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Asymmetric interaction will facilitate the evolution of cooperation

Science China(Life Sciences) 2010年第8期53卷 1041-1046页

作者： WANG RuiWu1, HE JunZhou1,2. WANG YaQiang1,2. SHI Lei1,3.& LI YaoTang1,2.1 State Key Laboratory of Genetic Resources and Evolution, {3. Institute of Zoology, Chinese Academy of Science, {3. 6502.3. China 2.School of {2. and Statistics,{3., kunming 650091, China 3.Statistics and {2. College,{3. of Finance and Economics, {3. 6502.1, China 1. State Key Laboratory of Genetic Resources and Evolution Kunming Institute of Zoology Chinese Academy of Science Kunming 650223 China2. School of Mathematics and Statistics Yunnan University Kunming 650091 China3. Statistics and Mathematics College Yunnan University of Finance and Economics Kunming 650221 China

Explaining the evolution of cooperation remains one of the greatest problems for both biology and social science. The classical theories of cooperation suggest that cooperation equilibrium or evolutionary stable strategy between partners can be maintained through genetic similarity or reciprocity relatedness. These classical theories are based on an assumption that partners interact symmetrically with equal payoffs in a game of cooperation interaction. However, the payoff between partners is usually not equal and therefore they often interact asymmetrically in real cooperative systems. With the Hawk–Dove model, we find that the probability of cooperation between cooperative partners will depend closely on the payoff ratio. The higher the payoff ratio between recipients and cooperative actors, the greater will be the probability of cooperation interaction between involved partners. The greatest probability of conflict between cooperative partners will occur when the payoff between partners is equal. The results show that this asymmetric relationship is one of the key dynamics of the evolution of cooperation, and that pure cooperation strategy (i.e., Nash equilibrium) does not exist in asymmetrical cooperation systems, which well explains the direct conflict observed in almost all of the well documented cooperation systems. The model developed here shows that the cost-to-benefit ratio of cooperation is also negatively correlated with the probability of cooperation interaction. A smaller cost-to-benefit ratio of cooperation might be created by the limited dispersal ability or exit cost of the partners involved, and it will make the punishment of the non-cooperative individuals by the recipient more credible, and therefore make it more possible to maintain stable cooperation interaction.

关键词： Hawk–Dove game evolutionarily stable strategy asymmetric cooperation mixed strategy Nash equilibrium

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A Series of Convex Functions on a Banach Space

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Acta Mathematica Sinica,English Series 1998年第1期14卷 77-84页

作者： Zheng Xiyin department of mathematics,{2.,{3., China

A series of convex functions on a Banach space is studied. The generalizations of the Moreau-Rockafellar theorem are given. As its application, the partial generalization of the Kuhn- Tucker theorem is obtained.

关键词： Pointwise convergence Locally uniform convergence Subdifferential Moreau-Rockafellar theorem Kuhn-Tucker theorem

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CYCLES CONTAINING MANY VERTICES OF SUBSETS IN GRAPHS WITH LARGE DEGREE SUMS AND NEIGHBORHOOD UNIONS

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Systems Science and Mathematical Sciences 2000年第4期13卷 432-445页

作者： LI Jianping (Institute of mathematics and department of mathematics,{3., kunming 650091, China) 云南大学数学所云南昆明 650091

Let G be a graph of order n and X V(G). G is called X-cyclable if G has an X-cycle, i.e., a cycle containing all vertices of X. Define the parameters a(X) = max{|S| S is an independent vertex set in G[X] induced by X}, σk(X) = min{∑ki=1dG(x.i| {x1, x1…, xk} is an independent vertex set in G[X]} and NCk(X) = min{|∪ki=1 NG(xi)| | {x1, x2.,xk} is an independent vertex set in G[X] }. Our main result is as follows: If G is a 1-tough graph and X V(G) with σ3.X)≥ n, then for every integer t ≥ 1, G has a cycle C containing at least min{|X|, (2.X| - n + 3. + 1 - t), |X| + NCt(X) - a(X)} venices of X, where δ(X) = [σ3.X)]. This result further extends previous results in H.J. Broersma et al. in terms of X-cyclability. We also obtain that if G is a 1-tough graph with σ3.(X) ≥ n, then for every integer t ≥ 1, G has a cycle containing at least min{|X|, (4|X|- 2.+4δ(X) + 1 - 2.), NCt (X) +NCt (X)} vertices of X, where NCt (X) = min{|N(I) ∩X|| I is an independent set of t vertices of X}. Analogous results are established for 2.connected graphs.

关键词： (X-)longest cycle (X-)dominating cycle hamiltonian graph vertex degree large degree sums neighborhood unions.

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Exponential attractors of the nonlinear wave equations

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Chinese Science Bulletin 1998年第16期43卷 1331-1335页

作者： DAI Zhengde 1 and MA Dacai 2.1. department of mathematics,{2., {3. 65003., China 2. department of mathematics, Shangrao Teachers College, Shangrao 3.4000, China department of mathematics Yunnan University Kunming China department of mathematics Shangrao Teachers College Shangrao China

The (E, E)-type exponential attractors for the nonlinear wave equation were obtained by using the decomposition of operators and finite covering *** results solves the open problem of Eden et al.

关键词： nonlinearity wave equations exponential attractors.

