COMPLETENESS FOR H_q~p(D) SPACE

Abstract Let D be arbitrary simply connected domain with at least two boundary points.We have introduced a kind of analytic functions' space H_■~V (D) (p≥1, q>0)and shown that it is a complete linear space with respect to the norm ■·||_(H_q~p(D)).     

Network analysis of eigenvalue problem for multilayer dielectric waveguide consisting of arbitrary number of layers

In this paper, the eigenvalue problem of a multilayer dielectric waveguide consisting of arbitrary number of layers is solved by the microwave network method. A general program with the function of computer graphics has been developed for analyzing the dispersion characteristics and the electromagnetic field distributions of an N layer dielectric waveguide. As examples of practical applications of the program, first, the dispersions and field patterns for the planar waveguides with refractive index of parabolic and exponential profiles are analyzed. Secondly, the procedure of mode conversion and mode separation in dielectric branching waveguides is vividly demonstrated through analyzing the field distributions of asymmetric multilayer dielectric structures and the general rules of mode conversion are discussed. The examples show that the present method possesses the advantages of versatility, rapidity, simplicity and accuracy.     

An intermediate distribution between Gaussian and Cauchy distributions

In this paper, we construct an intermediate distribution linking the Gaussian and the Cauchy distribution. We provide the probability density function and the corresponding characteristic function of the intermediate distribution. Because many kinds of distributions have no moment, we introduce weighted moments. Specifically, we consider weighted moments under two types of weighted functions: the cut-off function and the exponential function. Through these two types of weighted functions, we can obtain weighted moments for almost all distributions. We consider an application of the probability density function of the intermediate distribution on the spectral line broadening in laser theory. Moreover, we utilize the intermediate distribution to the problem of the stock market return in quantitative finance.     

Quantum Dynamics in the Fermi–Pasta–Ulam Problem

We study a quantum chain of oscillators with nonlinear quartic interactions, under the “narrow packet” approximation. We analyse the dynamics of quantum corrections and the conditions at which the quantum solution for average complex amplitude converges to the corresponding classical unstable solution which describes the four-wave decay processes of phonons. We develop an asymptotic theory by using a small quasiclassical parameter, and determine the characteristic time scale for which the evolution of decay processes is essentially specified by quantum effects. AMS Subject classification: Primary: 35F10 Secondary: 35Q40, 35B40     

基于柯西分布的视频图像序列背景建模和运动目标检测

提出了一种用于视觉监视系统的基于柯西分布的发光模型的光照不变变化检测方法.假定视频图像序列中每个背景图像像素点灰度观测值的时序变化由白噪声引起,利用建立的初始化背景高斯统计模型对每帧图像进行归一化,得到了背景像灰度比值的分布符合标准柯西分布的结论,解决了柯西分布的模型参量估计问题.在变化检测的基础上,YCbCr颜色空间的亮度、色调和饱和度被用来识别和消除由阴影和反光等引起的变化区域.结果表明,提出的背景建模方法对场景中各种光线变化、小的背景扰动等噪声具有稳健性,可以较为可靠地检测前景目标,识别和去除阴影和反光.     

Elastic behaviour of lead fluoride under pressure

The variation of the second-order elastic constants (SOECs) and the longitudinal and shear modulii with hydrostatic pressure for the lead fluoride (PbF₂) has been investigated for the first time by means of a three-body force potential (TBP) model. The significance of three-body interactions (TBI) has been clearly demonstrated in reproducing the elastic constant variations and the pressure derivatives of SOECs of PbF₂. The equation of state for this crystal has also been reported.     

Symmetry Reduction and Cauchy Problems for a Class of Fourth-Order Evolution Equations

We exploit higher-order conditional symmetry to reduce initial-value problems for evolution equations to Cauchy problems for systems of ordinary differential equations （ODEs）. We classify a class of fourth-order evolution equations which admit certain higher-order generalized conditional symmetries （GCSs） and give some examples to show the main reduction procedure. These reductions cannot be derived within the framework of the standard Lie approach, which hints that the technique presented here is something essential for the dimensional reduction of evolution equations.     

A competitive (dual) simplex method for the assignment problem

Where there is abundance of mystery and confusion in every direction, the truth seldom remains hidden for long. It's a matter of having plenty of angles to go at it from. Only the utterly simple crimes - the simplex crimes, you may say - have the trick of remaining baffling. - Sir John (from Michael Innes,The Open House (A Sir John Appleby Mystery), Penguin Books, 1974).A dual simplex method for the assignment problem leaves open to choice the activity (i,j) of rowi and columnj that is to be dropped in pivoting so long asx _ij < 0. A choice (i,j) over columnsj having at least 3 basic activities that minimizesx _ij is shown to converge in at most ( ₂ ^n-1 ) pivots, and at most O(n ³) time, and it is argued that on average the number of pivots is at mostn logn. Dedicated with affection to George B. Dantzig on the occasion of his seventieth birthday.