the laguerre and legendre polynomials from an operational point of view the use of the monomiality principle and of the associated operational calculus allows to reformulate the theory of laguerre and legendre polynomials from a unified point of view they are indeed shown to be particular cases of more general polynomials whose usefulness in purely mathematical and applied contexts is discussed the concepts introduced in the paper are also exploited to develop an elementary point of view on the theory of legendre and laguerre bessel functions

integral transforms and chebyshev like polynomials we use the integral representation method to derive the properties of chebyshev polynomials and of their generalized forms

associated laguerre konhauser polynomials quasi monomiality and operational identities abstract in this paper we exploit the monomiality principle to discuss and introduce a new class of laguerre konhauser polynomials we study their properties differential equations generating functions recurrence relations expansions and so on and discuss the link with ordinary case

existence and uniqueness of solutions of unilateral problems in orlicz spaces abstract in this paper we prove the existence and uniqueness of solutions of unilateral problems of the type div a x u f in the framework of orlicz spaces the main contribution of our work is proving the existence of a solution without any restriction on the n function m of the orlicz spaces

multi variable hermite matrix polynomials properties and applications abstract in this paper the multi variable hermite matrix polynomials are introduced by algebraic decomposition of exponential operators their properties are established using operational methods the matrix forms of the chebyshev and truncated polynomials of two variable are also introduced which are further used to derive certain operational representations and expansion formulae

finding mixed families of special polynomials associated with appell sequences abstract in this paper certain mixed special polynomial families associated with appell sequences are introduced and their properties are established further operational rules providing connections between these families and known special polynomials are established which are used to derive the identities and results for the members of these new families determinantal definitions of the polynomials associated with appell family are also derived the approach presented is general

analysis and approximation of the ginzburg landau model of superconductivity the authors consider the ginzburg landau model for superconductivity first some well known features of superconducting materials are reviewed and then various results concerning the model the resultant differential equations and their solution on bounded domains are derived then finite element approximations of the solutions of the ginzburg landau equations are considered and error estimates of optimal order are derived

some families of generating functions for the multiple orthogonal polynomials associated with modified bessel k functions the main object of this paper is to derive several substantially more general families of bilinear bilateral and mixed multilateral finite series relationships and generating functions for the multiple orthogonal polynomials associated with the modified bessel k functions also known as macdonald functions some special cases of the above statements are also given

certain results for the 2 variable apostol type and related polynomials in this article the 2 variable general polynomials are taken as base with apostol type polynomials to introduce a family of 2 variable apostol type polynomials these polynomials are framed within the context of monomiality principle and their properties are established certain summation formulae for these polynomials are also derived examples of some members belonging to this family are considered and numbers related to some mixed special polynomials are also explored

on a singular integral equation including a set of multivariate polynomials suggested by laguerre polynomials in this paper we introduce the class of polynomials z n 1 n j a x 1 x j r 1 r j suggested by the multivariate laguerre polynomials we give schlafli s contour integral representation and calculate the fractional order integral of these polynomials furthermore we obtain linear multilinear and mixed multilateral generating functions for them finally we construct a singular integral equation with z n 1 n j a x 1 x j r 1 r j in the kernel and obtain the solution in terms of multivariate analogue of the mittag leffler functions

generating functions involving hermite laguerre polynomials using operational methods in this paper some generating functions involving 3 variable hermite laguerre polynomials are derived by using operational methods further generating functions for the polynomials related to hermite laguerre polynomials are also obtained as applications of the main results

operational methods and laguerre gould hopper polynomials abstract in this paper the authors introduce the laguerre gould hopper polynomials by combining the operational methods with the principle of monomiality generating function series definition differential equation and certain other properties of laguerre gould hopper polynomials are derived further operational representations of these polynomials are established which are used to get integral representations and expansion formulae for these polynomials

an optimal linear solver for the jacobian system of the extreme type ii ginzburg landau problem this paper considers the extreme type ii ginzburg landau equations a nonlinear pde model for describing the states of a wide range of superconductors based on properties of the jacobian operator and an amg strategy a preconditioned newton krylov method is constructed after a finite volume type discretization numerical experiments are done for representative two and three dimensional domains strong numerical evidence is provided that the number of krylov iterations is independent of the dimension n of the solution space yielding an overall solver complexity of o n

