Minimal expansions in redundant number systems: Fibonacci bases and Greedy algorithms

We study digit expansions with arbitrary integer digits in base q (q integer) and the Fibonacci base such that the sum of the absolute values of the digits is minimal. For the Fibonacci case, we describe a unique minimal expansion and give a greedy algorithm to compute it. Additionally, transducers to calculate minimal expansions from other expansions are given. For the case of even integer bases q, similar results are given which complement those given in [6].     

A relaxed model and its homogenization for nematic liquid crystals in composite materials

We analyse a model for equilibrium configurations of composite systems of nematic liquid crystal with polymer inclusions, in the presence of an external magnetic field. We assume that the system has a periodic structure, and consider the relaxed problem on the unit length constraint of the nematic director field. The relaxation of the Oseen–Frank energy functional is carried out by including bulk as well as surface energy penalty terms, rendering the problem fully non‐linear. We employ two‐scale convergence methods to obtain effective configurations of the system, as the size of the polymeric inclusions tends to zero. We discuss the minimizers of the effective energies for, both, the constrained as well as the unconstrained models. Copyright © 2004 John Wiley & Sons, Ltd.     

The long‐time behaviour of the thermoconvective flow in a porous medium

For the Boussinesq approximation of the equations of coupled heat and fluid flow in a porous medium we show that the corresponding system of partial differential equations possesses a global attractor. We give lower and upper bounds of the Hausdorff dimension of the attractor depending on a physical parameter of the system, namely the Rayleigh number of the flow. Numerical experiments confirm the theoretical findings and raise new questions on the structure of the solutions of the system. Copyright © 2004 John Wiley & Sons, Ltd.     

Stress State of Multilayer Thin-Walled Elements with Interfacial Defects of Structure

Based on the discrete-structural theory of thin plates and shells, a calculation model for thin-walled elements consisting of a number of rigid anisotropic layers is put forward. It is assumed that the transverse shear and compression stresses are equal on the interfaces. Elastic slippage is allowed over the interfaces between adjacent layers. The solution to the problem is obtained in a geometrically nonlinear statement with account of the influence of transverse shear and compression strains. The stress-strain state of circular two-layer transversely isotropic plates, both without defects and with a local area of adhesion failure at their center, is investigated numerically and experimentally. It is found that the kinematic and static contact conditions on the interfaces of layered thin-walled structural members greatly affect the magnitude of stresses and strains. With the use of three variants of calculation models, in the cases of perfect and weakened contact conditions between layers, the calculation results for circular plates are compared. It is revealed that the variant suggested in this paper adequately reflects the behavior of layered thin-walled structural elements under large deformations. __________ Translated from Mekhanika Kompozitnykh Materialov, Vol. 41, No. 6, pp. 761–772, November–December, 2005.     

线性常微分方程组解的特征数的估计

复数域上线性系统ｘ＝Ａ（ｔ）ｘ，当Ａ（ｔ）＝（ａｉｊ（ｔ））ｎ×ｎ具有（ｎ，Ｎ，ｒ） 差异性质且ｒｎ时，解的特征数ｊ有估计λｊ－ｌｉｍｔ→∞１ｔ∫ｔｔ０Ｒｅａｊ（τ）ｄτｎ－１ｒ＋１－ｎｌｉｍｔ→∞１ｔ∫ｔｔ０Ａ（τ）ｄτ，ｊ＝１，２，…，ｎ，其中Ａ（ｔ）＝ｍａｘ｛｜ａｉｊ（ｔ）｜：ｉ，ｊ＝１，２，…，ｎ，ｉ≠ｊ．｝     

A Note on Geometric Structures of Linear Ordered Orthogonal Arrays and (T,M,S)-Nets of Low Strength

The equivalent geometrical configurations of linear ordered orthogonal arrays are determined when their strengths are 3 and 4. Existence of such geometrical configurations is investigated. They are also useful in the study of (T, M, S)-nets.     

激光调Q CAI

从激光调Q速率方程出发,分析推导了激光调Q过程中,腔内光子数与工作物质内反转粒子数间的关系.再根据激光调Q的过程中,对腔Q值控制方式不同,将激光调Q技术分为:转镜调Q、声光调Q、电光调Q、饱和吸收调Q和脉冲透射式调Q.用C语言进行了激光调Q CAI软件的开发研制,获得了将文学、图形、动画和计算融为一体的,直观而生动地将调Q的理论和过程再现于屏幕的CAI课件.介绍了课件的内容、结构及其特点.     

Luttinger liquid with asymmetric dispersion

We present an extension of the Tomonaga-Luttinger model in which left and right-moving particles have different Fermi velocities. We derive expressions for one-particle Green's functions, momentum-distributions, density of states, charge compressibility and conductivity as functions of both the velocity difference ε and the strength of the interaction β. This allows us to identify a novel restricted region in the parameter space in which the system keeps the main features of a Luttinger liquid but with an unusual behavior of the density of states and the static charge compressibility κ. In particular κ diverges on the boundary of the restricted region, indicating the occurrence of a phase transition. Received 20 May 2002 / Received in final form 23 August 2002 Published online 19 November 2002     

PACKING PAIRS BY QUINTUPLES:THE CASE OF ZERO CONGRUENCE MOD 4

ＰＡＣＫＩＮＧＰＡＩＲＳＢＹＱＵＩＮＴＵＰＬＥＳ：ＴＨＥＣＡＳＥＯＦＺＥＲＯＣＯＮＧＲＵＥＮＣＥＭＯＤ４ＹＩＮＪＩＡＮＸＩＮＧＡｂｓｔｒａｃｔ：ＬｅｔＤ（ｖ）ｄｅｎｏｔｅｔｈｅｍａｘｉｍｕｍｎｕｍｂｅｒｏｆｑｕｉｎｔｕｐｌｅｓｏｆａｖ－ｓｅｔｏｆｐｏ...     

Rank, term rank, and chromatic number

Let G be a graph with a nonempty edge set, and with rank rk(G), term rank Rk(G), and chromatic number χ(G). We characterize Rk(G) as being the maximum number of colors in certain proper colorings of G. In particular, we observe that χ(G)Rk(G), with equality holding if and only if (besides isolated vertices) G is either complete or a star. For a twin-free graph G, we observe the bound and we show that this bound is sharp.