Monte Carlo studies of the square Ising model with next-nearest-neighbor interactions

We apply a new entropic scheme to study the critical behavior of the square-lattice Ising model with nearest- and next-nearest-neighbor antiferromagnetic interactions. Estimates of the present scheme are compared with those of the Metropolis algorithm. We consider interactions in the range where superantiferromagnetic (SAF) order appears at low temperatures. A recent prediction of a first-order transition along a certain range (0.5–1.2) of the interaction ratio (R=J_nnn/J_nn) is examined by generating accurate data for large lattices at a particular value of the ratio (R=1). Our study does not support a first-order transition and a convincing finite-size scaling analysis of the model is presented, yielding accurate estimates for all critical exponents for R=1. The magnetic exponents are found to obey “weak universality” in accordance with a previous conjecture.     

非平面图的色数算法

本文对非平面无向简单图的点着色问题进行分析研究后,提出了一个点色数算法.该算法不仅给出了非平面图求点色数的方法,同时也解决了着色方法.并且对算法所涉及的有关性质定理给出了证明.     

Periodic Solutions of a Nonlinear Evolution Problem

In this paper we prove existence of periodic solutions to a nonlinear evolution system of second order partial differential equations involving the pseudo-Laplacian operator. To show the existence of periodic solutions we use Faedo-Galerkin method with a Schauder fixed point argument.     

一类正则锥在非线性奇异边值中的应用

本文构造了一个新的正则锥,运用非紧减算子的不动点定理,得到了一类非线性奇异边值问题正解的唯一性,改进了有关结果.     

Large deviations of sojourn times in processor sharing queues

This paper presents a large deviation analysis of the steady-state sojourn time distribution in the GI/G/1 PS queue. Logarithmic estimates are obtained under the assumption of the service time distribution having a light tail, thus supplementing recent results for the heavy-tailed setting. Our proof gives insight into the way a large sojourn time occurs, enabling the construction of an (asymptotically efficient) importance sampling algorithm. Finally our results for PS are compared to a number of other service disciplines, such as FCFS, LCFS, and SRPT. 2000 mathematics subject classification: 60K25.     

一类二阶常微分方程奇异边值问题多重解的至少个数

本文利用变分原理和Z2不变群指标研究了二阶常微分方程边值问题的多重解．得出了这类解个数的下界估计     

一种基于时域和频域特征的图像拼接方法

1 引言图像拼接是指将具有部分景物重合的图像进行无缝拼合,生成一张具有较宽视角的高分辨率图像的技术．现有的图像拼接技术主要有两类:基于区域的方法和基于特征的方法．基于区域的方法[1]通常是取参考图像中某一窗口中的点作为特征模板,建立描述     

Superconvergence of Continuous Finite Elements with Interpolated Coeffcients for Initial Value Problems of Nonlinear Ordinary Differential Equation

In this paper, n-degree continuous finite element method with interpolated coefficients for nonlinear initial value problem of ordinary differential equation is introduced and analyzed. An optimal superconvergence u-uh = O(hn+2), n ≥ 2, at (n + 1)-order Lobatto points in each element respectively is proved. Finally the theoretical results are tested by a numerical example.     

Avoided level crossings and singular points

Avoided crossings of discrete states as well as of resonance states are traced back to the existence of branch points (BPs) which are singular points in the complex energy plane. They cannot be identified with exceptional points. At a BP width bifurcation occurs, different Riemann sheets evolve and the levels do not cross anymore when the system is still further opened. The BPs are physically meaningful: they influence the dynamics of open as well as of closed quantum systems. The geometric phase that arises by encircling a BP, is different from the phase that appears by encircling a diabolic point. This is found to be true even for the two BPs into which the diabolic point is unfolded by opening the system. Presented at the 3rd International Workshop “Pseudo-Hermitian Hamiltonians in Quantum Physics”, Istanbul, Turkey, June 20–22, 2005.     

关于Poincare—Hopf的奇点指数公式

在一般的文献中，Poincare-Hopf的曲面奇点指数公式的证明需要利用Euler的曲面示性数公式。本文将通过微分方程的定性方法，直接证明了Poincare-Hopf的奇点指数公式，然后作为简单的应用可得到Euler的曲面示性数公式。