The structure and the sufficint and necessary conditions for generalized statistically self-similar sets

We constructed a class of generalized statistically self-similar sets and give the necessary and sufficent conditions to ensure a random recursive set being a generalized statistically self-similar set. The statistically self-similar sets defined by Hutchinson, Falconer, Graf are the special cases of ours. Foundation item: Supported by the National Natural Science Foundation of China Biography: DENG Ai-jiao (1974-), female, Ph.D. candidate, research interes: is in stochastic process and random ractal     

Oppenheim定理的推广

建立了（ＣＰ）Ｄｎ类复广义正定矩阵的Ｏｐｐｅｎｈｅｉｍ定理，推广了已有结果。     

所有子群皆循环或正规的有限2-群

研究了所有子群皆循环或正规的有限2群,并给出了其完全分类.     

Applications of Tauberian theorems in some problems in mathematical physics

We give some multidimensional Tauberian theorems for generalized functions and show examples of their application in mathematical physics. In particular, we consider the problems of stabilizing the solutions of the Cauchy problem for the heat kernel equation, multicomponent gas diffusion, and the asymptotic Cauchy problem for a free Schrödinger equation in the norms of different Banach spaces among others.     

Common fixed point theorems for expansion mappings in various spaces

We prove expansion mappings theorems in various spaces i.e., metric spaces, generalized metric spaces, probabilistic metric spaces and fuzzy metric spaces, which generalize the results of various authors like Daffer and Kaneko [11], Ahmad, Ashraf and Rhoades [1], Vasuki [38], Rhoades [31] and Wang, Li, Gao and Iseki [40] etc. In the memory of 65^th birthday anniversary of his Father Late Sh. Ram Phool Sharma     

A new auxiliary function method for solving the generalized coupled Hirota–Satsuma KdV system

In this letter, a new auxiliary function method is presented for constructing exact travelling wave solutions of nonlinear partial differential equations. The main idea of this method is to take full advantage of the solutions of the elliptic equation to construct exact travelling wave solutions of nonlinear partial differential equations. More new exact travelling wave solutions are obtained for the generalized coupled Hirota–Satsuma KdV system.     

最高阶元素个数为40的非可解群的分类

设$\varphi$为群${\rm Aut}(N)$的同态,记$H_\varphi\times N$为群$N$借助于群$H$的半直积.设$G$为有限不可解群,本文证明: 若$G$中最高阶元素个数为40, 则$G$同构于下列群之一:(1)~$Z_{4\varphi}\times A_5$,\,${\rm ker}\varphi=Z_2$; (2)~$D_{8\varphi}\times A_5,\,{\rm ker}\varphi=Z_2\times Z_2$; (3)~$G/N=S_5$, $N=Z(G)=Z_2$; (4)~$G/N=S_5$, $N=Z_2\times Z_2,\,N\cap Z(G)=Z_2$.     

Suzuki cross‐coupling reaction of aryl and heterocyclic bromides and aromatic polybromides on a Pd(II)‐hydrotalcite catalyst

The Suzuki cross‐coupling reaction of various bromine‐containing substrates and phenylboronic acid in toluene at 90 °C on a Pd(AcO)₂Py₂ catalyst supported on an Mg? Al hydrotalcite, using K₂CO₃ as the base, was studied. The conversion and selectivity results obtained for many of the substrates were excellent and similar to those provided by more active or even homogeneous catalysts. The reactions of aryl polybromides and phenylboronic acid gave the corresponding polyaromatic compounds in variable yields depending on the particular substrate. Arylation occurred in a consecutive manner by substitution of the different Br atoms. ICP‐MS measurements of the palladium content of the catalyst performed prior to and after the reaction revealed that part of the metal is incorporated into the bulk solution; therefore, the catalytic process is not purely heterogeneous. Copyright © 2008 John Wiley & Sons, Ltd.     

Nonexistence of local minima of supersolutions for the polyharmonic problems

In this note we study the nonexistence of local minima of the supersolutions of the polyharmonic equations on the balls under generalized homogeneous Dirichlet boundary conditions. Under suitable restriction on the dimensions, this means that a generalized clamped circular plate, which is pushed from below, cannot bend downwards even locally. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)