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Epidemic dynamics on complex networks

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Progress in Natural Science:Materials International 2006年第5期16卷 452-457页

作者： ZHOU Tao , FU Zhongqian, and WANG Binghong (department of Electronic Science and technology, university of Science and technology of china, hefei 23.026, china department of Modern Physics, university of Science and technology of china, hefei 23.026, china) department of Electronic Science and technology University of Science and Technology of China Hefei 230026 China department of Modern Physics University of Science and Technology of China Hefei 230026 China

Recently, motivated by the pioneer work in revealing the small-world effect and scale-free property of various real-life networks, many scientists devote themselves to studying complex networks. One of the ultimate goals is to understand how the topological structures affect the dynamics upon networks. In this paper, we give a brief review on the studies of epidemic dynamics on complex networks, including the description of classical epidemic models, the epidemic spread on small-world and scale-free networks, and network immunization. Finally, perspectives and some interesting problems are proposed.

关键词： epidemic dynamics complex networks critical value immunization small-world effect scale-free property.

Parabolic equation of the m-Laplacian with nonlinear boundary condition

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Chinese Science Bulletin 1998年第11期43卷 905-908页

作者： WANG Shu+ 1, 2, WANG Mingxin 3. XIE Chunhong 1 1. department of mathematics, Nanjing university, Nanjing 210093. {3. 2. department of mathematics, Henan university, Kaifeng 475001, {3. 3. department of Applied mathematics, Southeast university, department of Mathernntics Nanjing University Nanjing China department of mathematics Henan University Kaifeng China department of Applied mathematics Southeast University Nanjing China

The existence and nonexistence of global positive weak solutions of parabolic equation of the m-Laplician with nonlinear boundary condition are dealt with. The necessary and sufficient conditions on the existence of a... 详细信息

关键词： nonlinear boundary condition parabolic equation of m-Laplacian global solution blow-up.

The regular representation and regular covariant representation of crossed products of Woronowicz C^(*)-algebras

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Science china mathematics 2005年第9期48卷 1245-1259页

作者： ZHANG Xiaoxia~(1,2) & GUO Maozheng~(1,3. 1. School of Mathematical Sciences,Peking university,Beijing 100871,china 2. department of {3.,Yantai university,Yantai 264005,china 3. LMAM,Peking university,Beijing 100871,china School of Mathematical Sciences Peking University Beijing China department of mathematics Yantai University Yantai China LMAM Peking University Beijing China

In this paper,it is shown that the regular representation and regular covariant representation of the crossed products A×α G correspond to the twisted multiplicative unitary operators,where A is a Woronowicz C~*-algebra acted upon by a discrete group ***,it is also shown that the regular covariant C~*-algebra is the Woronowicz C~*-algebra which corresponds to a multiplicative ***,an explicit description of the multiplicative unitary operator for C(SU_q(2) )×α (?) is given in terms of those of the Woronowicz C~*-algebra C(SU_q(2) ) and the discrete group G.

关键词： multiplicative unitary operator, Woronowicz C*-algebra, crossed product.

Transitivity, mixing and chaos for a class of set-valued mappings

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Science china mathematics 2006年第1期49卷 1-8页

作者： LIAO Gongfu, WANG Lidong & ZHANG Yucheng Institute of mathematics, Jilin university, Changchun 13.012, china Institute of Nonlinear Information {3., Dalian Nations university, Dalian 116600, china department of mathematics, university of Science and {3. of china, hefei 23.026, china Institute of mathematics Jilin University Changchun China Institute of Nonlinear Information technology Dalian Nations University Dalian China department of mathematics University of Science and Technology of China Hefei China

Consider the continuous map f : x → X and the continuous map f of K,(X) into itself induced by f, where X is a metric space and K(X) the space of all non-empty compact subsets of x endowed with the Hausdorff metric. According to the questions whether the chaoticity of f implies the chaoticity of f posed by Roman-Flores and when the chaoticity of f implies the chaoticity of f posed by Fedeli, we investigate the relations between f and f in the related dynamical properties such as transitivity, weakly mixing and mixing, etc. And by using the obtained results, we give the satisfied answers to Roman-Flores's question and Fedeli's question.

关键词： set-valued mapping, transitivity, weak mixing, mixing, chaos.

Application of Fourier Slice Theorem in Wigner Operator Theory and New Complete Representation

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Communications in Theoretical Physics 2009年第11期52卷 829-831页

作者： WANG Tong-Tong~1 and FAN Hong-Yi~(2,3.1 School of mathematics and Physics, Huangshi Institute of technology, Huangshi 43.003. china2 {3. of Material Science and Engineering, university of Science and technology of china, hefei 23.026, china3.department of Physics, Shanghai Jiao Tong university, Shanghai 20003., china School of mathematics and Physics Huangshi Institute of Technology Huangshi 435003 China department of Material Science and Engineering University of Science and Technology of China Hefei 230026 China department of Physics Shanghai Jiao Tong University Shanghai 200030 China

By applying the Fourier slice theorem,S;（λ）=∫;P;（t）e;=F（λcosθ,λsinθ）,where P;（t）is aprojection of f（x,p）=（?）F（u,v）e;dudv along lines of constant,to the Wigner operator we are naturally led toa projection operator（pure state）,which results in a new complete *** Weyl orderimg formalism of theWigner operator is used in the derivation.

