In this paper, we present a fuzzy linguistic scale, which is characterized by triangular fuzzy numbers on [1/9, 9], for the comparison between two alternatives, and introduce a possibility degree formula for comparing...In this paper, we present a fuzzy linguistic scale, which is characterized by triangular fuzzy numbers on [1/9, 9], for the comparison between two alternatives, and introduce a possibility degree formula for comparing triangular fuzzy numbers. We utilize the fuzzy linguistic scale to construct a linguistic preference matrix, and propose a fuzzy induced ordered weighted geometric averaging (FIOWGA) operator to aggregate linguistic preference information. A method based on the fuzzy linguistic scale and FIOWGA operator for decision-making problems is presented. Finally, an illustrative example is given to verify the developed method and to demonstrate its feasibility and effectiveness.展开更多
This paper an cited instances in illustration of the incorrectness of the criteria of asymptotic stability of a class of nonlinear large seale system that L_j·T·Grujie gave in paper [1] by the comparison the...This paper an cited instances in illustration of the incorrectness of the criteria of asymptotic stability of a class of nonlinear large seale system that L_j·T·Grujie gave in paper [1] by the comparison theory and then corrected it,and has given the sufficient conditions of the asymptotic stability.展开更多
Fuzziness is one of the general characteristics of human thinking and objective things. Introducing fuzzy techniques into decision-making yields very good results. Fuzzy consistent matrix has many excellent characteri...Fuzziness is one of the general characteristics of human thinking and objective things. Introducing fuzzy techniques into decision-making yields very good results. Fuzzy consistent matrix has many excellent characteristics, especially cen- ter-division transitivity conforming to the reality of the human thinking process in decision-making. This paper presents a new approach for creating fuzzy consistent matrix from mutual supplementary matrix in fuzzy decision-making. At the same time, based on the distance between individual fuzzy consistent matrix and average fuzzy consistent matrix, a kind of combined opera- tion for several fuzzy consistent matrixes is presented which reflects most opinions of experienced experts. Finally, a practical example shows its flexibility and practicability further.展开更多
In this paper,we first give the solution concept of the fuzzy matrix equation =. Secondly,we discuss the property of the solution and give the method of solving the fuzzy matrix equation A=. Finally,we present an appl...In this paper,we first give the solution concept of the fuzzy matrix equation =. Secondly,we discuss the property of the solution and give the method of solving the fuzzy matrix equation A=. Finally,we present an application of solving fuzzy matrix equation A= to the fuzzy linear regression analysis,establish a new model of fuzzy linear regression,and introduce a new method of estimating parameters.展开更多
The notion of weak Doi-Hopfπ-datum and weak Doi-Hopfπ-module are given as generalizations of an ordinary weak Doi-Hopf datum and weak Doi-Hopf module introduced in (Boehm, 2000), also as a generalization of a Doi-...The notion of weak Doi-Hopfπ-datum and weak Doi-Hopfπ-module are given as generalizations of an ordinary weak Doi-Hopf datum and weak Doi-Hopf module introduced in (Boehm, 2000), also as a generalization of a Doi-Hopfπ-module introduced in (Wang, 2004). Then we also show that the functor forgetting action or coaction has an adjoint. Furthermore we explain how the notion of weak Doi-Hopfπ-datum is related to weak smash product. This paper presents our preliminary results on weak Doi-Hopf group modules.展开更多
The MacCormack method is applied to the analysis of multiconductor transmission lines by intro- ducing a new technique that does not require decoupling. This method can be used to analyze a wide range of problems and ...The MacCormack method is applied to the analysis of multiconductor transmission lines by intro- ducing a new technique that does not require decoupling. This method can be used to analyze a wide range of problems and does not have to consider the matrix forms of distributed parameters. We have developed soft- ware named MacCormack Transmission Line Analyzer based on the proposed method. Numerical examples are presented to demonstrate the accuracy and efficiency of the method and illustrate its application to analyz- ing multiconductor transmission lines.展开更多
