Influence of the Interaction between Two Neighboring Periodically Curved Fibers on the Stress Distribution in a Composite Material

A method is developed for a stress analysis in an infinite elastic body containing two neighboring periodically cophasaly curved fibers located along two parallel lines. The stress distribution is studied when the body is loaded at infinity by uniformly distributed normal forces in the fiber direction. The investigation is carried out within the framework of a piecewise homogeneous body model with the use of exact three-dimensional equations of elasticity theory. Numerical results related to the stress distribution considered and the influence of interaction between the fibers on this distribution are given.     

Pearson-χ~2距离的若干性质

本文对数理统计中常用的 Pearson- χ2距离的分析特性进行了讨论 ,得到了这一距离的一些解析性质 ,最后我们还给出了几个常用距离的关系 .     

On the number of full levels in tries

We study the asymptotic distribution of the fill‐up level in a binary trie built over n independent strings generated by a biased memoryless source. The fill‐up level is the number of full levels in a tree. A level is full if it contains the maximum allowable number of nodes (e.g., in a binary tree level k can have up to 2^k nodes). The fill‐up level finds many interesting applications, e.g., in the internet IP lookup problem and in the analysis of level compressed tries (LC tries). In this paper, we present a complete asymptotic characterization of the fill‐up distribution. In particular, we prove that this distribution concentrates on one or two points around the most probably value k = ?log_1/qn ? log log log n + 1 + log log(p/q)?, where p > q = 1 ? p is the probability of generating the more likely symbol (while q = 1 ? p is the probability of the less likely symbol). We derive our results by analytic methods such as generating functions, Mellin transform, the saddle point method, and analytic depoissonization. We also present some numerical verification of our results. © 2004 Wiley Periodicals, Inc. Random Struct. Alg., 2004     

Upper and lower bounds for the energy of bipartite graphs

Using Lagrange's multiplier rule, we find upper and lower bounds of the energy of a bipartite graph G, in terms of the number of vertices, edges and the spectral moment of fourth order. Moreover, the upper bound is attained in a graph G if and only if G is the graph of a symmetric balanced incomplete block design (BIBD). Also, we determine the graphs for which the lower bound is sharp.     

Numerical calculations of temperature distribution of double layer metallic surface treated by laser beams

A mathematical model of laser beam treatment of double layer alloys (Ni/Fe, Al/Fe and Cr/Fe systems) describing the effect of laser beam on different physical and geometrical parameters of coated layer system has been adapted. The numerical solutions of the non-homogeneous heat-transport differential equation could estimate the temperature of the treated region.The suggested model allows investigation of the temperature distribution as a function of treated surface and laser parameters. The physical parameters of the treated materials were taken as functions of temperature due to the change in the temperature of the treated double layer materials.     

Directed Motion of a Molecular Motor Based on the Four-State Model with Unequal Substeps

A periodic one-dimensional four-state hopping model is proposed. In the model, the substeps betweenarbitrary adjacent states are unequal, and an explicit solution of the master equation is first obtained for the probabilitydistribution as a function of the time and position for any initial distribution with all the transients included. Next, thetransient behaviors in the initial period of time and the characteristic time to reach the steady state for the molecularmotor are discussed. Finally, we compare the steady state results to experiments and illustrate qualitatively the kineticbehaviors of a molecular motor under external load F.     

Electron–hole recombination luminescence in LiYF4:U single crystal

Photoluminescence (PL), photostimulated luminescence (PSL), thermally stimulated luminescence (TSL) and electron paramagnetic resonance (EPR) studies were carried out on LiYF₄:U⁴⁺ and pure LiYF₄ crystals. The PL and EPR investigations have identified the presence of Eu³⁺, Tb³⁺ and Gd³⁺ ions in both of these crystals possibly due to their existence in the starting materials. The luminescence observed during afterglow, PSL and TSL revealed that emission occurs at wavelength positions 382, 413, 437 and 544 nm, which are characteristic of Tb³⁺ ions. The present investigations using PSL and TSL in combination with PL studies before and after gamma irradiation have revealed that selective energy transfer to Tb³⁺ ions occurs during electron–hole recombination processes like PSL and TSL. Even though other luminescent ions (U⁴⁺ and Eu³⁺) are present in the system and U⁴⁺/U³⁺ ions are participating in electron capture/release processes, the selective energy transfer results in Tb³⁺ ions acting as luminescence centers.     

Large deviation for the empirical eigenvalue density of truncated Haar unitary matrices

Let U_m be an m×m Haar unitary matrix and U_[m,n] be its n×n truncation. In this paper the large deviation is proven for the empirical eigenvalue density of U_[m,n] as m/n→λ and n→∞. The rate function and the limit distribution are given explicitly. U_[m,n] is the random matrix model of quq, where u is a Haar unitary in a finite von Neumann algebra, q is a certain projection and they are free. The limit distribution coincides with the Brown measure of the operator quq.     

燃煤烟气中As、Se、Pb的形态分布及S、Cl元素对其形态分布的影响

基于化学热力学平衡分析方法，计算分析了燃煤烟气中重金属As、Se、Pb的形态分布规律，研究了S、Cl等元素对As、Se、Pb的形态分布规律的影响。结果表明，氧化性气氛下，As以As₂O₅、As₄O₆、AsO等氧化物的形式存在；Se主要以SeO₂形式存在；Pb在1000 K以下主要是固态PbSO₄，1200 K以上为气态PbO。还原性气氛下，As在较低温度时为固态As₂S₂，900-1400 K以As₂、AsS、AsN气体共存，2000 K以上全部转化为气态AsO。Se在1100 K以下主要以气态H₂Se存在，1100 K开始生成SeS和Se₂气体，1800 K时主要是气态Se和少量气态SeO；Pb在中低温时主要是PbS，1800 K以上气态Pb为主要存在形态。S在还原性气氛下增大了AsS（g）、PbS（g）、SeS（g）的比例，氧化性气氛下对As、Se、Pb形态分布基本无影响；Cl无论在氧化还是还原气氛下对As、Se影响均较小，但对Pb的形态分布影响较大。