HARMONIC MAPS AND FUNDAMENTAL GROUPS OF NONPOSITIVELY CURVEDRIEMANNIAN MANIFOLDS

Ｔｈｅｔｈｅｏｒｙｏｆｈａｒｍｏｎｉｃｍａｐｓｉｎｔｏａｃｏｍｐａｃｔｎｏｎｐｏｓｉｔｉｖｅｌｙｃｕｒｖｅｄｔａｒｇｅｔｉｓｗｅｌｌ-ｄｅｖｅｌｏｐｅｄ.ＴｈｅｅｘｉｓｔｅｎｃｅｏｆｓｕｃｈａｈａｒｍｏｎｉｃｍａｐｐｉｎｇｉｎａｎｙｇｉｖｅｎｈｏｍｏｔｏｐｙｃｌａｓｓｉｓｅｓｔａｂｌｉｓｈｅｄｂｙＥｅｌｌｓａｎｄＳａｍｐｓｏｎ[1]ｉｎ1964,ａｎｄｌａｔｅｒ,ｉｎ1967,Ｈａｒｔｍａｎ[2]ｇａｖｅａｐｒｏｏｆｏｆｔｈｅｕｎｉｑｕｅｎｅｓｓ.Ｔｈｉｓｐａｐｅｒｉｓｄｅｖｏｔｅｄｔｏａｎａｐｐｌｉｃａｔｉｏｎｏ…     

向量集值优化超有效解的对偶问题

借助于Contingent切锥和集值映射的上图而引入的有关集值映射的Contingent切导数，对约束集值优化问题的超有效解建立了最优性Kuhn Tucker必要及充分性条件,借此建立了向量集值优化超有效解的Wolfe型和Mond Weir型对偶定理.     

The isolated critical value phenomenon in local－global riddling bifurcation

A chaotic synchronized system of two coupled skew tent maps is discussed in this paper. The locally and globally riddled basins of the chaotic synchronized attractor are studied. It is found that there is a novel phenomenon in the local－global riddling bifurcation of the attractive basin of the chaotic synchronized attractor in some specific coupling intervals. The coupling parameter corresponding to the locally riddled basin has a single value which is embedded in the coupling parameter interval corresponding to the globally riddled basin, just like a breakpoint. Also, there is no relation between this phenomenon and the form of the chaotic synchronized attractor. This phenomenon is found analytically. We also try to explain it in a physical sense. It may be that the chaotic synchronized attractor is in the critical state, as it is infinitely close to the boundary of its attractive basin. We conjecture that this isolated critical value phenomenon will be common in a system with a chaotic attractor in the critical state, in spite of the system being discrete or differential.     

自相似集之间的等变映射

定义了复射动力系统以及它们之间等变映射的概念 ,在此基础上又引出了自相似集之间等变映射的概念并讨论了在此类映射的映射下自相似集象的 Hausdorff维数的状态 .     

p阶Feigenbaum映射

A continuous map f from the unit closed interval into itself is called a p-order Feigenbaum's map if fp(λx) = λf(x),f(O)=1 and f|[λ,1] is univallecular. In this paper, some characterizations of p order Feigenbaum's maps are discussed and the existence for both types of such maps is proven.     

Hochschild Cohomologies of the Algebra of Smooth Functions

Based on the previously developed technique using the Laplace transformation of distributions with compact support, we calculate the Hochschild cohomologies of the algebra of smooth functions on a finite-dimensional real vector space with coefficients in the adjoint representation.     

Gated Polling Systems with Lévy Inflow and Inter-Dependent Switchover Times: A Dynamical-Systems Approach

We study asymmetric polling systems where: (i) the incoming workflow processes follow general Lévy-subordinator statistics; and, (ii) the server attends the channels according to the gated service regime, and incurs random inter-dependentswitchover times when moving from one channel to the other. The analysis follows a dynamical-systems approach: a stochastic Poincaré map, governing the one-cycle dynamics of the polling system is introduced, and its statistical characteristics are studied. Explicit formulae regarding the evolution of the mean, covariance, and Laplace transform of the Poincaré map are derived. The forward orbit of the maps transform – a nonlinear deterministic dynamical system in Laplace space – fully characterizes the stochastic dynamics of the polling system. This enables us to explore the long-term behavior of the system: we prove convergence to a (unique) steady-state equilibrium, prove the equilibrium is stationary, and compute its statistical characteristics.     

改进的自组织映射(SOM)蛋白质折叠算法和计算实现

蛋白质结构预测是生物信息学中的重要研究方向．为了研究蛋白质折叠的机理,人们引入了只考虑蛋白质疏水核心和亲水外围位置导致能量差别的简化HP模型．即使是求解二维HP模型已被证明是一个NP完全问题,因此需要设计有效的近似算法来求解较大规模的HP模型．从旅行商问题(TSP)的求解看,自组织映射是构造近似算法的有效工具．本文将归一化的F-W自组织模型应用到蛋白质二维HP问题的求解中,结合为克服多重映射构造的局部线搜索算法．数值试验表明,该算法改进了现有的HP模型的SOM求解算法, 只需很少的迭代步数就能找到最低能量构象．这一改进算法可以成为进一步研究的基础．     

Maps Preserving Zeros of xy*

For a prime ring A with involution, we explore the characterization of additive bijective maps φ: A → A such that φ(x)φ(y)* = 0 whenever xy* = 0. In particular, we show that if A is prime, unital, and generated by nontrivial idempotents, then there is a *-monomorphism g of A into Q, and an element r ∈ A such that φ(x) = rg(x) for all x ∈ A.     

三角代数上初等映射的可加性

本文主要研究了三角代数上的初等映射的可加性.利用矩阵分块理论,证明了三角代数上的初等映射是可加的.