蒙特卡罗哈密顿新方案及其检验

蒙特卡罗哈密顿方法(MCH)是研究量子理论的数值模拟新方法, 其优点是可求出超出基态的能谱和波函数. 旧MCH方案需要自由粒子的信息, 较难推广应用于格点规范理论. 本文提出克服这个困难的新方案. 首先介绍这一方案的思想, 并以1维量子力学模型V(x)=μ²x²+λx⁴(其中μ²< 0,λ>0)为例说明实现这一新方案的具体计算步骤和方法.     

资产组合的CVaR风险的敏感度分析

基于CVaR风险计量技术，分别给出了正态和t分布情形下资产组合的CVaR值，对一般情形下风险资产组合的CVaR风险关于头寸的敏感度进行了分析，研究了其经济意义。     

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.     

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).     

Schwinger Formula Revisited

We apply the formal W.K.B. method in the complex plane to the quantum field theory to obtain the Schwinger formula for spin and spinless particles; i.e., we obtain the probability that the vacuum state remains unchanged in presence of a constant electric field. Finally, from Schwinger formula we calculate the probability that n pairs are produced.     

CreditRisk+模型下商业银行经济资本配置研究

对金融资产风险的度量与经济资本的分配应该体现分散化效应,传统的V aR方式不能保证分散化效应的次可加性.本文讨论了基于T a ilV aR这一新的风险度量与经济资本分配标准,并在违约率均值不变情况下,对C red itR isk+模型下的商业银行经济资本分配进行了实证分析.     

Flow Search Approach and New Bounds for the m-Step Linear Conjugate Gradient Algorithm

A flow search approach is presented in this paper. In the approach, each iterative process involves a subproblem, whose variables are the stepsize parameters. Every feasible solution of the subproblem corresponds to some serial search stages, the stepsize parameters in different search stages may interact mutually, and their optimal values are determined by evaluating the total effect of the interaction. The main idea of the flow search approach is illustrated via the minimization of a convex quadratic function. Based on the flow search approach, some properties of the m-step linear conjugate gradient algorithm are analyzed and new bounds on its convergence rate are also presented. Theoretical and numerical results indicate that the new bounds are better than the well-known ones.     

On norms of composition operators acting on Bergman spaces

For arbitrary composition operators acting on a general Bergman space we improve the known lower bound for the norm and also generalize a related recent theorem of D.G. Pokorny and J.E. Shapiro. Next, we obtain a geometric formula for the norms of composition operators with linear fractional symbols, thus extending a result of C. Cowen and P. Hurst and revealing the meaning of their computation. Finally, we obtain a lower bound for essential norm of an arbitrary composition operator related to the well-known criterion of B. MacCluer and J.H. Shapiro. As a corollary, norms and essential norms are obtained for certain univalently induced noncompact composition operators in terms of the minimum of the angular derivative of the symbol.     

An “Instrumental Approach” to Study the Integration of a Computer Tool Into Mathematics Teaching: the Case of Spreadsheets

This article reports on research focused on the integration of a specific computer tool, the spreadsheet, into mathematics teaching. After presenting some important results obtained by research in this area, we revisit these in the light of an instrumental approach, which we perceive as essential to analyse the construction of mathematical meanings in spreadsheet environments and to understand better the questions of technological integration. Then, these theoretical elements are used in order to design an exploratory experiment with grade 7 pupils and analyse its results.