鞅差几何级数的重对数律

设｛Ｘｋ，Ｆｋ，ｋ≥０｝是（Ω，Ｆ，Ｐ）上的鞅差序列，在本文中我们讨论了以｛Ｘｋ｝为系数的幂级数Ｓ（β＝Σ∞ｋ＝０βｋＸｋ，当β↑１时的渐近行为，本文证明了：如果│Ｘｋ│≤ｃ，Ｅ（Ｘ＾２ｋ│Ｆｋ－１）＝１，则有下面的重对数律成立ｌｉｍβ↑１√１－β＾２／√２ｌｏｇｌｏｇ（１－β＾２）－１Ｓ（β）＝１ａ．ｓ。     

亚纯函数的幅角分布及其增长性

本文考虑了亚纯函数的幅角分布及其增长性的关系，得到了如下定理：设ｆ（ｚ）为亚纯函数，下级μ（μ〈＋∞，ａｒｇｚ＝θｋ（ｋ＝１，２，…，ｑ；０≤θ１〈θ２〈…〈θｑ〈２π，θｑ＋１＝θ１＋２π）为ｑ（１≤ｑ〈＋∞）条半直线使对Ａ↓ε〉０有：ｌｉｍｒ→∞↑－ｌｏｇ＋ｎ↑－（∪ｋ＝１↑ｑΩ↑－（θｋ＋ε，θｋ＋１－ε；ｒ），ｆ＝ｘ）／ｌｏｇｒ≤ρ〈＋∞ ｘ＝０，∞则当存在一非负整数ｌ使ｆ＾（ｌ）（ｚ）（     

连通的欧拉生成子图

本文证明了：若G是一个p顶点的、2－边－连通简单图，其边数，q≥(p-4↑ 2) 7，则除K2，5外，G有连通的欧拉生成子图。当q=(p-r↑ 2）＋6和κ′（G）＝2时，本文给出了全部6个极图。     

临界增长的半线性椭圆方程的一个奇异扰动问题

本文考虑下面的奇异扰动问题－Δｕ＝ｕ２－１＋εｕ，ｘ∈Ω；ｕ＞０，ｘ∈Ω；ｕ＝０，ｘ∈Ω，其中Ω是ＲＮ的一个有界区域，Ｎ５，２＝２ＮＮ－２本文证明了当ｘ０是Ｈ（ｘ，ｘ）的一个严格局部极小点时，其中Ｈ（ｘ，ｙ）是Ｇｒｅｅｎ函数的正则部分，则所考虑的问题在ε＞０充分小时，存在解ｕε满足｜Ｄｕε｜２ＳＮ／２δｘ０，这里，Ｓ是Ｓｏｂｏｌｅｖ嵌入Ｈ１（ＲＮ）Ｌ２（ＲＮ）的最佳常数     

一类离散型奇异积分算子

设｛αｋ｝∞ｋ＝－∞为正数缺项序列，满足ｉｎｆｋαｋ＋１／ｄｋ＝α＞１，Ω（ｙ′）为Ｂｅｓｏｖ空间Ｂ０，１１（Ｓｎ－１）上的函数，其中Ｓｎ－１为Ｒｎ（ｎ２）上的单位球面．本文证明：若∫Ｓｎ－１Ω（ｙ′）ｄσ（ｙ′）＝０，则离散型奇异积分ＴΩ（ｆ）（ｘ）＝∑∞ｋ＝－∞∫Ｓｎ－１ｆ（ｘ－αｋｙ′）Ω（ｙ′）ｄσ（ｙ′）和相关的极大算子ＴΩ（ｆ）（ｘ）＝ｓｕｐＮ∑∞ｋ＝Ｎ∫Ｓｎ－１ｆ（ｘ－αｋｙ′）Ω（ｙ′）ｄσ（ｙ′）均在Ｌ２（Ｒｎ）上有界．上述结果推广了Ｄｕｏａｎｄｉｋｏｅｔｘｅａ和ＲｕｂｉｏｄｅＦｒａｎｃｉａ［１］在Ｌ２情形下的一个结果     

