We build a computer program to reconstruct convex bodies using even L_(p)surface area measures for p≥1.Firstly,we transform the minimization problem Pi,which is equivalent to solving the even L_(p)Minkowski problem,i...We build a computer program to reconstruct convex bodies using even L_(p)surface area measures for p≥1.Firstly,we transform the minimization problem Pi,which is equivalent to solving the even L_(p)Minkowski problem,into a convex optimization problem P4 with a finite number of constraints.This transformation makes it suitable for computational resolution.Then,we prove that the approximate solutions obtained by solving the problem P4 converge to the theoretical solution when N and k are sufficiently large.Finally,based on the convex optimization problem P_(4),we provide an algorithm for reconstructing convex bodies from even L_(p)surface area measures,and present several examples implemented using MATLAB.展开更多
The mid-facet of a simplex in n-dimensional Euclidean space which was introduced quite recently is an important geometric element. An analytic expression for the mid-facet area of a simplex is firstly given. In order ...The mid-facet of a simplex in n-dimensional Euclidean space which was introduced quite recently is an important geometric element. An analytic expression for the mid-facet area of a simplex is firstly given. In order to obtain the expression,the exterior differential method was presented. Furthermore, the properties of the mid-facets of a simplex analogous to median lines of a triangle (such as for all mid-facets of a simplex,there exists another simplex such that its edge-lengths equal to these mid-facets area respectively, and all of the mid-facets of a simplex have a common point) were proved. Finally, by applying the analytic expression, a number of inequalities which combine edge-lengths, circumradius, median line, bisection area and facet area with the mid-facet area for a simplex were established.展开更多
A kind of integrable coupling of soliton equations hierarchy with self-consistent sources associated with s/（4） has been presented （Yu F J and Li L 2009 Appl. Math. Comput. 207 171; Yu F J 2008 Phys. Lett. A 372 6...A kind of integrable coupling of soliton equations hierarchy with self-consistent sources associated with s/（4） has been presented （Yu F J and Li L 2009 Appl. Math. Comput. 207 171; Yu F J 2008 Phys. Lett. A 372 6613）. Based on this method, we construct two integrable couplings of the soliton hierarchy with self-consistent sources by using the loop algebra sl（4）. In this paper, we also point out that there are some errors in these references and we have corrected these errors and set up new formula. The method can be generalized to other soliton hierarchy with self-consistent sources.展开更多
In this article, an SIRS epidemic model spread by vectors （mosquitoes） which have an incubation time to become infectious is formulated. It is shown that a disease-free equilibrium point is globally stable if no end...In this article, an SIRS epidemic model spread by vectors （mosquitoes） which have an incubation time to become infectious is formulated. It is shown that a disease-free equilibrium point is globally stable if no endemic equilibrium point exists. Further, the endemic equilibrium point （if it exists） is globally stable with a respect ＂weak delay＂. Some known results are generalized.展开更多
The authors establish some inequalities about the dual mixed volumes of star bodies in Rn. These inequalities are the analogue in the Brunn-Minkowski theory of the inequalities of Marcus-Lopes and Bergstrom about symm...The authors establish some inequalities about the dual mixed volumes of star bodies in Rn. These inequalities are the analogue in the Brunn-Minkowski theory of the inequalities of Marcus-Lopes and Bergstrom about symmetric functions of positive reals.展开更多
A numerical method for simulating the motion and deformation of an axisymmetric bubble or drop rising or falling in another infinite and initially stationary fluid is developed based on the volume of fluid （VOF） met...A numerical method for simulating the motion and deformation of an axisymmetric bubble or drop rising or falling in another infinite and initially stationary fluid is developed based on the volume of fluid （VOF） method in the frame of two incompressible and immiscible viscous fluids under the action of gravity, taking into consideration of surface tension effects. A comparison of the numerical results by this method with those by other works indicates the validity of the method. In the frame of inviseid and incompressible fluids without taking into consideration of surface tension effects, the mechanisms of the generation of the liquid jet and the transition from spherical shape to toroidal shape during the bubble or drop deformation, the increase of the ring diameter of the toroidal bubble or drop and the decrease of its cross-section area during its motion, and the effects of the density ratio of the two fluids on the deformation of the bubble or drop are analysed both theoretically and numerically.展开更多
We present a novel and effective method for controlling epidemic spreading on complex networks, especially on scale-free networks. The proposed strategy is performed by deleting edges according to their significances ...We present a novel and effective method for controlling epidemic spreading on complex networks, especially on scale-free networks. The proposed strategy is performed by deleting edges according to their significances （the significance of an edge is defined as the product of the degrees of two nodes of this edge）. In contrast to other methods, e.g., random immunization, proportional immunization, targeted immunization, acquaintance immunization and so on, which mainly focus on how to delete nodes to realize the control of epidemic spreading on complex networks, our method is more effective in realizing the control of epidemic spreading on complex networks, moreover, such a method can better retain the integrity of complex networks.展开更多
By a transformation between a Painlevé integrable variable coefficient KdV equation and the standard KdV equation, we derive the Lax pair and infinitely many conservation laws of the variable coefficient KdV equa...By a transformation between a Painlevé integrable variable coefficient KdV equation and the standard KdV equation, we derive the Lax pair and infinitely many conservation laws of the variable coefficient KdV equation from the counterparts of the KdV equation.展开更多
