Let G be a discrete group with a neutral element and H be a quasitriangular Hopf G-coalgebra over a field k. Then the relationship between G-grouplike elements and ribbon elements of H is considered. First, a list of ...Let G be a discrete group with a neutral element and H be a quasitriangular Hopf G-coalgebra over a field k. Then the relationship between G-grouplike elements and ribbon elements of H is considered. First, a list of useful properties of a quasitriangular Hopf G-coalgebra and its Drinfeld elements are proved. Secondly, motivated by the relationship between the grouplike and ribbon elements of a quasitriangular Hopf algebra, a special kind of G-grouplike elements of H is defined. Finally, using the Drinfeld elements, a one-to-one correspondence between the special G-grouplike elements defined above and ribbon elements is obtained.展开更多
In this paper, the eigenfunction method established by Chen Jin-quan is used to compute the C-G coefficients in regard to the coupling between symmetry points and lines in the first Brillouin zone of the structure D6h...In this paper, the eigenfunction method established by Chen Jin-quan is used to compute the C-G coefficients in regard to the coupling between symmetry points and lines in the first Brillouin zone of the structure D6h^1, space group. Therewith, the wave vector selection rule and the C-G series, are also given as the middle result of computing the C-G coefficients.展开更多
The eigenfunction method put forward by Chen Jin-quan is illustrated. We apply this theory to the space group D1_ 6h. The selection rules of this space are worked out in the points of higher symmetry A,K,H in the firs...The eigenfunction method put forward by Chen Jin-quan is illustrated. We apply this theory to the space group D1_ 6h. The selection rules of this space are worked out in the points of higher symmetry A,K,H in the first Brillion Zone. The C-G coefficients are calculated for K.HA.展开更多
The links of Motoman HP6 arc welding robot are considered as an open kinematic chain which consists of a series of rotational joints through concatenation. One end of the open chain is fixed to the base or the earth, ...The links of Motoman HP6 arc welding robot are considered as an open kinematic chain which consists of a series of rotational joints through concatenation. One end of the open chain is fixed to the base or the earth, and the other end which is free fastens the end executor to complete various duties. Each link of this arc welding robot has four kinds of Denavit-Hartenberg parameters: common normal length between two adjacent links, angle of two adjacent joints, distance between the crossing of common normal length and two joints axes, and angle of two adjacent links. The displacement relation between each link of the Motoman HP6 arc welding robot is introduced, and the kinematic positive-going solution and the kinematic passive-going solution are calculated.展开更多
A transition diagram is used to describe the behavior of systems. Birth-death equations were derived from transition diagram depicting the state of the birth-death processes. Queue models and characteristics of queue ...A transition diagram is used to describe the behavior of systems. Birth-death equations were derived from transition diagram depicting the state of the birth-death processes. Queue models and characteristics of queue models are also derivable from birth-death processes. These queue models consist of mathematical formulas and relationships that can be used to determine the operating characteristics （performance measures） for a waiting line. Schematic and transition diagrams of different single server queue models were shown. Relationships between birth-death processes, waiting lines （queues） and transition diagrams were given. While M/M/I/K queue model states was limited by K customers and had （K＋I） states, M/M/1/1 queue model had only two states. M/G/1/∝/∝ and M/M/1/∝/∝ shared similar characteristics. Many ideal queuing situations employ M/M/1 queueing model.展开更多
We consider a Lotka-Volterra prey-predator model with cross-diffusion and Holling type-II functional response.The main concern is the existence of positive solutions under the combined effect of cross-diffusion and Ho...We consider a Lotka-Volterra prey-predator model with cross-diffusion and Holling type-II functional response.The main concern is the existence of positive solutions under the combined effect of cross-diffusion and Holling type-II functional response.Here,a positive solution corresponds to a coexistence state of the model.Firstly,we study the sufficient conditions to ensure the existence of positive solutions by using degree theory and analyze the coexistence region in parameter plane.In addition,we present the uniqueness of positive solutions in one dimension case.Secondly,we study the stability of the trivial and semi-trivial solutions by analyzing the principal eigenvalue of the corresponding linearized system,and then we characterize the stable/unstable regions of semi-trivial solutions in parameter plane.展开更多
There are two algebraic lower bounds of the number of n-periodic points of a self-map f ： M →4 M of a compact smooth manifold of dimension at least 3： NFn（f） = min{#Fix（gn）;g - f; g continuous} and NJDn（f） = ...There are two algebraic lower bounds of the number of n-periodic points of a self-map f ： M →4 M of a compact smooth manifold of dimension at least 3： NFn（f） = min{#Fix（gn）;g - f; g continuous} and NJDn（f） = min{#Fix（gn）;g - f; g smooth}. In general, NJDn（f） may be much greater than NFn（f）. We show that for a self-map of a semi-simple Lie group, inducing the identity fundamental group homomorphism, the equality NFn（f） = NJDn（f） holds for all n →← all eigenvalues of a quotient cohomology homomorphism induced by f have moduli ≤ 1.展开更多
基金The National Natural Science Foundation of China(No.11371088)the Natural Science Foundation of Jiangsu Province(No.BK2012736)the Fundamental Research Funds for the Central Universities(No.KYZZ0060)
文摘Let G be a discrete group with a neutral element and H be a quasitriangular Hopf G-coalgebra over a field k. Then the relationship between G-grouplike elements and ribbon elements of H is considered. First, a list of useful properties of a quasitriangular Hopf G-coalgebra and its Drinfeld elements are proved. Secondly, motivated by the relationship between the grouplike and ribbon elements of a quasitriangular Hopf algebra, a special kind of G-grouplike elements of H is defined. Finally, using the Drinfeld elements, a one-to-one correspondence between the special G-grouplike elements defined above and ribbon elements is obtained.
