Banach空间逼近紧性与预报算子连续性的几何条件

首先给出 Banach空间为逼近紧的几何特征 .然后用随机变量组成的 Banach空间及空间中预报集的几何性质给出预报算子连续的条件 .     

Compactness Conditions for the Green Operator in Lp(ℝ) Corresponding to a General Sturm–Liouville Operator

We consider the equation ℝ, where , for ℝ, (ℝ), (ℝ), (ℝ), (ℝ) := C(ℝ)). We give necessary and sufficient conditions under which, regardless of , the following statements hold simultaneously: I) For any (ℝ) Equation (0.1) has a unique solution (ℝ) where $\int ^{\infty}_{-\infty}$ ℝ. II) The operator (ℝ) → (ℝ) is compact. Here is the Green function corresponding to (0.1). This result is applied to study some properties of the spectrum of the Sturm–Liouville operator.     

复正定矩阵的充要条件

本文研究Hermite正定矩阵、实正定矩阵的推广概念复正定矩阵,给出了复方阵复正定性的一些充分必要条件。     

The Nemitskii Operator in Holder Spaces: Some Necessary and Sufficient Conditions

The Nemitskii operator in the Hölder spaces C^0, () with an open bounded subset of Rⁿ, is studied; necessary and sufficientconditions are given for boundedness, uniform continuity, anduniformly continuous differentiability on bounded sets.     

Sufficient Conditions for the Existence of Disintegrations

Let be a probability space and a partition of . A necessary and sufficient condition is given for the existence of a -additive and measurable disintegration of P on . It is also shown that P admits a -additive (but not measurable) disintegration on whenever is a standard space and the set (₁, ₂):₁ and ₂ are in the same element of } is coanalytic in ×. Finally, sufficient statistics (in the classical Fisherian sense) are investigated by using -additive disintegrations as conditional probabilities.     

复函数奇偶性判定的几个充分必要条件

研究复函数奇偶性的判定方法,得出了几个充分必要条件,可为此类函数的运算和进一步的分析研究提供有用的参考.     

Sufficient Conditions for Nonsmooth r-Invexity

In this paper, some sufficient conditions are derived for nonsmooth r-invexity with respect to Clarke's generalized directional derivatives. Some notions including nearly convex-like mappings and nearly convex sets are used to obtain the results.     

非奇H-矩阵的充分条件

非奇H矩阵是具有广泛实际背景的重要矩阵类,但实际判断一个矩阵是否为非奇H矩阵却是困难的.该文给出非奇H矩阵的两个实用且适用范围较广的充分条件. 数值例子说明了结果的优越性.     

Sufficient Conditions for Irregular Wavelet Frames

Finding verifiable conditions for wavelet systems to be wavelet frames is among the core problems in wavelet analysis. In this paper, we give some simple and sufficient conditions that ensure a multidimensional irregular wavelet system to be a frame or a weighted frame. Quantitative results are provided, and explicit frame bounds are given.     

关于p叶近于凸性的充分条件

Let Ap(n)(p, n∈N={1,2,...}) denote the class of functions of the form f(z)=zp+ap+nzp+n+... which are analytic in the unit disc E={z:|z|＜1}. By using the method of differential subordinations we give some sufficient conditions for a function f(z)∈Ap(n) to be a certain subclass Rp(n,k) of p-valently close-to-convexity functions.     

Jacobson猜想成立的某些充分条件

Jacobson在文献[1]给出了一个猜想:若(L,[p])为限制李代数,且x^[p]n(x)=x,?x∈L,n(x)>0,则L是交换李代数.至今为止,人们还不知此猜想是否正确.本文分别证明这个猜想在p映射为p半线性映射或者域F为代数闭域条件下的正确性.     

Arrow-Mangasarian Sufficient Conditions for Controlled Semimartingales

Abstract

This article shows a version of Arrow's generalization of Manga-sarian's sufficient conditions valid for controlled stochastic differential equations driven by semimartingales. The infinite horizon case is covered. An example is given.     

隐稳定的充分条件

本文分析隐稳定矩阵的充分条件,得到几个关于低阶隐稳定矩阵扩充高阶后仍保持隐稳定的结果．     

非光滑最优化问题的充分条件

§l引言 考虑如下最优化问题: fNP、) /n““,(。) 、 Iz E R一{z E E‘/口(z)≤0,^(z)一0},其中,:驴一E,g一(9∥“,‰)’:E。一13",h一(^∥一,^,)”:驴一E’并且f,g。(1≤。≤,,,‘),hjL I≤j≤p)均是E。上的局部Lipsehitz函数. 最近,唐焕文等在[1]中提出了广义伪凸函数并在[2]中利用这类函数讨论了非光滑最优化问题解的充分条件.在这篇文章里,我们提出几类,“义凸性函数,在这些凸性条件下我们证明了非光滑最优化问题(NP)的解的允分条件,它包括Kuhn—Tucker允分条件和FritzJohn允分条件.§2概念 设D是驴的一个开子集,一个实值函数…     

与相对论Boltzmann方程中的输运算子有关的紧性

该文给出了一个与相对论Boltzmann方程中的输运算子有关的紧性的结果，它是一个类似于DiPerna和Lions在非相对论情况下给出的紧性的结果的推广，在研究相对论Boltzmann方程中起着很重要的作用．