离散随机变量序列的强偏差定理

利用分析方法建立了用不等式表示的用对数似然比刻划的任意相依离散随机变量序列的强偏差定理,作为推论得到了更一般的离散随机变量序列加权和的强大数定律.     

变质量质点的动能定理与软绳问题

给出变量质点的动能定理和一对反推内力作功的表达式,并由此给出软绳问题的正确解。     

Existence of multiplicity harmonic and subharmonic solutions for second‐order quasilinear equation via Poincaré‐Birkhoff twist theorem

In this paper, we investigate the existence and multiplicity of harmonic and subharmonic solutions for second‐order quasilinear equation where , g satisfies the superlinear condition at infinity. We prove that the given equation possesses harmonic and subharmonic solutions by using the phase‐plane analysis methods and a generalized version of the Poincaré‐Birkhoff twist theorem.     

Approximation of signals from local averages

This work is concerned with approximation of a signal from local averages. It improves a result of Butzer and Lei [P.L. Butzer, J. Lei, Approximation of signals using measured sampled values and error analysis, Commun. Appl. Anal. 4 (2000) 245–255].     

UNIQUENESS PROBLEM WITH TRUNCATED MULTIPLICITIES OF MEROMORPHIC MAPPINGS FOR MOVING TARGETS

In this article,two uniqueness theorems of meromorphic mappings on moving targets with truncated multiplicities are proved.     

高阶柯西中值定理中间点的渐近性及误差估计

利用洛必达法则研究长度趋于零和长度趋于无穷大的两类区间上高阶柯西值定理中间点的渐近性及其误差估计.     

随机条件概率的一个极限性质与条件矩母函数方法

设Ｘｎ,ｎ〉０是在ｓ＝１,２,…,Ｎ中取值的一列随机变量,ｐｋ（ｘｋ↓ｘ０,…ｘｋ－１）＝ｐ（Ｘｋ＝ｘｋ↓Ｘ０＝ｘｋ－１＝ｘｋ－１）。本文得到随机概率｛ｐｋ（Ｘｋ↓Ｘ０,…Ｘｋ－１）,１〈ｋ〈ｎ↓）的调和平均ａ．ｅ．收敛的一个定理．证明中提出了将关开网的微分法和条件矩母函数的工具应用于强极限定理的研究的一种途径。     

Blocking analysis andT(1) theorem

TheT(1) theorem with a weak condition on the distribution kernel is proved by using a new method—blocking analysis. It improves a result of Meyer’s. Project supported by the National Natural Science Foundation of China (Grant No. 19631080) and the Foundation of Advanced Research Center, Zhongshan University.     

Manifestations of topological effects in graphene

Graphene is a monoatomic layer of graphite with carbon atoms arranged in a two-dimensional honeycomb lattice configuration. It has been known for more than 60 years that the electronic structure of graphene can be modelled by two-dimensional massless relativistic fermions. This property gives rise to numerous applications, both in applied sciences and in theoretical physics. Electronic circuits made out of graphene could take advantage of its high electron mobility that is witnessed even at room temperature. In the theoretical domain the Dirac-like behaviour of graphene can simulate high energy effects, such as the relativistic Klein paradox. Even more surprisingly, topological effects can be encoded in graphene such as the generation of vortices, charge fractionalisation and the emergence of anyons. The impact of the topological effects on graphene's electronic properties can be elegantly described by the Atiyah–Singer index theorem. Here we present a pedagogical encounter of this theorem and review its various applications to graphene. A direct consequence of the index theorem is charge fractionalisation that is usually known from the fractional quantum Hall effect. The charge fractionalisation gives rise to the exciting possibility of realising graphene based anyons that unlike bosons or fermions exhibit fractional statistics. Besides being of theoretical interest, anyons are a strong candidate for performing error free quantum information processing.     

Bolzano's Theorems for Holomorphic Mappings

The existence of a zero for a holomorphic functions on a ball or on a rectangle under some sign conditions on the boundary generalizing Bolzano's ones for real functions on an interval is deduced in a very simple way from Cauchy's theorem for holomorphic functions.A more complicated proof,using Cauchy's argument principle,provides uniqueness of the zero,when the sign conditions on the boundary are strict.Applications are given to corresponding Brouwer fixed point theorems for holomorphic functions.Extensions to holomorphic mappings from Cn to Cn are obtained using Brouwer degree.