Oscillation of certain partial difference equations

In this paper we consider a class of nonlinear delay partial difference equations and a class of linear delay partial difference equations with variable coefficients, which may change sign. We obtain oscillation criteria for these equations. There are no results for the oscillation of these equations up to now.     

Idealization of a decomposition theorem

In 1986, Tong [13] proved that a function f : (X,τ)→(Y,φ) is continuous if and only if it is α-continuous and A-continuous. We extend this decomposition of continuity in terms of ideals. First, we introduce the notions of regular-I-closed sets, A _I-sets and A _I -continuous functions in ideal topological spaces and investigate their properties. Then, we show that a function f : (X,τ,I)→(Y, φ) is continuous if and only if it is α-I-continuous and A _I-continuous. This revised version was published online in June 2006 with corrections to the Cover Date.     

Rn上的非初等变换群及其极限集

该文对高维非初等Mò'bius变换群进行了研究,得到了一些重要性质,给出了几个关于离散准则和代数收敛性的定理.     

一类递归集的Hausdorff维数及Bouligand维数

本文给出递归集的Ｈａｕｓｄｏｒｆｆ维数的下界估计，并由此确定了一类递归集的维数，所获结果包含并推广了Ｂｅｄｆｏｒｄ，Ｄｅｋｋｉｎｇ及文志英、钟红柳等人的有关结果。     

Baum-Katz-Nagaev type results for martingales

We obtain a Baum-Katz-Nagaev type theorem for bounded martingale difference sequences that have more than a second moment, and prove that the celebrated Hsu-Robbins-Erd?s theorem fails for martingales.     

差分系统基于两种度量的极端稳定性

首先引入了差分系统基于两种度量的极端稳定性概念 ,然后建立了一些关于差分系统 ( h0 ,h)极端稳定性 (极端一致稳定性 ,极端渐近稳定性 ,极端一致渐近稳定性 )的判定准则 .在所得到的定理中 ,对△ V的限制较弱 ,特别地 ,△V甚至可以恒为正 ,从而便于实际应用 .     

On a question of Gross

Using the notion of weighted sharing of sets we prove two uniqueness theorems which improve the results proved by Fang and Qiu [H. Qiu, M. Fang, A unicity theorem for meromorphic functions, Bull. Malaysian Math. Sci. Soc. 25 (2002) 31-38], Lahiri and Banerjee [I. Lahiri, A. Banerjee, Uniqueness of meromorphic functions with deficient poles, Kyungpook Math. J. 44 (2004) 575-584] and Yi and Lin [H.X. Yi, W.C. Lin, Uniqueness theorems concerning a question of Gross, Proc. Japan Acad. Ser. A 80 (2004) 136-140] and thus provide an answer to the question of Gross [F. Gross, Factorization of meromorphic functions and some open problems, in: Proc. Conf. Univ. Kentucky, Lexington, KY, 1976, in: Lecture Notes in Math., vol. 599, Springer, Berlin, 1977, pp. 51-69], under a weaker hypothesis.     

New Constructions of Disjoint Distinct Difference Sets

New constructions of regular disjoint distinct difference sets (DDDS) are presented. In particular, multiplicative and additive DDDS are considered.     

Molecular Orbital Calculations on 2, 4, 6-Trinitrotoluene

Three ab initio calculations (HF/6-3IG, HF/6-3IG*, and HF/6-3IG**) on 2,4,6-trinitrotoluene were made, The results compare well with xray data, except dihedral angles of NO₂ relative to the plane of the benzene ring. The deviations are attributed to packing forces and steric effects in the crystal. The most stable structure was a torsional angle 10° of the methyl top with the benzene ring, unlike toluene. The rotational barriers of the methyl top and the 4-nitro group are small. Hydrogen bonding, dipole moments and total atomic charges arc calculated.     

Mixed methods on quadrilaterals and hexahedra

We describe a new family of discrete spaces suitable for use with mixed methods on certain quadrilateral and hexahedral meshes. The new spaces are natural in the sense of differential geometry, so all the usual mixed method theory, including the hybrid formulation, carries over to these new elements with proofs unchanged. Because transforming general quadrilaterals into squares introduces nonlinearity and because mixed methods involve the divergence operator, the new spaces are more complicated than either the corresponding Raviart-Thomas spaces for rectangles or corresponding finite element spaces for quadrilaterals. The new spaces are also limited to meshes obtained from a rectangular mesh through the application of a single global bilinear transformation. Despite this limitation, the new elements may be useful in certain topologically regular problems, where initially rectangular grids are deformed to match features of the physical region. They also illustrate the difficulties introduced into the theory of mixed methods by nonlinear transformations.