The Schubert polynomials lift the Schur basis of symmetric polynomials into a basis for Z[x1, x2, . . .]. We suggest the prism tableau model for these polynomials. A novel aspect of this alternative to earlier results is that it directly invokes semistandard tableaux; it does so as part of a colored tableau amalgam. In the Grassmannian case, a prism tableau with colors ignored is a semistandard...

We study Thom polynomials associated with Lagrange singularities. We expand them in the basis of Q̃-functions. This basis plays a key role in the Schubert calculus of isotropic Grassmannians. We prove that the Q̃-function expansions of Thom polynomials of Lagrange singularities have always nonnegative coefficients. This is an analog of a result on Thom polynomials of mapping singularities and Sch...

We present the Maple implementations of two algorithms developed by M. Zhou and F. Winkler for computing a relative Gröbner basis of a finitely generated difference-differential module and we use this to compute the bivariate difference-differential dimension polyomial of the module with respect to the natural bifiltration of the ring of difference-differential operators. An overview regarding ...

For radial basis function interpolation of scattered data in IR d , the approximative reproduction of high-degree polynomials is studied. Results include uniform error bounds and convergence orders on compact sets. x1. Introduction We consider interpolation of real-valued functions f deened on a set IR d ; d 1. These functions are interpolated on a set X := fx 1 ; : : : ; x N X g of N X 1 pairw...

this paper presents discrete galerkin method for obtaining the numerical solution of higher even-order integro-differential equations with variable coefficients. we use the generalized jacobi polynomials with indexes corresponding to the number of homogeneous initial conditions as natural basis functions for the approximate solution. numerical results are presented to demonstrate the effectiven...

In paper [4], transformation matrices mapping the Legendre and Bernstein forms of a polynomial of degree n into each other are derived and examined. In this paper, we derive a matrix of transformation of Chebyshev polynomials of the first kind into Bernstein polynomials and vice versa. We also study the stability of these linear maps and show that the Chebyshev–Bernstein basis conversion is rem...

We show that the action of classical operators associated to the Mac-donald polynomials on the basis of Schur functions, S λ [X(t − 1)/(q − 1)], can be reduced to addition in λ−rings. This provides explicit formulas for the Macdonald polynomials expanded in this basis as well as in the ordinary Schur basis, S λ [X], and the monomial basis, m λ [X].

We constructmultiple representations relative to different bases of the generalized Tschebyscheff polynomials of second kind. Also, we provide an explicit closed from of The generalized Polynomials of degree r less than or equal n in terms of the Bernstein basis of fixed degree n. In addition, we create the change-of-basis matrices between the generalized Tschebyscheff of the second kind polyno...

A new basis {irk(z)}t.o for discrete analytic polynomials is presented for which the series 2k-o ak7Tk(z) converges absolutely to a discrete analytic function in the upper right quarter lattice whenever lim | ak \" k = 0. Introduction Let Z be the group of integers and consider functions / : Z X Z ^ C such that (1.1) f(x, y) + if(x + 1, y) / (* + 1, y + 1) if(x, y + 1) = 0 for every (x, y ) £ Z...

In this paper we show that the Kazhdan–Lusztig polynomials (and, more generally, parabolic KL polynomials) for the group Sn coincide with the coefficients of the canonical basis in nth tensor power of the fundamental representation of the quantum group Uqslk. We also use known results about canonical bases for Uqsl2 to get a new proof of recurrent formulas for KL polynomials for maximal parabol...