BIFURCATION SOLUTION BRANCHESAND THEIR NUMERICAL APPROXIMATIONS OF A SEMI-LINEAR ELLIPTIC PROBLEM WITH TWO PARAMETERS

1.IntroductionConsidertheequationdependingontheparametersA,pER,wheref'R-Rands:R-RaresmoothoddfunctionandLetS'u(x)-u(T--x),r={S,I}.Then(l.l)isr-equivalent.Theequality(l.Za)isjustanormalizationoffatx=0.WeintroduceaSobolevspaceX:=Ha(0,7),anddefineamappingT'gEL'(0,T)u'=TaEXimplicitly'Aweakformof(1.1)inXxRZisDuetof(0)~0,theproblem(1.3)(resp.(1))hasatrivialsolutioncurveIfwerestrictp=0,then(l.3)reducestoaproblemwithsingleparameteranditsbifurcationsonthetrivialsolutioncurveCOarewellknown,…     

Nilpotent sign patterns of a given index

A sign pattern is said to be nilpotent of index k if all real matrices in its qualitative class are nilpotent and their maximum nilpotent index equals k. In this paper, we characterize sign patterns that are nilpotent of a given index k. The maximum number of nonzero entries in such sign patterns of a given order is determined as well as the sign patterns with this maximum number of nonzero entries.     

Government-provided annuities under insolvency risk

This paper seeks to determine whether governments should intervene in the private annuity market by directly providing public insurance in the form of annuities when both the government and the insurance companies could default. It is found that, although the government could default, intervening by means of an annuity can improve social welfare if the insurance companies could default and the expected return on the public annuity is greater than the rate of return on a risk-free bond. We also find that, under actuarially fair pricing, the government should provide more in terms of a public annuity than the optimal amount of the annuity that the individual purchases in the private market if the government is less likely to default on the public annuity than an insurance company would in the case of a private annuity.     

Decomposition and removability properties of John domains

In this paper we characterize John domains in terms of John domain decomposition property. In addition, we also show that a domain D in ℔ ⁿ is a John domain if and only if DP is a John domain, where P is a subset of D containing finitely many points of D. The best possibility and an application of the second result are also discussed.     

Wm∨Pn的交叉数

在Klesc M给出的联图W_3 V P_n的交叉数的基础上,继续对联图Wm V Pn（m=4,5）的交叉数cr进行了研究,得到了cr（W3 V Pn）=Z（5,n）＋n＋「n/2＋1」以及cr（W5 V Pn）=Z（6,n）＋n＋3[n/2」＋1,n≥2.     

ON THE 3D VISCOUS PRIMITIVE EQUATIONS OF THE LARGE-SCALE ATMOSPHERE

This paper is devoted to considering the three-dimensional viscous primitive equations of the large-scale atmosphere. First, we prove the global well-posedness for the primitive equations with weaker initial data than that in [11]. Second, we obtain the existence of smooth solutions to the equations. Moreover, we obtain the compact global attractor in V for the dynamical system generated by the primitive equations of large-scale atmosphere, which improves the result of [11].     

The project scheduling problem with production and consumption of resources: A list-scheduling based algorithm

The paper deals with algorithms for applying classical list scheduling to a project scheduling problem where the units of resources are produced or consumed at the occurrence of precedence-related events. It is shown that the feasibility variant of the project scheduling problem is NP-complete. Moreover, polynomial-time scheduling algorithms are devised for the three cases where the occurrence time sequence of all events or the consuming events or the producing events is given in advance. By enumerating these sequences (called linear orders), one obtains a list-scheduling based algorithm for minimizing the makespan of a project scheduling problem with production and consumption of resources.     

无穷级亚纯函数的公共值与奇异方向

f（z）为无穷级亚纯函数,且σ（f）〈∞。本文证明了复平内存在奇异方向,f（z）与其k阶导函数f（k）（z）（k≥3）在这方向所对应的任意小角域内至多有两个不同的有穷公‘共值。     

Vacuum solution and quasineutral limit of semiconductor drift-diffusion equation

The first half of this paper is concerning with the nonlinear drift-diffusion semiconductor model in d (d?3) dimensional space. The global estimate is achieved on the evolution of support of solution and the finite speed of propagation. The proof is based on the estimate of the weighted norm with special designed weight functions. In the second half, we prove the quasineutral limit locally for 1-dimensional standard drift-diffusion model with discontinuous, sign-changing doping profile.