用元素法把二重积分直接化为单积分

根据积分区域和被积函数情况,用曲线（或直线,射线）分割积分区域,构建区域元素一元微分,把二重积分直接化为单积分．此种方法可简化二重积分的计算,有必要编写入微积分教材中．     

关于简单MCD图

设G是阶为n的简单图，若G中没有两个等长圈且具有最大可能的边数，则称G为简单MCD图。本文通过引进路分解概念给出了两个关于图中圈数的结果并应用它们证明了下述定理：若G是简单MCD图，则G不是2连通可平面图且对所有整数n，除七个例外，G不是阶为n的含有同胚于K4的2连通图。     

Optimal Control of Some Simple Deterministic Epidemic Models

Using control variables such as the level of medicare programme effort and the level of inoculation programme effort, three simple mathematical models of epidemics are transformed into optimal control problems. These are multi-state problems with the state variables as numbers of infectives and susceptibles and with the objective function being minimization of the total present value of the social or economic costs of infectives and medical controls. The problems are analysed with the framework of the maximum principle to obtain or, at least, partially characterize the optimal policies over time.     

On Integral Fusion Categories with Low-Dimensional Simple Objects

Let k be an algebraically closed field of characteristic zero. In this article, we consider an integral fusion category over k in which the Frobenius–Perron dimensions of its simple objects are at most 3. We prove that such fusion category is of Frobenius type. In addition, we also prove that such fusion category is not simple.     

On Simple MIX game

We consider zero-sum game which is called Simple MIX game. Each of two players (I and II) draws a number (x andy respectively) according to a uniform distribution on [0, 1]. After observing his number each player can then choose to offer or not offer to exchange his number for the other player's number. Conditions for an exchange are the following: 1) both players must offer for a trade to occur with certainty; 2) if only one player offers, a trade occurs with probabilityp. A player's payoff is equal to 1, 0 or — 1 if the value of the number which he finally gets is greater, equal or less than the number of his opponent. In the present paper we shall investigate Simple MIX game in which both of the players can obtain additional information about the opponent's number. Besides, we consider two-stage variant of this game.     

On Tensor Products of Simple Modules for Simple Groups

In an attempt to get some information on the multiplicative structure of the Green ring we study algebraic modules for simple groups, and associated groups such as quasisimple and almost-simple groups. We prove that, for almost all groups of Lie type in defining characteristic, the natural module is non-algebraic. For alternating and symmetric groups, we prove that the simple modules in p-blocks with defect groups of order p ² are algebraic, for p?≤?5. Finally, we analyze nine sporadic groups, finding that all simple modules are algebraic for various primes and sporadic groups.     

On Some Groups with Finite Involution Saturated with Finite Simple Groups

In the paper, on the basis of the notion of saturation introduced in [1], we give a characterization of locally finite simple groups with an Abelian Sylow 2-subgroup in the classes of mixed and periodic groups. A part of the main results was announced in [2]. Theorem 2 of the paper generalizes results of [3, 4].     

On Real Simple Left-symmetric Algebras

In this article, we commence to study the real (simple) left-symmetric algebras. From the known classification of certain complex (semi)simple left-symmetric algebras, we classify their corresponding real forms. We not only obtain the classification of real simple left-symmetric algebras in low dimensions, but also find certain examples of real simple left-symmetric algebras in higher dimensions. In particular, there exists a complex simple left-symmetric algebra without any real form. We also give a geometric construction for a class of real simple left-symmetric algebras. At last, we apply the classification results to study some structures related to geometry.     

On Armendariz Rings and Matrix Rings with Simple 0-Multiplication

We introduce and study subrings with simple 0-multiplication of matrix rings in the context of Armendariz rings. In this way we extend several known results in the area.     

On Finite Linear Spaces with Almost Simple Flag-Transitive Automorphism Groups

This paper contains a classification of finite linear spaces with an automorphism group which is an almost simple group of Lie type acting flag-transitively. This completes the proof of the classification of finite flag-transitive linear spaces announced in [BDDKLS].     

On Optimal Lattice Decompositions

A lattice decomposition lemma by H. Rosenthal is given an optimal refinement, both in the real and in the complex valued setting.     

On Infinitesimally Optimal Paths

The concept of infinitesimal optimality is specified for discrete dynamic extremal problems.     

On Optimal Random Nets

The possibility to approximate bounded linear mappings between Banach spaces depends on the degree of compactness. One way to measure this degree of compactness is the scale of entropy numbers, cf. (B. Carl and I. Stephani: 1990. "Entropy, Compactness and the Approximation of Operators," Cambridge Univ. Press, Cambridge). In the usual (worst-case) setting of numerical analysis this scale has been studied for a long time. Recent research is concerned with the study of the so-called average-case and randomized (Monte Carlo) settings. We propose the respective counterparts of the entropy numbers in these settings and obtain their behavior for Sobolev embeddings. It turns out that, at least in this situation, randomly chosen nets may not improve the approximability of operators in the Monte Carlo setting. However, we can use the results to improve previous estimates for average Kolmogorov numbers, as obtained in (P. Mathé, 1991, J. Complexity7, 261-281).     

On Optimal Codes Over the Field with Five Elements

In this paper, we prove the nonexistence of Griesmer codes over the field of five elements for k = 4 and d = 33, 83, 163, 164.     

Optimal Network Design for Wireless Local Area Network

Network design for wireless local area networks is an important issue in the deployment of these networks. Research activities are presently being undertaken in two major areas: determining the location of base stations (BSs) and assigning the frequency channels for these stations. Our BS location problem selects a set of BSs to provide the best demand area coverage and maximize the signal level and physical area attendance priority. Adequate channel assignment reduces signal interference and improves network throughput. This paper reports a real world experiment where we applied the concepts of two classical outdoor problems namely the optimal BS location problem and the fixed channel assignment problem to build a WLAN into an indoor environment. We propose a mathematical model that we solve by a commercial software and report the computational results.     

A Simple Nearly Optimal Restart Scheme For Speeding Up First-Order Methods

Foundations of Computational Mathematics - We present a simple scheme for restarting first-order methods for convex optimization problems. Restarts are made based only on achieving specified...     

On a Series with Simple Zeros of ζ(s)

Mathematical Notes -     

带有无限到达源的Re-entrant Line的稳定性

用Foster判别准则,Weiss[13]给出了带有无限到达源的两站三步re-entrant line的稳定性的充分条件．本文用两种不同的方法得到了其稳定性的充分必要条件,即: 二维随机游动方法和Foster判别准则．同时,我们又用流体模型方法得到了系统稳定的充分条件,大大地简化了Weiss[13]的证明．     

On Simple Exponential Sets of Polynomials

In this paper, it is shown that certain classes of regular functions of several complex variables be represented by exponential sets of polynomials in hyperelliptical regions. Moreover, an upper bound for the order of exponential set is given.