非定常概周期系统局部结构稳定的充要条件

本文给出：如果一致概周期函数ｆ（ｔ，ｘ）满足：ｉ）ｆ（ｔ，０）＝０；ｉｉ）Ｄｘｆ（ｔ，ｘ）在Ｒ×Ｄ上有界（Ｄ是Ｒｎ中含原点的一个区域）；ｉｉｉ）对ｔ一致成立，那么系统关于Ｂ１（所有满足ｉ），ｉｉ）的一致概周期函数全体所成之集按范数构成的赋范线性空间）在原点邻域局部结构稳定的充要条件是它的零解变分系统在Ｒ上具有指数型二分性．进而得到系统关于Ｂ１在原点邻域局部结构稳定是可继承的．并推出这类结构稳定的系统在Ｂ１的某子空间中是处处稠密的．     

强相关平稳Gauss过程高水平穿过和最大值的弱收敛

设｛ξ（ｔ），ｔ≥０｝是强相关不可微Ｇａｕｓ过程，即其相关函数Ｒ（ｔ）满足：Ｒ（ｔ）ｌｏｇｔ→γ＞０（ｔ→∞）和Ｒ（ｔ）＝１－Ｃ｜ｔ｜^α＋ｏ（｜ｔ｜^α）（ｔ→０），且０＜α≤２，Ｃ＞０．本文建立了｛ξ（ｔ），ｔ≥０｝对一个和多个高水平的ε-上穿点过程的极限定理，并给出了最大值的极限分布和局部ε-最大值的联合渐近分布．     

恰有t行含s圈正元的布尔方阵的幂敛指数

设Ｄｎ，ｓ（ｔ）是恰有ｔ行含ｓ圈正元的ｎ阶布尔方阵的集合，ｓｔｎ．本文给出了当ｓ＝１或ｓ为素数时Ｄｎ，ｓ（ｔ）中矩阵的幂敛指数的一个上界，证明了除ｔ＞ｎ－ｓ（ｎ－１）＋１／４－３／２，且ｓ与ｎ不互素外，这个上界可以达到，对Ｄｎ，ｓ（ｔ）中幂敛指数达到这个上界的矩阵作了部分刻划．     

一类连续半鞅型随机微分方程解的随机稳定性

本文利用Ｌｙａｐｕｎｏｖ函数方法，讨论了时齐Ｄｏｌｅａｎｓ－Ｄａｄｅｒ－Ｐｒｏｔｔｅｒ方程ｄＸ＿ｔ＝σ（Ｘ＿ｔ）ｄＭ＿ｔ＝ｂ（Ｘ＿ｔ）ｄＡ＿ｔ＋（（Ｍ＿ｔ）为连续局部平方可积鞅；（Ａ＿ｔ）为连续有限变差过程）平凡解的随机稳定性。本文建立了随机稳定性的判定定理并给出了相应的Ｌｙａｐｕｎｏｖ函数的一种具体形式。     

关于M／M~［r］／1系统的一个注记

徐光辉［１，第六章§１］讨论了成批服务系统Ｍ／Ｍ［ｒ］／１，并在ｌｉｍＰｊ（ｔ）＝Ｐｊ＞０假设下，求出马氏过程Ｎ（ｔ）的平稳分布｛Ｐｉ｝，李文琦等在［２，Ｐ１６８８］指出［１．Ｐ２１８—２１９］给出的关于ｌｉｍＰｊ（ｔ）＝Ｐｊ＞０的证明是不准确的，并利用Ｆｏｓｔｅｒ判别法给出Ｎ（ｔ）的遍历性的严格证明。本文指出Ｎ（ｔ）的遍历性可由Ｐｉｊ（△ｔ）的表达式及Ｔａｋａｃｓ［４，Ｐ９４定理２］推出。     