体上的矩阵方程AX—XB=C与AX±XB=±C

设Ｆ和Ω分别是一个任意的体和一个具有对合反自同构的有限维中心代数且ｃｈａｒΩ≠２．本研究体上的下列矩阵方程：ＡＸ－ＸＢ＝Ｃ，（１）ＡＸ－ＸＢ＝Ｃ，（２）ＡＸ＋ＸＢ＝－Ｃ（３）分别给出了在Ω上（１）有一般解，（２）自共轭解及（３）有斜自共轭解的充要条件，并将Ｗ．Ｅ．Ｒｏｔｈ的相似定理推广到了任意的体Ｆ上。     

关于МОФОНЪКО不等式的精确性

证明了如下定理：设Φ（ｚ）＝Σ↑ｎ↓ｕ＝１∏↑ｔ↓ｉ＝１ｆｉ＾ａ＾ｕｉ０…（ｆｉ＾（ｋｉ））＾ａｉｋｉ＾ｕ／Σ↑ｍ↓ｖ＝１∏↑ｔ↓ｉ＝１ｆｉ＾ｂ＾ｖｉ０…（ｆｉ＾（ｋｉ））＾ｂｉｋｉ＾ｖ其中ｆｉ（ｚ），（１≤ｉ≤ｔ）是亚纯函数，ａｉｊ＾ｕ，ｂｉｊ＾ｖ为非负整数，则有Ｔ（ｒ，Φ）≤Σ↑ｔ↓ｉ＝１｛［Ｓｉ＋ｏ（１）］ｍ（ｒ，ｆｉ）＋［△ｉ＝ｕｉ＋ｏ（１）］Ｎ（ｒ，ｆｉ）＋（△ｉ－Ｓｉ）Ｎ↑－（ｒ，ｆｉ     

市场经济下随机经济模型

本文探讨了市场经济下，经济发展的随机规律性；在假设市需求｛Ｄ↑－＾（ｎ）（ω）｝ｎ≥１为独立随机向量族的条件下，证明了产出向量Ｙ（ｎ，ω）是一个马氏过程。     

有界对称域上混合范数空间的乘子变换

本文考虑了Ｃ＾ｎ中有界对称域Ω上的混合范数空间Ｈｐ，ｑ，ａ（Ω）它包含许多重要的函数空间，如Ｈａｒｄｙ空间、Ｂｅｒｇｍａｎ空间、缓慢增长的函数空间以及Ｂｐｑ，研究了Ｈｐ，ｑ，ａ（Ω）中函数的现人类 乘子变 得到了Ｈｐ，ｑ，ａ（Ω）中的Ｈａｒｄｙ－Ｌｉｔｔｌｅｗｏｏｄ定理。这些结果均推了以前一系列结论。     

随机微分方程终值问题的弱解(英)

设｛Wt．Ft．t∈［0．T］｝为概率空间（Ω，P）上的标准α维Brown运动，为由它生成的自然σ－代数流．本文讨论了如下随机微分方程终值问题弱解的存在性：其中ξ∈L2（Ω，P；Rn），g：［0，T」×Rn×Rnd→Rn为有界可测函数．此外，还讨论了它在金融市场期权定价问题中的应用．     

The relationship between integer and real solutions of constrained convex programming

We prove the following theorem which gives a bound on the proximity of the real and the integer solutions to certain constrained optimization programs.     

An O(n 2) Active Set Algorithm for Solving Two Related Box Constrained Parametric Quadratic Programs

Recently, O(n ²) active set methods have been presented for minimizing the parametric quadratic functions (1/2)x Dx–a x+| x–c| and (1/2)x Dx–a x+(/2)( x–c)², respectively, subject to lxb, for all nonnegative values of the parameter . Here, D is a positive diagonal n×n matrix, and a are arbitrary n-vectors, c is an arbitrary scalar; l and b are arbitrary n-vectors such that lb. In this paper, we show that each one of these algorithms may be used to simultaneously solve both parametric programs withno additional computational cost.     

