Deviation of Upper Bounds of Critical Temperature of Two-Dimensional O(N) Spin Models

Critical temperature of the classical O(N) spin model in two dimensions is investigated. We show that no phase transition exists in the system if the inverse temperature is less than _c=_c(N), where _c(N) is a constant such that _c(N) > const. N log N.     

四元数体上Minkowski不等式与Bergstrom不等式

我们对四元数体上自共轭半正定矩阵按广义Ｓｃｈｕｒ补给出了Ｂｅｒｇｓｔｒｏｍ不等式的推广。然后应用自共轭半正定矩阵的Ｂｅｒｇｓｔｒｏｍ不等式得到了Ｍｉｎｋｏｗｓｋｉ不等式,我们的结果修正了重行列不等式的一些错误。     

On the modified discrete KP equation with self-consistent sources

The modified discrete KP equation is the Bäcklund transformation for the Hirota’s discrete KP equation or the Hirota-Miwa equation. We construct the modified discrete KP equation with self-consistent sources via source generation procedure and clarify the algebraic structure of the resulting coupled modified discrete KP system by presenting its discrete Gram-type determinant solutions. It is also shown that the commutativity between the source generation procedure and Bäcklund transformation is valid for the discrete KP equation. Finally, we demonstrate that the modified discrete KP equation with self-consistent sources yields the modified differential-difference KP equation with self-consistent sources through a continuum limit. The continuum limit of an explicit solution to the modified discrete KP equation with self-consistent sources also gives the explicit solution for the modified differential-difference KP equation with self-consistent sources.     

Novel Wronskian Condition and New Exact Solutions to a （3＋1）-Dimensional Generalized KP Equation

Utilizing the Wronskian technique, a combined Wronskian condition is established for a （3＋1）-dimensional generalized KP equation. The generating functions for matrix entries satisfy a linear system of new partial differential equations. Moreover, as applications, examples of Wronskian determinant solutions, including N-soliton solutions, periodic solutions and rational solutions, are computed.     

伏安法测电阻时安培表采用内、外接法的判定条件

导出了在物理实验中用伏安法测电阻时安培表采用内、外接法的判定条件,并在实验上给予了验证．     

Hill-Type Formula and Krein-Type Trace Formula for Hamiltonian Systems

In this paper, we give a survey on the Hill-type formula and its applications.Moreover, we generalize the Hill-type formula for linear Hamiltonian systems and Sturm-Liouville systems with any self-adjoint boundary conditions, which include the standard Neumann, Dirichlet and periodic boundary conditions. The Hill-type formula connects the infinite determinant of the Hessian of the action functional with the determinant of matrices which depend on the monodromy matrix and boundary conditions. Further, based on the Hill-type formula, we derive the Krein-type trace formula. As applications, we give nontrivial estimations for the eigenvalue problem and the relative Morse index.     

一道行列式证明题的多种证明方法

针对线性代数教材中一道行列式证明题,利用行列式的性质,给出多种证明方法,旨在启发学生对相关行列式计算或证明题的解题方法进行探索．     

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.     

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.