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GLOBAL ATTRACTIVITY IN A PERIODIC DELAY SINGLE SPECIES MODEL

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Systems Science and Mathematical Sciences 2000年第1期13卷 1-6页

作者： LI Yong kun (department of mathematics,{2.,{3., China) 云南大学数学系云南昆明 650091

***[1]illtroducedthefollowingdelayLotka-Volterratypesinglespeciespopulationgrowthmodel:wherea,b,ctTarerealconstants,anda>0,c>0,***>0,b0,(l.1)exhibitstheso--calledAlic... 详细信息

***[1]illtroducedthefollowingdelayLotka-Volterratypesinglespeciespopulationgrowthmodel:wherea,b,ctTarerealconstants,anda>0,c>0,***>0,b0,(l.1)exhibitstheso--calledAlic...

关键词： Single species population growth positive periodic solution global attractivity foedholm mapping.

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OUTLIERS AND INFLUENTIAL OBSERVATIONS IN A RIDGE MEAN SHIFT REGRESSION

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Systems Science and Mathematical Sciences 1995年第1期8卷 12-26页

作者： PAN Jianxin (Institute of Applied mathematics, yunnan Province,{2., China)XIONG Haiyan ({3. of mathematics, yunnan university,{2., China) 云南省应用数学所云南昆明 650091 云南大学数学系云南昆明

ＯＵＴＬＩＥＲＳＡＮＤＩＮＦＬＵＥＮＴＩＡＬＯＢＳＥＲＶＡＴＩＯＮＳＩＮＡＲＩＤＧＥＭＥＡＮＳＨＩＦＴＲＥＧＲＥＳＳＩＯＮＰＡＮＪｉａｎｘｉｎ（ＩｎｓｔｉｔｕｔｅｏｆＡｐｐｌｉｅｄＭａｔｈｅｍａｔｉｃｓ，Ｙｕｎｎａｎ... 详细信息

ＯＵＴＬＩＥＲＳＡＮＤＩＮＦＬＵＥＮＴＩＡＬＯＢＳＥＲＶＡＴＩＯＮＳＩＮＡＲＩＤＧＥＭＥＡＮＳＨＩＦＴＲＥＧＲＥＳＳＩＯＮＰＡＮＪｉａｎｘｉｎ（ＩｎｓｔｉｔｕｔｅｏｆＡｐｐｌｉｅｄＭａｔｈｅｍａｔｉｃｓ，ＹｕｎｎａｎＰｒｏｖｉｎｃｅ，Ｋｕｎｍｉｎｇ６...

关键词： Outliers influential observations ridge mean shift regression ridge residuals.

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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 {2., Nanjing 2.0093. China {3., Henan {2., Kaifeng 475001, China 3. department of Applied mathematics, Southeast {2., 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.

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CAS-MCSCF Study on the Ground State of the Ditungsten Molecule(W_2.

引用

Chinese Chemical Letters 1997年第4期8卷 347-350页

作者： GUO Liang LI Xue Yan TU Shu Shan DAI(department of Chemistry, yunnan university, {2.. {3. 650091) yunnan UNIV DEPT CHEMKUNMING 650091YUNNANPEOPLES R CHINA

Complete active space multiconfiguration self-consisten-field (CAS-MCSCF)calculations are carried out on the ground stae() of W_2. The spectroscopic properties(Re=2.078A. De=4.2.4eV and ωe=3.4.3.m-1) and the poential... 详细信息

关键词： CAS-MCSCF Study on the Ground State of the Ditungsten Molecule W2

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Ab Initio Study of the Excited State Decomposition Reactions of Monothioformic Acid

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Chinese Chemical Letters 1998年第5期9卷 459-461页

作者： Xiao Guang XIE Huai CAO (Modem Biological Center, yunnan university Kunndng 650091)Xian Jun BI ({2. of Chemistry, {3. Normal university kunming 650092.Shu Shan DAI ({2. of Chemistry, yunnan university Kunndng 650091) yunnan Univ Modern Biol Ctr Kunming 650091 Peoples R China yunnan Normal Univ Dept Chem Kunming 650092 Peoples R China yunnan Univ Dept Chem Kunming 650091 Peoples R China

The possible excited state decomposition reactions (dehydrogensulfidation, dehydration, and dehydrogenation) of the four tautomers of monothioformic acid have been investigated by ab initio methods with 6-3.G** basis sets at the CIS level. The activation energies of the four excited state reactions are 42.57, 42.49, 56.90, 47.73.kcal/mol, and are respectively lower than that of the ground states by 2..52. 2..98, 2..2., and 2..10 kcal/mol.

关键词： monothioformic acid excited state decomposition reaction ab initio

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ON THE ESTIMATIONS OF BOUNDS FOR DETERMINANT OF HADAMARD PRODUCT OF H-MATICES

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Journal of Computational mathematics 2001年第4期19卷 365-370页

作者： Yao-tang Li (department of Mathemotics, Yuunan university,{2., China) Ji-cheng Li (department of mathematics, Xian Jiaotong university, Xian 71049, China) 云南大学云南昆明 650091 西安交通大学陕西西安 710049

In this paper, some estimations of bounds for determinant of Hadamard product of H-matrices are given. The main result is the following: if A= (aij) and B=(bij) are nonsingular H-matrices of order n and ∏in=1, aiibii> 0, and Ak and Bk, k = 1, 2.…,n, are the k× k leading principal submatrices of A and B, respectively, then where M(Ak) denotes the comparison mains of Ak.

关键词： H-matrix Determinant Hadamard product.

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