一类q-级数恒等式的新证法

本文利用一个已知的变换公式及其它基本超几何函数的求和公式，给出了一类ｑ级数恒等式的新的更简单的证明，并建立了该类恒等式的一般形式．     

空间l1(Xn)中的弱紧性

本文首先讨论空间l₁(X_n)中的弱收敛性，然后给出了l₁(X_n)中弱紧性的几种等价刻画，同时对l_p(X_n)（１＜ｐ＜∞）中的弱紧性也得到了类似的结果．     

K-f环上格序模的张量积

研究(?)Ｒ_ｉ的由Ｒ_ｉ（ｉ＝１，２，…，ｐ）的序所诱导的序，证明(?)Ｒ_ｉ在一定条件下作成一个有单位元的ｆ环，并在有单位元的Ｋ-ｆ环上的格序模范畴中引入保格Ｒ₁(?)Ｒ₂映射，进一步定义了张量积，使张量积概念在不同序环的序模范畴得到拓展．     

自全国各地100多位理事Road Machinery Branch of China Highway and Transportation Society He

In this paper, a three dimensional ratio-dependent chemostat model with periodically pulsed input is considered. By using the discrete dynamical system determined by the stroboscopic map and Floquet theorem, an exact periodic solution with positive concentrations of substrate and predator in the absence of prey is obtained. When β is less than some critical value the boundary periodic solution (xs(t), 0, zs(t)) is locally stable, and when β is larger than the critical value there are periodic oscillations in substrate, prey and predator. Increasing the impulsive period τ, the system undergoes a series of period-doubling bifurcation leading to chaos, which implies that the dynamical behaviors of the periodically pulsed ratio-dependent predator-prey ecosystem are very complex.     

一类非牛顿渗流方程爆破界的估计

本文利用拟线性常微分方程解的非存在性定理得到了一类拟线性反应扩散方程(非牛顿渗流方程)爆破界的估计,从而推广了半线性反应扩散方程(牛顿渗流方程)相应结果.     

等式与界约束非线性优化信赖域算法的全局收敛

§ 1　ＩｎｔｒｏｄｕｃｔｉｏｎＣｏｎｓｉｄｅｒｔｈｅｆｏｌｌｏｗｉｎｇｎｏｎｌｉｎｅａｒｏｐｔｉｍｉｚａｔｉｏｎｐｒｏｂｌｅｍ :ｍｉｎｉｍｉｚｅｆ(ｘ)ｓｕｂｊｅｃｔｔｏＣ(ｘ) =0 ,　ａ≤ｘ≤ｂ ,( 1 .1 )ｗｈｅｒｅｆ(ｘ) :Ｒｎ→Ｒ ,Ｃ(ｘ) =(ｃ1(ｘ) ,ｃ2 (ｘ) ,...,ｃｍ(ｘ) ) Ｔ:Ｒｎ→Ｒｍ ａｒｅｔｗｉｃｅｃｏｎｔｉｎｕｏｕｓｌｙｄｉｆｆｅｒｅｎｔｉａｂｌｅ,ｍ≤ｎ ,ａ ,ｂ∈Ｒｎ.Ｔｒｕｓｔｒｅｇｉｏｎａｌｇｏｒｉｔｈｍｓａｒｅｖｅｒｙｅｆｆｅｃｔｉｖｅｆｏｒｓｏｌｖｉｎｇｎｏｎｌｉｎｅａｒｏｐｔｉｍｉ…     

两类惯量惟一的对称符号模式

§ 1　 IntroductionA sign pattern(matrix) A is a matrix whose entries are from the set{ +,-,0 } .De-note the setofall n× n sign patterns by Qn.Associated with each A=(aij)∈ Qnis a class ofreal matrices,called the qualitative class of A,defined byQ(A) ={ B =(bij)∈ Mn(R) |sign(bij) =aijfor all i and j} .　　 For a symmetric sign pattern A∈ Qn,by G(A) we mean the undirected graph of A,with vertex set { 1 ,...,n} and (i,j) is an edge if and only if aij≠ 0 .A sign pattern A∈ Qnis a do…     

正交共轭滤波器的构造

It is very importent for generating an orthonormal multiwavelet system to construct a conjugate quadrature filter(CQF). In this paper, a general method of deriving a length-L 1 conjugate quadrature filter from a length-L conjugate quadrature filter and vice versa is obtained. As a special case, we study generally the construction of any length-L 1 compactly supported symmetric-antisymmetric orthonormal multiwavelet system with multiplicity 2 from a length-L multiwavelet system and vice versa. Examples of conjugate quadrature filter are given.     

w-DENSITY AND w-BALANCED PROPERTY OF WEIGHTED GRAPHS

§ 1　IntroductionAll graphsconsidered in this paperare finite undirected ones withoutloops ormultipleedges.Our terminology and notation are standard exceptas indicated.A good reference forany undefined terms is[1 ] .Let G be a graph with vertex set V( G) and edge set E( G) .The density of G is definedbyd( G) =ε( G)ν( G) ,whereν( G) andε( G) denote| V( G) | and| E( G) | ,respectively.G is said to be balanced iffor each subgraph H of G we have d( H )≤ d( G) ,where V( H ) is assum…     

Fréchet空间上的一些等距逼近问题

本文主要讨论Ｆｒéｃｈｅｔ空间上ε－等距线性算子的等距逼近问题，证明了任意有限维Ｆｒéｃｈｅｔ空间之间的等距逼近问题都是肯定的；无穷维Ｆｒéｃｈｅｔ空间（ｓ）空间上的等距逼近问题也是肯定的．