On the Distribution of Weakly Composite Numbers

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Dissipativity and stability for semilinear anomalous diffusion equations involving delays

We analyze the dissipativity and stability of solutions to a class of semilinear anomalous diffusion equations involving delays. The existence of absorbing set, the stability, and weak stability will be shown under suitable assumptions on the nonlinearity. Our analysis is based on new Halanay-type inequality, local estimates, and fixed-point arguments.     

A NOTE ON NONAUTONOMOUS KLEIN-GORDON-SCHR(O)DINGER EQUATIONS WITH HOMOGENEOUS DIRICHLET BOUNDARY CONDITION

This note discusses the long time behavior of solutions for nonautonomous weakly dissipative Klein-Gordon-Schrodinger equations with homogeneous Dirichlet bound-ary condition. The authors prove the existence of compact kernel sections for the associated process by using a suitable decomposition of the equations.     

C-半群的弱渐近概周期运动

讨论了Bnanch空间上C-半群的弱渐近概周期(WAAP)运动,进而得到其表示定理和扰动定理.     

多叶函数的Krzyz定理

设α是单叶函数ｆ（ｚ）的Ｈａｙｍａｎ指数，Ｋｒｚｙｚ证明了（１－ｒ）＾３Ｍ（ｒ，ｆ＇）→２α（ｒ→１）。本文将这个结果推广到多叶函数ｆ（ｚ）的ｎ次导数ｆ＾（ｎ）（ｚ）的情形，我们所使用的方法与Ｋｒｚｙｚ的不同。     

Extrapolation method for solving weakly singular nonlinear Volterra integral equations of the second kind

Based on a new generalization of discrete Gronwall inequality in [L. Tao, H. Yong, A generalization of discrete Gronwall inequality and its application to weakly singular Volterra integral equality of the second kind, J. Math. Anal. Appl. 282 (2003) 56-62], Navot's quadrature rule for computing integrals with the end point singularity in [I. Navot, A further extension of Euler-Maclaurin summation formula, J. Math. Phys. 41 (1962) 155-184] and a transformation in [P. Baratella, A. Palamara Orsi, A new approach to the numerical solution of weakly singular Volterra integral equations, J. Comput. Appl. Math. 163 (2004) 401-418], a new quadrature method for solving nonlinear weakly singular Volterra integral equations of the second kind is presented. The convergence of the approximation solution and the asymptotic expansion of the error are proved, so by means of the extrapolation technique we not only obtain a higher accuracy order of the approximation but also get a posteriori estimate of the error.     

Characterization of the Nonemptiness and Compactness of Solution Sets in Convex and Nonconvex Vector Optimization

As a consequence of an abstract theorem proved elsewhere, a vector Weierstrass theorem for the existence of a weakly efficient solution without any convexity assumption is established. By using the notion (recently introduced in an earlier paper) of semistrict quasiconvexity for vector functions and assuming additional structure on the space, new existence results encompassing many results appearing in the literature are derived. Also, when the cone defining the preference relation satisfies some mild assumptions (but including the polyhedral and icecream cones), various characterizations for the nonemptiness and compactness of the weakly efficient solution set to convex vector optimization problems are given. Similar results for a class of nonconvex problems on the real line are established as well.Research supported in part by Conicyt-Chile through FONDECYT 104-0610 and FONDAP-Matemáticas Aplicadas II.     

板模型具广义边界条件的迁移算子的渐近点谱及其聚点

研究非均匀介质、各向异性和连续能量的板模型迁移算子 A在广义边界条件下的的渐近点谱及其聚点 .在 Lp(1 p <+∞ ) 空间获得了算子 A的渐近点谱以及谱聚点的分布等新的结果 .     

板模型迁移算子的渐近点谱及其聚点(英文)

In this paper we investigate the asymptotic spectrum and accumulation of a transport operator A in slab geometry with continuous energy, anisotropic scattering and inhomogeneous medium. In L^p （1 ≤ p 〈 ＋∞） space we show a series of new results for the asymptotic point spectrum and accumulation of A.     

