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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 college of mathematics and information science Shaanxi Normal University Xi’an 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

Theoretical study of the mechanism for C-H bond activation in spin-forbidden reaction between Ti^+ and C_2H_4

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science china Chemistry 2009年第3期52卷 295-303页

作者： LV LingLing1, LIU XinWen1, YUAN Kun1, WANG XiaoFang1 & WANG YongCheng2 1 college of Life science and Chemistry, Tianshui normal university, Tianshui 741001, china 2 college of Chemistry and Chemical Engineering, northwest normal university, lanzhou 730070, china college of Life science and Chemistry Tianshui Normal University Tianshui China college of Chemistry and Chemical Engineering Northwest Normal University Lanzhou China

The mechanism of the spin-forbidden reaction Ti+(4F, 3d24s1) + C2H4 → TiC2H2+ (2A2) + H2 on both doublet and quartet potential energy surfaces has been investigated at the B3LYP level of theory. Crossing points between the potential energy surfaces and the possible spin inversion process are discussed by means of spin-orbit coupling (SOC) calculations. The strength of the SOC between the low-lying quartet state and the doublet state is 59.3 cm-1 in the intermediate complex IM1-4B2. Thus, the changes of its spin multiplicity may occur from the quartet to the doublet surface to form IM1- 2A1, leading to a sig-nificant decrease in the barrier height on the quartet PES. After the insertion intermediate IM2, two dis-tinct reaction paths on the doublet PES have been found, i.e., a stepwise path and a concerted path. The latter is found to be the lowest energy path on the doublet PES to exothermic TiC2H2+ (2A2) + H2 products, with the active barrier of 4.52 kcal/mol. In other words, this reaction proceeds in the following way: Ti++C2H4 →4IC→IM1-4B2→4,2ISC→IM1- 2A1→[2TSins]→IM2→[2TSMCTS]→IM5→TiC2H2+(2A2)+H2.

关键词： Ti+(4F) and C2H4 spin-forbidden reaction mechanism spin-orbit coupling (SOC) concerted path

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 college of Physics and information Engineering Hebei Normal University Shijiazhuang China college of mathematics and information science Hebei Normal University Shijiazhuang 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 China college of mathematics and information science Hebei Normal University Shijiazhuang 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) 湖南师范大学理学院湖南长沙 410081

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 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

Remarks on Vertex-Distinguishing IE-Total Coloring of Complete Bipartite Graphs K4,n and Kn,n

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Journal of Mathematical Research with Applications 2012年第2期32卷 157-166页

作者： Xiang’en CHEN,Xiaoqing XIN,Wenyu HE college of mathematics and information science,northwest normal university,Gansu 730070,P.R.china college of mathematics and information science Northwest Normal University Gansu 730070

Let G be a simple *** IE-total coloring f of G refers to a coloring of the vertices and edges of G so that no two adjacent vertices receive the same *** C(u) be the set of colors of vertex u and edges incident to u under *** an IE-total coloring f of G using k colors,if C(u)=C(v) for any two different vertices u and v of V(G),then f is called a k-vertex-distinguishing IE-total-coloring of G,or a k-VDIET coloring of G for *** minimum number of colors required for a VDIET coloring of G is denoted by χ ie vt (G),and it is called the VDIET chromatic number of *** will give VDIET chromatic numbers for complete bipartite graph K4,n (n≥4),K n,n (5≤ n ≤ 21) in this article.

关键词： graphs IE-total coloring vertex-distinguishing IE-total coloring vertex-distinguishing IE-total chromatic number complete bipartite graph.

The environmental signal of an early Holocene pollen record from the Shiyang River basin lake sediments, NW china

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Chinese science Bulletin 2002年第4期47卷 267-273页

作者： ZHU Yan, CHEN Fahu & Madsen Davidcollege of geography and Environment, northwest normal university, lanzhou 730070, china National Key Laboratory of West Environmental System, lanzhou university, lanzhou 730000, china Utah Geological Surv college of geography and Environment Northwest Normal University Lanzhou China National Key Laboratory of West Environmental System Lanzhou University Lanzhou China Utah Geological Survey Utah USA

Pollen analyses of 85 samples from the San-jiaocheng section well along the margin of a palaeolake at the end of the Shiyang River, NW china, show that Picea and Sabina dominate the pollen assemblage. Together they reach as high as 40%-60%, with the percentage of Picea varying inversely with that of Sabina. Similar results were obtained from another section in the Shiyang River drainage. Using modern ecological habitat relationship analogues, pol-len transport characteristics, and the overall pollen assem-blage, we propose that both Picea and Sabina pollen were transported by the river from the mountains at the upper reaches of the Shiyang River, and that the assemblage is more indicative of changes in upland vegetation than of local conditions near the section. This interpretation is supported by pollen data derived from surface samples, water samples, and riverbed samples. Using a moisture indicator (the Picea to Sabina ratio) and calculated pollen concentrations, we identify a series of

关键词： NW china The environmental signal of an early Holocene pollen record from the Shiyang River basin lake sediments

Sol-gel preparation and characterization of Co_3O_4 nanocrystals

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Journal of university of science and Technology Beijing 2003年第1期10卷 54-57页

作者： Jinzhang Gao, Yanchun Zhao, Wu Yang, Jianniao Tian, Fei Guan. and Yongjun MaChemistry and Chemical Engineering college, northwest normal university, lanzhou 730070, china NW normal Univ Chem & Chem Engn Coll Lanzhou 730070 Peoples R China

A new citrate acid-hydrazine sol-gel route for preparation of Co3O4 nanoparticles has been developed. Co3O4 nanoparticles with different particle-sizes and morphology were prepared at different heat-treatment temperatures and the pure cubic nanocrystals of Co3O4 were obtained at 600℃. The synthesis process was monitored by infrared spectroscopy (IR), thermal gravimetric and differential thermal analysis (TG-DTA). The structure and morphology of Co3O4 nanocrystals were characterized by X-ray powder diffraction (XRD), transmission electron microscopy (TEM) and X-ray-photoelectron spectroscopy (XPS). The infrared absorption bands blue-shifted with particle size decreasing, which could be attributed to increasing surface effect. XPS results showed that predominant species at surface layers of Co3O4 nanocrystals are octahedral Co (Ⅲ).

关键词： sol-gel route nanocrystals cobalt oxide