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…     

具超前变元的二阶微分方程三点边值问题的正解

§ 1　 IntroductionRecently,certain three-point boundary value problems for nonlinear ordinarydifferential equations have been studied by many authors[1— 6] .However,few papers havebeen published on the same problems for nonlinear functional differential equations.In thispaper,we are concerned with the following second order differential equation with anadvanced argumentu″(t) +λa(t) f(u(h(t) ) ) =0 ,t∈ (0 ,1 ) (1 .1 )with the three-point boundary conditionsu(0 ) =0 ,αu(η) =u(1 ) ,(1 .2 )…     

具有功能反应的两斑块扩散时滞竞争系统正周期解的存在性

§ 1　ＩｎｔｒｏｄｕｃｔｉｏｎＦｏｒｍａｎｙｓｐｅｃｉｅｓｔｈｅｓｐａｔｉａｌｆａｃｔｏｒｓａｒｅｉｍｐｏｒｔａｎｔｉｎｐｏｐｕｌａｔｉｏｎｄｙｎａｍｉｃｓ .Ｔｈｅｔｈｅｏｒｅｔｉｃａｌｓｔｕｄｙｏｆｓｐａｔｉａｌｄｉｓｔｒｉｂｕｔｉｏｎｈａｓｂｅｅｎｅｘｔｅｎｓｉｖｅｌｙｓｔｕｄｉｅｄｉｎｍａｎｙｐａｐｅｒｓ .Ｍｏｓｔｏｆｔｈｅｐｒｅｖｉｏｕｓｐａｐｅｒｓｆｏｃｕｓｅｄｏｎｔｈｅｃｏｅｘｉｓｔｅｎｃｅｏｆｐｏｐｕｌａｔｉｏｎｓｍｏｄｅｌｌｅｄｂｙｓｔｓｔｅｍｓｏｆｏｒｄｉｎａｒｙｄｉｆｆｅｒｅ…     

一个来自振动理论反问题的矩阵方程

§ 1　ＩｎｔｒｏｄｕｃｔｉｏｎＬｅｔＲｎ×ｍｄｅｎｏｔｅｔｈｅｒｅａｌｎ×ｍｍａｔｒｉｘｓｐａｃｅ ,Ｒｎ×ｍｒ ｉｔｓｓｕｂｓｅｔｗｈｏｓｅｅｌｅｍｅｎｔｓｈａｖｅｒａｎｋｒ ,ＯＲｎ×ｎｔｈｅｓｅｔｏｆａｌｌｎ×ｎｏｒｔｈｏｇｏｎａｌｍａｔｒｉｃｅｓ,ＳＲｎ×ｎ(ＳＲｎ×ｎ≥ ,ＳＲｎ×ｎ>)ｔｈｅｓｅｔｏｆａｌｌｎ×ｎｒｅａｌｓｙｍｍｅｔｒｉｃ (ｓｙｍｍｅｔｒｉｃｐｏｓｉｔｉｖｅｓｅｍｉｄｅｆｉｎｉｔｅ ,ｐｏｓｉｔｉｖｅｄｅｆｉｎｉｔｅ)ｍａｔｒｉｃｅｓ.ＴｈｅｎｏｔａｔｉｏｎＡ>0 (≥ 0 ,<0 ,≤ 0 )ｍ…     

直径不超过4的树的割宽

§ 1　IntroductionThe cutwidth problem for graphs,as well as a class of optimal labeling and embed-ding problems,have significant applications in VLSI designs,network communicationsand other areas (see [2 ] ) .We shall follow the graph-theoretic terminology and notation of [1 ] .Let G=(V,E)be a simple graph with vertex set V,| V| =n,and edge set E.A labeling of G is a bijec-tion f:V→ { 1 ,2 ,...,n} ,which can by regarded as an embedding of G into a path Pn.Fora given labeling f of G,th…     

WEIGHTED APPROXIMATION ON SZASZ—TYPE OPERATORS

In this paper, we use weighted modules ω(?)(f,t)w to study the pointwise approximation on Szasz-type operators, and obtain the direct and converse theorem, as well as characterizations of the pointwise approximation of Jacobi-weighted Szasz-type operators.     

A Fair Allocation of County Cricket Opponents

Each team in the English County Cricket Championship plays against some other teams twice a year, and others only once. This paper describes a case study whose aim was to overcome this inherent unfairness by producing a four-year schedule of opponents which was as fair as possible, and could be easily seen to be fair, while still allowing for traditional rivalries. The schedule also needed to be satisfactory in regard to several other constraints and objectives. Various simple heuristics were used; these are described in some detail. Of particular interest is the effectiveness of a ‘local non-worsening’ approach when the objective is to find any feasible solution. This is equivalent to simulated annealing at a constant temperature of absolute zero.     

The sense of smell,its signalling pathways,and the dichotomy of cilia and microvilli in olfactory sensory cells

Smell is often regarded as an ancillary perception in primates, who seem so dominated by their sense of vision. In this paper, we will portray some aspects of the significance of olfaction to human life and speculate on what evolutionary factors contribute to keeping it alive. We then outline the functional architecture of olfactory sensory neurons and their signal transduction pathways, which are the primary detectors that render olfactory perception possible. Throughout the phylogenetic tree, olfactory neurons, at their apical tip, are either decorated with cilia or with microvilli. The significance of this dichotomy is unknown. It is generally assumed that mammalian olfactory neurons are of the ciliary type only. The existence of so-called olfactory microvillar cells in mammals, however, is well documented, but their nature remains unclear and their function orphaned. This paper discusses the possibility, that in the main olfactory epithelium of mammals ciliated and microvillar sensory cells exist concurrently. We review evidence related to this hypothesis and ask, what function olfactory microvillar cells might have and what signalling mechanisms they use.