A Geometric Problem and the Hopf Lemma. Ⅱ

Abstract A classical result of A. D. Alexandrov states that a connected compact smooth n-dimensional manifold without boundary, embedded in ℝⁿ⁺¹, and such that its mean curvature is constant, is a sphere. Here we study the problem of symmetry of M in a hyperplane X_n+1 =constant in case M satisfies: for any two points (X′,X_n+1), on M, with , the mean curvature at the first is not greater than that at the second. Symmetry need not always hold, but in this paper, we establish it under some additional conditions. Some variations of the Hopf Lemma are also presented. Several open problems are described. Part I dealt with corresponding one dimensional problems. (Dedicated to the memory of Shiing-Shen Chern) * Partially supported by NSF grant DMS-0401118.     

A.H.柯尔莫戈洛夫

本文简要阐述了当代著名数学家,苏联的柯尔莫戈洛夫的生平及其对数学、科学和教育作出的贡献.     

On A. Lino, W. Demelo and C. C. Pugh''''s Conjecture (Part 1)

For Lienard's equation or its equivalent system (?)=y-F(x),(?)=-x,(F(x)=integral from n=0 to x (f(ξ)dξ)). (*) there were quite a few papers studied (*) to have some limit cycles. Although there were few papers studied (*) to have at most m limit cycles, but good results were given already. A. Lino, W. Demelo and C. C. Pugh conjectured following fact: when f(x)=sum from N (a_ix~i) (N=2n+1,2n+2),system (*) has at most n limit cycles.     

The Life and Work of R.A. Rankin (1915–2001)

Robert Alexander Rankin, an eminent Scottish number theorist and, for several decades, one of the world's foremost experts in modular forms, died on January 27, 2001 in Glasgow at the age of 85. He was one of the founding editors of The Ramanujan Journal. For this and the next two issues of the The Ramanujan Journal, many well-known mathematicians have prepared articles in Rankin's memory. In this opening paper, we provide a short biography of Rankin and discuss some of his major contributions to mathematics. At the conclusion of this article, we provide a complete list of Rankin's doctoral students and a complete bibliography of all of Rankin's writings divided into five categories: (1) Research and Expository Papers; (2) Books; (3) Books Edited; (4) Obituaries; (5) Other Writings.     

A NOTE ON A PROBLEM OF BOAS R.P.

To answer the rest part of the problem of Boas R. P. on derivative of poiyaomial, it is shown that if p(s) is a polynomial of degree n such that ■|p(z)|≤1 and. p(s)≠0 in |z|≤k, 0相似文献   

A RAMARK ON A THEOREM OF T.D.NARANG

In 1966,M.Edelstein[2] generalized a result of M.a.Draseselsk[3] by replace”uniformly convex Banach space with strictly convex Banach~~     

A note on a theorem of W. Gaschütz and N. Itô

Given a finite groupG andp an odd prime number, we conclude thatO ^p(G)G isp-nilpotent when for every subgroupH ofG of orderp there exists a subgroupK ofG such thatG=HK andH permutes with every subgroup ofK.     

Jungck＇s Common Fixed Point Theorem and E.A Property

We prove that （E.A） property buys the required containment of range of one mapping into the range of other in common fixed point considerations up to a pair of mappings. While proving our results, we utilize the idea of implicit functions due to Popa, keeping in view their unifying power.     

Extension of E.A. Barbashin’s and N.N. Krasovskii’s stability theorems to controlled dynamical systems

The known theorems by E.A. Barbashin and N.N. Krasovskii (1952) about the asymptotic and global stability of an equilibrium state for an autonomous system of differential equations are extended to nonautonomous differential inclusions with closed-valued (but not necessarily compact-valued) right-hand sides, where the equilibrium state is a weakly invariant (with respect to solutions of the inclusion) set. The statements are formulated in terms of the Hausdorff-Bebutov metric, the dynamical system of translations corresponding to the right-hand side of the differential inclusion, and the weakly invariant set corresponding to the inclusion.     

Appendix to Cluster-Cyclic Quivers with Three Vertices and the Markov Equation,by A. Beineke,Th. Brűstle and L. Hille

The relation between the Markov constant of an acyclic cluster algebra of rank 3 and the dimension of the first Hochschild cohomology group of the corresponding hereditary algebra will be shown.     

Contents of Vol.23 Ser.A

No.1入Iareh 2008 Applieation of a neural network optimization eombinatorial predietion model to 011一gas yield forecasting···················，··，··············‘········……DENG Ybng DU Zhi一min LUY‘n一ni(l) 5     

Contents of Vol.17 Ser.A

No.1　 March 2 0 0 2The Weak Exponential Asym ptotic Stability of Impulsive Differential SystemFeng Weizhen　 Chen Yongshao ( 1 )……………………………………………………………………………………Existence of a Single Rub- Impact Period- n Motion for the Rotor Systems with Rigid ConstraintsLi Qunhong　 L u Qishao ( 7)……………………………………………………………………………………………Positive Periodic Solution of Single Species Model with Feedback Regulation and Infinite DelayLi X…     

A Comment on a Necessary and Sufficient Condition for Transitive Permutation Group by P.J.Cameron

P.J. Cameron had mentioned that "It can be shown that a permutation group is transitive if and only if its centralizer in the symmetric group is semiregular, and vice versa (Wielandt, page 9)."[1] The latter is true, i.e. G≤S_Ω is semiregular(?)Cs_Ω(G) is transitive. [cf. 2] But in the former statement fails, i.e. Cs_Ω(G) is semiregular(?)G≤S_Ω is transitive. In this note we give a series of the