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弱鞅的Whittle型不等式及其应用

山东大学学报（理学版） 2011年第9期46卷 112-116,121页

作者：龚小兵四川省高等学校数值仿真重点实验室四川内江641112 内江师范学院数学与信息科学学院四川内江641112

首先得到了弱鞅的Whittle型不等式,它包含弱鞅的Hajek-Renyi型不等式,然后利用此不等式证明了弱鞅的强大数定律。

关键词：弱鞅 Whittle型不等式 Hajek-Renyi型不等式强大数定律

Fuzzy controllers based on some fuzzy implication operators and their response functions

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Progress in Natural science:Materials International 2004年第1期14卷 16-21页

作者： LI Hongxing 1*, YOU Fei 1 and PENG Jiayin 2(1. Department of mathematics, Beijing normal university, Beijing 100875, china 2. Department of mathematics, neijiang Teacher's college, neijiang 641112, china) Beijing normal Univ Dept Math Beijing 100875 Peoples R China

The fuzzy controllers constructed by 23 fuzzy implication operators based on CRI algorithm and their response functions are discussed. The conclusions show that the fuzzy controllers constructed by 9 fuzzy implication operators are universal approximators to continuous functions and can be used in practical fuzzy control systems. And these 9 fuzzy implication operators except for Einstein operator intersection are all the adjoint pairs of some fuzzy implication operators. Besides, there are 3 other fuzzy controllers formed by fuzzy implication operators being regarded approximately as fitted functions.

关键词： fuzzy implication operators CRI algorithm fuzzy controllers response functions universal approximators

Dark energy from logarithmically modified gravity and deformed Coleman-Weinberg potential

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Research in Astronomy and Astrophysics 2011年第7期11卷 759-766页

作者： Ahmad Rami El-Nabulsi Department of Nuclear and Energy Engineering Cheju National University college of mathematics and information sciences Neijiang Normal University

Recent astrophysical measurements strongly suggest the existence of a missing energy component dubbed dark energy that is responsible for the current accelerated expansion of the universe.A new class of modified gravity theory is introduced which yields a universe accelerating in time and dominated by dark *** new modified gravity model constructed here concurrently includes a Gauss-Bonnet invariant term,barotropic fluid with a time-dependent equation of state parameter,a Coleman-Weinberg（CW） potential-like expression V（φ） =ξφm lnφn and a new Einstein-Hilbert term f（R,φ） =E（φ） R which depends on both the scalar curvature and the scalar fieldφthrough a generic logarithmic function E（φ） =lnφ.Here m and n take different values from the standard CW potential andξis a real parameter. It was shown that the presence of these terms provides many useful features which are discussed in some detail.

关键词： dark energy—gravitation—equation of state

Variational iteration method for solving time-fractional diffusion equations in porous the medium

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Chinese Physics B 2012年第12期21卷 118-122页

作者：吴国成 Key Laboratory of Numerical Simulation of Sichuan Province Neijiang Normal UniversityNeijiang 641112China college of Water Resources and Hydropower Sichuan UniversityChengdu 610065China

The variational iteration method is successfully extended to the case of solving fractional differential equations, and the Lagrange multiplier of the method is identified in a more accurate way. Some diffusion models with fractional derivatives are investigated analytically, and the results show the efficiency of the new Lagrange multiplier for fractional differential equations of arbitrary order.

关键词： time-fractional diffusion equation Captuo derivative Riemann-Liouville derivative,variational iteration method Laplace transform

Short cycle structures for graphs on surfaces and an open problem of Mohar and Thomassen

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science china mathematics 2006年第2期49卷 212-224页

作者： REN Han & DENG Mo Department of mathematics, East china normal university, Shanghai 200062, china college of mathematics & information science, Northwest normal university, Lanzhou 730070, china 1. Department of mathematics East China Normal University Shanghai 200062 China 2. college of mathematics & information science Northwest Normal University Lanzhou 730070 China

In this paper we investigate cycle base structures of a (weighted) graph and show that much information of short cycles is contained in an MCB (i.e., minimum cycle base). After setting up a Hall type theorem for base-transformation, we give a sufficient and necessary condition for a cycle base to be an MCB. Furthermore, we show that the structure of MCB in a (weighted)graph is unique. The property is also true for those having a longest length (although much work has been down in evaluating MCB, little is known for those having a longest length). We use those methods to find out some unknown properties for short cycles sharing particular properties in (unweighted) graphs. As applications, we determine the structures of short cycles in an embedded graph and show that there exist polynomially bounded algorithms in finding a shortest contractible cycle and a shortest two-sided cycle provided such cycles exist. Those answer an open problem of B. Mohar and C. Thomassen.

