for signal processing applications such as interpolation differentiation filtering noise reduction and data compressions is considered the b spline coefficients are obtained through a linear transformation which unlike other commonly used transforms is space invariant and can be implemented efficiently by linear filtering the same property also applies for the indirect b spline transform as well as for the evaluation of approximating representations using smoothing or least squares splines the filters associated with these operations are fully characterized by explicitly evaluating their transfer functions for b splines of any order applications to differentiation filtering smoothing and least squares approximation are examined the extension of such operators for higher dimensional signals such as digital images is 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

quantum harmonic oscillator algebra and link invariants associated with the q deformation of the harmonic oscillator algebra we define an infinite dimensional braid group representation on the hilbert space of the harmonic oscillator and an extended yang baxter system in the sense of turaev the corresponding link invariant is computed in some particular cases and coincides with the inverse of the alexander conway polynomial the r matrix of uq h4 can be interpreted as defining a baxterization of the intertwiners for semicyclic representations of su 2 q at q e2 i n in the n limit finally we define new multicolored braid group representations and study their relation to the multivariable alexander conway polynomial

lie bialgebra quantizations of the oscillator algebra and their universal r matrices all coboundary lie bialgebras and their corresponding poisson lie structures are constructed for the oscillator algebra generated by quantum oscillator algebras are derived from these bialgebras by using the lyakhovsky and mudrov formalism and for some cases quantizations at both algebra and group levels are obtained including their universal r matrices

the braided heisenberg group the braided groups and braided matrices b r for the solution r of the yang baxter equation associated to the quantum heisenberg group are computed it is also shown that a particular extension of the quantum heisenberg group is dual to the heisenberg universal enveloping algebra uq h and this result is used to derive an action of uq h on the braided groups the various covariance properties are then demonstrated using the braided heisenberg group as an explicit example in addition the braided heisenberg group is found to be self dual finally a physical application to a system of n braided harmonic oscillators is discussed an isomorphism is found between the n fold braided and unbraided tensor products and the usual free time evolution is shown to be equivalent to an action of a primitive generator of uq h on the braided tensor product

the yang baxter equation and invariants of links on considere le fait que l on peut construire des invariants d isotopie p et f pour des liens en utilisant certaines solutions des equations de yang baxter

a nonlinear deformed su 2 algebra with a two color quasitriangular hopf structure nonlinear deformations of the enveloping algebra of su 2 involving two arbitrary functions of j0 and generalizing the witten algebra were introduced some time ago by delbecq and quesne in the present paper the problem of endowing some of them with a hopf algebraic structure is addressed by studying in detail a specific example referred to as aq 1 this algebra is shown to possess two series of n 1 dimensional unitary irreducible representations where n 0 1 2 to allow the coupling of any two such representations a generalization of the standard hopf axioms is proposed by proceeding in two steps in the first one a variant and extension of the deforming functional technique is introduced variant because a map between two deformed algebras suq 2 and aq 1 is considered instead of a map between a lie algebra and a deformed one and extension because use is made of a two valued functional whose inverse is singular as a result the hopf structure of suq 2 is carried over to aq 1 ther

on warped product gradient yamabe solitons abstract the purpose of this article is to study gradient yamabe solitons on top of warped product manifolds first we prove triviality results in the case of a bounded warping function on a noncompact base and then for compact base in order to provide nontrivial examples we consider the base conformal to a semi euclidean space which is invariant under the action of a translation group and then we characterize steady solitons we use this method to give infinitely many explicit examples of complete steady gradient yamabe solitons

solutions to a singularly perturbed supercritical elliptic equation on a riemannian manifold concentrating at a submanifold abstract given a smooth riemannian manifold m g we investigate the existence of positive solutions to the equation e 2 g u u u p 1 on m which concentrate at some submanifold of m as e 0 for supercritical nonlinearities we obtain a positive answer for some manifolds which include warped products using one of the projections of the warped product or some harmonic morphism we reduce this problem to a problem of the form e 2 div h c x h u a x u b x u p 1 with the same exponent p on a riemannian manifold m h of smaller dimension so that p turns out to be subcritical for this last problem then applying lyapunov schmidt reduction we establish existence of a solution to the last problem which concentrates at a point as e 0