Magnetic behavior of the bond random mixed compound FE(BR x I1−x )2(x = 0.9) with Mössbauer spectroscopy

The bond random mixed compound Fe(Br_0.9I_0.1)₂ has been studied by magnetization and Mössbauer measurements. Although the zero-field cooled and field-cooled magnetization variations are not like a typical spin glass one, the Mössbauer spectrum below Néel temperature shows a hyperfine field distribution. It implies that the 10% FeI₂ mixed in FeBr₂ can be induced by the bond random effect which causes the sample to exhibit a spin glass-like behavior.     

Recognition of the Finite Simple Groups F 4(2m) by Spectrum

The spectrum of a finite group is the set of its element orders. A finite group G is said to be recognizable by spectrum, if every finite group with the same spectrum as G is isomorphic to G. The purpose of the paper is to prove that for every natural m the finite simple Chevalley group F ₄(2 ^m ) is recognizable by spectrum.     

Vassiliev invariants for braids on surfaces

We show that Vassiliev invariants separate braids on a closed oriented surface, and we exhibit a universal Vassiliev invariant for these braids in terms of chord diagrams labeled by elements of the fundamental group of the surface.

     

Mass‐lumping or not mass‐lumping for eigenvalue problems

In this article we analyze the effect of mass‐lumping in the linear triangular finite element approximation of second‐order elliptic eigenvalue problems. We prove that the eigenvalue obtained by using mass‐lumping is always below the one obtained with exact integration. For singular eigenfunctions, as those arising in non convex polygons, we prove that the eigenvalue obtained with mass‐lumping is above the exact eigenvalue when the mesh size is small enough. So, we conclude that the use of mass‐lumping is convenient in the singular case. When the eigenfunction is smooth several numerical experiments suggest that the eigenvalue computed with mass‐lumping is below the exact one if the mesh is not too coarse. © 2003 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 19: 653–664, 2003     

Maximum norms of random sums and transient pattern formation

Many interesting and complicated patterns in the applied sciences are formed through transient pattern formation processes. In this paper we concentrate on the phenomenon of spinodal decomposition in metal alloys as described by the Cahn-Hilliard equation. This model depends on a small parameter, and one is generally interested in establishing sharp lower bounds on the amplitudes of the patterns as the parameter approaches zero. Recent results on spinodal decomposition have produced such lower bounds. Unfortunately, for higher-dimensional base domains these bounds are orders of magnitude smaller than what one would expect from simulations and experiments. The bounds exhibit a dependence on the dimension of the domain, which from a theoretical point of view seemed unavoidable, but which could not be observed in practice.

In this paper we resolve this apparent paradox. By employing probabilistic methods, we can improve the lower bounds for certain domains and remove the dimension dependence. We thereby obtain optimal results which close the gap between analytical methods and numerical observations, and provide more insight into the nature of the decomposition process. We also indicate how our results can be adapted to other situations.

     

Escape Through a Small Opening: Receptor Trafficking in a Synaptic Membrane

We model the motion of a receptor on the membrane surface of a synapse as free Brownian motion in a planar domain with intermittent trappings in and escapes out of corrals with narrow openings. We compute the mean confinement time of the Brownian particle in the asymptotic limit of a narrow opening and calculate the probability to exit through a given small opening, when the boundary contains more than one. Using this approach, it is possible to describe the Brownian motion of a random particle in an environment containing domains with small openings by a coarse grained diffusion process. We use the results to estimate the confinement time as a function of the parameters and also the time it takes for a diffusing receptor to be anchored at its final destination on the postsynaptic membrane, after it is inserted in the membrane. This approach provides a framework for the theoretical study of receptor trafficking on membranes. This process underlies synaptic plasticity, which relates to learning and memory. In particular, it is believed that the memory state in the brain is stored primarily in the pattern of synaptic weight values, which are controlled by neuronal activity. At a molecular level, the synaptic weight is determined by the number and properties of protein channels (receptors) on the synapse. The synaptic receptors are trafficked in and out of synapses by a diffusion process. Following their synthesis in the endoplasmic reticulum, receptors are trafficked to their postsynaptic sites on dendrites and axons. In this model the receptors are first inserted into the extrasynaptic plasma membrane and then random walk in and out of corrals through narrow openings on their way to their final destination.     

A boundary element method for the calculation of noise barrier insertion loss in the presence of atmospheric turbulence

Atmospheric turbulence is an important factor that limits the amount of attenuation a barrier can provide in the outdoor environment. It is therefore important to develop a reliable method to predict its effect on barrier performance. The boundary element method (BEM) has been shown to be a very effective technique for predicting barrier insertion loss in the absence of turbulence. This paper develops a simple and efficient modification of the BEM formulation to predict the insertion loss of a barrier in the presence of atmospheric turbulence. The modification is based on two alternative methods: (1) random realisations of log-amplitude and phase fluctuations of boundary sources and (2) de-correlation of source coherence using the mutual coherence function (MCF). An investigation into the behaviours of these two methods is carried out and simplified forms of the methods developed. Some systematic differences between the predictions from the methods are found. When incorporated into the BEM formulation, the method of random realisations and the method of MCF de-correlation provide predictions that agree well with predictions by the parabolic equation method and by the scattering cross-section method on a variety of thin barrier configurations.     

一些随机重合点定理

本文引入了一种满足更一般的收缩不等式的多重函数类,并证明了属于该类的可测多重函数对的一些随机重合点定理。     

Discrete limit theorems for general Dirichlet series. III

Here we prove a limit theorem in the sense of the weak convergence of probability measures in the space of meromorphic functions for a general Dirichlet series. The explicit form of the limit measure in this theorem is given. Partially supported by Lithuanian Foundation of Studies and Science     

B值随机变量阵列加权和的完全收敛性

设{X_ni:1≤i≤n,n≥1}为行间独立的B值r.v.阵列,g(z)是指数为1/p的正则变化函数,r>0,{ani 1≤t≤n,n≥1}为实数阵列,本文得到了使(?)成立的条件,推广并改进了Stout及Sung等的著名结论.