In this paper,Noether symmetry and Mei symmetry of discrete nonholonomic dynamical systems with regular and the irregular lattices are investigated.Firstly,the equations of motion of discrete nonholonomic systems are ...In this paper,Noether symmetry and Mei symmetry of discrete nonholonomic dynamical systems with regular and the irregular lattices are investigated.Firstly,the equations of motion of discrete nonholonomic systems are introduced for regular and irregular lattices.Secondly,for cases of the two lattices,based on the invariance of the Hamiltomian functional under the infinitesimal transformation of time and generalized coordinates,we present the quasi-extremal equation,the discrete analogues of Noether identity,Noether theorems,and the Noether conservation laws of the systems.Thirdly,in cases of the two lattices,we study the Mei symmetry in which we give the discrete analogues of the criterion,the theorem,and the conservative laws of Mei symmetry for the systems.Finally,an example is discussed for the application of the results.展开更多
Some characterizations of preregular operators between two Banach lattices are presented. Then several sufficient conditions for preregular operators being regular are given, and some related results are also obtained.
In this paper,we introduce and investigate the strongly regular relation.Then we give the relational representations and an intrinsic characterization of strongly algebraic lattices via mapping relation and strongly r...In this paper,we introduce and investigate the strongly regular relation.Then we give the relational representations and an intrinsic characterization of strongly algebraic lattices via mapping relation and strongly regular relation.展开更多
To reveal the occurrence state and enrichment regularity of the dispersed element indium in pyrite, the petrology,mineralogy, geochemistry, and mineral physics were researched detailedly. The results suggest that the ...To reveal the occurrence state and enrichment regularity of the dispersed element indium in pyrite, the petrology,mineralogy, geochemistry, and mineral physics were researched detailedly. The results suggest that the structure of pyrite is mainlycomposed of massive structure, disseminated structure, vein structure, reticular structure, comb structure and so on. Generally, thepyrite coexists with sphalerite, marmatite, pyrrhotite, chalcopyrite, galena, and arsenopyrite. And the texture of pyrite primarilyconsists of the metasomatic texture, solid solution texture, idiomorphic?hypidiomorphic granular texture, and disseminated texture.The content of indium in pyrite ranges from 0.491×10?6 to 65.1×10?6 with an average value of 14.38×10?6. Yet, the indium content inthe Gaofeng deposit is higher than that in the Dafulou and Tongkeng deposit, showing a particularly significant supernormalenrichment. Besides, the cadmium content in pyrite is also higher than other dispersed elements, and similarly the abnormalenrichment of cadmium in the Gaofeng deposit is also very significant. An obvious positive correlation exists between In and Cd, orTl, but a negative correlation between In and Re. It is difficult to find out a positive or negative correlation between In and Ga. Theelement zinc is of great importance to the enrichment of indium, which can possibly facilitate to the migration and crystallization of dispersed element indium.展开更多
A method to construct strongly non regular order bounded operators from a classical Banach lattice C into any separable Banach lattice F without Dedekind σ completeness is presented in this paper. A r...A method to construct strongly non regular order bounded operators from a classical Banach lattice C into any separable Banach lattice F without Dedekind σ completeness is presented in this paper. A result concerning the order bounded norm and the regular norm is also contained.展开更多
Let E and F be Banach lattices. It is known that if every continuous linear operator from E into F is regular, then, under some mild assumptions on E or F, either E is lattice isomorphic to an AL-space or F is lattice...Let E and F be Banach lattices. It is known that if every continuous linear operator from E into F is regular, then, under some mild assumptions on E or F, either E is lattice isomorphic to an AL-space or F is lattice isomorphic to an AM-space. Here we present a characterization on an AL-space E such that every bounded linear operator from E into a Banach lattice is regular. A counterexample is also provided, which shows that the results are unexpected even if the domain is an AL-space or the range space is an AM-space.展开更多