Fiber Bragg grating under transverse force on a small grating section is studied by numerical simulation and experimentation. A numerical simulation based on the transfer matrix method is used to calculate the consequ...Fiber Bragg grating under transverse force on a small grating section is studied by numerical simulation and experimentation. A numerical simulation based on the transfer matrix method is used to calculate the consequent changes in reflected spectrum. The reflected spectra of the FBG subjected to the transverse force split into two main peaks, and the split point shifted linearly and periodically versus the applied force. The split point is shifted in the bandwidth with the period of 11N, and the sensitivity of the split point wavelength shift versus the applied force is 0.05 nm/N in one period. The experimental results show good agreement with the simulation analysis.展开更多
Considering the level distribution of soil layers, the soils surrounding pile are simulated with level finite layer elements. Supposing that the vertical deformation of the soil elements surrounding pile varies in the...Considering the level distribution of soil layers, the soils surrounding pile are simulated with level finite layer elements. Supposing that the vertical deformation of the soil elements surrounding pile varies in the form of exponent function with radial distance, and considering the nonlinear constitutive relation of stress and strain, the stiffness matrix is established. The mechanics behavior of the pile—soil interface is simulated with a nonlinear interface element. This method can truly express the behavior of the pile-soil system. The load-settlement relation Q-S curves of two big diameter prototype piles on bearing test are analyzed, and satisfying results are obtained. This method is reasonable in theory and feasible in engineering.展开更多
The performance of analytical derivative and sparse matrix techniques applied to a traditional dense sequential quadratic programming (SQP) is studied, and the strategy utilizing those techniques is also presented.Com...The performance of analytical derivative and sparse matrix techniques applied to a traditional dense sequential quadratic programming (SQP) is studied, and the strategy utilizing those techniques is also presented.Computational results on two typical chemical optimization problems demonstrate significant enhancement in efficiency, which shows this strategy is promising and suitable for large-scale process optimization problems.展开更多
The modal back-scattering matrix can be extracted from reverberation data. For high frequency cases the ’window smoothed’ processing has been proposed by E. C. Shang, T. F. Gao and D. J. Tang (2002) to extract the ...The modal back-scattering matrix can be extracted from reverberation data. For high frequency cases the ’window smoothed’ processing has been proposed by E. C. Shang, T. F. Gao and D. J. Tang (2002) to extract the ’window averaged’ back-scattering matrix. It is pointed out in this paper that in order to inverse the ’window averaged’ back-scattering matrix by changing the source depth data we have to assume that the matrix is not related to the source depth, and the numerical simulation on the question has been conducted.展开更多
This paper deals with the numerical simulation of incompressible turbulent boundary flow of a flat plate with the pseudo-spectral matrix method. In order to appear more than 10 nodes in the turbulent base-stratum and ...This paper deals with the numerical simulation of incompressible turbulent boundary flow of a flat plate with the pseudo-spectral matrix method. In order to appear more than 10 nodes in the turbulent base-stratum and transition of 43×43 computational grids,a coordinate transformation is put up from physical panel to computational panel. Several zero turbulent models are computed comparatively. The results are credible when comparing with the previous methods.展开更多
This paper is an improvement over beta-Nakagami distribution developed by Shittu and Adepoju (2013). Here we propose the addition of one parameter to the two parameter continuous Nakagami-m distribution (Nakagami, ...This paper is an improvement over beta-Nakagami distribution developed by Shittu and Adepoju (2013). Here we propose the addition of one parameter to the two parameter continuous Nakagami-m distribution (Nakagami, 1960) that was designed for modeling the fading of radio signals. The resulting distribution referred to as Exponentiated Nakagami (ENAK) distribution is a generalization of the classical Nakagami distribution. The statistical properties of the proposed distribution such as moments, moment generating function, the asymptotic behavior among others were investigated. The method of maximum likelihood is used to estimate the model parameters and the observed information matrix is derived. A real data set is used to compare the new model with the class of Nakagami distributions. Our findings showed that the Exponentiated Nakagami distribution is more flexible than beta-Nakagami distribution with better representation and less computational effort.展开更多
