formulae expressing explicitly the coefficients of an expansion of double jacobi polynomials which has been partially differentiated an arbitrary number of times with respect to its variables in terms of the coefficients of the original expansion are stated and proved. extension to expansion of triple jacobi polynomials is given. the results for the special cases of double and triple ultraspher...

Studying Jone’s polynomials in node theories, their generalization and their connections with ”vertex models” in two-dimensional statistical mechanics, Witten presents Hoph algebra deformations of the universal enveloping algebra su(2). There is a family of associative algebras depending on a real parameter p. These algebras are given by the generators E0, E+, E− and relations [2]: pE0E+ − 1 p ...

For a given arbitrary triangulation of R, we construct an interpolating operator which is exact for the polynomials in two variables of total degree ≤ 2. This operator is local, in the sense that the information around an interpolation node are taken from a small region around this point. We study the remainder of the interpolation formula. MSC 2000: 41A63, 41A05, 41A25, 41A80, 47A57.

We study the total weight of weighted matchings in segment graphs, which is related to a question concerning generalized Chebyshev polynomials introduced by Vauchassade de Chaumont and Viennot and, more recently, investigated by Kim and Zeng. We prove that weighted matchings with sufficiently large node-weight cannot have equal total weight.

background: sentinel  lymph  node  biopsy  has  shown  to  be  a  good  alternative procedure  for  axillary  lymph  node  dissection  and  to lead  to  lower  frequency  of morbidity, though this technique has its own side effects. it needs especial equipment and may not be available in some medical centers, especially in developing countries. this study aimed to identify a subgroup of patient...

The twoand all-terminal reliabilities of the Brecht-Colbourn ladder and the generalized fan have been calculated exactly for arbitrary size as well as arbitrary individual edge and node reliabilities, using transfer matrices of dimension four at most. While the all-terminal reliabilities of these graphs are identical, the special case of identical edge (p) and node (ρ) reliabilities shows that ...

Polynomial interpolation is a classical method to approximate continuous functions by polynomials. To measure the correctness of the approximation, Lebesgue constants are introduced. For a given node system X = {x1 < . . . < xn+1} (xj ∈ [a, b]), the Lebesgue function λn(x) is the sum of the modulus of the Lagrange basis polynomials built on X. The Lebesgue constant Λn assigned to the function λ...

The main goal of the present paper is to construct some families of the Carlitz's $q$-Bernoulli polynomials and numbers. We firstly introduce the modified Carlitz's $q$-Bernoulli polynomials and numbers with weight ($_{p}$. We then define the modified degenerate Carlitz's $q$-Bernoulli polynomials and numbers with weight ($alpha ,beta $) and obtain some recurrence relations and other identities...

In this contribution, we study multivariate polynomial interpolation and quadrature rules on non-tensor product node sets linked to Lissajous curves and Chebyshev varieties. After classifying multivariate Lissajous curves and the interpolation nodes related to these curves, we derive a discrete orthogonality structure on these node sets. Using this discrete orthogonality structure, we can deriv...

This article is a survey on recent research on bivariate polynomial interpolation on the node points of Lissajous curves. The resulting theory is a generalization of the generating curve approach developed for Lagrange interpolation on the Padua points. After classifying the different types of Lissajous curves, we give a short overview on interpolation and quadrature rules defined on the node p...