To deeply understand the emergence of cooperation in natural,social and economical systems,we present an improved fitness evaluation mechanism with memory in spatial prisoner's dilemma game on regular lattices.In ...To deeply understand the emergence of cooperation in natural,social and economical systems,we present an improved fitness evaluation mechanism with memory in spatial prisoner's dilemma game on regular lattices.In our model,the individual fitness is not only determined by the payoff in the current game round,but also by the payoffs in previous round bins.A tunable parameter,termed as the memory strength(μ),which lies between 0 and 1,is introduced into the model to regulate the ratio of payoffs of current and previous game rounds in the individual fitness calculation.When μ = 0,our model is reduced to the standard prisoner's dilemma game;while μ = 1 represents the case in which the payoff is totally determined by the initial strategies and thus it is far from the realistic ones.Extensive numerical simulations indicate that the memory effect can substantially promote the evolution of cooperation.For μ < 1,the stronger the memory effect,the higher the cooperation level,but μ = 1 leads to a pathological state of cooperation,but can partially enhance the cooperation in the very large temptation parameter.The current results are of great significance for us to account for the role of memory effect during the evolution of cooperation among selfish players.展开更多
The authors give finite dimensional exponential solutions of the bigraded Toda hierarchy （BTH）. As a specific example of exponential solutions of the BTH, the authors consider a regular solution for the （1, 2）-BTH...The authors give finite dimensional exponential solutions of the bigraded Toda hierarchy （BTH）. As a specific example of exponential solutions of the BTH, the authors consider a regular solution for the （1, 2）-BTH with a 3 × 3-sized Lax matrix, and discuss some geometric structures of the solution from which the difference between the （1, 2）- BTH and the original Toda hierarchy is shown. After this, the authors construct another kind of Lax representation of （N, 1）-BTH which does not use the fractional operator of Lax operator. Then the authors introduce the lattice Miura transformation of （N, 1）-BTH which leads to equations depending on one field, and meanwhile some specific examples which contain the Volterra lattice equation （a useful ecological competition model） are given.展开更多
基金Project supported by the National Outstanding Young Scientist Fund of China (Grant No. 10725209)the National Natural Science Foundation of China (GrantNos. 11072218 and 11272287)the Natural Science Foundation of Zhejiang Province,China (Grant No. Y6110314)
文摘In this paper,Noether symmetry and Mei symmetry of discrete nonholonomic dynamical systems with regular and the irregular lattices are investigated.Firstly,the equations of motion of discrete nonholonomic systems are introduced for regular and irregular lattices.Secondly,for cases of the two lattices,based on the invariance of the Hamiltomian functional under the infinitesimal transformation of time and generalized coordinates,we present the quasi-extremal equation,the discrete analogues of Noether identity,Noether theorems,and the Noether conservation laws of the systems.Thirdly,in cases of the two lattices,we study the Mei symmetry in which we give the discrete analogues of the criterion,the theorem,and the conservative laws of Mei symmetry for the systems.Finally,an example is discussed for the application of the results.
文摘Some characterizations of preregular operators between two Banach lattices are presented. Then several sufficient conditions for preregular operators being regular are given, and some related results are also obtained.
基金Supported by the National Natural Science Foundation of China(10861007)
文摘In this paper,we introduce and investigate the strongly regular relation.Then we give the relational representations and an intrinsic characterization of strongly algebraic lattices via mapping relation and strongly regular relation.
