A new multivariate Toda hierarchy of nonlinear partial differential equations adapted to biorthogonal polynomials is discussed. This integrable associated with non-standard biorthogonality. Wave and Baker functions, linear equations, Lax Zakharov–Shabat KP type appropriate reductions, Darboux or spectral transformations, bilinear involving transformations are presented.

We present a construction of a gradient recovery operator based on an oblique projection, where the basis functions of two involved spaces satisfy a condition of biorthogonality. The biorthogonality condition guarantees that the recovery operator is local. 1. Introduction. One reason for the success of the finite element method for solving partial differential equations is that a reliable a pos...

In this paper we construct a flatlet biorthogonal multiwavelets System. Then, we use this system for numerical solution of Integro-differential equations. The good properties of this system, i.e., biorthogonality and more vanishing moments lead to efficient and accurate solutions. Some test problems with known solutions are presented and the numerical results are given to show the efficiency of...

In this paper, the existence, regularity and biorthogonality of the solution of the nonhomogeneous reenement equation (x) = X k2Z Z d 0 c k (2x ? k) + G(x); x 2 IR d are considered. Also new class of biorthogonal wavelet basis on a non-uniform grid is constructed.

Let G be a countable group of unitary operators on a complex separable Hilbert space H. We give a characterization of biorthogonality among Riesz multiwavelets in terms of certain invariant properties of their associated core spaces. A large family of non-biorthogonal Riesz multiwavelets is exhibited. We also discuss some results on linear perturbation of orthonormal multiwavelets.

We construct a family of continuous biorthogonal functions related to an elliptic analogue of the Gauss hypergeometric function. The key tools used for that are the elliptic beta integral and the integral Bailey chain introduced earlier by the author. Relations to the Sklyanin algebra and elliptic analogues of the Faddeev modular double are discussed in detail.

A family of continuous biorthogonal functions related to an elliptic analog of the Gauss hypergeometric function is constructed. The key tools used for that are the elliptic beta integral and the integral Bailey chain introduced earlier by the author. The relationship with the Sklyanin algebra and elliptic analogs of the Faddeev modular double are discussed in detail. §

This paper is devoted to the analysis of the behaviour, in nite precision arithmetic, of the quasi-minimal residual method without look ahead for the solution of linear systems Ax = b where A is a real or complex matrix of order n. In exact arithmetic, the behaviour of the method as applied to symmetric deenite matrices is well understood; but results about convergence usually suppose that the ...

We analyze polarization changes of light diffracted on a planar chiral array from the standpoint of the Lorentz reciprocity lemma and find biorthogonality in the polarization eigenstates for waves diffracting though the grating in the opposite direction. Both reciprocal and nonreciprocal components in the polarization azimuth rotation of the diffracted light are identified. The structural chira...

We define operational logical relations between terms of a polymorphically typed functional language and low-level programs for a variant SECD machine. The relations, defined using biorthogonality and step-indexing, give extensional and compositional specifications expressing when low-level code and machine values realize typed source-level terms. We prove the correctness of a compiler and of s...