文摘In this paper, the eigenfunction method established by Chen Jin-quan is used to compute the C-G coefficients in regard to the coupling between symmetry points and lines in the first Brillouin zone of the structure D6h^1, space group. Therewith, the wave vector selection rule and the C-G series, are also given as the middle result of computing the C-G coefficients.
文摘The eigenfunction method put forward by Chen Jin-quan is illustrated. We apply this theory to the space group D1_ 6h. The selection rules of this space are worked out in the points of higher symmetry A,K,H in the first Brillion Zone. The C-G coefficients are calculated for K.HA.
文摘The links of Motoman HP6 arc welding robot are considered as an open kinematic chain which consists of a series of rotational joints through concatenation. One end of the open chain is fixed to the base or the earth, and the other end which is free fastens the end executor to complete various duties. Each link of this arc welding robot has four kinds of Denavit-Hartenberg parameters: common normal length between two adjacent links, angle of two adjacent joints, distance between the crossing of common normal length and two joints axes, and angle of two adjacent links. The displacement relation between each link of the Motoman HP6 arc welding robot is introduced, and the kinematic positive-going solution and the kinematic passive-going solution are calculated.
文摘A transition diagram is used to describe the behavior of systems. Birth-death equations were derived from transition diagram depicting the state of the birth-death processes. Queue models and characteristics of queue models are also derivable from birth-death processes. These queue models consist of mathematical formulas and relationships that can be used to determine the operating characteristics （performance measures） for a waiting line. Schematic and transition diagrams of different single server queue models were shown. Relationships between birth-death processes, waiting lines （queues） and transition diagrams were given. While M/M/I/K queue model states was limited by K customers and had （K＋I） states, M/M/1/1 queue model had only two states. M/G/1/∝/∝ and M/M/1/∝/∝ shared similar characteristics. Many ideal queuing situations employ M/M/1 queueing model.
基金supported by National Natural Science Foundation of China(Grant No.11201380)the Fundamental Research Funds for the Central Universities(Grant No.XDJK2012B007)+2 种基金Doctor Fund of Southwest University(Grant No.SWU111021)Educational Fund of Southwest University(Grant No.2010JY053)National Research Foundation of Korea Grant funded by the Korean Government(Ministry of Education,Science and Technology)(Grant No.NRF-2011-357-C00006)
文摘We consider a Lotka-Volterra prey-predator model with cross-diffusion and Holling type-II functional response.The main concern is the existence of positive solutions under the combined effect of cross-diffusion and Holling type-II functional response.Here,a positive solution corresponds to a coexistence state of the model.Firstly,we study the sufficient conditions to ensure the existence of positive solutions by using degree theory and analyze the coexistence region in parameter plane.In addition,we present the uniqueness of positive solutions in one dimension case.Secondly,we study the stability of the trivial and semi-trivial solutions by analyzing the principal eigenvalue of the corresponding linearized system,and then we characterize the stable/unstable regions of semi-trivial solutions in parameter plane.
基金supported by the National Science Center,Poland(Grant No.UMO2014/15/B/ST1/01710)
文摘There are two algebraic lower bounds of the number of n-periodic points of a self-map f ： M →4 M of a compact smooth manifold of dimension at least 3： NFn（f） = min{#Fix（gn）;g - f; g continuous} and NJDn（f） = min{#Fix（gn）;g - f; g smooth}. In general, NJDn（f） may be much greater than NFn（f）. We show that for a self-map of a semi-simple Lie group, inducing the identity fundamental group homomorphism, the equality NFn（f） = NJDn（f） holds for all n →← all eigenvalues of a quotient cohomology homomorphism induced by f have moduli ≤ 1.