In order to solve the flow mismatch problem between pumping source output and workload demand,a novel configuration of D + A combined multi-pump controlled hydraulic system,similar to a pump-controlled system,is propo...In order to solve the flow mismatch problem between pumping source output and workload demand,a novel configuration of D + A combined multi-pump controlled hydraulic system,similar to a pump-controlled system,is proposed for a large power hydraulic system in this study. This novel configuration consists of several parallel fixed displacement pumps of different sizes and proportional variable displacement pumps,which is controlled by digital signal( on/off) and analog signal respectively( D + A pumps). The system flow is divided into two parts,one is the total flow from fixed displacement pumps,and the other is the rest desired flow supplied by variable displacement pumps to smooth and improve the demand flow. First,basic design principles and evaluation indicators of the proposed system are introduced. Then,a flow state matrix of the binary-coding digital pumps( 1: 2: 4) is obtained to provide the control signals of pumps. Experimental results show that the system output flow tracks well with acceptable flow deviation,though a little lag behind input signal.展开更多
In this paper,the finite-difference time-domain(FDTD)algorithm is employed to simulate microwave pulse coupling into the rectangular cavity with aperture arrays.In the case in which the long-side of the slot in apertu...In this paper,the finite-difference time-domain(FDTD)algorithm is employed to simulate microwave pulse coupling into the rectangular cavity with aperture arrays.In the case in which the long-side of the slot in aperture arrays is perpendicular to the incident electrical field,and the electrical distribution of each center of slot in the aperture arrays in the process of microwave pulse coupling into the rectangular cavity with aperture arrays is analyzed in detail. We find that the effect of field enhancement of the slot in the middle of all the slots which distribute in the direction parallel to the incident electrical field is minimum and increases in turn from the middle to both sides symmetrically. We also find that the effect of field enhancement of the slot in the middle of all the slots which distribute in the direction perpendicular to the incident electrical field is maximum and decreases in turn from the middle to both sides symmetrically.In the same time,we investigate the factors that influence the effect of field enhancement of the center of each slot and the coupling electrical distribution in the cavity,including the number of slots and the spacing between slots.展开更多
In modern days, biodegradable polymeric matrix used as the kingpin of local drug delivery system is in the center of attention. This work is concentrated on the formulation of mathematical model elucidating degradatio...In modern days, biodegradable polymeric matrix used as the kingpin of local drug delivery system is in the center of attention. This work is concentrated on the formulation of mathematical model elucidating degradation of drug-loaded polymeric matrix followed by drug release to the adjacent biological tissues. Polymeric degradation is penciled with mass conservation equations. Drug release phenomenon is modeled by considering solubilization dynamics of drug particles, diffusion of the solubilized drug through polymeric matrix along with reversible dissociation/recrystallization process. In the tissue phase, reversible dissociation/association along with internalization processes of drug are taken into account. For this, a two-phase spatio-temporal model is postu- lated, which has ensued to a system of partial differential equations. They are solved analytically with appropriate choice of initial, interface and boundary conditions. In order to reflect the potency of the advocated model, the simulated results are analogized with corresponding experimental data and found laudable agreement so as to validate the applicability of the model considered. This model seems to foster the delicacy of the mantle enacted by important drug kinetic parameters such as diffusion coefficients, mass transfer coefficients, particle binding and internalization parameters, which is illustrated through local sensitivity analysis.展开更多
