一个平面弹性问题的虚位移原理和Locking-Free非协调有限元方法

证明了平面弹性问题的虚位移原理,提出了一个新的非协调有限元解决纯位移边界条件下的Locking现象,该方法是Robust和Optimal,证明了能量模的收敛性,并且证明了误差估计结果与参数λ无关.     

PbTe纳米晶高压热电性能的研究

 利用自建的400 t四柱双缸液压机,研究了PbTe纳米晶在0~0.8 GPa压力范围内热电性能随压力的变化。实验结果表明：PbTe纳米晶电导率随压力的增加而增加,而热电动势随压力的增加而减小,两者随压力的变化具有可逆性;PbTe纳米晶具有极高的热电动势,在常压下达到565 μV/K,在0.8 GPa压力下,材料的电导率为常压下的4倍,热电动势仅降低20%,功率因子则达到常压下的3倍。研究表明,高压能显著提高PbTe纳米晶的热电性能。利用第一性原理计算了0.4~4.0 GPa压力范围内材料的简约费米能级,计算结果与实验结果相吻合。     

A Reflection Principle and an Orthogonal Decomposition in Clifford Algebras

In this article we investigate spaces of functions defined in a domain Ω ? R with values in the Clifford algebra R _n. According to an inner product an orthogonal decomposition is proved. By this decomposition, we obtain a subspace A ₂(Ω) of regular functions with respect to the Dirac operator. In the orthogonal complement the Dirac equation with homogeneous boundary values is solvable. The decomposition can be proved in two ways: by a reflection principle and by Sobolev's regularity theorem. It will turn out, that the existence of the orthogonal decomposition and Sobolev's theorem is equivalent. So also a reflection principle will be proved, which describes the jump behavior of a Cauchy type integral. By the reflection principle, a countable dense subset of A ₂(Ω) can be obtained. Further considerations lead to a minimal generating system, by which the Bergman kernel function can be obtained. As a conclusion we also obtain Runge's theorem.     

Lipschitzian Regularity of Minimizers for Optimal Control Problems with Control-Affine Dynamics

We study the Lagrange Problem of Optimal Control with a functional and control-affine dynamics = f(t,x) + g(t,x)u and (a priori) unconstrained control u∈ \bf R ^m . We obtain conditions under which the minimizing controls of the problem are bounded—a fact which is crucial for the applicability of many necessary optimality conditions, like, for example, the Pontryagin Maximum Principle. As a corollary we obtain conditions for the Lipschitzian regularity of minimizers of the Basic Problem of the Calculus of Variations and of the Problem of the Calculus of Variations with higher-order derivatives. Accepted 15 March 1999     

气相色谱-质谱法和主成分投影分析法用于烟用香精的分析和质量控制

采用同时蒸馏萃取法及气相色谱-质谱法对 AB6 香精中挥发性成分进行了提取分离与测定.定性了 15 种成分,占总成分的 80.5%(截除溶剂峰),其中 4 种主要组分在10个不同批次样品中含量的相对标准偏差分别为 3.9%,6.1%,5.7%和 2.2%,由此构成合格样品库,并采用主成分投影分析法有效地区分了掺有溶剂的 AB6 香精与 AB6 香精的合格样品,随着溶剂量的增加它们之间的距离越远,同时,不同品种的香精样品之间也具有显著的差异.气相色谱-质谱法分析和主成分投影分析法可用于香精的质量控制.     

On positive homogeneity and comonotonic additivity of the principle of equivalent utility under Cumulative Prospect Theory

Investigating the principle of equivalent utility under Cumulative Prospect Theory, Kałuszka and Krzeszowiec (2012) established characterizations of several important properties of the premium. It turns out that the results concerning positive homogeneity and comonotonic additivity are in general not true. The aim of this paper is to present modified and essentially generalized versions of the mentioned above results.     

一类单位圆上的Chebyshev权的Cauchy型求积公式

在本文中,我们首先给出一些基本的结果和一些概念,然后给出单位圆上带Cheby shev权的一些Cauchy主值积分的求积公式,最后给出了它们的误差估计.     

Generalized random energy model

This paper applies the large deviation technique to a general tree formulation of Generalized Random Energy Model. The similarities and dissimilarities between the exponential and the Gaussian model are discussed. Formulae for limiting free energies, characterization of energy functions are obtained. Limiting case of the tree structure and randomization of the trees are also investigated.     

Nonlinear models of suspension bridges

Nonlinear variational equations describing one type of suspension bridges are proposed and studied. The variational equations describe the behaviour of road bed, main cables and cable stays. The road bed is described by two functions connected with vertical and horizontal deformation of any cross section. The main cable is considered to be perfectly flexible and inextensible. The cable stays only resist tensile forces. The variational equations are derived from the principle of minimum potential energy. The existence of solution is based on the Brouwer Fixed Point Theorem. The local uniqueness and continuous dependence on the data represented by gravitational forces acting on the road bed are studied. The local results are based on the Implicit Function Theorem for Banach spaces. A certain stability criterion for suspension bridges is formulated and this criterion indicates how to influence the stability of suspension bridges.