Effects of a Degeneracy in the Competition Model: Part II. Perturbation and Dynamical Behaviour

This is the second part of our study on the competition model where the coefficient functions are strictly positive over the underlying spatial region Ω except b(x), which vanishes in a nontrivial subdomain of Ω, and is positive in the rest of Ω. In part I, we mainly discussed the existence of two kinds of steady-state solutions of this system, namely, the classical steady-states and the generalized steady-states. Here we use these solutions to determine the dynamics of the model. We do this with the help of the perturbed model where b(x) is replaced by b(x)+ε, which itself is a classical competition model. This approach also reveals the interesting relationship between the steady-state solutions (both classical and generalized) of the above system and that of the perturbed system.     

Coloring of Double Disk Graphs

We study the problem of minimizing the number of colors for vertex-coloring of double disk graphs and in this note, show a polynomial-time 31-approximation for the problem, which improves an existing result.     

Kp,q-factorization of complete bipartite graphs

Let K _m,nbe a complete bipartite graph with two partite sets having m and n vertices, respectively. A K _p,q-factorization of K _m,n is a set of edge-disjoint K _p,q-factors of K _m,n which partition the set of edges of K _m,n. When p = 1 and q is a prime number, Wang, in his paper “On K _1,k -factorizations of a complete bipartite graph” (Discrete Math, 1994, 126: 359—364), investigated the K _1,q -factorization of K _m,nand gave a sufficient condition for such a factorization to exist. In the paper “K _1,k -factorizations of complete bipartite graphs” (Discrete Math, 2002, 259: 301—306), Du and Wang extended Wang’s result to the case that q is any positive integer. In this paper, we give a sufficient condition for K _m,n to have a K _p,q-factorization. As a special case, it is shown that the Martin’s BAC conjecture is true when p : q = k : (k+ 1) for any positive integer k.     

水母雪莲化学成分的研究（Ⅱ）

前文已报道从水母雪莲(Saussurea Medusa Maxim)中分得4种黄酮甙,本文报道另外6种化合物的分离和鉴定。 1 化合物Ⅰ—Ⅳ物化性质及分离鉴定 1.1 化合物Ⅰ 黄色结晶,m.p.:249～251℃,水解所得甙元鉴定为木樨草素,纸层析检出鼠李糖和葡萄糖。MS(FAB):m/z 595(M~++1),287(M~++H-葡萄糖基-鼠李糖)。化合物I与木樨草素的~(13)C NMR比较,C_6、C_8、C_(10)分别向低场位移1.1、1.0、1.8 ppm,而C,向高场移动     

A modal analysis for the dynamic response of fluid-structure systems

In this paper a theory of modal analysis for the dynamic response of fluid-structure systems is presented. A pair of generalized eigenvalue equations with three real symmetric matrices and their relationships are derived from the finite element equations in the form of structural displacements and fluid velocity potential. Generalized orthogonality relations of modal vectors are then developed. The response of the system to external excitation is derived in closed form by modal expansion. Two examples of the solution are given for illustration.     

Temperature elevation generated by a focused Gaussian ultrasonic beam at a tissue-bone interface

When a focused Gaussian ultrasonic beam in soft tissue normally impinges on the boundary of a contiguous bone, reflection and transmission occur. Taking account of the reflection, the steady-state temperature elevation along the beam axis for this case was calculated. The effect of perfusion is also included.     

Preparation and properties of the single 110 K phase Bi(Pb)-Sr-Ca-Cu-O superconductor

The single 110 K phase Bi(Pb)–Sr–Ca–Cu–O superconductor was made by sintering in air. Its zero-resistance temperature is 106 K, and it is an orthorhombic cell witha=5.403 Å,b=5.412 Å andc=37.062 Å. It formed around the low-T _c phase. The forming period of the 110 K phase can be shortened by multiple sintering and grinding. If PbO is mixed into the samples after the 85 K phase has formed, the forming rate of the 110 K phase can be increased significantly. EDAX analysis of grain composition confirms that the Pb atoms enter the unit cell, and probably Pb cations replace some Ca cations.     

二元光学反／衍混合Schmidt望远系统光学设计

针对空间光学系统轻型的特点，采用衍射光学元件取代Ｓｃｈｍｉｄｔ校正板来校正系统像差，设计了一个二元光学反／衍混合Ｓｃｈｍｉｄｔ望远系统。光学系统的通光孔径为＝２００ｍｍ，相对孔径Ｆ／＃＝１．９，波长λ＝４．３μｍ，视场２ω＝１０°。光学设计采用ＯＳＬＯｓｉｘ软件。光学设计结果：空间频率ν≤６０ｃｙｃｌｅｓ／ｍｍ时，调制传递函数ＭＴＦ≥０．４。