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D(β)-vertex-distinguishing total coloring of graphs

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science china mathematics 2006年第10期49卷 1430-1440页

作者： ZHANG Zhongfu,LI Jingwen,CHEN Xiang’en,YAO Bing, WANG Wenjie & QIU Pengxiang Institute of Applied Mathematic, lanzhou Jiaotong university, lanzhou 73.070, china college of mathematics and information science, northwest normal university, lanzhou 73.070, china college of information and Electrical Engineering, lanzhou Jiaotong university, lanzhou 73.070, china Institute of Applied Mathematic Lanzhou Jiaotong University Lanzhou 730070 China college of mathematics information science Northwest Normal University Lanzhou 730070 China college of information Electrical Engineering Lanzhou Jiaotong University Lanzhou 730070 China

A new concept of the D(β)-vertex-distinguishing total coloring of graphs, i.e., the proper total coloring such that any two vertices whose distance is not larger than β have different color sets, where the color set of a vertex is the set composed of all colors of the vertex and the edges incident to it, is proposed in this paper. The D(2)-vertex-distinguishing total colorings of some special graphs are discussed, meanwhile, a conjecture and an open problem are presented.

关键词： graph, total coloring, D(β)-vertex-distinguishing total coloring, D(β)-vertexdistinguishing total chromatic number.

On adjacent-vertex-distinguishing total coloring of graphs

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science china mathematics 2005年第3期48卷 289-299页

作者： ZHANG Zhongfu, CHEN Xiang’en, LI Jingwen, YAO Bing, LU Xinzhong & WANG Jianfang college of mathematics and information science, northwest normal university, lanzhou 73.070, china Department of Computer, lanzhou normal college, lanzhou 73.070, china Institute of Applied mathematics, lanzhou Jiaotong university, lanzhou 73.070, china college of information and Electrical Engineering, lanzhou Jiaotong university, lanzhou 73.070, china Institute of Applied mathematics, Chinese Academy of sciences, Beijing 100080, china 1. college of mathematics and information science Northwest Normal University 730070 Lanzhou China 2. Department of Computer Lanzhou Normal College 730070 Lanzhou China 3. Institute of Applied mathematics Lanzhou Jiaotong University 730070 Lanzhou China 4. college of information and Electrical Engineering Lanzhou Jiaotong University 730070 Lanzhou China 5. Institute of Applied mathematics Chinese Academy of Sciences 100080 Beijing China

In this paper, we present a new concept of the adjacent-vertex-distinguishing total coloring of graphs (briefly, AVDTC of graphs) and, meanwhile, have obtained the adjacent-vertex-distinguishing total chromatic number... 详细信息

关键词： graph, proper total coloring, adjacent-vertex-distinguishing total coloring, adjacent-vertex-distinguishing total chromatic number.

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

Borel probabilistic and quantitative logic

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science china(information sciences) 2011年第9期54卷 1843-1854页

作者： ZHOU HongJun & WANG GuoJun 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

The present paper introduces the notion of the probabilistic truth degree of a formula by means of Borel probability measures on the set of all valuations,endowed with the usual product topology,in classical two-valued propositional *** approach not only overcomes the limitations of quantitative logic,which require the probability measures on the set of all valuations to be the countably infinite product of uniform probability measures,but also remedies the drawback that probability logic behaves only *** is proved that the notions of truth degree,random truth degree in quantitative logic and the probability of formulas in probability logic can all be brought as special cases into the unified framework of the probabilistic truth *** quantitative logic and probability logic are *** also proves a one-to-one correspondence between deductively closed theories and topologically closed subsets of the space of all valuations,and a one-to-one correspondence between probabilistic truth degree functions and Borel probability measures on the space of all *** second part of the present paper proposes an axiomatic definition of the probabilistic truth degree,and it is finally proved that each probabilistic truth degree function is represented by a unique Borel probability measure on the space of all valuations in the way given in the first *** a theory which we call probabilistic and quantitative logic in the framework of classical propositional logic is established.

关键词： probabilistic truth degree finite separation property probability logic quantitative logic probabilistic and quantitative logic

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

ON THE LEAST SQUARES PROBLEM OF A MATRIXEQUATION

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Journal of Computational mathematics 1999年第6期17卷 589-594页

作者： An-ping Liao(college of science, Hunan normal university, Changsha 410081, china) Hunan normal Univ Coll Sci Changsha 410081 Peoples R China

Least squares solution of F=PG with respect to positive semidefinite symmetric P is considered,a new necessary and sufficient condition for solvablity is given,and the expression of solution is derived in the some special cases. Based on the expression, the least spuares solution of an inverse eigenvalue problem for positive semidefinite symmetric matrices is also given.

关键词： least squares solution matrix equation inverse eigenvalue problem positive semidefinite symmetric matrix

L_p-mixed intersection bodies

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science china mathematics 2008年第12期51卷 2172-2188页

作者： ZHAO ChangJian Department of information and mathematics sciences, college of science, china Jiliang university, Hangzhou 310018, china Department of information and mathematics sciences College of Science China Jiliang University Hangzhou 310018 China

In this paper the author first introduce a new concept of Lp-dual mixed volumes of star bodies which extends the classical dual mixed volumes. Moreover, we extend the notions of Lp- intersection body to Lp-mixed intersection body. Inequalities for Lp-dual mixed volumes of Lp-mixed intersection bodies are established and the results established here provide new estimates for these type of inequalities.

关键词： L p -dual mixed volumes L p -intersection bodies L p -mixed intersection bodies 52A40