Solution of certain weakly singular integral equations of the first kind with indefinite parameters

In this paper we study a two-dimensional weakly singular integral equation of the first kind with logarithmic kernel. We construct a pair of spaces of the desired elements and the right-hand sides, where we prove the correctness of the problem under consideration and obtain inversion formulas for the integral operator.     

合肥光源交错刀片型光位置检测器的研制

为了减小同步光尺寸对同步光位置检测器灵敏度的影响,合肥光源新研制了一种交错刀片型光位置检测器,并使用成熟的商业化产品Libera Photon进行后续的数据处理和输出。基于传统计算光位置信号的差比和方法,提出了比值和对数比两种新的计算方法,理论模拟了3种计算方法下交错刀片型光位置检测器的性能。在线标定结果与理论计算结果相符,并在机器研究光束线进行了初步的应用研究。     

几何凸(凹)函数积分的上(下)界比较及其一般结果

运用齐次函数的分析性质,在基本不等式中插入了一个齐次加权"平均",推广加细了基本不等式.作为特例,得到了加权的对数,指数平均不等式,从而部分解决了文[1]提出的问题.     

Finitely convergent cutting planes for concave minimization

In 1964 Tuy introduced a new type of cutting plane, the concavity cut, in the context of concave minimization. These cutting planes, which are also known as convexity cuts, intersection cuts and Tuy cuts, have found application in several algorithms, e.g., branch and bound algorithm, conical algorithm and cutting plane algorithm, and also in algorithms for other optimization problems, e.g., reverse convex programming, bilinear programming and Lipschitzian optimization. Up to now, however, it has not been possible to either prove or disprove the finite convergence of a pure cutting plane algorithm for concave minimization based solely on these cutting planes. In the present paper a modification of the concavity cut is proposed that yields deeper cutting planes and ensures the finite convergence of a pure cutting plane algorithm based on these cuts.     

Exponential convergence rate in Boltzmann-Shannon entropy

This paper deals with the optimal exponential convergence rate β to the equilibrium state in Boltzmann-Shannon entropy for general Markov semigroups. We prove a variational formula of β, and then discuss the relation among β, spectral gap λ and logarithmic Sobolev constant α, which is read as λ≥β≥α.     

Exponential convergence rate in entropy

The exponential convergence rate in entroy is studied for symmetric forms, with a special attention to the Markov chain with a state space having two points only. Some upper and lower bounds of the rate are obtained and five examples with precise or qualitatively exact estimates are presented.      

An exactly solved model of three-dimensional surface growth in the anisotropic KPZ regime

We generalize the surface growth model of Gates and Westcott to arbitrary inclination. The exact steady growth velocity is of saddle type with principal curvatures of opposite sign. According to Wolf, this implies logarithmic height correlations, which we prove by mapping the steady state of the surface to world lines of free fermions with chiral boundary conditions.     

A method for portfolio choice

This paper shows how one can use the theory of hidden Markov models for portfolio optimization. We illustrate our method by a ball and urn experiment. An application to historical data is examined. Copyright © 2003 John Wiley & Sons, Ltd.     

On a characterization question for symmetric random variables

If X₁, X₂ are independent with common density g symmetric about zero, then $\text{P(X}{}_1\text{+ αX}{}_2\text{> 0) =}\text{1}\text{2}$ for all real α. We provide a counter example to show that the converse is false and thus settle a question posed by Burdick (1972).     

关于对数平均的若干极限定理

关于算术平均和几何平均极限定理在许多文献中有所研究,本文主要给出对数平均大数定律成立的若干充分条件.