3类图完美匹配的数目

图的完美匹配计数问题是匹配理论研究中的一个重要课题,此问题有很强的物理学和化学背景．但是,一般图的完关匹配计数问题却是NP-困难的．用划分、求和、再递推的方法给出了三类特殊图完美匹配数目的计算公式．     

东亚北部地区气温的冬季-冬季再现特征研究

对东亚北部(40—50°N,100—130°E)区域1953—2012年大气温度的冬季-夏季-次年冬季(简称冬季-冬季)的季节变化特征进行了初步研究.结果表明:2008年以来,该区域的气温从低层至高层(1000—400 h Pa)连续三年出现冬季偏冷-夏季偏暖-次年冬季偏冷的典型特征,20世纪50—60年代亦有类似情况;而20世纪90年代则出现了与此相反的冬季偏暖-夏季偏冷-次年冬季偏暖的变化特征.将这种典型的气温季节变化特征定义为一种新的变化机理:冬季-冬季再现(WWR).根据1953—2012年的历年变化情况将这60年划分为四种不同的类型:负(正)冬季-冬季再现(negative/positive WWR)型和负(正)冬季-冬季非再现(negative/positive non-WWR)型.其中,气温表现为WWR型的年份共计23年,出现概率近40%,并且该WWR特征是相对独立于El Nio-南方涛动指数的变化而存在的.对不同类型年份的位势高度场、垂直速度场及其850 h Pa风场进行的合成分析表明:对于WWR型,高层(500 h Pa)至低层(1000 h Pa)的大气内部动力过程具有与气温相匹配的冬季-冬季的再现特征;而non-WWR型则没有出现类似的特征,从而在一定程度验证了WWR存在的可能性.WWR的提出为进一步开展当前全球增暖背景下冬季低温事件的频发提供了一个新的思路.     

An infinite family of Legendrian torus knots distinguished by cube number

For a knot K the cube number is a knot invariant defined to be the smallest n for which there is a cube diagram of size n for K. There is also a Legendrian version of this invariant called the Legendrian cube number. We will show that the Legendrian cube number distinguishes the Legendrian left hand torus knots with maximal Thurston-Bennequin number and maximal rotation number from the Legendrian left hand torus knots with maximal Thurston-Bennequin number and minimal rotation number.     

Phase retrieval from spectral interferograms including a stationary-phase point

We report on a simple processing procedure to retrieve the phase from spectral interferograms including a stationary-phase point. First, the numerical simulations are performed to demonstrate high precision of the phase retrieval from the spectral interferogram. Second, the feasibility of the procedure is confirmed in processing the experimental data from a dispersive Michelson interferometer comprising a cube beam splitter and a plate made of BK7 optical glass. From the retrieved spectral phase, the effective thickness of the BK7 optical glass is determined precisely.     

Approximation by Discrete GB-Splines

This paper addresses the definition and the study of discrete generalized splines. Discrete generalized splines are continuous piecewise defined functions which meet some smoothness conditions for the first and second divided differences at the knots. They provide a generalization both of smooth generalized splines and of the classical discrete cubic splines. Completely general configurations for steps in divided differences are considered. Direct algorithms are proposed for constructing discrete generalized splines and discrete generalized B-splines (discrete GB-splines for short). Explicit formulae and recurrence relations are obtained for discrete GB-splines. Properties of discrete GB-splines and their series are studied. It is shown that discrete GB-splines form weak Chebyshev systems and that series of discrete GB-splines have a variation diminishing property.     

一类两个指标的非常系数线性递推式之解

根据代数方程的求解原理 ,利用传统的数学归纳方法 ,通过严密的推导得到了一类两个指标的非常系数线性递推式的显式解 ,从而为解决与之相关的定解问题 ,提供了一个统一、具体的计算公式 .     

The Number of Solutions of Polynomial-Exponential Equations

We will give explicit bounds for the numberof solutions of polynomial-exponential equations.In contrast to earlier work, the bounds areindependent of the coefficients of the equations,and they are of only single exponential growthin the number of coefficients.     

Semiclassical Calculation of Recurrence Spectra of He Rydberg Atom in Strong External Fields

Using core-scattered closed-orbit theory and region-splitting iterative method, we calculated the scaled recurrence spectra of helium atom in parallel electric and magnetic fields. Closed orbits in the corresponding classical system have also been obtained. When we search the closed orbits, in order to remove the Coulomb singularity of the classical Hamiltonian motion equations, we implement the Kustaanheimo-Stiefel transformation, which transforms the system from a three-dimensional to a four-dimensional one. The Fourier transformed spectrum of helium atom has allowed direct comparison between peaks in such plot and the scaled action values of closed orbits. The results are compared with those of the hydrogen case, which shows that the core-scattered effects play an important role in the recurrence spectra of the multi-electron Rydberg atom.     

Semiclassical calculation of the recurrence spectra of He Rydberg atom in perpendicular electric and magnetic fields

Closed orbit theory is a semiclassical technique for explaining the spectra of Rydberg atoms in external fields. By developing the closed orbit theory from two degrees of freedom to three non-separable degrees of freedom, we calculated the recurrence spectra of He Rydberg atom in perpendicular electric and magnetic fields. The closed orbits in the corresponding classical system have also been obtained. Fourier transformed spectra of He atoms have allowed direct comparison between the resonance peaks and the scaled action values of closed orbits, whereas the nonhydrogenic resonance can be explained in terms of the new orbits created by the core scattering. The semiclassical result is in good agreement with the quantum spectra, which suggests that our method is correct.     

Linear recurrence relations in the algebra of matrices and applications

We study here some linear recurrence relations in the algebra of square matrices. With the aid of the Cayley–Hamilton Theorem, we derive some explicit formulas for Aⁿ (nr) and e^tA for every r×r matrix A, in terms of the coefficients of its characteristic polynomial and matrices A^j, where 0jr−1.