numerical approximations of the ginzburg landau models for superconductivity in this paper we review various methods for the numerical approximations of the ginzburg landau models of superconductivity particular attention is given to the different treatment of gauge invariance in both the finite element finite difference and finite volume settings representative theoretical results typical numerical simulations and computational challenges are presented generalizations to other relevant models are also discussed

variational inequalities in orlicz sobolev spaces on etudie l existence de solutions d inegalites variationnelles associees a des operateurs differentiels elliptiques

generalized polynomials and associated operational identities we use operational identities to introduce multivariable laguerre polynomials we explore the wealth of differential equations they satisfy we analyze their properties and the link with legendre type polynomials

the approximation properties of generalized bernstein polynomials of two variables the positive linear operators of bernstein type of two variables are considered and the theorems about approximation and about the order of approximation of the sequence of these operators are established

algebraic multigrid solvers for complex valued matrices in the mathematical modeling of real life applications systems of equations with complex coefficients often arise while many techniques of numerical linear algebra e g krylov subspace methods extend directly to the case of complex valued matrices some of the most effective preconditioning techniques and linear solvers are limited to the real valued case here we consider the extension of the popular algebraic multigrid method to such complex valued systems the choices for this generalization are motivated by classical multigrid considerations evaluated with the tools of local fourier analysis and verified on a selection of problems related to real life applications

bivariate mittag leffler functions arising in the solutions of convolution integral equation with 2d laguerre konhauser polynomials in the kernel abstract recently the 2d laguerre konhauser polynomials were introduced in 1 in the present paper first of all we propose another bivariate polynomial family which is bi orthonormal with the 2d laguerre konhauser polynomials then we consider a convolution integral equation with 2d laguerre konhauser polynomials in the kernel and we obtain its solution by introducing a new family of bivariate mittag leffler functions furthermore we introduce a double fractional integral operator including bivariate mittag leffler functions in the kernel this integral operator includes the double riemann liouville fractional integral operator we investigate its transformation properties on the continuous function and lebesgue summable function spaces also the semigroup property of the operator is investigated we further study some miscelenenous properties of 2d laguerre konhauser polynomials and bivariate mittag leffler functions such as generating function schlafli s integral represantation finally we approximate to the image of any bivariate continuous function under the action of the proposed double integral operators

some properties of hermite based sheffer polynomials abstract in this paper the concepts and the formalism associated with monomiality principle and sheffer sequences are used to introduce family of hermite based sheffer polynomials some properties of hermite sheffer polynomials are considered further an operational formalism providing a correspondence between sheffer and hermite sheffer polynomials is developed furthermore this correspondence is used to derive several new identities and results for members of hermite sheffer family

existence results for some unilateral problems without sign condition with obstacle free in orlicz spaces abstract we prove the existence results in the setting of orlicz spaces for the unilateral problem associated to the following equation a u g x u u f where a is a leray lions operator acting from its domain d a w 0 1 l m into its dual while g x u u is a nonlinear term having a growth conditions with respect to u and no growth with respect to u but does not satisfy any sign condition the right hand side f belongs to l 1 and the obstacle is a measurable function

some properties of legendre gould hopper polynomials and operational methods abstract in this paper the author introduces the legendre gould hopper polynomials by combining the operational methods with the principle of monomiality generating functions series definition differential equation and certain other properties of legendre gould hopper polynomials are derived further operational representations of these polynomials are established which are used to get integral representations and expansion formulae certain summation formulae for these polynomials are also obtained

bilateral generating functions and operational methods bilateral generating functions are those involving products of different types of polynomials we show that operational methods offer a powerful tool to derive these families of generating functions we study cases relevant to products of hermite polynomials with laguerre legendre and other polynomials we also propose further extensions of the method which we develop here

generalized and mixed type gegenbauer polynomials abstract in this paper a new generalized form of the gegenbauer polynomials is introduced by using the integral representation method further the hermite gegenbauer and the laguerre gegenbauer polynomials are introduced by using the operational identities associated with the generalized hermite and laguerre polynomials of two variables