关键词： Wigner operator Fourier slice theorem new complete representation

Comparison study of trapped water in human erythrocytes by EPC and DSC method and its application

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Science china(Technological Sciences) 2004年第3期47卷 343-351页

作者： ZHAO Gang1, HE Liqun1, GUO Xiaojie2, LIU Zhong3. LUO Dawei1,3.& GAO Dayong1,3.1. Cryobiomedical Engineering Research Institute, department of Thermal Science and Energy Engineering, university of Science and technology of {3., hefei 23.027, {3. 2. Red Cross Blood Center of hefei, hefei 23.022, {3. 3. department of Mechanical Engineering, university of Kentucky, Lexington, KY 40506-0108, USA Cryobiomedical Engineering Research Institute Department of Thermal Science and Energy Engineering University of Science and Technology of China Hefei 230027 China Red Cross Blood Center of Hefel Hefei 230022 China department of Mechanical Engineering University of Kentucky Lexington KY 40506-0108 United States

The novel differential scanning calorimetry method for determining trapped water volume of human red blood cell during freezing process has been reexamined. Results show that the final erythrocyte volume is 53. of its isotonic volume after freezing to -40℃. An electronic particle counter (MultisizerTM III, Beckman Coulter Inc., USA) was used to measure cell volume changes in response to hypertonic solution. Using this approach, when extracellular solution was 3.86 mOsm, the equilibrium cell volume was found to be 57% of its isotonic value. Both results indicate that 3.%—40% of intracellular water is trapped and cannot respond to osmotic difference between intra- and extracellular solution. These findings are consistent with the published data: at least 20%—3.% of the isotonic cell water volume is retained within RBCs during freezing. Some applications of the values of trapped water are addressed.

关键词： differential scanning calorimeter/DSC, electronic particle counter/EPC, cell volumetric change, red blood cell/RBC/erythrocyte

s-ordering operator expansions of quantum-mechanical fundamental representations and their applications

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Science china(Physics,Mechanics & Astronomy) 2011年第12期54卷 2150-2154页

作者： FAN HongYi 1,3., XU YeJun 2 & YUAN HongChun 3.4 1 department of Materials Science and Engineering, university of Science and technology of {3., hefei 23.026, {3. 2 department of Physics Electronic and Engineering, Chizhou university, Chizhou 247000, {3. 3.department of Physics, Shanghai Jiao Tong university, Shanghai 20003., {3. 4 College of Optoelectronic Engineering, Changzhou Institute of technology, Changzhou 213.02, {3. department of Materials Science and Engineering University of Science and Technology of China Hefei China department of Physics Shanghai Jiao Tong University Shanghai China department of Physics Electronic and Engineering Chizhou University Chizhou China College of Optoelectronic Engineering Changzhou Institute of Technology Changzhou China

We show that the quantum-mechanical fundamental representations, say, the coordinate representation, the coherent state representation, the Fan-Klauder entangled state representation can be recast into s-ordering operator expansion, which is elegant in form and has many applications in deriving new operator identities. This demonstrates that Dirac's symbolic method can be merged into Newton-Leibniz integration theory in a broad way.

关键词： s-ordering operator expansion operator identities quantum mechanical representation

Optimal Replenishment Problem for Items with Polynomial Demand During Their Life Period

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Journal of Systems Engineering and Electronics 1999年第2期10卷 9-14页

作者： Zhou Yongwu(department of mathematics, hefei {3. of technology,23.009, P. R. china) department of mathematics Hefei University of Technology 230009 P. R. China

In this paper, a deterministic lot-sizing model is developed for an item during its lifeperiod. A demand for the item is approximated by a special polynomial function. And shortages areallowed to occur in the proposed model. A simple dynamic programming method is presented forgenerating the optimal replenishment policy. A numerical example is used to illustrate the solutionprocedure for the special case with quadric demand. Sensitivity analysis for parameters is alsoincluded.

关键词： Dynamic programming Inventory Polynomial demand.

Estimation of an Important Constant in Sieve Method

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Acta Mathematica Sinica,English Series 1994年第1期10卷 1-3页

作者： Xie Sheng-gang department of mathematics university of Science and {3. of china hefei,23.027 china department of mathematics University of Science and Technology of China Hefei China

ζk is one of the most important constant in the siève *** paper gives the relatively accurate lower bound and upper bound on it,that is,3.1/kck,where c=1.22... and k>16.

ζk is one of the most important constant in the siève *** paper gives the relatively accurate lower bound and upper bound on it,that is,3.sup>-1/kck,where c=1.22... and k>16.

关键词： exp Estimation of an Important Constant in Sieve Method