金纳米粒子光学性质中的尺寸和形状效应

纳米尺度的金属及半导体呈现出特殊的光学、电学及磁学性质,采用近年发展起来的离散偶极近似(DDA)的方法,我们分析了金纳米粒子的尺寸及形状对其光学性质的影响。粒子周围介质的影响在文中亦作了分析。计算结果显示,金纳米粒子的等离子体吸收带同时受到粒子尺寸和形状的影响,但来自形状的影响更为明显。与米氏理论及扩展的甘氏理论相比较,DDA方法在粒子尺寸不再远小于入射光波长的时候更准确,并能应用于任何形状的纳米粒子。理论计算与实验结果能较好的吻合。     

A modular integer GCD algorithm

This paper describes the first algorithm to compute the greatest common divisor (GCD) of two n-bit integers using a modular representation for intermediate values U, V and also for the result. It is based on a reduction step, similar to one used in the accelerated algorithm [T. Jebelean, A generalization of the binary GCD algorithm, in: ISSAC '93: International Symposium on Symbolic and Algebraic Computation, Kiev, Ukraine, 1993, pp. 111–116; K. Weber, The accelerated integer GCD algorithm, ACM Trans. Math. Softw. 21 (1995) 111–122] when U and V are close to the same size, that replaces U by (U−bV)/p, where p is one of the prime moduli and b is the unique integer in the interval (−p/2,p/2) such that . When the algorithm is executed on a bit common CRCW PRAM with O(nlognlogloglogn) processors, it takes O(n) time in the worst case. A heuristic model of the average case yields O(n/logn) time on the same number of processors.     

因素空间理论与知识表示的数学框架(XⅢ)──描述架中概念的结构(2)

本文是［１，１２］的继续，研究描述架中概念的结构；本文讨论后半部分，内容涉及概念内涵与外延的转换，清晰关系的内投影与内变换，概念的结构＊以及有关问题的注记。     

CONVERGENCE OF SOLUTIONS FOR A CLASS OF DIFFERENCE EQUATIONS WITH VARIABLE DELAY

Ｃｏｎｓｉｄｅｒｔｈｅｄｉｆｅｒｅｎｃｅｅｑｕａｔｉｏｎｗｉｔｈａｖａｒｉａｂｌｅｄｅｌａｙｘｎ－ｘｎ－１＝Ｆ（ｘｎ，ｘｒ（ｎ），ｎ＝ｎ０，ｎ０＋１，…（１）ｗｈｅｒｅ（Ｈ１）：Ｆ∈Ｃ（Ｒ×Ｒ，Ｒ），Ｆ（ｕ，ｖ）ｉｓｄｅｃｒｅａｓｉｎｇｗｉｔｈｒｅｓ...     

Three-dimensional integrable models and associated tangle invariants

In this paper we show that the Boltzmann weights of the three-dimensional Baxter-Bazhanov model give representations of the braid group if some suitable spectral limits are taken. In the trigonometric case we classify all possible spectral limits which produce braid group representations. Furthermore, we prove that for some of them we get cyclotomic invariants of links and for others we obtain tangle invariants generalizing the cyclotomic ones.     

内参量热力学中的应变参量分析

以连续体的各力学守恒定律和熵函数为基础,给出了完备的变形体内参量热力学的表述框架。讨论了将热力学状态参量分划为外参量和内参量的必要性和依据,论证了热力学内参量和非弹性变形的关系以及将各种类型的非弹性应变列为内参量的数学条件。给出了考虑非弹性变形的内参量热力学基本方程,讨论了熵平衡和熵产生的关系方程和行为特性。引入两种定义的变形体自由能函数的表述方程,给出了各相应的状态方程组。     

A Survey on Explicit Representation Formulae for Fundamental Solutions of Linear Partial Differential Operators

In the present article, we aim at treating the existence of fundamental solutions of linear partial differential operators with constant coefficients from the viewpoint of setting up explicit formulae yielding fundamental solutions.     

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.     

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.