“String” formulation of the dynamics of the forward interest rate curve

We propose a formulation of the term structure of interest rates in which the forward curve is seen as the deformation of a string. We derive the general condition that the partial differential equations governing the motion of such string must obey in order to account for the condition of absence of arbitrage opportunities. This condition takes a form similar to a fluctuation-dissipation theorem, albeit on the same quantity (the forward rate), linking the bias to the covariance of variation fluctuations. We provide the general structure of the models that obey this constraint in the framework of stochastic partial (possibly non-linear) differential equations. We derive the general solution for the pricing and hedging of interest rate derivatives within this framework, albeit for the linear case (we also provide in the appendix a simple and intuitive derivation of the standard European option problem). We also show how the “string” formulation simplifies into a standard N-factor model under a Galerkin approximation. Received: 30 January 1998 / Revised: 12 February 1998 / Accepted: 16 February 1998     

（Φ，Δ）型概率收缩与Menger PN－空间中非线性算子方程的解

本文在Ｍｅｎｓｅｒ概率赋范空间中引入了（Φ，Δ）型概率收缩的概念，研究了Ｍｅｎｇｅｒ概率赋范空间中具有这类概率收缩的非线性算子方程的解的存在性与唯一性．发展和改进了引文［１］、［４～８］的相应结果．     

Absorption spectra and the nature of complexes in the polyvinyl Alcohol-Nickel (II) chloride system

We have used electronic spectroscopy in the 160–1100 nm range to study the polyvinyl alcohol-nickel(II) chloride system. Based on the results obtained, we hypothesize formation of mixed-ligand complexes of the type [Ni(H₂O)_6-nCl_n]^2-n (n = 0, 1,..., 5) in the polyvinyl alcohol matrix. Transformation of the coordination sphere as the NiCl₂ concentration changes is apparent both in the region of the d-d transition bands (350–1100 nm) and in the region of the charge transfer bands (160–250 nm). We propose assigning the absorption bands separated by mathematical treatment to complexes of specific compositions. __________ Translated from Zhurnal Prikladnoi Spektroskopii, Vol. 73, No. 1, pp. 136–138, January–February, 2006.     

氩等离子体物态方程的TF简化模型

对于高温高压下氩等离子体的电离度和物态方程,本文给出了一种基于Thomas-Feimi(TF)统计模型的简化计算新方法:首先将TF模型电离势的数值结果进行函数逼近,给出一个便于数值求解的计算电离度的近似计算方法,并由此计算了局部热动平衡下的氩等离子体在10～1000 eV高温范围内的物态方程.计算结果与国外报道的其他几种理论模型的计算结果均符合很好,与实验值也吻合较好.本文所提出的简单模型也适用于计算混合物物态方程,可以在电磁发射技术领域中的强电离等离子体中有更为广阔的应用前景.     

New numerical methods and some applied aspects of the p-regularity theory

The theory of p-regularity is applied to optimization problems and to singular ordinary differential equations (ODE). The special variant of the method of the modified Lagrangian function proposed by Yu.G. Evtushenko for constrained optimization problems with inequality constraints is justified on the basis of the 2-factor transformation. An implicit function theorem is given for the singular case. This theorem is used to show the existence of solutions to a boundary value problem for a nonlinear differential equation in the resonance case. New numerical methods are proposed including the p-factor method for solving ODEs with a small parameter.     

解初值问题y″=g(x，y)的含参数块方法

1引言对于二阶常微分方程的初值问题y″=g(x,y),y(x_0)=y_0,y′(x_0)=y_0′,x_0(?)x(?)T(1)的数值解法的研究引起人们的广泛兴趣．对于直接积分(1),自从1976年J．D．Lambert和I．A．Waston提出二阶P-稳定方法和1978年G．Dahlquist证明P-稳定常系数线性多步方法的最高相容阶不超过2的重要结论以来,截止目前,已积累了许多高于2阶的P-稳定方法．例如,修正的Numerov方法,混合法(特殊形式RK的方法),多导法,Obrechkoff方法,显式RKN方法,单隐方法和对角隐式RKN方法等(顺便指出,文献[5,16]中所说的高阶方法的相容阶均不超过4)．所有这些方法,有些相     

动态广义球对称含荷黑洞的统计熵

利用改进了的brickwall膜模型,计算了动态广义球对称含荷黑洞的熵,研究结果表明,对于动态黑洞,将黑洞熵表示为与视界面积成正比时,则比例系数总与动态黑洞的视界速度有关 关键词： 广义球对称黑洞 黑洞熵 brick-wall膜模型 WKB近似     

Interplay of charge, spin, orbital and lattice correlations in colossal magnetoresistance manganites

We derive a realistic microscopic model for doped colossal magnetoresistance manganites, which includes the dynamics of charge, spin, orbital and lattice degrees of freedom on a quantum mechanical level. The model respects the SU(2) spin symmetry and the full multiplet structure of the manganese ions within the cubic lattice. Concentrating on the hole doped domain ( 0≤x≤0.5) we study the influence of the electron-lattice interaction on spin and orbital correlations by means of exact diagonalisation techniques. We find that the lattice can cause a considerable suppression of the coupling between spin and orbital degrees of freedom and show how changes in the magnetic correlations are reflected in dynamic phonon correlations. In addition, our calculation gives detailed insights into orbital correlations and demonstrates the possibility of complex orbital states. Received 4 September 2002 / Received in final form 8 November 2002 Published online 31 December 2002     

Orbital-selective Mott-insulator transition in Ca 2 - x Sr x RuO 4

The electronic structures of the metallic and insulating phases of the alloy series Ca_2-xSr_xRuO₄ ( 0 ? x ? 2) are calculated using LDA, LDA+U and Dynamical Mean-Field Approximation methods. In the end members the groundstate respectively is an orbitally non-degenerate antiferromagnetic insulator (x = 0) and a good metal (x = 2). For x > 0.5 the observed Curie-Weiss paramagnetic metallic state which possesses a local moment with the unexpected spin S = 1/2, is explained by the coexistence of localized and itinerant Ru-4d-orbitals. For 0.2 < x < 0.5 we propose a state with partial orbital and spin ordering. An effective model for the localized orbital and spin degrees of freedom is discussed. The metal-insulator transition at x = 0.2 is attributed to a switch in the orbital occupation associated with a structural change of the crystal. Received 27 July 2001