关于叶果洛夫定理证明的一个注记

给出了一种函数列收敛的等价刻画,并利用此等价刻画来给出实变函数中叶果洛夫定理的另一种证明方法.     

Existence theorems for second-order discrete boundary value problems

This article is concerned with the existence of solutions of boundary value problems for nonlinear second-order difference equations of the type , where δ>0 is the ratio of odd positive integers, {p_n} and {q_n} are real sequences. The authors apply the Linking Theorem and the Mountain Pass Lemma in the critical point theory and give some new results for the existence of solutions.     

A unified proof on existence of homoclinic orbits for some semilinear ordinary differential equations with periodic potentials

This paper gives a direct, short and unified proof of Rabinowitz's Theorem, Grossinho-Minhós-Tersian's Theorem and Tersian-Chaparova's Theorems on existence of homoclinic orbits for second order periodic Hamiltonian systems, fourth and sixth order periodic ordinary differential equations, respectively, by Brezis-Nirenberg type Mountain Pass Lemma.     

An almost periodic noncommutative Wiener's Lemma

We develop a theory of almost periodic elements in Banach algebras and present an abstract version of a noncommutative Wiener's Lemma. The theory can be used, for example, to derive some of the recently obtained results in time-frequency analysis such as the spectral properties of the finite linear combinations of time-frequency shifts.     

Estimates of oscillatory integrals with stationary phase and singular amplitude: Applications to propagation features for dispersive equations

In this paper, we study time‐asymptotic propagation phenomena for a class of dispersive equations on the line by exploiting precise estimates of oscillatory integrals. We propose first an extension of the van der Corput Lemma to the case of phases which may have a stationary point of real order and amplitudes allowed to have an integrable singular point. The resulting estimates provide optimal decay rates which show explicitly the influence of these two particular points. Then we apply these abstract results to solution formulas of a class of dispersive equations on the line defined by Fourier multipliers. Under the hypothesis that the Fourier transform of the initial data has a compact support or an integrable singular point, we derive uniform estimates of the solutions in space‐time cones, describing their motions when the time tends to infinity. The method permits also to show that symbols having a restricted growth at infinity may influence the dispersion of the solutions: we prove the existence of a cone, depending only on the symbol, in which the solution is time‐asymptotically localized. This corresponds to an asymptotic version of the notion of causality for initial data without compact support.     

Some general univalence criteria for a family of integral operators

The main object of the present paper is to discuss some extensions of univalence conditions for a family of integral operators. Several other closely-related results are also considered. Many known univalence conditions are shown to follow upon specializing the parameters involved in our main results.     

A Relative Filtration Index and Fibers of Normal Primes in Extensions of Finite Type

For an extension R A of commutative Noetherian rings the behavior of the associated morphism of topological spaces Spec A Spec R is often measured by its behavior on each of its fibers. Specifically, one studies the 'splitting' (or 'branching') and the 'ramification' that occurs in each fiber. In the classical constructions of faithfully flat analytic extensions (e.g., completion or Henselization) of excellent local rings the splitting and ramification properties are fairly well understood; see EGA IV [6, 18.10], Nagata [13, Sect. 37] or Raynaud [15, Ch. IX]. The strongest results are usually achieved for fibers over a 'normal point' of Spec R, that is, over p Spec R such that R/p is a normal domain [e.g., the property of a normal prime p in a local ring to be 'unibranched', i.e., the Henselization of R/p is a (normal) domain].     

On the Pósa-Seymour conjecture

Paul Seymour conjectured that any graph G of order n and minimum degree at least contains the k^th power of a Hamilton cycle. We prove the following approximate version. For any ϵ ≥ 0 and positive integer k, there is an n₀ such that, if G has order n ≥ n₀ and minimum degree at least $(\frac{k}{k+1} + \epsilon )n$, then G contains the k^th power of a Hamilton cycle. © 1998 John Wiley & Sons, Inc. J. Graph Theory 29: 167–176, 1998     

A multilinear Phelps' Lemma

We prove a multilinear version of Phelps' Lemma: if the zero sets of multilinear forms of norm one are `close', then so are the multilinear forms.

     

On test sets for nonlinear integer maximization

A finite test set for an integer optimization problem enables us to verify whether a feasible point attains the global optimum. In this paper, we establish several general results that apply to integer optimization problems with nonlinear objective functions.