In this paper, we analyze a nonlinear mathematical model of the HIV/AIDS and screening of unaware infectives on the transmission dynamics of the disease in a homoge- neous population with constant immigration of susce...In this paper, we analyze a nonlinear mathematical model of the HIV/AIDS and screening of unaware infectives on the transmission dynamics of the disease in a homoge- neous population with constant immigration of susceptibles incorporating use of condom, screening of unaware infectives and treatment of the infected. We consider constant con- trols and thereafter by incorporating the theory of Volterra-Lyapunov stable matrices into the classical method of Lyapunov functions, we present an approach for global stability analysis of HIV/AIDS. The analysis and results presented in this paper make building blocks toward a comprehensive study and deeper understanding of the funda- mental mechanism in HIV/AIDS. A numerical study of the model is also carried out to investigate the analytical results.展开更多
The Cellular Automaton(CA) modeling and simulation of solid dynamics is a long-standing difficult problem.In this paper we present a new two-dimensional CA model for solid dynamics.In this model the solid body is repr...The Cellular Automaton(CA) modeling and simulation of solid dynamics is a long-standing difficult problem.In this paper we present a new two-dimensional CA model for solid dynamics.In this model the solid body is represented by a set of white and black particles alternatively positioned in the x-and y-directions.The force acting on each particle is represented by the linear summation of relative displacements of the nearest-neighboring particles.The key technique in this new model is the construction of eight coefficient matrices.Theoretical and numerical analyses show that the present model can be mathematically described by a conservative system.So,it works for elastic material.In the continuum limit the CA model recovers the well-known Navier equation.The coefficient matrices are related to the shear module and Poisson ratio of the material body.Compared with previous CA model for solid body,this model realizes the natural coupling of deformations in the x-and y-directions.Consequently,the wave phenomena related to the Poisson ratio effects are successfully recovered.This work advances significantly the CA modeling and simulation in the field of computational solid dynamics.展开更多
In this paper, an SEIR epidemic model with vaccination is formulated. The results of our mathematical analysis indicate that the basic reproduction number plays an important role in studying the dynamics of the system...In this paper, an SEIR epidemic model with vaccination is formulated. The results of our mathematical analysis indicate that the basic reproduction number plays an important role in studying the dynamics of the system. If the basic reproduction number is less than unity, it is shown that the disease-free equilibrium is globally asymptotically stable by comparison arguments. If it is greater than unity, the system is permanent and there is a unique endemic equilibrium. In this case, sufficient conditions are established to guarantee the global stability of the endemic equilibrium by the theory of the compound matrices. Numerical simulations are presented to illustrate the main results.展开更多
We show that two module homomorphisms for groups and Lie algebras established by Xi(2012)can be generalized to the setting of quasi-triangular Hopf algebras.These module homomorphisms played a key role in his proof of...We show that two module homomorphisms for groups and Lie algebras established by Xi(2012)can be generalized to the setting of quasi-triangular Hopf algebras.These module homomorphisms played a key role in his proof of a conjecture of Yau(1998).They will also be useful in the problem of decomposition of tensor products of modules.Additionally,we give another generalization of result of Xi(2012)in terms of Chevalley-Eilenberg complex.展开更多
基金The National Natural Science Foundation of China(79970093) the Ph.D. Dissertation Foundation of Southeast University- NARI-Relays Electric Co. Ltd.
文摘In this paper, we present a fuzzy linguistic scale, which is characterized by triangular fuzzy numbers on [1/9, 9], for the comparison between two alternatives, and introduce a possibility degree formula for comparing triangular fuzzy numbers. We utilize the fuzzy linguistic scale to construct a linguistic preference matrix, and propose a fuzzy induced ordered weighted geometric averaging (FIOWGA) operator to aggregate linguistic preference information. A method based on the fuzzy linguistic scale and FIOWGA operator for decision-making problems is presented. Finally, an illustrative example is given to verify the developed method and to demonstrate its feasibility and effectiveness.