奇异半线性发展方程的局部Cauchy问题

本文在Ｂａｎａｃｈ空间Ｅ中讨论如下问题ｄｕｄｔ＋１ｔσＡｕ＝Ｊ（ｕ），０＜ｔＴ，ｌｉｍｔ→０＋ｕ（ｔ）＝０，其中ｕ：（０，Ｔ］Ｅ，Ａ是与ｔ无关的线性算子．（－Ａ）是Ｅ上Ｃ０半群｛Ｔ（ｔ）｝ｔ０的无穷小生成元，常数σ１，Ｊ是一个非线性映射ＥＪ→Ｅ．它满足局部Ｌｉｐｓｃｈｉｔｚ条件．我们证明了当其Ｌｉｐｓｃｈｉｔｚ常数ｌ（ｒ）满足一定条件时．问题（Ｓ）有局部解，且在某函类中解唯一．设Ｊ（ｕ）＝｜ｕ｜γ－１ｕ＋ｆ（ｘ）（γ＞１），Ｅ＝Ｌｐ，ＥＪ＝Ｌｐγ时得到了与Ｗｅｉｓｌｅｒ［２］在非奇异情形类似的结果．     

具有较一般分支特征的超布朗运动轨道性质

本文研究具有较一般分支特征的超布朗运动｛Ｘ（ｔ）｝ｔ０的轨道性质．首先给出了它的一个击中概率的表达式，其次找到了它的支集蔓延速度的估计式及证明了支撑过程的右连续性，从而验证了Ｄａｗｓｏｎ，Ｄ．Ａ．等人的猜想     

L~2空间中的Bernstein─Markov不等式及其最佳常数（Ⅱ）

继［１５］．本中考虑了带不同权函数空间中的Ｂｅｒｎｓｔｃｉｎ－Ｍａｒｋｏｖ不等式，给出了其最佳常数；最后还得到相应的反向Ｂｅｒｎｓｔｃｉｎ－Ｍａｒｋｏｖ不等式．     

一类多指标随机过程样本轨道的Hausdorff维数

设｛Ｘ（ｔ，ｗ）；ｔ∈［０，１］Ｎ｝是Ｒｄ值轨道连续的随机过程，在条件：存在常数０＜α＜１，Ｍ＞０，β≥ｄ使　下，我们得到了Ｘ关于紧集的象和图以及水平集的Ｈａｕｓｄｏｒｆｆ维数的最佳上界，同时在条件：存在常数ａ．α，ｄ＇＞０使　下，我们获得了Ｘ关于紧集的象和图的Ｈａｕｓｄｏｒｆｆ维数的最佳下界以及存在平方可积的局部时．     

Nest代数的某些范数闭理想

设Ｒ＿Ｎ是Ｎｅｓｔ代数ａｌｇＮ的Ｊａｃｏｂｓｏｎ根，用表示由；生成的ａｌｇＮ的范数闭双边理想。Ｊ．Ｒ．Ｒｉｎｇｒｏｓｅ［１，定理５．４］给出了Ｒ＿Ｎ的Ｋ１ｎｇｒｏｓｅ特征，本文将给出具有广义Ｒｉｎｇｒｏｓｅ特征的充分必要条件，这个结果是［１］中的Ｒｉｎｇｒｏｓｅ准则在上的一般化     

On the existence of local times: A geometric study

We present a general study relating the geometry of the graph of a real function to the existence of local times for the function. The general results obtained are applied to Gaussian processes, and we show that with probability 1 the sample functions of a nondifferentiable stationary Gaussian process with local times will be Jarnik functions. This extends earlier works of Lifschitz and Pitt, which gave examples of Gaussian processes without local times. An example is given of a Jarnik function without local times, thus answering negatively a question raised by Geman and Horowitz.     

广义de Sitter空间中的类时超曲面

利用奇点理论研究广义de Sitter空间中的类时超曲面.介绍类时超曲面的局部微分几何,定义了广义de Sitter高斯像及广义de Sitter高度函数,研究广义deSitter高度函数族的性质及广义de Sitter高斯像的几何意义,介绍了一种证明高度函数为Morse族的新方法.最后研究了类时超曲面的通有性质.     

