Existence and regularity of solutions for some partial functional integrodifferential equations in Banach spaces

In this work, we study the existence and regularity of solutions for some partial functional integrodifferential equations in Banach spaces. We suppose that the undelayed part admits a resolvent operator in the sense given by Grimmer in [R. Grimmer, Resolvent operators for integral equations in a Banach space, Transaction of American Mathematical Society 273 (1982) 333–349]. The delayed part is assumed to be locally Lipschitz. Firstly, we show the existence of the mild solutions. Secondly, we give sufficient conditions ensuring the existence of the strict solutions.     

软件再生系统解的渐近稳定性分析

用补充变量的方法建立了各状态之间转移概率服从一般分布的软件再生系统的数学模型 .并用泛函分析中的 C0 半群理论对系统算子的谱点分布情况作了研究 ,证明了系统算子的谱点均位于复平面左半平面且在虚轴上除 0点外均为系统算子的正则点 ,作为线性算子半群稳定性的一个直接结果 ,得出了软件再生系统解的渐近稳定性     

一维连续时间Markov分枝过程的密度演化方程

本文通过建立密度演化方程 ,将一维连续时间Markov分枝过程问题转化为确定性的方法来研究 ,用C0 半群理论证明了密度解的存在性和唯一性 ,并介绍了求密度解及其母函数表达式的方法 ,得到了一些有益的结果     

Two-Parametric Compound Binomial Approximations

We consider two-parametric compound binomial approximation of the generalized Poisson binomial distribution. We show that the accuracy of approximation essentially depends on the symmetry or shifting of distributions and construct asymptotic expansions. For the proofs, we combine the properties of norms with the results for convolutions of symmetric and shifted distributions. In the lattice case, we use the characteristic function method. In the case of almost binomial approximation, we apply Steins method.__________Published in Lietuvos Matematikos Rinkinys, Vol. 44, No. 4, pp. 443–466, October–December, 2004.     

On the Existence of Solutions of Quasivariational Inclusion Problems

Quasivariational inclusion problems are formulated and sufficient conditions on the existence of solutions are shown. As special cases, we obtain several results on the existence of solutions of general vector ideal, proper, Pareto, weak quasioptimization problems, quasivariational inequalities, and vector quasiequilibrium problems. Further, we prove theorems on the existence for solutions of systems of these inclusions. As a corollary, we obtain an ideal minimax theorem concerning vector functions.     

⊕-Cofinitely Supplemented Modules

Let R be a ring and M a right R-module. M is called -cofinitely supplemented if every submodule N of M with M/N finitely generated has a supplement that is a direct summand of M. In this paper various properties of the -cofinitely supplemented modules are given. It is shown that (1) Arbitrary direct sum of -cofinitely supplemented modules is -cofinitely supplemented. (2) A ring R is semiperfect if and only if every free R-module is -cofinitely supplemented. In addition, if M has the summand sum property, then M is -cofinitely supplemented iff every maximal submodule has a supplement that is a direct summand of M.     

Almost flat locally finite coverings of the sphere

For any subset A of the unit sphere of a Banach space X and for [0,2) the notion of -flatness is introduced as a measure of non-flatness of A. For any positive , construction of locally finite tilings of the unit sphere by -flat sets is carried out under suitable -renormings of X in a quite general context; moreover, a characterization of spaces having separable dual is provided in terms of the existence of such tilings. Finally, relationships between the possibility of getting such tilings of the unit sphere in the given norm and smoothness properties of the norm are discussed.     

The Brownian loop soup

We define a natural conformally invariant measure on unrooted Brownian loops in the plane and study some of its properties. We relate this measure to a measure on loops rooted at a boundary point of a domain and show how this relation gives a way to chronologically add Brownian loops to simple curves in the plane.Cornell University; Research supported in part by the National Science FoundationUniversité Paris-Sud and IUFMathematics Subject Classification (2000):60J65, 81T40     

On Fraenkel’s <Emphasis Type="Italic">N</Emphasis>-Heap Wythoff’s Conjectures

The N-heap Wythoffs game is a two-player impartial game with N piles of tokens of sizes Players take turns removing any number of tokens from a single pile, or removing (a₁,..., a_N) from all piles - a_i tokens from the i-th pile, providing that where is the nim addition. The first player that cannot make a move loses. Denote all the P-positions (i.e., losing positions) by Two conjectures were proposed on the game by Fraenkel [7]. When are fixed, i) there exists an integer N₁ such that when . ii) there exist integers N₂ and _2 such that when , the golden section.In this paper, we provide a sufficient condition for the conjectures to hold, and subsequently prove them for the three-heap Wythoffs game with the first piles having up to 10 tokens.AMS Subject Classification: 91A46, 68R05.     

On the quantifier complexity of Δ<Subscript> n+1</Subscript> (T)– induction

In this paper we continue the study of the theories I _n+1 (T), initiated in [7]. We focus on the quantifier complexity of these fragments and theirs (non)finite axiomatization. A characterization is obtained for the class of theories such that I _n+1 (T) is _n+2 –axiomatizable. In particular, I _n+1 (I _n+1 ) gives an axiomatization of Th _n+2 (I _n+1 ) and is not finitely axiomatizable. This fact relates the fragment I _n+1 (I _n+1 ) to induction rule for _n+1 –formulas. Our arguments, involving a construction due to R. Kaye (see [9]), provide proofs of Parsons conservativeness theorem (see [16]) and (a weak version) of a result of L.D. Beklemishev on unnested applications of induction rules for _n+2 and _n+1 formulas (see [2]).Research partially supported by grant PB96–1345 (Spanish Goverment)Mathematics Subject Classification (2000): 03F30, 03H15