乘方的指数与其幂的位数的关系

为了探究乘方的指数与其幂的位数的关系,定义了几个有关的新概念,并且证明了两个关于乘方以及进制进位的定理,由此建立起关于乘方以及进制进位的理论体系,其中包括进位理论中判定乘方的指数与其幂的位数是否存在周期规律的判别法,以及进位规律的求解法和四条相关的性质.     

树的最大特征值的上界的一个注记

设T是一个树,V是T的顶点集．记dv是υ∈V的度,△是T的最大顶点度．设υ∈V且dw=1．记k=ew+1,这里ew是w的excentricity．设δj′= max{dυ:dist(υ,w)=j},j=1,2,…,k-2,我们证明和这里μ1(T)和λ1(T)分别是T的Laplacian矩阵和邻接矩阵的最大特征值．特别地,记δo′=2．     

计算Hamilton矩阵特征值的一个稳定的有效的保结构的算法

提出了一个稳定的有效的保结构的计算Hamilton矩阵特征值和特征不变子空间的算法,该算法是由SR算法改进变形而得到的。在该算法中,提出了两个策略,一个叫做消失稳策略,另一个称为预处理技术。在消失稳策略中,通过求解减比方程和回溯彻底克服了Bunser Gerstner和Mehrmann提出的SR算法的严重失稳和中断现象的发生,两种策略的实施的代价都非常低。数值算例展示了该算法比其它求解Hamilton矩阵特征问题的算法更有效和可靠。     

不同的公理不同的几何

一位语文老师在博客上写反思.他在教《自相矛盾》这则寓言时,有学生站起来反驳:有这么傻的人么?太不可信了吧.面对这样大胆质疑的学生,这位老师不知如何处理为好! 现在的学生比以前更敢想敢做了.     

纯正的群的正则带的构造

本文研究纯正的群的正则带.在给出这类半群的若干特征后,建立了纯正的群的正则带的构造定理.作为应用,同时给出了纯正的群的右拟正规带的构造定理.     

多维的一般的BBM-Burgers方程解的逐点估计

研究R~n中一般的BBM-Burgers方程解的渐进行为.运用Green函数法和Fourier分析方法得到了在非零常状态u~*附近小扰动解的逐点估计,作为一个推论,又得到了L~p(R~n)(1≤p∞)空间解的最佳的衰减估计.     

自由群的直积的检验元素的注记

本文研究了自由群的直积的检验元素,通过对直积的自同态的分解,得到了直积中的元素为检验元素的充分必要条件,改进了O'neill和Turner的结果.此外,构造了两类具体的检验元素.     

证明圆的切线的常用策略

圆的切线是初中数学的重点内容之一,也是中考的主要考察对象.本文举例介绍证明圆的切线的几种常用策略.一、当讨论的问题涉及圆的半径r及圆心到直线的距离d这样的数量关系时,往往可以     

某类群的增广理想的基底及其商群的结构

本文研究了一类具有完全正规子群的有限群之增广理想及增广商群结构的问题.利用完全群的一些性质及数学归纳法,得到了此类群任意次增广理想的一组基底,并且解决了增广商群的结构问题.     

相同的性质不同的表述

文[1]《2010年四川卷理科20题的引申》一文给出并证明了这样一个性质(表述1.1),这里以焦点在x轴上的椭圆为例.     

矩阵的正规化

本文考虑ｎ阶复矩阵可嵌入到ｎ＋１阶的正规矩阵的条件．证明了ｎ＞２阶的复矩阵不一定可嵌入到ｎ＋１阶的正规矩阵,而２阶复矩阵总可嵌入到３阶正规矩阵中．本文还证明了任意ｎ阶复方阵可嵌入到２ｎ阶正规矩阵中     

On different geometric formulations of Lagrangian formalism

We consider two geometric formulations of Lagrangian formalism on fibred manifolds: Krupka's theory of finite order variational sequences, and Vinogradov's infinite order variational sequence associated with the -spectral sequence. On one hand, we show that the direct limit of Krupka's variational bicomplex is a new infinite order variational bicomplex which yields a new infinite order variational sequence. On the other hand, by means of Vinogradov's -spectral sequence, we provide a new finite order variational sequence whose direct limit turns out to be the Vinogradov's infinite order variational sequence. Finally, we provide an equivalence of the two finite order and infinite order variational sequences modulo the space of Euler-Lagrange morphisms.     

Gompertz分布顺序统计量的一些随机比较

考虑两组相互独立的来自非齐次总体Gompertz分布的样本,给出了最小顺序统计量的反向失效率序、散度序以及凸变换序之间的比较和最大顺序统计量的普通随机序的比较.     

向量优化中有效点的存在性

分别在有pre-order的无线性结构的集合和拓扑空间中，给出了有效点的存在性。作为应用，讨论了向量优化问题中解的存在性。最后给出了紧、弱紧、锥紧、锥半紧、上序紧、下序紧、上序半紧、准上序半紧和准下序半紧等之间的关系。     

Steiner triple systems of order 19 and 21 with subsystems of order 7

Steiner triple systems (STSs) with subsystems of order 7 are classified. For order 19, this classification is complete, but for order 21 it is restricted to Wilson-type systems, which contain three subsystems of order 7 on disjoint point sets. The classified STSs of order 21 are tested for resolvability; none of them is doubly resolvable.     

Some new results on convolutions of heterogeneous gamma random variables

Convolutions of independent random variables often arise in a natural way in many applied areas. In this paper, we study various stochastic orderings of convolutions of heterogeneous gamma random variables in terms of the majorization order [p-larger order, reciprocal majorization order] of parameter vectors and the likelihood ratio order [dispersive order, hazard rate order, star order, right spread order, mean residual life order] between convolutions of two heterogeneous gamma sets of variables wherein they have both differing scale parameters and differing shape parameters. The results established in this paper strengthen and generalize those known in the literature.     

Concerning Order of Convergence for Subdivision

We discuss order of convergence for subdivision algorithms, in the scalar-valued and the vector-valued case. In order to find the generic order, the usual definition of convergence order is extended, refering to a proper quasi interpolant operator whose representation on polynomial spaces can be constructively determined with recourse to properties of the subdivision mask. Assuming stability and smoothness of the limit functions, the approximation order of the quasi interpolant operator determines the order of convergence of subdivision.     

Embedding of function spaces of variable order of differentiation in function spaces of variable order of integration

The paper deals with embeddings of function spaces of variable order of differentiation in function spaces of variable order of integration. Here the function spaces of variable order of differentiation are defined by means of pseudodifferential operators.     

Projective planes of order 12 do not have a collineation group of order 4

In this paper, we prove that there are no projective planes of order 12 admitting a collineation group of order 4. This yields that the order of any collineation group of a projective plane of order 12 is 1, 2, or 3.     

Estimates for The Hyper-Order of Solutions of Certain Linear Differential Equations

In this article, the authors study the growth of certain second order linear differential equation f″＋A（z）f′＋B（z）f=0 and give precise estimates for the hyperorder of solutions of infinite order. Under similar conditions, higher order differential equations will be considered.