文摘This paper an cited instances in illustration of the incorrectness of the criteria of asymptotic stability of a class of nonlinear large seale system that L_j·T·Grujie gave in paper [1] by the comparison theory and then corrected it,and has given the sufficient conditions of the asymptotic stability.
基金Project (No. 20040335129) supported by the Specialized Research Fund for the Doctoral Program of Higher Education (SRFDP) China
文摘Fuzziness is one of the general characteristics of human thinking and objective things. Introducing fuzzy techniques into decision-making yields very good results. Fuzzy consistent matrix has many excellent characteristics, especially cen- ter-division transitivity conforming to the reality of the human thinking process in decision-making. This paper presents a new approach for creating fuzzy consistent matrix from mutual supplementary matrix in fuzzy decision-making. At the same time, based on the distance between individual fuzzy consistent matrix and average fuzzy consistent matrix, a kind of combined opera- tion for several fuzzy consistent matrixes is presented which reflects most opinions of experienced experts. Finally, a practical example shows its flexibility and practicability further.
文摘In this paper,we first give the solution concept of the fuzzy matrix equation =. Secondly,we discuss the property of the solution and give the method of solving the fuzzy matrix equation A=. Finally,we present an application of solving fuzzy matrix equation A= to the fuzzy linear regression analysis,establish a new model of fuzzy linear regression,and introduce a new method of estimating parameters.
基金Project supported by the Program for New Century Excellent Talents in University (No. 04-0522), the National Science Foundation of Zhejiang Province of China (No. 102028), and the Cultivation Fund of the Key Scientific and Technical Innovation Project, Ministry of Education of China (No. 704004)
文摘The notion of weak Doi-Hopfπ-datum and weak Doi-Hopfπ-module are given as generalizations of an ordinary weak Doi-Hopf datum and weak Doi-Hopf module introduced in (Boehm, 2000), also as a generalization of a Doi-Hopfπ-module introduced in (Wang, 2004). Then we also show that the functor forgetting action or coaction has an adjoint. Furthermore we explain how the notion of weak Doi-Hopfπ-datum is related to weak smash product. This paper presents our preliminary results on weak Doi-Hopf group modules.
文摘The MacCormack method is applied to the analysis of multiconductor transmission lines by intro- ducing a new technique that does not require decoupling. This method can be used to analyze a wide range of problems and does not have to consider the matrix forms of distributed parameters. We have developed soft- ware named MacCormack Transmission Line Analyzer based on the proposed method. Numerical examples are presented to demonstrate the accuracy and efficiency of the method and illustrate its application to analyz- ing multiconductor transmission lines.
基金This paper was supported by China National Science Foundation(60377002) .
文摘Fiber Bragg grating under transverse force on a small grating section is studied by numerical simulation and experimentation. A numerical simulation based on the transfer matrix method is used to calculate the consequent changes in reflected spectrum. The reflected spectra of the FBG subjected to the transverse force split into two main peaks, and the split point shifted linearly and periodically versus the applied force. The split point is shifted in the bandwidth with the period of 11N, and the sensitivity of the split point wavelength shift versus the applied force is 0.05 nm/N in one period. The experimental results show good agreement with the simulation analysis.
文摘Considering the level distribution of soil layers, the soils surrounding pile are simulated with level finite layer elements. Supposing that the vertical deformation of the soil elements surrounding pile varies in the form of exponent function with radial distance, and considering the nonlinear constitutive relation of stress and strain, the stiffness matrix is established. The mechanics behavior of the pile—soil interface is simulated with a nonlinear interface element. This method can truly express the behavior of the pile-soil system. The load-settlement relation Q-S curves of two big diameter prototype piles on bearing test are analyzed, and satisfying results are obtained. This method is reasonable in theory and feasible in engineering.
基金Supported by the National Natural Science Foundation of China(No.29906010).