φ混合样本下帕累托分布参数的经验贝叶斯分析

在弱平稳φ混合样本下,讨论了Pareto分布参数的经验Bayes（EB）单边检验问题,构造了参数的经验Bayes检验函数,证明了它具有渐近最优（a.o.）性,并且获得了收敛速度。     

Tauberian Theorem for the Stieltjes Transform

Under weak constraints on the positive functions to be compared, we derive their asymptotic equivalence at infinity as a consequence of the asymptotic equivalence of their Stieltjes transforms at infinity.     

弱P—正则半群

在本文中,我们刻画弱P－正则半群上的最大幂等分离同余,并且证明了有超C－集的弱P－正则半群S[P]是拟P－正则当且仅当它同构于WB（p)[P^*]和某个弱正则^*-半群T的织积,其中B是S[P]的半带,最后,我们获得,在一般情况下,WB(p)[P]的弱P－正则半群但不是P－正则半群的条件。     

Weakly pre-<Emphasis Type=”Italic”>I-</Emphasis>open sets and decomposition of continuity

Summary We establish a general sharp inequality which holds for the family of conformally flat submanifolds in real space form. We show that this inequality does not hold for arbitrary submanifolds in real space forms. We also provide several applications of the inequality.     

C-半群的弱稳定性

引入了C-半群的个体弱稳定性和弱稳定性的概念,给出了弱稳定性的一个充分条件.     

ON WELL-POSEDNESS OF THE MULTIOBJECTIVE GENERALIZED GAME

§1　IntroductionHadamard type well-posedness and Tikhonov type well-posedness are two main typesof concepts of well-posedness. At the beginning of last century,Hadamard firstintroduced the concept of well-posedness in study of optimal problem. Hadamard typewell-posedness of a problem means the continuous dependence of the solution on the dataof such problem. Later,Tikhonov introduced another concept of well-posedness.Tikhonov type well-posedness deals with the behavior ofa prescribed class …     

Eberlein mulian定理在局部凸空间中的推广

设（Ｅ，Ｔ）是一个分离的局部凸空间．本文主要结果是：（１）如果（Ｅ，Ｔ）是次可分的，那么ＡＥ是相对弱紧集Ａ是相对弱可数紧集Ａ是相对弱序列紧集．（２）如果（Ｅ，Ｔ）是强次可分且（Ｅ，β（Ｅ，Ｅ））是桶型空间，那么ＡＥ是相对弱紧集Ａ是相对弱可数紧集Ａ是相对弱序列紧集．     

A construction of weakly inverse semigroups

Let S° be an inverse semigroup with semilattice biordered set E° of idempotents and E a weakly inverse biordered set with a subsemilattice Ep = { e ∈ E ｜ arbieary f ∈ E, S（f , e） loheain in w（e）} isomorphic to E° by θ：Ep→E°. In this paper, it is proved that if arbieary f, g ∈E, f ←→ g→→ f°θD^s° g°θand there exists a mapping φ from Ep into the symmetric weakly inverse semigroup P J（E∪ S°） satisfying six appropriate conditions, then a weakly inverse semigroup ∑ can be constructed in P J（S°）, called the weakly inverse hull of a weakly inverse system （S°, E, θ, φ） with I（∑） ≌ S°, E（∑） ∽- E. Conversely, every weakly inverse semigroup can be constructed in this way. Furthermore, a sufficient and necessary condition for two weakly inverse hulls to be isomorphic is also given.     

Dynamical systems disjoint from any minimal system

Furstenberg showed that if two topological systems and are disjoint, then one of them, say , is minimal. When is nontrivial, we prove that must have dense recurrent points, and there are countably many maximal transitive subsystems of such that their union is dense and each of them is disjoint from . Showing that a weakly mixing system with dense periodic points is in , the collection of all systems disjoint from any minimal system, Furstenberg asked the question to characterize the systems in . We show that a weakly mixing system with dense regular minimal points is in , and each system in has dense minimal points and it is weakly mixing if it is transitive. Transitive systems in and having no periodic points are constructed. Moreover, we show that there is a distal system in .

Recently, Weiss showed that a system is weakly disjoint from all weakly mixing systems iff it is topologically ergodic. We construct an example which is weakly disjoint from all topologically ergodic systems and is not weakly mixing.

     

拟共形映射和弱Cigar域

设f是R~n到R~n上的同胚,本文证明了f是拟共形映射的充要条件是f将R~n中的任一弱Cigar域映成R~n中的弱Cigar域。