Elliptic fibers over non-perfect residue fields

Kodaira and Néron classified and described the geometry of the special fibers of the Néron model of an elliptic curve defined over a discrete valuation ring with a perfect residue field. Tate described an algorithm to determine the special fiber type by manipulating the Weierstrass equation. In the case of non-perfect residue fields, we discover new fiber types which are not on the Kodaira-Néron list. We describe these new types and extend Tate's algorithm to deal with all discrete valuation rings. Specifically, we show how to translate a Weierstrass equation into a form where the reduction type may be easily determined. Having determined the special fiber type, we construct the regular model of the curve with explicit blow-up calculations. We also provide tables that serve as a simple reference for the algorithm and which succinctly summarize the results.     

Subgame Consistent Cooperative Solutions in Stochastic Differential Games

Subgame consistency is a fundamental element in the solution of cooperative stochastic differential games. In particular, it ensures that: (i) the extension of the solution policy to a later starting time and to any possible state brought about by the prior optimal behavior of the players would remain optimal; (ii) all players do not have incentive to deviate from the initial plan. In this paper, we develop a mechanism for the derivation of the payoff distribution procedures of subgame consistent solutions in stochastic differential games with transferable payoffs. The payoff distribution procedure of the subgame consistent solution can be identified analytically under different optimality principles. Demonstration of the use of the technique for specific optimality principles is shown with an explicitly solvable game. For the first time, analytically tractable solutions of cooperative stochastic differential games with subgame consistency are derived.     

条形码技术的国际发展趋势及我国的对策

介绍了供应链管理中的一个得力工具——条形码技术，对这一技术进行了剖析，分析了条形码技术的国际发展趋势以及在我国的应用现状，最后针对我国在实现条形码技术时所遇到的各种问题提出了一些建议。     

On the United Theory of the Family of Euler-Halley Type Methods with Cubical Convergence in Banach Spaces

The convergence problem of the family of Euler-Halley methods is considered under the Lipschitz condition with the L-average, and a united convergence theory with its applications is presented.     

更新时间概率模型及其无偏估计定理的论证

本文提出应用小参数法 ,探讨 Markov链中相邻两次更新时刻内稀疏事件的概率估计问题 .建立了三种最重要的具有更新时间的概率模型 .通过小参数的引入和对概率式的幂展开 ,进而推证出幂渐近展开系数的模型估算法 .论证了无偏估计的重要定理 ,给出了概率估计式和无偏估计精度 .亦将许多算法扩展到Markov链的任意状态空间     

Propagator matrices as matrices of power''s series. II. It''s relationship with HF''s stability problem and alternative solutions

Some non-singlet quasi-instabilities (QIs) cases that arise in the calculation of NMR-J parameters are analyzed within response theory. The relationship between ‘very close to zero’ eigenvalues of the principal propagator and the rate of convergency for specific coupling pathways is shown by a power series implemented to calculate the principal propagator matrix. A natural criterion for the analysis of the stability problem emerges from that series. This is more general and accurate compared with previous proposals. Its relationship with π-type molecular orbitals is given. We present an alternative scheme to minimize the effects of non-singlet QIs in such a way that the NMR-J parameters become close to the best theoretical calculations for H₂CX (X=CH₂, NH and O).     

HUA’S THEOREM WITH FIVE ALMOSTE QUAL PRIME VARIABLES

§1. IntroductionIn the additive theory of prime numbers, one studies the representation of positive in-tegers by powers of primes. For the quadratic case, Hua [1] proved that each large integercongruent to 5 modulo 24 can be written as the sum of ?ve squ…     

线性规划的符号跟踪算法

分析了只含一个约束条件的线性规划最优基变量的特征，将其运用到搜寻含m个约束条件的线性规划的最优基变量，从而提出了线性规划的符号跟踪算法，为线性规划求解提供了新途径。     

A purely algebraic characterization of the hyperreal numbers

The hyperreal numbers of nonstandard analysis are characterized in purely algebraic terms as homomorphic images of a suitable class of rings of functions.

     

关于折射率对散射光场分布影响的研究

根据Mie散射理论,采用理论计算和实验相结合的手法,研究了光散射现象以及散射介质的折射率对散射光场分布的影响.通过对空气中不同折射率的散射介质形成的散射光场光强的实验比较,论证了散射介质折射率的实部变化对散射光强的影响不大,其主要影响是通过对相位的变化来实现的,也即散射介质折射率的虚部变化对光强的影响很大,在实际应用中不可忽略.这一结论对以散射光场的分布为基础的各种研究具有一定的指导意义.