On Discrete Zariski-Dense Subgroups of Algebraic Groups

We investigate under which conditions an algebraic group G defined over a locally compact field k admitr a subgroup Γ? G(k) which is dense in the Zariski topology, but discerte in the topology induced by the locally compact topology on k. For non—solvable groups we provide a complete answer.     

弱1—凸对策及其解的性质

本文提出了一类特殊的ｎ人合作对策模型─—弱１—凸对策，研究了弱１—凸对策的解的性质，并证明弱１—凸对策的解满足所有常见的公理化特征．     

Ant colony optimization: Introduction and recent trends

Ant colony optimization is a technique for optimization that was introduced in the early 1990's. The inspiring source of ant colony optimization is the foraging behavior of real ant colonies. This behavior is exploited in artificial ant colonies for the search of approximate solutions to discrete optimization problems, to continuous optimization problems, and to important problems in telecommunications, such as routing and load balancing. First, we deal with the biological inspiration of ant colony optimization algorithms. We show how this biological inspiration can be transfered into an algorithm for discrete optimization. Then, we outline ant colony optimization in more general terms in the context of discrete optimization, and present some of the nowadays best-performing ant colony optimization variants. After summarizing some important theoretical results, we demonstrate how ant colony optimization can be applied to continuous optimization problems. Finally, we provide examples of an interesting recent research direction: The hybridization with more classical techniques from artificial intelligence and operations research.     

Modeling of radiative heat transfer in an axisymmetric cylindrical enclosure with participating medium

Radiative heat transfer in an axisymmetric enclosure with absorbing, emitting, and scattering medium is studied here by using the different methods such as MDOM, FVM, and MFVM with emphasis on the treatment of angular derivative term, which appears in curvilinear coordinates due to angular redistribution. After final discretization equation for MFVM is introduced by using the step scheme and directional weights, the present approach is validated by applying it to three different benchmarking problems with absorbing, emitting, and scattering medium. All of the results presented here support its accuracy as well as moderate efficiency. Finally, the present approaches are applied to a truncated cone-shaped enclosure as a body-fitted geometry case.     

Carnot-Caratheodory空间中的变换论

Klein发表著名的埃尔兰根纲领,由群论角度研究了空间变换群的不变量,从而引进了各种不同的几何学．本文利用Felix Klein的观念,研究Carnot-Caratheodory空间{M,Q,g}(又称为次黎曼流形)上的类似问题,给出了次黎曼流形中的共形不变量和射影不变量．本文给出的共形和射影不变量可视为黎曼情形的一种自然推广．由于次黎曼流形与黎曼流形之间有着本质的差异,故此,本文通过次黎曼流形上存在的唯一非完整联络(Nonholonomic connections)来刻画所提的问题．     

抽运激光在光靶中的局域及其对X射线激光特性的影响

新型X射线靶设计为:由SiO2和TiO2组成具有12个周期的一维光子晶体,在它的中间嵌入光靶材料层作为缺陷层,SiO2,TiO2和光靶层的光学厚度分别为λ4、λ4和λ2,λ为抽运激光波长.与普通平板光靶相比,当抽运光垂直照射到这种光靶时,靶层内部的光强将提高2个数量级,所以抽运激光的阈值强度将降低2个数量级,这有利于X射线激光的小型化.在同样的抽运激光照射下,X射线激光的强度将提高4个数量级,转换效率也将提高约4个数量级.由于平均电离度随抽运激光强度的提高而提高,所以采用这种光靶有利于使X射线激光向短波长推进. 关键词： X射线激光 光子晶体 光波局域     

基于频域方法的三维物体分层重现

基于频域方法实现了数字记录和再现三维物体离轴全息图.通过频谱对应关系求得各个面的频谱分布,使用数字滤波方法,成功地消除了零级衍射和共轭像;通过改变再现距离,分别获取了三维物体各个截面的再现像.     

~ Transform Demonstration of Dark Soliton Solutions Found by Inverse Scattering

One of the basic problems about the inverse scattering transform for solving a completely integrable nonlinear evolutions equation is to demonstrate that the Jost solutions obtained from the inverse scattering equations of Cauchy integral satisfy the Lax equations. Such a basic problem still exists in the procedure of deriving the dark soliton solutions of the NLS equation in normal dispersion with non-vanishing boundary conditions through the inverse scattering transform. In this paper, a pair of Jost solutions with same analytic properties are composed to be a 2 × 2 matrix and then another pair are introduced to be its right inverse confirmed by the Liouville theorem. As they are both 2 × 2 matrices, the right inverse should be the left inverse too, based upon which it is not difficult to show that these Jost solutions satisfy both the first and second Lax equations. As a result of compatibility condition, the dark soliton solutions definitely satisfy the NLS equation in normal dispersion with non-vanishing boundary conditions.     

Estimating Invariant Probability Densities for Dynamical Systems

Knowing a probability density (ideally, an invariant density) for the trajectories of a dynamical system allows many significant estimates to be made, from the well-known dynamical invariants such as Lyapunov exponents and mutual information to conditional probabilities which are potentially more suitable for prediction than the single number produced by most predictors. Densities on typical attractors have properties, such as singularity with respect to Lebesgue measure, which make standard density estimators less useful than one would hope. In this paper we present a new method of estimating densities which can smooth in a way that tends to preserve fractal structure down to some level, and that also maintains invariance. We demonstrate with applications to real and artificial data.