In this paper we give a characterization of pointwise and uniform convergence of sequences of homogeneous polynomials on a Banach space by means of the convergence of their level sets. Results are obtained both in the real and the complex cases, as well as some generalizations to the nonhomogeneous case and to holomorphic functions in the complex case. Kuratowski convergence of closed sets is u...

This work concerns controlled Markov chains with denumerable state space, (possibly) unbounded cost function, and an expected average cost criterion. Under a Lyapunov function condition, together with mild continuity-compactness assumptions, a simple necessary and sufficient criterion is given so that the relative value functions and differential costs produced by the value iteration scheme con...

Infection by Epstein-Barr virus (EBV) generates several types of latency with different profiles of gene expression but with expression of Epstein-Barr nuclear antigen 1 (EBNA-1) in common. The BamHI Q promoter (Qp) is used for the transcription of EBNA-1 mRNA in type I latency, which is an EBV infection state exemplified by Burkitt's lymphoma (BL). However, Qp is inactive in type III latency, ...

Abstract We prove asymptotic stability of steady-state solutions to the Navier–Stokes equations in whole space. One novelties this work consists considering perturbations that show a distinct pointwise behavior (in space and time) correspond initial data only belonging suitable weighted Lebesgue spaces.

In this article we summarize recent results on a priori error estimates for space-time finite element discretizations of linear-quadratic parabolic optimal control problems. We consider the following three cases: problems without inequality constraints, problems with pointwise control constraints, and problems with state constraints pointwise in time. For all cases, error estimates with respect...

This paper investigates higher order wave-type equations of the form [Formula: see text], where the symbol [Formula: see text] is a real, non-degenerate elliptic polynomial of the order [Formula: see text] on [Formula: see text]. Using methods from harmonic analysis, we first establish global pointwise time-space estimates for a class of oscillatory integrals that appear as the fundamental solu...

It is known that accumulation points of a pointwise bounded sequence (f n) n of continuous functions on a Polish space are pointwise limits of subsequences if all accumulation points are Borel. Here we present a quantitative variant of this result: For 0 0 and any accumulation point f there is a subsequence (f nk) k with lim sup k jf(x) ? f nk (x)j 0 for all x provided that every accumulation p...

Epstein-Barr virus (EBV) nuclear antigen 1 (EBNA-1) is the essential protein for maintenance of the EBV episome and establishment of latency. The BamHI Q promoter (Qp) is used for the transcription of EBNA-1 mRNA in type I and type II latency, which are EBV infection states exemplified by Burkitt's lymphoma and nasopharyngeal carcinoma. However, Qp is inactive in type III latency, and other pro...

A criterion for the maximum possible pointwise convergence rate in Birkhoff’s ergodic theorem semiflows a Lebesgue space is obtained. It proved that higher rates of this are impossible.

Finite difference approximations of the second derivative in space appearing in, parabolic, incompletely parabolic systems of, and second order hyperbolic, partial differential equations are considered. If the solution is pointwise bounded, we prove that finite difference approximations of those classes of equations can be closed with two orders less accuracy at the boundary without reducing th...