Subcubic Growth of the Averaged Dehn Function for a Class 2 Nilpotent Group

We show that the averaged Dehn function with respect to each finite presentation of an arbitrary finitely generated class 2 nilpotent group is subcubic. For the finite rank 2 free class 2 nilpotent group this implies the subasymptoticity of the averaged Dehn function in the sense of M. Gromov, confirming his conjecture.Original Russian Text Copyright © 2005 Romankov V. A.The author was supported by the Russian Foundation for Basic Research (Grant 04-01-00489) and the Scientific Program Universities of Russia of the Ministry for Education of the Russian Federation (Grant 362-05).__________Translated from Sibirskii Matematicheskii Zhurnal, Vol. 46, No. 3, pp. 663–672, May–June, 2005.     

左群的强半格的Cayley图

研究了左群的强半格的Cayley图的结构和性质,给出了一个有向图是左群强半格的Cayley图的充分条件,若限制左群是群,则可以得到Clfford半群的Cayley图的相应结果,从而推广了关于此类半群的Cayley图的一些主要结论.     

Normality of Tetravalent Cayley Graphs of Odd Prime-cube Order and Its Application

Let p be an odd prime. In this paper we prove that all tetravalent connected Cayley graphs of order p^3 are normal. As an application, a classification of tetravalent symmetric graphs of odd prime-cube order is given.     

The diameters of almost all Cayley digraphs

1.IntroductionLetGbeagroupandSasubsetofGnotcontainingtheidentity,1ofG.TheCayleydigraphofGwithrespecttoS,denotedbyX(G,S),isadigraphwhosevertexsetisGandforx,yEG,thereisanarcfromxtoyinX(G,S)ifandonlyifx--laES.IfS=S--',thenX(G,S)isactuallyagraphcalledCayleygraph.ThereisadiversityofliteratureonCnyleygraphsandCayleydigraphs.Themostlyinvestigatedsubjectsaretheconnectivityll'2],theHamiltonianpropertiesl3],theisomorphismsI4]andthediameterIS'6].Recelltly,someauthorsproposedtouseCayleygraph…     

On the Normality of Cayley Digraphs of Valency 2 on Non-Abelian Group of Odd Order

In this paper, we prove that the Cayley digraph = Cay(G, S) of valency 2 on non-abelian group G of odd order is normal if the automorphism group of A(), a graph constructed from by using the method presented in the paper, is primitive on the vertices set V(A(). We also prove that the Cayley digraphs of valency 2 on non-abelian group of order pq² are normal, where p and q are distinct odd primes.AMS Subject Classification (2000) 05C25 20B25Supported by the National Natural Science Foundation of China (Grant no. 19971086) and the Doctoral Program Foundation of the National Education Department of China.     

完全正则半群的Cayley表示

本文利用点集映射和等价关系得出了完全正则半群的Ｃａｙｌｅｙ表示，从而解决了１９８７年Ｍ．Ｐｅｔｒｉｃｈ提出的一个公开问题．作为特例，还得到完全单半群的ｃａｙｌｅｙ表示．     

Explicit and approximate solutions of second order elliptic differential equations in hilbert and banach spaces

An explicit closed-form solution for an abstract elliptic equation in Hilbert or Banach space is presented. Using this explicit representation we propose an approximation with the accuracy automatically depending on the smoothness of the initial data.