Ramification of valuations

In this paper we develop a very explicit theory of ramification of general valuations in algebraic function fields. In characteristic zero and arbitrary dimension, we obtain the strongest possible generalization of the classical ramification theory of local Dedekind domains. We further develop a ramification theory of algebraic functions fields of dimension two in positive characteristic. We prove that local monomialization and simultaneous resolution hold under very mild assumptions, and give pathological examples.     

On the Continuity of Characteristic Functionals and Sparse Stochastic Modeling

The characteristic functional is the infinite-dimensional generalization of the Fourier transform for measures on function spaces. It characterizes the statistical law of the associated stochastic process in the same way as a characteristic function specifies the probability distribution of its corresponding random variable. Our goal in this work is to lay the foundations of the innovation model, a (possibly) non-Gaussian probabilistic model for sparse signals. This is achieved by using the characteristic functional to specify sparse stochastic processes that are defined as linear transformations of general continuous-domain white Lévy noises (also called innovation processes). We prove the existence of a broad class of sparse processes by using the Minlos–Bochner theorem. This requires a careful study of the regularity properties, especially the \(L^p\) -boundedness, of the characteristic functional of the innovations. We are especially interested in the functionals that are only defined for \(p<1\) since they appear to be associated with the sparser kind of processes. Finally, we apply our main theorem of existence to two specific subclasses of processes with specific invariance properties.     

Asymptotic properties of general autoregressive models and strong consistency of least-squares estimates of their parameters

This paper establishes several almost sure asymptotic properties of general autoregressive processes. By making use of these properties, we obtain a proof of the strong consistency of the least-squares estimates of the parameters of the process without any assumption on the roots of the characteristic polynomial.     

Constrainedn-person games

The usual properties of a characteristic function game were derived byvon Neumann andMorgenstern from the properties of a game in normal form. In this paper we give a linear programming principle for the calculation of the characteristic function. The principle is a direct application ofCharnes' linear programming method for the calculation of the optimal strategies and the value of a two-person zero-sum game. The linear programming principle gives another method for proving the standard properties of a characteristic function when it is derived from a game in normal form. Using an idea originated byCharnes for two person games, we develop the concept of a constrainedn-person game as a simple, practical extension of ann-person game. However the characteristic function for a constrainedn-person game may not satisfy properties, such as superadditivity, usually associated with a characteristic function.     

A method for approximating pairwise comparison matrices by consistent matrices

In several methods of multiattribute decision making, pairwise comparison matrices are applied to derive implicit weights for a given set of decision alternatives. A class of the approaches is based on the approximation of the pairwise comparison matrix by a consistent matrix. In the paper this approximation problem is considered in the least-squares sense. In general, the problem is nonconvex and difficult to solve, since it may have several local optima. In the paper the classic logarithmic transformation is applied and the problem is transcribed into the form of a separable programming problem based on a univariate function with special properties. We give sufficient conditions of the convexity of the objective function over the feasible set. If such a sufficient condition holds, the global optimum of the original problem can be obtained by local search, as well. For the general case, we propose a branch-and-bound method. Computational experiments are also presented.     

Stability of the Minimizers of Least Squares with a Non-Convex Regularization. Part I: Local Behavior

Many estimation problems amount to minimizing a piecewise C^m objective function, with m ≥ 2, composed of a quadratic data-fidelity term and a general regularization term. It is widely accepted that the minimizers obtained using non-convex and possibly non-smooth regularization terms are frequently good estimates. However, few facts are known on the ways to control properties of these minimizers. This work is dedicated to the stability of the minimizers of such objective functions with respect to variations of the data. It consists of two parts: first we consider all local minimizers, whereas in a second part we derive results on global minimizers. In this part we focus on data points such that every local minimizer is isolated and results from a C^m-1 local minimizer function, defined on some neighborhood. We demonstrate that all data points for which this fails form a set whose closure is negligible.