New light on Hensel''s lemma

The historical development of Hensel's lemma is briefly discussed (Section 1). Using Newton polygons, a simple proof of a general Hensel's lemma for separable polynomials over Henselian fields is given (Section 3). For polynomials over algebraically closed, valued fields, best possible results on continuity of roots (Section 4) and continuity of factors (Section 6) are demonstrated. Using this and a general Krasner's lemma (Section 7), we give a short proof of a general Hensel's lemma and show that it is, in a certain sense, best possible (Section 8). All valuations here are non-Archimedean and of arbitrary rank. The article is practically self-contained.     

12-Ring Network Coordination Polymer——{[Cu(C_4N_2H_(10))_4]_2·H_4V_4O_(14)}_n Formed by Linking cyclo-[H_4V_4O_(14)]~(4-) with Cu(C_4N_2H_(10))~(2+)_4 Cation Clusters

IntroductionThe interest in polyoxometalates that are widelyused in medical chemistry, catalyst reactions, and ma-terial sciences stems from their complicated aggregatesformed by means of corner-, edge- and face-sha-ring[1—4]. The exploitation of new str…     

“Optimization of aircraft maintenance/support infrastructure using genetic algorithms—level of repair analysis”

Level of repair analysis (LORA) is an approach used during the design stage of complex equipment for analysis of the cost effectiveness of competing maintenance strategies. LORA is carried as a part of the life cycle cost and cost of ownership analysis and plays a significant role in minimizing the life cycle cost and cost of ownership of the capital equipment. Since many purchasing decisions of complex equipment are based on cost of ownership, it has become essential to carry out LORA to compete in the market. In this paper, we develop a mathematical model for LORA and propose a solution methodology based on genetic algorithms. The concept is illustrated using a hypothetical aircraft engine.     

Velocity Quantization Approach of the One-Dimensional Dissipative Harmonic Oscillator

Given a constant of motion for the one-dimensional harmonic oscillator with linear dissipation in the velocity, the problem to get the Hamiltonian for this system is pointed out, and the quantization up to second order in the perturbation approach is used to determine the modification on the eigenvalues when dissipation is taken into consideration. This quantization is realized using the constant of motion instead of the Hamiltonian. PACS: 03.20.+i, 03.30.+p, 03.65.−w,03.65.Ca     

激光穿透焊的三维数值模拟

本文对激光穿透焊进行了三维数值模拟，除考虑焊接速度影响外，还研究了Ｍａｒａｎｇｏｎｉ对流对熔池流动与传热的影响。将三维数值模拟结果与相应的二维模拟结果进行了比较，结果表明，Ｍａｒａｎｇｏｎｉ对流对熔池的形成有很大的影响，因此不可忽略。本文还给出了估计激光穿透焊中蒸气孔尺寸与焊接热效率的方法。     

Diophantine Undecidability of Function Fields of Characteristic Greater than 2, Finitely Generated over Fields Algebraic over a Finite Field

Let F be a function field of characteristic p > 2, finitely generated over a field C algebraic over a finite field C _p and such that it has an extension of degree p. Then Hilbert's Tenth Problem is not decidable over F.     

时滞差分系统基于两种度量的稳定性分析

本文建立了一些关于时滞差分系统（h0,h）稳定性（一致稳定性，渐近稳定性，一致渐近稳定性）的判定准则。在所得到的定理中，去除了△V为常负的限制，特别地，△V甚至可以恒为正，从而大大改进了已有结果，并更加便于应用。     

标的股价服从混合过程的期权定价公式及有限元算法

本文将马尔科夫跳跃过程叠加于 Ito过程 ,形成混合过程 ,并用该过程来刻画股价走势情况。而后在标的股价服从混合过程的基础上 ,推导出了欧式看涨期权的定价公式 ,并对美式看跌期权定价给出了有限元算法。     

Cooperative games of choosing partners and forming coalitions in the marketplace

Two games of interacting between a coalition of players in a marketplace and the residual players acting there are discussed, along with two approaches to fair imputation of gains of coalitions in cooperative games that are based on the concepts of the Shapley vector and core of a cooperative game. In the first game, which is an antagonistic one, the residual players try to minimize the coalition's gain, whereas in the second game, which is a noncooperative one, they try to maximize their own gain as a coalition. A meaningful interpretation of possible relations between gains and Nash equilibrium strategies in both games considered as those played between a coalition of firms and its surrounding in a particular marketplace in the framework of two classes of n-person games is presented. A particular class of games of choosing partners and forming coalitions in which models of firms operating in the marketplace are those with linear constraints and utility functions being sums of linear and bilinear functions of two corresponding vector arguments is analyzed, and a set of maximin problems on polyhedral sets of connected strategies which the problem of choosing a coalition for a particular firm is reducible to are formulated based on the firm models of the considered kind.     

外加电场下激光诱导Al等离子体特性的实验研究

由Q-Nd:YAG脉冲激光(波长1.06μm,脉宽10 ns)烧蚀Al靶产生等离子体.观测了在低气压和直流电场条件下的Al等离子体发射光谱.研究了激光功率密度和直流电场对各谱线强度的影响,分析了谱线半高全宽与外加电压,等离子体电子温度与激光能量的变化规律.结果表明,直流电场对铝原子谱线强度有显著的增强,铝原子谱线的半高全宽与直流电场的外加电压基本上呈线性关系.