基金Projects(41202051,41672076)supported by the National Natural Science Foundation of ChinaProject(2015CX008)supported by the Innovation-driven Plan in Central South University,China+4 种基金Project(2016JJ1022)supported by Hunan Provincial Natural Science Outstanding Youth Foundation of ChinaProject(CSUZC201601)supported by the Open-End Fund for the Valuable and Precision Instruments of Central South University,ChinaProject(2014T70886)supported by the Special Program of the Postdoctoral Science Foundation of ChinaProject(2012M521721)supported by China Postdoctoral Science FoundationProject(XKRZ[2014]76)supported by the Platform of Scientific and Technological Innovation for Hunan Youth,China
文摘To reveal the occurrence state and enrichment regularity of the dispersed element indium in pyrite, the petrology,mineralogy, geochemistry, and mineral physics were researched detailedly. The results suggest that the structure of pyrite is mainlycomposed of massive structure, disseminated structure, vein structure, reticular structure, comb structure and so on. Generally, thepyrite coexists with sphalerite, marmatite, pyrrhotite, chalcopyrite, galena, and arsenopyrite. And the texture of pyrite primarilyconsists of the metasomatic texture, solid solution texture, idiomorphic?hypidiomorphic granular texture, and disseminated texture.The content of indium in pyrite ranges from 0.491×10?6 to 65.1×10?6 with an average value of 14.38×10?6. Yet, the indium content inthe Gaofeng deposit is higher than that in the Dafulou and Tongkeng deposit, showing a particularly significant supernormalenrichment. Besides, the cadmium content in pyrite is also higher than other dispersed elements, and similarly the abnormalenrichment of cadmium in the Gaofeng deposit is also very significant. An obvious positive correlation exists between In and Cd, orTl, but a negative correlation between In and Re. It is difficult to find out a positive or negative correlation between In and Ga. Theelement zinc is of great importance to the enrichment of indium, which can possibly facilitate to the migration and crystallization of dispersed element indium.
文摘A method to construct strongly non regular order bounded operators from a classical Banach lattice C into any separable Banach lattice F without Dedekind σ completeness is presented in this paper. A result concerning the order bounded norm and the regular norm is also contained.
文摘Let E and F be Banach lattices. It is known that if every continuous linear operator from E into F is regular, then, under some mild assumptions on E or F, either E is lattice isomorphic to an AL-space or F is lattice isomorphic to an AM-space. Here we present a characterization on an AL-space E such that every bounded linear operator from E into a Banach lattice is regular. A counterexample is also provided, which shows that the results are unexpected even if the domain is an AL-space or the range space is an AM-space.
基金Supported by the National Natural Science Foundation of China under Grant Nos. 61203138,60904063Innovation Fund for Technology Based Firms in Tianjin
文摘To deeply understand the emergence of cooperation in natural,social and economical systems,we present an improved fitness evaluation mechanism with memory in spatial prisoner's dilemma game on regular lattices.In our model,the individual fitness is not only determined by the payoff in the current game round,but also by the payoffs in previous round bins.A tunable parameter,termed as the memory strength(μ),which lies between 0 and 1,is introduced into the model to regulate the ratio of payoffs of current and previous game rounds in the individual fitness calculation.When μ = 0,our model is reduced to the standard prisoner's dilemma game;while μ = 1 represents the case in which the payoff is totally determined by the initial strategies and thus it is far from the realistic ones.Extensive numerical simulations indicate that the memory effect can substantially promote the evolution of cooperation.For μ < 1,the stronger the memory effect,the higher the cooperation level,but μ = 1 leads to a pathological state of cooperation,but can partially enhance the cooperation in the very large temptation parameter.The current results are of great significance for us to account for the role of memory effect during the evolution of cooperation among selfish players.
基金supported by the National Natural Science Foundation of China(Nos.11201251,10971109)the Natural Science Foundation of Zhejiang Province(No.LY12A01007)the K.C.Wong Magna Fundin Ningbo University
文摘The authors give finite dimensional exponential solutions of the bigraded Toda hierarchy （BTH）. As a specific example of exponential solutions of the BTH, the authors consider a regular solution for the （1, 2）-BTH with a 3 × 3-sized Lax matrix, and discuss some geometric structures of the solution from which the difference between the （1, 2）- BTH and the original Toda hierarchy is shown. After this, the authors construct another kind of Lax representation of （N, 1）-BTH which does not use the fractional operator of Lax operator. Then the authors introduce the lattice Miura transformation of （N, 1）-BTH which leads to equations depending on one field, and meanwhile some specific examples which contain the Volterra lattice equation （a useful ecological competition model） are given.
