Bcklund变换与n孤子解

本文首先证明了KdV方程与sine-Gordon方程不同形式的Backlund变换是相互等价的;其次从双线性导数形式的Backlund变换出发给出多孤子解的Hirota表示与Wronski行列式表示,并利用Vandermonde行列式说明这两种孤子解的表示是一致的.     

图像的色彩分割技术在等差线处理中的应用研究

提出一种基于图像色彩分割的等差线提取新技术,即采用彩色图像卡和摄像机,以白光照射下应力模型在圆偏振光场中等差线条纹的颜色为标志,采用符合人类视觉特征的HSI颜色空间来表示图像的颜色特征,根据“最小色差准则”对等差线进行颜色聚类,实现等差线的快速、准确提取。     

The number of bound states of a one-particle Hamiltonian on a three-dimensional lattice

We consider the Hamiltonian , describing the motion of one quantum particle on a three-dimensional lattice in an external field. We investigate the number of eigenvalues and their arrangement depending on the value of the interaction energy for μ ≥ 0 and λ ≥ 0. __________ Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 158, No. 3, pp. 425–443, March, 2009.     

Elliptic enumeration of nonintersecting lattice paths

We enumerate lattice paths in the planar integer lattice consisting of positively directed unit vertical and horizontal steps with respect to a specific elliptic weight function. The elliptic generating function of paths from a given starting point to a given end point evaluates to an elliptic generalization of the binomial coefficient. Convolution gives an identity equivalent to Frenkel and Turaev's summation. This appears to be the first combinatorial proof of the latter, and at the same time of some important degenerate cases including Jackson's and Dougall's summation. By considering nonintersecting lattice paths we are led to a multivariate extension of the summation which turns out to be a special case of an identity originally conjectured by Warnaar, later proved by Rosengren. We conclude with discussing some future perspectives.     

Some inequalities for characteristic functions. II

Recently we established Matysiak and Szablowski's conjecture [V. Matysiak, P.J. Szablowski, Theory Probab. Appl. 45 (2001) 711-713] about a lower bound of real-valued characteristic functions. In this paper, applying an alternative approach we are able to give explicitly the ranges of argument for which the obtained inequalities hold true for general characteristic functions.     

{Omega}-Admissible Theory

Arakelov and Faltings developed an admissible theory on regulararithmetic surfaces by using Arakelov canonical volume formson the associated Riemann surfaces. Such volume forms are inducedfrom the associated Kähler forms of the flat metric onthe corresponding Jacobians. So this admissible theory is inthe nature of Euclidean geometry, and hence is not quite compatiblewith the moduli theory of Riemann surfaces. In this paper, wedevelop a general admissible theory for arithmetic surfaces(associated with stable curves) with respect to any volume form.In particular, we have a theory of arithmetic surfaces in thenature of hyperbolic geometry by using hyperbolic volume formson the associated Riemann surfaces. Our theory is proved tobe useful as well: we have a very natural Weil function on themoduli space of Riemann surfaces, and show that in order tosolve the arithmetic Bogomolov-Miyaoka-Yau inequality, it issufficient to give an estimation for Petersson norms of somemodular forms. 1991 Mathematics Subject Classification: 11G30,11G99, 14H15, 53C07, 58A99.     

有理样条不可约解的行列式表示

１引言在文［１］中,对于剖分ａ＝ｘ０＜ｘ１＜…＜ｍｎ＝ｂ及给定的ｙ０,ｙ１,…,　…,Ｌ＋Ｍ－１,我们构造了有理样条Ｓ［Ｌ,Ｍ（ｘ）Ｑ［Ｌ,Ｍ］为次数不超过ｍ的多项式全体．在［１］中,已经讨论了Ｓ［Ｌ,Ｍ］（ｘ）的存在性,并指出：若问题（１）（２）（３）可解,则解唯一这里总假设问题（１）（２）（３）可解．２有理样条解不可约的充要条件由Ｓ［Ｌ,Ｍ］（ｘ）的依区间递推算法（见［１］）,我们只需讨论［ｘ０,ｘ１］上的情形．当［Ｘ０,ｘ１］时,将Ｓ［Ｌ,Ｍ］　（ｘ）,Ｐ［Ｌ,Ｍ］　（ｘ）和Ｑ［Ｌ,Ｍ］（…     

求条件极值的一种新方法

利用线性代数的理论方法,对多元函数求条件极值的拉格朗日乘数法加以改进,建立了求条件极值的一种新方法     

基于NSGAII的协同产品开发项目自动协商决策

供应链环境下的协同产品开发项目中,核心企业与合作企业之间,需要对项目工期、预算和质量进行协商。科学高效的协商决策方法有助于协同产品开发项目参与各方实现双赢的协商目标。采用多Agent系统建立了协商问题的框架,构建了协商Agent以自身效用最大化和与对方建议相似度最大化为目标的多目标反建议模型;提出了基于NSGAII的自动协商决策算法,算法采用了正整数和小数混合的实数编码方式,并在遗传操作中增加了约束限制,剔除不可行个体。计算机仿真实验结果表明了算法对提高协商成功率和协商效果的有效性,说明了协商Agent可接受的最低效用值对于协商结果的影响。     

Improved second derivative test for relative extrema

In this note, a modified Second Derivative Test is introduced for the relative extrema of a single variable function. This improved test overcomes the difficulty of the second derivative vanishing at the critical point, while in contrast the traditional test fails for this case. A proof for this improved Second Derivative Test is presented, followed by an example.