文摘The performance of analytical derivative and sparse matrix techniques applied to a traditional dense sequential quadratic programming (SQP) is studied, and the strategy utilizing those techniques is also presented.Computational results on two typical chemical optimization problems demonstrate significant enhancement in efficiency, which shows this strategy is promising and suitable for large-scale process optimization problems.
文摘The modal back-scattering matrix can be extracted from reverberation data. For high frequency cases the ’window smoothed’ processing has been proposed by E. C. Shang, T. F. Gao and D. J. Tang (2002) to extract the ’window averaged’ back-scattering matrix. It is pointed out in this paper that in order to inverse the ’window averaged’ back-scattering matrix by changing the source depth data we have to assume that the matrix is not related to the source depth, and the numerical simulation on the question has been conducted.
文摘This paper deals with the numerical simulation of incompressible turbulent boundary flow of a flat plate with the pseudo-spectral matrix method. In order to appear more than 10 nodes in the turbulent base-stratum and transition of 43×43 computational grids,a coordinate transformation is put up from physical panel to computational panel. Several zero turbulent models are computed comparatively. The results are credible when comparing with the previous methods.
文摘This paper is an improvement over beta-Nakagami distribution developed by Shittu and Adepoju (2013). Here we propose the addition of one parameter to the two parameter continuous Nakagami-m distribution (Nakagami, 1960) that was designed for modeling the fading of radio signals. The resulting distribution referred to as Exponentiated Nakagami (ENAK) distribution is a generalization of the classical Nakagami distribution. The statistical properties of the proposed distribution such as moments, moment generating function, the asymptotic behavior among others were investigated. The method of maximum likelihood is used to estimate the model parameters and the observed information matrix is derived. A real data set is used to compare the new model with the class of Nakagami distributions. Our findings showed that the Exponentiated Nakagami distribution is more flexible than beta-Nakagami distribution with better representation and less computational effort.
基金Supported by the National Natural Science Foundation of China(No.51575471)the Key Project of Natural Science Foundation of Hebei Province(No.E2016203264)
文摘In order to solve the flow mismatch problem between pumping source output and workload demand,a novel configuration of D + A combined multi-pump controlled hydraulic system,similar to a pump-controlled system,is proposed for a large power hydraulic system in this study. This novel configuration consists of several parallel fixed displacement pumps of different sizes and proportional variable displacement pumps,which is controlled by digital signal( on/off) and analog signal respectively( D + A pumps). The system flow is divided into two parts,one is the total flow from fixed displacement pumps,and the other is the rest desired flow supplied by variable displacement pumps to smooth and improve the demand flow. First,basic design principles and evaluation indicators of the proposed system are introduced. Then,a flow state matrix of the binary-coding digital pumps( 1: 2: 4) is obtained to provide the control signals of pumps. Experimental results show that the system output flow tracks well with acceptable flow deviation,though a little lag behind input signal.
文摘In this paper,the finite-difference time-domain(FDTD)algorithm is employed to simulate microwave pulse coupling into the rectangular cavity with aperture arrays.In the case in which the long-side of the slot in aperture arrays is perpendicular to the incident electrical field,and the electrical distribution of each center of slot in the aperture arrays in the process of microwave pulse coupling into the rectangular cavity with aperture arrays is analyzed in detail. We find that the effect of field enhancement of the slot in the middle of all the slots which distribute in the direction parallel to the incident electrical field is minimum and increases in turn from the middle to both sides symmetrically. We also find that the effect of field enhancement of the slot in the middle of all the slots which distribute in the direction perpendicular to the incident electrical field is maximum and decreases in turn from the middle to both sides symmetrically.In the same time,we investigate the factors that influence the effect of field enhancement of the center of each slot and the coupling electrical distribution in the cavity,including the number of slots and the spacing between slots.