关键词： cycle base facial cycle graph embedding.

Quantum secret sharing between multiparty and multiparty with four states

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science china(Physics,Mechanics & Astronomy) 2007年第5期50卷 572-580页

作者： YAN FengLi1, GAO Ting2 & LI YouCheng1 1 college of Physics and information Engineering, Hebei normal university, Shijiazhuang 050016, china 2 college of mathematics and information science, Hebei normal university, Shijiazhuang 050016, china 1. college of Physics and information Engineering Hebei Normal University Shijiazhuang 050016 China 2. college of mathematics and information science Hebei Normal University Shijiazhuang 050016 China

A protocol of quantum secret sharing between multiparty and multiparty with four states was presented. It was shown that this protocol can nullify the Trojan horse attack with a multi-photon signal, the fake-signal attack with Einstein-Podolsky- Rosen pairs, the attack with single photons, and the attack with invisible photons. In addition, the upper bounds of the average success probabilities were given for dishonest agent eavesdropping encryption using the fake-signal attack with any two-particle entangled states.

关键词： quantum secret sharing, security, Einstein-Podolsky-Rosen pairs

Near generalized balanced tournament designs with block sizes 4 and 5

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science china mathematics 2009年第9期52卷 1927-1938页

作者： SHAN XiuLing1, 2 1 Department of mathematics, Beijing Jiaotong university, Beijing 100044, china 2 college of mathematics and information science, Hebei normal university, Shijiazhuang 050016, china Department of mathematics Beijing Jiaotong University Beijing 100044 China college of mathematics and information science Hebei Normal University Shijiazhuang 050016 China

A near generalized balanced tournament design, or an NGBTD(k,m) in short, is a (km+1,k,k-1)-BIBD defined on a (km+1)-set V . Its blocks can be arranged into an m×(km+1) array in such a way that (1) the blocks in every column of the array form a partial parallel class partitioning V\{x} for some point x, and (2) every element of V is contained in precise k cells of each row. In this paper, we completely solve the existence of NGBTD(4,m) and almost completely solve the existence of NGBTD(5,m) with four exceptions.

关键词： near generalized balanced tournament designs frame generalized doubly resolvable packing constructions existence 05B05

Lyapunov exponents for continuous random transformations

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science china mathematics 2010年第2期53卷 413-424页

作者： ZHU YuJun & ZHANG JinLian college of mathematics and information science, Hebei normal university, Shijiazhuang 050016, china 1. college of mathematics and information science Hebei Normal University Shijiazhuang 050016 China

In this paper, the concept of Lyapunov exponent is generalized to random transformations that are not necessarily differentiable. For a class of random repellers and of random hyperbolic sets obtained via small pertur... 详细信息

关键词： random transformation Lyapunov exponent multiplicative ergodic theorem random repeller random hyperbolic set

Duality properties between spectra and tilings

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science china mathematics 2010年第5期53卷 270-280页

作者： LI JianLin college of mathematics and information science,Shaanxi normal university,Xi’an 710062,china 1. college of mathematics and information science Shaanxi Normal University Xi’an 710062 China

Spectra and tilings play an important role in analysis and geometry *** relations between spectra and tilings have bafied the mathematicians for a long *** conjectures,such as the Fuglede conjecture,are placed on the establishment of relations between spectra and tilings,although there are no desired *** the present paper we derive some characteristic properties of spectra and tilings which highlight certain duality properties between them.

关键词： spectral pair periodic set packing and covering tiling pair