A remark on the Kochen-Specker theorem and some characterizations of the determinant on sets of Hermitian matrices

In this paper we describe the general forms of all (nonlinear) continuous functionals on the sets of positive definite, positive semi-definite and Hermitian matrices which are multiplicative on the commuting elements. As a consequence, we obtain some new characterizations of the determinant on those classes of matrices.

     

对正项级数敛散性判别法的关系的一些探讨

先对正项级数敛生判别法的粗细与强弱问题进行了辨析，然后建立了三个有关正项级数剑散判别的命题，分别比较了三组判别法之间的强弱关系。     

On the Exceptional Zeros of Rankin–Selberg L-Functions

The main objects of study in this article are two classes of Rankin–Selberg L-functions, namely L(s,f×g) and L(s, sym²(g)× sym²(g)), where f,g are newforms, holomorphic or of Maass type, on the upper half plane, and sym²(g) denotes the symmetric square lift of g to GL(3). We prove that in general, i.e., when these L-functions are not divisible by L-functions of quadratic characters (such divisibility happening rarely), they do not admit any LandauSiegel zeros. Such zeros, which are real and close to s=1, are highly mysterious and are not expected to occur. There are corollaries of our result, one of them being a strong lower bound for special value at s=1, which is of interest both geometrically and analytically. One also gets this way a good bound onthe norm of sym²(g).     

半正二阶三点边值问题的解和正解

考察了非线性二阶三点边值问题的n个解和正解的存在性,其中允许非线性项有一个负的下界并且n是一个任意的自然数．主要结论表明该问题可以具有n个解或者正解,只要非线性项在某些有界集上的“高度”是适当的．     

DIRICHLET BOUNDARY VALUE PROBLEMS FOR SECOND-ORDER QUASI-LINEAR DIFFERENTIAL EQUATIONS WITH CHANGING SIGN NONLINEARITIES

This paper is concerned with the existence of positive solutions of two-point Dirichlet singular and nonsingular boundary problems for second-order quasi-linear differential equations with changing sign nonlinearities.     

动态等值论在文学翻译中的应用

美国的尤金·奈达博士(Dr.Eugene A. Nida)的动态等值论(Dynamic Equivalence)被许多学者推崇为评判译文质量优劣的标准以及翻译所追求的最终目标.在运用奈达的"动态等值"论来指导文学翻译时,应注意的问题是,译文如果要准确传递原文信息就要充分体现原作者的美学意图,这样才能使译文受众获得和原文受众基本一致的感觉.     

改编的好作品难得的好教材--叶露生钢琴曲《蓝花花的故事》探微

叶露生改编的钢琴曲<蓝花花的故事>成功地利用了原始民歌音调,采用变奏形式,运用钢琴语言,塑造了以蓝花花为主人公的多个形象,情感丰富,爱憎分明,是一部改编的好作品,难得的好教材.     

关于正定可对称化线性代数方程组的预对称正则化算法

1引言考虑线性代数方程组A_x=b,A∈R~(n×n)非奇异,x,b∈R~n(1)的求解．当系数矩阵是大型稀疏的正定可对称化矩阵,文[1,2]讨论了一类预对称共轭梯度算法(LRSCG算法是其中之一),这类算法的实质是利用非对称的系数矩阵可对称化的性质,并结合共轭梯度法而构造的一种预处理的共轭梯度法[12,16,17]．但非对称的系数     

覆氧或氧离子轰击下固体表面二次正离子发射的研究

通过对离子轰击下固体表面电离过程重新考虑认为，在固体表面覆氧或氧离子轰击下除表面原子的直接电离外，激发态双原子间电子交换和断键亦起重要作用。在此基础上修正了局部热力学平衡模型，得到了一个包含各类离子内配分函数、电离能、金属－氧原子键断键能以及表面金属原子与氧原子结合份数等参数决定的新电离几率分析表达式。应用该分析表达式解释了金属表面覆氧、氧离子轰击金属、化合物半导体表面二次离子发射中氧增强效应、充氧量对二次离子发射的影响及其基体效应等实验现象。并由此得到了元素相对灵敏度因子的分析表达式，对化合物半导体及一些陶瓷材料表面二次离子质谱分析中元素灵敏度因子随元素电离能变化曲线给予了相应的物理解释。     

Triple Positive Solutions of Boundary Value Problems for High-order Fractional Differential Equation at Resonance with Singularities

In this paper, we investigate the existence of triple positive solutions of boundary value problems for high-order fractional differential equation at resonance with singularities by using the fixed point index theory and the Leggett-Williams theorem. The spectral theory and some new height functions are also employed to establish the existence of triple positive solutions. The nonlinearity involved is arbitrary fractional derivative, and permits singularity.