文摘In modern days, biodegradable polymeric matrix used as the kingpin of local drug delivery system is in the center of attention. This work is concentrated on the formulation of mathematical model elucidating degradation of drug-loaded polymeric matrix followed by drug release to the adjacent biological tissues. Polymeric degradation is penciled with mass conservation equations. Drug release phenomenon is modeled by considering solubilization dynamics of drug particles, diffusion of the solubilized drug through polymeric matrix along with reversible dissociation/recrystallization process. In the tissue phase, reversible dissociation/association along with internalization processes of drug are taken into account. For this, a two-phase spatio-temporal model is postu- lated, which has ensued to a system of partial differential equations. They are solved analytically with appropriate choice of initial, interface and boundary conditions. In order to reflect the potency of the advocated model, the simulated results are analogized with corresponding experimental data and found laudable agreement so as to validate the applicability of the model considered. This model seems to foster the delicacy of the mantle enacted by important drug kinetic parameters such as diffusion coefficients, mass transfer coefficients, particle binding and internalization parameters, which is illustrated through local sensitivity analysis.
文摘In this paper, we analyze a nonlinear mathematical model of the HIV/AIDS and screening of unaware infectives on the transmission dynamics of the disease in a homoge- neous population with constant immigration of susceptibles incorporating use of condom, screening of unaware infectives and treatment of the infected. We consider constant con- trols and thereafter by incorporating the theory of Volterra-Lyapunov stable matrices into the classical method of Lyapunov functions, we present an approach for global stability analysis of HIV/AIDS. The analysis and results presented in this paper make building blocks toward a comprehensive study and deeper understanding of the funda- mental mechanism in HIV/AIDS. A numerical study of the model is also carried out to investigate the analytical results.
基金Supported by the Science Foundations of China Academy of Engineering Physics under Grant Nos. 2012B0101014 and 2011A0201002National Natural Science Foundation of China under Grant Nos. 11075021,91130020,and 11202003Foundation of State Key Laboratory of Explosion Science and Technology
文摘The Cellular Automaton(CA) modeling and simulation of solid dynamics is a long-standing difficult problem.In this paper we present a new two-dimensional CA model for solid dynamics.In this model the solid body is represented by a set of white and black particles alternatively positioned in the x-and y-directions.The force acting on each particle is represented by the linear summation of relative displacements of the nearest-neighboring particles.The key technique in this new model is the construction of eight coefficient matrices.Theoretical and numerical analyses show that the present model can be mathematically described by a conservative system.So,it works for elastic material.In the continuum limit the CA model recovers the well-known Navier equation.The coefficient matrices are related to the shear module and Poisson ratio of the material body.Compared with previous CA model for solid body,this model realizes the natural coupling of deformations in the x-and y-directions.Consequently,the wave phenomena related to the Poisson ratio effects are successfully recovered.This work advances significantly the CA modeling and simulation in the field of computational solid dynamics.
基金This work was supported by the National Natural Science Foundation of China (11371368), the Nature Science Foundation for Young Scientists of Hebei Province, China (A2013506012) and Basic Courses Department of Mechanical Engineering College Foundation (JCKY1507).
文摘In this paper, an SEIR epidemic model with vaccination is formulated. The results of our mathematical analysis indicate that the basic reproduction number plays an important role in studying the dynamics of the system. If the basic reproduction number is less than unity, it is shown that the disease-free equilibrium is globally asymptotically stable by comparison arguments. If it is greater than unity, the system is permanent and there is a unique endemic equilibrium. In this case, sufficient conditions are established to guarantee the global stability of the endemic equilibrium by the theory of the compound matrices. Numerical simulations are presented to illustrate the main results.
基金supported by National Natural Science Foundation of China (Grant No. 11501546)
文摘We show that two module homomorphisms for groups and Lie algebras established by Xi(2012)can be generalized to the setting of quasi-triangular Hopf algebras.These module homomorphisms played a key role in his proof of a conjecture of Yau(1998).They will also be useful in the problem of decomposition of tensor products of modules.Additionally,we give another generalization of result of Xi(2012)in terms of Chevalley-Eilenberg complex.