LMI优化问题的择一性定理与对偶

考虑目标函数是线性函数约束条件为线性矩阵不等式的LMI优化问题,讨论了LMI优化问题中的四个择一性定理.每种类型的择一性定理包含两个线性不等式和(或)等式系统,一个原始系统和一个对偶系统.弱择一性定理说明两系统中至多只有其一有解;基于凸集分离理论得到的强择一性定理说明两系统有且仅有其一有解.并在此基础上推导了LMI优化...     

半参数回归模型小波估计的弱收敛速度

本文研究了误差为鞅差序列情形下的半参数回归模型.利用小波方法,在相当一般的条件下,得到了参数、非参数估计量的弱收敛速度.     

Superconducting and magnetic properties of Nb/Pd 1-xFex/Nb triple layers

The superconducting and magnetic properties of Nb/Pd_1-xFe_x/Nb triple layers with constant Nb layer thickness d_Nb=200 ? and different interlayer thicknesses 3 ?≤ d_PdFe ≤ ? are investigated. The thickness dependence of the magnetization and of the superconducting transition temperature shows that for small iron concentration x the Pd_1-xFe_x layer is likely to be in the paramagnetic state for very thin films whereas ferromagnetic order is established for x ≥ 0.13. The parallel critical field B_c2||(T){B_{c2||}}(T) exhibits a transition from two-dimensional (2D) behavior where the Nb films are coupled across the interlayer, towards a 2D behavior of decoupled Nb films with increasing d_PdFeand/or x. This transition allows a determination of the penetration depth x_F{\xi _F} of Cooper pairs into the Pd_1-xFe_x layer as a function of x. For samples with a ferromagnetic interlayer x_F{\xi _F} is found to be independent of x.     

Convex duality for finite-fuel problems in singular stochastic control

Upon introducing a finite-fuel constraint in a stochastic control system, the convex duality formulation can be set up to represent the original singular control problem as a minimization problem over the space of vector measures at each level of available fuel. This minimization problem is imbedded tightly into a related weak problem, which is actually a mathematical programming problem over a convex,w*-compact space of vector-valued Radon measures. Then, through the Fenchel duality principle, the dual for the finite-fuel control problems is to seek the maximum of smooth subsolutions to a dynamic programming variational inequality. The approach is basically in the spirit of Fleming and Vermes, and the results of this paper extend those of Vinter and Lewis in deterministic control problems to the finite-fuel problems in singular stochastic control. Meanwhile, we also obtain the characterization of the value function as a solution to the dynamic programming variational inequality in the sense of the Schwartz distribution.The author is much indebted to Professor Wendell H. Fleming for his constant support and many helpful discussions during the preparation of this paper.     

A central limit theorem for the sojourn times of strongly ergodic Markov chains

Let X_n be an irreducible aperiodic recurrent Markov chain with countable state space I and with the mean recurrence times having second moments. There is proved a global central limit theorem for the properly normalized sojourn times. More precisely, if $\text{t}{}^{\mathrm{(n}}\text{)}{}_{\mathrm{i}}\text{=Σ}{}^{\mathrm{n}}{}_{\mathrm{k=1}}\text{i}\text{?}{}_{\mathrm{i}}\text{(X}{}_{\mathrm{k}}\text{)}$, then the probability measures induced by {t⁽ⁿ⁾_i/√n?√nπ_i}_i?I(π_i being the ergotic distribution) on the Hilbert-space of square summable I-sequences converge weakly in this space to a Gaussian measure determined by a certain weak potential operator.     

Optimality for set functions with values in ordered vector spaces

Let (X, , ) be a finite atomless measure space,L a convex subfamily of , andY andZ locally convex Hausdorff topological vector spaces which are ordered by the conesC andD, respectively. LetF:LY beC-convex andG:LZ beD-convex set functions. Consider the following optimization problem (P): minimizeF(), subject to L andG() _D . The paper generalizes the Moreau-Rockafellar theorem with set functions. By applying this theorem, a Kuhn-Tucker type optimality condition and a Fritz John type optimality condition for problem (P) are established. The duality theorem for problem (P) is also studied.This work was partially supported by National Science Council, Taipei, Taiwan. This paper was written while the first author was visiting at the University of Iowa, 1987-88.The authors would like to express their gratitude to the two anonymous referees for their valuable comments. Also, they would like to thank Professor P. L. Yu for his encouragement and suggestions which improved the material presented here considerably.     

^143Pm高自旋态研究

通过熔合蒸发反应^129Te(^19F,4nγ）布居了^143Pm的高自旋态,利用在束γ谱学方法,对^143Pm的高自旋态核结构进行了研究,测量了γ射线单谱和γ－γ符合谱,并进行了γ射线各向异性以及DCO比率分析,建立了激发高能达10535．4keV的能级纲图,其中包括新发现的32条γ射线和17个新能级,用弱耦合模型对^143Pm的晕态能级结构进行了解释。     

Limit Gaussian Behavior of the Solutions of the Multidimensional Burger'; Equation with Weak-Dependent Initial Conditions

Asymptotic normality of the solutions of the initial-value problems for multidimensional Burgers' equation with weakly dependent possible non-Gaussian initial condition is proved.     

Polynomial continuity on

A mapping between Banach spaces is said to be polynomially continuous if its restriction to any bounded set is uniformly continuous for the weak polynomial topology. A Banach space has property (RP) if given two bounded sequences , we have that for every polynomial on whenever for every polynomial on ; i.e., the restriction of every polynomial on to each bounded set is uniformly sequentially continuous for the weak polynomial topology. We show that property (RP) does not imply that every scalar valued polynomial on must be polynomially continuous.

     

Weak continuity of Riemann integrable functions in Lebesgue-Bochner spaces

In general, Banach space-valued Riemann integrable functions defined on [0, 1] （equipped with the Lebesgue measure） need not be weakly continuous almost everywhere. A Banach space is said to have the weak Lebesgue property if every Riemann integrable function taking values in it is weakly continuous almost everywhere. In this paper we discuss this property for the Banach space LX^1 of all Bochner integrable functions from [0, 1] to the Banach space X. We show that LX^1 has the weak Lebesgue property whenever X has the Radon-Nikodym property and X＊ is separable. This generalizes the result by Chonghu Wang and Kang Wan [Rocky Mountain J. Math., 31（2）, 697-703 （2001）] that L^1[0, 1] has the weak Lebesgue property.