Nonexistence of bounded energy solutions for a critical exponent problem

In this paper, we discuss positive solutions for certain weighted elliptic equations with critical Sobolev exponent in R^N. The weights depend on a positive parameter γ, which is allowed to increase to infinity. While for small values of γ solutions are completely classified, an attempt to such a classification is much more difficult for large values of the parameter. In the present work we prove the nonexistence of solutions with bounded energy as γ increases to infinity. We also prove a multiplicity result for high energy solutions.     

Gliding motion of bacteria on power‐law slime

The present investigation deals with an undulating surface model for the motility of bacteria gliding on a layer of non‐Newtonian slime. The slime being the viscoelastic material is considered as a power‐law fluid. A hydrodynamical model of motility involving an undulating cell surface which transmits stresses through a layer of exuded slime to the substratum is examined. The non‐linear differential equation resulting from the balance of momentum and mass is solved numerically by a finite difference method with an iteration technique. The manner in which the various exponent values of the power‐law flow affect the structure of the boundary layer is delineated. A comparison is made of the power‐law fluid with the Newtonian fluid. For the power‐law fluid with respect to different power‐law exponent values, shear‐thinning and shear‐thickening effects can be observed, respectively. Copyright © 2004 John Wiley & Sons, Ltd.     

Operator geometric stable laws

Operator geometric stable laws are the weak limits of operator normed and centered geometric random sums of independent, identically distributed random vectors. They generalize operator stable laws and geometric stable laws. In this work we characterize operator geometric stable distributions, their divisibility and domains of attraction, and present their application to finance. Operator geometric stable laws are useful for modeling financial portfolios where the cumulative price change vectors are sums of a random number of small random shocks with heavy tails, and each component has a different tail index.     

The origin of preferential attachment and the generalized preferential attachment for weighted networks

In this paper, we first discuss the origin of preferential attachment. Then we establish the generalized preferential attachment (GPA) which has two new properties; first, it encapsulates both the topological and weight aspects of a network, which makes it is neither entirely degree preferential nor entirely weight preferential. Second, it can tell us not only the chance that each already-existing vertex being connected but also how much weight each new edge has. The GPA can generate four power-law distributions, besides the three for vertex degrees, vertex strengths, and edge weights, it yields a new power-law distribution for the subgraph degrees.     

一种城市路灯合理排布的优化设计方法

文章借助于物理模型和数学计算分析，给出了一种优化的城市路灯排列的设计方法．利用该方法优化出的路灯排列方式（如三角型排列），与现在普遍采用的对称排列方式相比，可以在满足人们交通安全和正常工作生活的条件下，达到节省电力能源的效果；或者是在能源耗费相同的条件下，能提供更高、更均匀的照明度．     

Occurrence, Repetition and Matching of Patterns in the Low-temperature Ising Model

We continue our study of the exponential law for occurrences and returns of patterns in the context of Gibbsian random fields. For the low-temperature plus-phase of the Ising model, we prove exponential laws with error bounds for occurrence, return, waiting and matching times. Moreover we obtain a Poisson law for the number of occurrences of large cylindrical events and a Gumbel law for the maximal overlap between two independent copies. As a by-product, we derive precise fluctuation results for the logarithm of waiting and return times. The main technical tool we use, in order to control mixing, is disagreement percolation     

股市收益率的极限分布

本文提出了一个描述股市收益率与成交量变化率的关系的非线性统计模型.通过这个模型我们证明了收益率序列{rn}依参数不同分别依分布收敛于指数列维稳定分布和列维稳定分布.     

Stopping power measurements of Si in polycarbonate detectors

The rate of energy loss of the impinging ion as it passes through succeeding layers of the target material gives information regarding the nature of the material and helps to calculate the range of the ions in a thick target in which the ions are stopped. In the present work, the range of 118 MeV ²⁸Si was measured in different types of polycarbonates, viz. Makrofol-N, Makrofol-G and Makrofol-KG, using the nuclear track technique. Polyallyldiglycol carbonate (PADC) was used as the backing detector. The experimental values of range and energy-loss rate are compared with the theoretical values obtained from different computer codes, viz. BENTON, HUBERT, RANGE, TRIM’98 and SRIM’03.     

基于二元光学设计的高能激光窗口的初步探讨

对非均匀近场强度分布影响强激光远场聚焦效果的原因进行了分析。对高能激光窗口进行了二元光学设计。提高了光束强度分布的均匀性,改善了光束质量。介绍了二元光学设计的基本原理,采用随机并行扰动爬山法对窗口的位相分布、变换后的光束强度分布、衍射效率和光束均匀性进行了计算。计算结果表明,基于二元光学设计的激光窗口能有效地改善光束强度分布的均匀性,提高了发射光束的质量。     

A power law distribution in patients’ lengths of stay in hospital

The distribution of patients’ lengths of stay in English hospitals is measured by using routinely collected data from 11 years. It is found to be well approximated by a power law distribution spanning over more than three decades. To explain this observation, a theoretical resource allocation model is presented. It is based on iterative long-term scheduling of hospital beds, and its main assumption is that future beds are allocated preferentially. This represents a situation where different parts of the health care system compete for resources, with bargaining powers proportional to current resource levels.