Consider a scalar, nonlinear conservative difference scheme satisfying the entropy condition. It is shown that difference schemes containing more numerical viscosity will necessarily converge to the unique, physically relevant weak solution of the approximated conservative equation. In particular, entropy satisfying convergence follows for E schemes—those containing more numerical viscosity tha...

where 1 sp < co. This definition is far from being intrinsic. For an intrinsic definition of WrTp(Mm, N”) see [ 11. In this space, beside the standard topology induced by the norm (1. ]ll,p, we also have weak topology and weak convergence. Let fk, f E W’~p(Mm), where 1 < p < co. We say that fk converges to f in weak topology iff fk + f in Lp and the set (lIVfk[lp)k is bounded. Weak convergence ...

The weak convergence of orthogonal polynomials is given under conditions on the asymptotic behaviour of the coefficients in the three-term recurrence relation. The results generalize known results and are applied to several systems of orthogonal polynomials, including orthogonal polynomials on a finite set of points.

Motivated by the theory of inhomogeneous Markov chains, we determine a sufficient condition for the convergence to 0 of a general product formed from a sequence of real or complex matrices. When the matrices have a common invariant subspace H, we give a sufficient condition for the convergence to 0 on H of a general product. Our result is applied to obtain a condition for the weak ergodicity of...

the process of economic globalization and integration has had a tremendous growth in recent years and the convergence of various economic sectors, including the financial markets is increasingly in the spotlight. this increasing trend has strengthened investors&apos; interests in the subject of convergence among the world&apos;s stock markets and investors experimentally show a passion for unde...

We prove phase-space mixing for solutions to Liouville’s equation integrable systems. Under a natural non-harmonicity condition, we obtain weak convergence of the distribution function with rate ⟨time⟩−1. In one dimension, also study case where this condition fails at certain energy, showing that still holds but slower rate. When and functions have higher regularity, can be faster.

This paper is aimed at sharpen a weak invariance principle for stationary sequences in Doukhan & Louhichi (1999). Our assumption is both beyond mixing and the causal θ-weak dependence in Dedecker and Doukhan (2003); those authors obtained a sharp result which improves on an optimal one in Doukhan et alii (1995) under strong mixing. We prove this result and we also precise convergence rates unde...