Large time behavior of the solutions to the Boltzmann equation with specular reflective boundary condition

In this paper a half space problem for the one-dimensional Boltzmann equation with specular reflective boundary condition is investigated. It is shown that the solution of the Boltzmann equation time-asymptotically converges to a global Maxwellian under some initial conditions. Furthermore, a time-decay rate is also obtained.     

Artificial time integration

Many recent algorithmic approaches involve the construction of a differential equation model for computational purposes, typically by introducing an artificial time variable. The actual computational model involves a discretization of the now time-dependent differential system, usually employing forward Euler. The resulting dynamics of such an algorithm is then a discrete dynamics, and it is expected to be “close enough” to the dynamics of the continuous system (which is typically easier to analyze) provided that small – hence many – time steps, or iterations, are taken. Indeed, recent papers in inverse problems and image processing routinely report results requiring thousands of iterations to converge. This makes one wonder if and how the computational modeling process can be improved to better reflect the actual properties sought. In this article we elaborate on several problem instances that illustrate the above observations. Algorithms may often lend themselves to a dual interpretation, in terms of a simply discretized differential equation with artificial time and in terms of a simple optimization algorithm; such a dual interpretation can be advantageous. We show how a broader computational modeling approach may possibly lead to algorithms with improved efficiency. AMS subject classification (2000)  65L05, 65M32, 65N21, 65N22, 65D18     

X分形晶格上Gauss模型的临界性质

采用实空间重整化群变换的方法,研究了2维和d(d>2)维X分形晶格上Gauss模型的临界性质.结果表明:这种晶格与其他分形晶格一样,在临界点处,其最近邻相互作用参量也可以表示为K=bqiqi(qi是格点i的配位数,bqi是格点i上自旋取值的Gauss分布常数)的形式;其关联长度临界指数v与空间维数d(或分形维数df)有关.这与Ising模型的结果存在很大的差异. 关键词： X分形晶格 重整化群 Gauss模型 临界性质     

非晶硅薄膜的低温快速晶化及其结构分析

在镀铝的廉价玻璃衬底上高速沉积的非晶硅薄膜在不同的温度下退火10min.退火温度为500℃时,薄膜表面形成了硅铝的混合相,非晶硅薄膜开始呈现了晶化现象 退火温度为550℃时,大部分(约80%)的非晶硅晶化为多晶硅,平均晶粒尺寸为500nm 退火温度为600℃时,几乎所有的非晶硅都转化为多晶硅,其平均晶粒尺寸约为15μm.     

On Characterizations of Proper Efficiency for Nonconvex Multiobjective Optimization

In this paper, nonconvex multiobjective optimization problems are studied. New characterizations of a properly efficient solution in the sense of Geoffrion's are established in terms of the stability of one scalar optimization problem and the existence of an exact penalty function of a scalar constrained program, respectively. One of the characterizations is applied to derive necessary conditions for a properly efficient control-parameter pair of a nonconvex multiobjective discrete optimal control problem with linear constraints.     

CP violation and extra dimensions

It is shown that new sources of CP violation can be generated in models with more than one extra dimension. In the supersymmetric models on the space-time , where the radius moduli have auxiliary vacuum expectation values and the supersymmetry breaking is mediated by the Kaluza–Klein states of the gauge supermultiplets, we analyze the gaugino masses and trilinear couplings for two scenarios and obtain the result that there exist relative CP violating phases among the gaugino masses and trilinear couplings. Received: 10 October 2001 / Published online: 20 December 2001     

遥感傅里叶变换红外光谱的大气层析技术

遥感傅里叶变换红外光谱层析技术是一项新的气体分析技术，它可用于构造气体浓度峰图形，定量分析工业污染气体总释放量等方面，随着算法的不断优化，在重构气体在空间的分布方面，遥感傅里叶变换红外光谱层析技术正在不断成长。     

Global Optimization of Stochastic Black-Box Systems via Sequential Kriging Meta-Models

This paper proposes a new method that extends the efficient global optimization to address stochastic black-box systems. The method is based on a kriging meta-model that provides a global prediction of the objective values and a measure of prediction uncertainty at every point. The criterion for the infill sample selection is an augmented expected improvement function with desirable properties for stochastic responses. The method is empirically compared with the revised simplex search, the simultaneous perturbation stochastic approximation, and the DIRECT methods using six test problems from the literature. An application case study on an inventory system is also documented. The results suggest that the proposed method has excellent consistency and efficiency in finding global optimal solutions, and is particularly useful for expensive systems.     

Improving Construction for Connected Dominating Set with Steiner Tree in Wireless Sensor Networks

The connected dominating set plays an important role in ad hoc wireless networking. Many constructions for approximating the minimum connected dominating set have been proposed in the literature. In this paper, we propose a new one with Steiner tree, which produces approximation solution within a factor of 6.8 from optimal. This approximation algorithm can also be implemented distributedly.     

A note on the computational complexity of graph vertex partition

A stable set of a graph is a vertex set in which any two vertices are not adjacent. It was proven in [A. Brandstädt, V.B. Le, T. Szymczak, The complexity of some problems related to graph 3-colorability, Discrete Appl. Math. 89 (1998) 59-73] that the following problem is NP-complete: Given a bipartite graph G, check whether G has a stable set S such thatG-Sis a tree. In this paper we prove the following problem is polynomially solvable: Given a graph G with maximum degree 3 and containing no vertices of degree 2, check whether G has a stable set S such thatG-Sis a tree. Thus we partly answer a question posed by the authors in the above paper. Moreover, we give some structural characterizations for a graph G with maximum degree 3 that has a stable set S such that G-S is a tree.