Binary fuzzy goal programming

Goal programming is an important technique for solving many decision/management problems. Fuzzy goal programming involves applying the fuzzy set theory to goal programming, thus allowing the model to take into account the vague aspirations of a decision-maker. Using preference-based membership functions, we can define the fuzzy problem through natural language terms or vague phenomena. In fact, decision-making involves the achievement of fuzzy goals, some of them are met and some not because these goals are subject to the function of environment/resource constraints. Thus, binary fuzzy goal programming is employed where the problem cannot be solved by conventional goal programming approaches. This paper proposes a new idea of how to program the binary fuzzy goal programming model. The binary fuzzy goal programming model can then be solved using the integer programming method. Finally, an illustrative example is included to demonstrate the correctness and usefulness of the proposed model.     

On ℓp programming

Our paper treats the primal and dual program of ?_p programming. ?_p programming is a generalization of ?_p approximation problems. There is a strict connection between ?_p programming and geometrical programming, because in both of them geometrical inequality plays a fundamental role. The structure of our paper follows that of Klafszkys [1].In the first Sections duality theorems are proved, which play an important role in mathematical programming. Most of these results can be found in Petersons and Eckers [3,4,5], but our proofs are much more simple and we show these fundamental properties more detailed.Afterwards the relation between the Lagrange function and the optimal solution pair is investigated. Regularity is investigated as well and we show the marginal value of ?_p programming. In the end linear programming ?_p constrained ?_p approximation problems, the quadratically constrained quadratic programming and compromise programming are shown as special cases of ?_p programming.     

Solving multi-level multi-objective linear programming problems through fuzzy goal programming approach

In this paper, two new algorithms are presented to solve multi-level multi-objective linear programming (ML-MOLP) problems through the fuzzy goal programming (FGP) approach. The membership functions for the defined fuzzy goals of all objective functions at all levels are developed in the model formulation of the problem; so also are the membership functions for vectors of fuzzy goals of the decision variables, controlled by decision makers at the top levels. Then the fuzzy goal programming approach is used to achieve the highest degree of each of the membership goals by minimizing their deviational variables and thereby obtain the most satisfactory solution for all decision makers.     

Composite geometric programming

Geometric programming is based on functions called posynomials, the terms of which are log-linear. This class of programs is extended from the composition of an exponential and a linear function to an exponential and a convex function. The resulting duality theory for composite geometric programs retains many of the qualities of geometric programming duality, while at the same time encompassing new areas of application. As an application, composite geometric programming is applied to exponential geometric programming. A pure dual is developed for the first time and used to solve a problem from the literature.This research was supported by the Air Force Office of Scientific Research, Grant No. AFOSR-83-0234.     

A method for finding well-dispersed subsets of non-dominated vectors for multiple objective mixed integer linear programs

We present an algorithm for generating a subset of non-dominated vectors of multiple objective mixed integer linear programming. Starting from an initial non-dominated vector, the procedure finds at each iteration a new one that maximizes the infinity-norm distance from the set dominated by the previously found solutions. When all variables are integer, it can generate the whole set of non-dominated vectors.     

On dual solutions of the linear assignment problem

For the linear assignment problem we describe how to obtain different dual solutions. It turns out that a shortest path algorithm can be used to compute such solutions with several interesting properties that enable to do better post-optimality analysis.Two examples illustrate how different dual solutions can be used in the context of the traveling salesman problem.     

An O(n) algorithm for quadratic knapsack problems

An algorithm is presented which solves bounded quadratic optimization problems with n variables and one linear constraint in at most O(n) steps. The algorithm is based on a parametric approach combined with well-known ideas for constructing efficient algorithms. It improves an O(n log n) algorithm which has been developed for a more restricted case of the problem.