Biorthogonality and integration

Biorthogonality and Integration

Semantic Barbs and Biorthogonality

We use the framework of biorthogonality to introduce a novel semantic definition of the concept of barb (basic observable) for process calculi. We develop a uniform basic theory of barbs and demonstrate its robustness by showing that it gives rise to the correct observables in specific process calculi which model synchronous, asynchronous and broadcast communication regimes.

Nonhomogeneous Reenement Equation: Existence, Regularity and Biorthogonality

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.

Biorthogonality of the Lagrange interpolants

The Newton-Lagrange interpolation is a well-known problem in elementary calculus. Recall basic facts concerning this problem [6], [2]. Let Ak, k = 0, 1, 2, . . . and ak, k = 0, 1, 2, . . . be two arbitrary sequences of complex numbers (we assume that all ak are distinct ak 6= aj if k 6= j. By interpolation polynomial we mean a n-degree polynomial Pn(z) whose values at points a0, a1, . . . , an ...

Loss of biorthogonality and linear system solvers

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 ...