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921.
QingXin Meng 《中国科学A辑(英文版)》2009,52(7):1579-1588
The paper is concerned with a stochastic optimal control problem in which the controlled system is described by a fully coupled
nonlinear forward-backward stochastic differential equation driven by a Brownian motion. It is required that all admissible
control processes are adapted to a given subfiltration of the filtration generated by the underlying Brownian motion. For
this type of partial information control, one sufficient (a verification theorem) and one necessary conditions of optimality
are proved. The control domain need to be convex and the forward diffusion coefficient of the system can contain the control
variable.
This work was partially supported by Basic Research Program of China (Grant No. 2007CB814904), National Natural Science Foundation
of China (Grant No. 10325101) and Natural Science Foundation of Zhejiang Province (Grant No. Y605478, Y606667) 相似文献
922.
The regioselectivity of 1,3-dipolar cycloadditions between (4-substituted)benzonitrile oxides and methyl propiolate cannot be rationalized on the basis of the electron demand of the reactants or frontier molecular-orbital theory. To this problem, we have applied a quantitative formulation of the hard-soft acid-base principle developed within the density functional theory. Global and local reactivity indices were computed at B3LYP/6-311+G(d,p) level. The details of charge transfer upon the reactive encounter have been elucidated, and the computed regioselectivity has been shown to be in good agreement with experimental data. 相似文献
923.
Christopher G. Jesudason 《Journal of mathematical chemistry》2006,39(1):201-230
Chemical and other reaction theories involving thermodynamical equilibrium states utilize statistical mechanical equilibrium
density distributions. Here, a definition of heat-work transformation termed thermo-mechanical coherence is first made, and
it is conjectured that most molecular bonds have the above heat-work transformation property, which models a chemical bond
as a “centrifugal heat engine”, where the internal energy state need not correspond to any of the standard equilibrium densities.
Expressions are derived for the standard Gibbs free energy, enthalpy, and entropy where the bond coordinates need not conform
to a non-degenerate Boltzmann state, since bond breakdown and formation are processes that have direction, whereas equilibrium
distributions are derived when the Hamiltonian is of fixed form, which is not the case for chemical reactions using localized
Hamiltonians. The empirically determined Gibbs free energy from a known molecular dynamics simulation of a dimer reaction
, accords rather well with the theoretical estimate. A relation connecting the rate of reaction with the equilibrium constant
and other kinetic parameters is derived and could place the commonly observed linear relationship between the logarithms of
the rate constant and equilibrium constant on a firmer theoretical footing. These relationships could include analogues of
the Hammett correlations used extensively in physical organic chemistry, as well as others which are temperature dependent.
One prediction of the principles developed here is that the equilibrium standard reaction free energy is more dependent on
the height of the intermolecular potential than its depth, so that the sign of the ΔG
θ can change for varying barrier height with fixed well depth, which may appear counter-intuitive. All the above developments
can be tested directly in simulations and therefore provides a fertile ground for further research with significant implications
on how standard states are determined in relation to the direction of chemical reaction.This work treats the molecular bond
using standard thermodynamics as if it were a system, and it is anticipated that with the advent of single-molecule science
and experiment, that might be one direction in which molecular statistical thermodynamics would develop. 相似文献
924.
The correspondence principle asserts that quantum mechanics resembles classical mechanics in the high-quantum-number limit. In the past few years, many papers have been published on the extension of both quantum mechanics and classical mechanics into the complex domain. However, the question of whether complex quantum mechanics resembles complex classical mechanics at high energy has not yet been studied. This paper introduces the concept of a local quantum probability density ρ(z) in the complex plane. It is shown that there exist infinitely many complex contours C of infinite length on which ρ(z) dz is real and positive. Furthermore, the probability integral is finite. Demonstrating the existence of such contours is the essential element in establishing the correspondence between complex quantum and classical mechanics. The mathematics needed to analyze these contours is subtle and involves the use of asymptotics beyond all orders. 相似文献
925.
在粘聚元或者粘聚域模型中,能够预测混合失效模式(mixed mode)的粘聚律是通过关联界面的法向分离和切向分离来建立的.考虑完全剪切失效机制的Xu-Needleman粘聚律是目前文献中应用最多的关联粘聚律之一.基于该文提出的粘聚律一致关联准则,采用界面分离功分析法,证明了考虑剪切失效机制的Xu-Needleman粘聚律在混合失效模式下,属于非一致关联粘聚律.理论分析证明,考虑剪切失效的Xu-Needleman粘聚律仅在界面的法向分离功与切向分离功相等的情况下能够正确刻画混合失效模式.基于粘聚律一致关联准则,在考虑剪切失效的Xu-Needleman粘聚律的基础上,进行修正提出一种一致关联粘聚律(CCC).分析证明,这种修正的一致关联粘聚律克服了原有Xu-Needleman粘聚律非一致关联的弊端,能够更好刻画混合失效模式下的破坏行为. 相似文献
926.
通过构造新的对偶向量, 用空间的环向坐标数学上比拟Hamilton体系的时间变量,在平面弹性扇形域问题中导出了一个斜对角Hamilton算子. 该算子具有主对角元为零,斜对角元是非零对称算子的结构特性. 得到两个独立的、对称的子正交关系.恰当选择对偶向量后, 直角坐标系下各向同性平面弹性问题的新正交关系被推广到极坐标情形. 根据控制微分方程的弱(积分)形式及相应的边界条件,建立了对应边值问题的变分原理, 并提出了相应的泛函表达式. 相似文献
927.
A new control law is proposed to asymptotically stabilize the chaotic neuron system based on LaSalle invariant principle. The control technique does not
require analytical knowledge of the system dynamics and operates without an explicit knowledge of the desired steady-state position. The well-known modified Hodgkin-Huxley (MHH) andHindmarsh-Rose (HR) model neurons are taken as examples to verify the implementation of our method. Simulation results show the proposed control law is effective. The outcome of this study is significant since it is helpful to understand the learning process
of a human brain towards the information processing, memory and abnormal discharge of the brain neurons. 相似文献
928.
929.
Wen-Xiu MA 《Frontiers of Mathematics in China》2013,8(5):1139-1156
A class of trilinear differential operators is introduced through a technique of assigning signs to derivatives and used to create trilinear differential equations. The resulting trilinear differential operators and equations are characterized by the Bell polynomials, and the superposition principle is applied to the construction of resonant solutions of exponential waves. Two illustrative examples are made by an algorithm using weights of dependent variables. 相似文献
930.
地基土的变形模量值不仅和土层所受的先期固结压力大小直接相关, 还受桩土作用产生的附加体积应变的影响.首先, 针对岩土散体材料分析其本构关系的主要影响因素, 研究模量随埋藏深度和体积应变的变化规律, 并对Duncan-Chang本构模型进行抗拉模量值修正.其次, 综合考虑岩土材料拉压模量不等修正以及桩土作用位移边界特点, 应用变分理论推导桩土作用造成的位移、应变和应力场理论解答.最后, 应用已有的经典土压力理论和小孔扩张理论对理论推导结果进行对比和分析验证.研究结果对桩基础设计施工、相应环境保护措施的选择和设计有较大的指导作用. 相似文献