Based on fractional isospectral problems and general bilinear forms, the gener-alized fractional trace identity is presented. Then, a new explicit Lie algebra is introduced for which the new fractional integrable coup...Based on fractional isospectral problems and general bilinear forms, the gener-alized fractional trace identity is presented. Then, a new explicit Lie algebra is introduced for which the new fractional integrable couplings of a fractional soliton hierarchy are derived from a fractional zero-curvature equation. Finally, we obtain the fractional Hamiltonian structures of the fractional integrable couplings of the soliton hierarchy.展开更多
The symmetry constraint and binary nonlinearization of Lax pairs for the super classical-Boussinesq hierarchy is obtained. Under the obtained symmetry constraint, the n-th flow of the super classical-Boussinesq hierar...The symmetry constraint and binary nonlinearization of Lax pairs for the super classical-Boussinesq hierarchy is obtained. Under the obtained symmetry constraint, the n-th flow of the super classical-Boussinesq hierarchy is decomposed into two super finite-dimensional integrable Hamiltonian systems, defined over the super-symmetry manifold with the corresponding dynamical variables x and tn. The integrals of motion required for Liouville integrability are explicitly given.展开更多
Associated with the concepts of the Lp-mixed quermassintegrals, the Lp-mixed volume, and the Lp-dual mixed volume, we establish inequalities for the quermassintegrals of the Lp-projection body and the Lp-centroid body...Associated with the concepts of the Lp-mixed quermassintegrals, the Lp-mixed volume, and the Lp-dual mixed volume, we establish inequalities for the quermassintegrals of the Lp-projection body and the Lp-centroid body. Further, the general results for the Shephard problem of the Lp-projection body and the Lp-centroid body are obtained.展开更多
This work aims to study the N-coupled Hirota equations in an optical fiber under the zero boundary condition at infinity. By analyzing the spectral problem, a matrix Riemann–Hilbert problem on the real axis is strict...This work aims to study the N-coupled Hirota equations in an optical fiber under the zero boundary condition at infinity. By analyzing the spectral problem, a matrix Riemann–Hilbert problem on the real axis is strictly established. Then, by solving the presented matrix Riemann–Hilbert problem under the constraint of no reflection,the bright multi-soliton solutions to the N-coupled Hirota equations are explicitly gained.展开更多
Some strong laws of large numbers for the frequencies of occurrence of states and ordered couples of states for nonsymmetric Markov chain fields （NSMC） on Cayley trees are studied. In the proof, a new technique for ...Some strong laws of large numbers for the frequencies of occurrence of states and ordered couples of states for nonsymmetric Markov chain fields （NSMC） on Cayley trees are studied. In the proof, a new technique for the study of strong limit theorems of Markov chains is extended to the case of Markov chain fields, The asymptotic equipartition properties with almost everywhere （a,e.） convergence for NSMC on Cayley trees are obtained,展开更多
In this paper, we study the dynamical behaviour of an epidemic on complex networks with population mobility. In our model, the number of people on each node is unrestricted as the nodes of the network are considered a...In this paper, we study the dynamical behaviour of an epidemic on complex networks with population mobility. In our model, the number of people on each node is unrestricted as the nodes of the network are considered as cities, communities, and so on. Because people can travel between different cities, we study the effect of a population＇s mobility on the epidemic spreading. In view of the population＇s mobility, we suppose that the susceptible individual can be infected by an infected individual in the same city or other connected cities. Simulations are presented to verify our analysis.展开更多
This article discusses spherical pulse like solutions of the system of semilinear wave equations with the pulses focusing at a point and emerging outgoing in three space variables. In small initial data case, it shows...This article discusses spherical pulse like solutions of the system of semilinear wave equations with the pulses focusing at a point and emerging outgoing in three space variables. In small initial data case, it shows that the nonlinearities have a strong effect at the focal point. Scattering operator is introduced to describe the caustic crossing. With the aid of the L^∞ norms, it analyzes the relative errors in approximate solutions.展开更多
Dynamics of three nonisospectral nonlinear Schrdinger equations(NNLSEs), following different time dependencies of the spectral parameter, are investigated. First, we discuss the gauge transformations between the stand...Dynamics of three nonisospectral nonlinear Schrdinger equations(NNLSEs), following different time dependencies of the spectral parameter, are investigated. First, we discuss the gauge transformations between the standard nonlinear Schrdinger equation(NLSE) and its first two nonisospectral counterparts, for which we derive solutions and infinitely many conserved quantities. Then, exact solutions of the three NNLSEs are derived in double Wronskian terms. Moreover,we analyze the dynamics of the solitons in the presence of the nonisospectral effects by demonstrating how the shapes,velocities, and wave energies change in time. In particular, we obtain a rogue wave type of soliton solutions to the third NNLSE.展开更多
This article introduces the concept of commutative semigroups of almost asymptotically nonexpansive-type mappings in a Banach space X which has the Opial property and whose norm is UKK, and establishes the weak conver...This article introduces the concept of commutative semigroups of almost asymptotically nonexpansive-type mappings in a Banach space X which has the Opial property and whose norm is UKK, and establishes the weak convergence theorems for almostorbits of this class of commutative semigroups. The author improves, extends and develops some recent and earlier results.展开更多
The PC synchronization of a class of chaotic systems is investigated in this paper. The drive system is assumed to have only one state variable available. By constructing proper observers, some novel criteria for PC s...The PC synchronization of a class of chaotic systems is investigated in this paper. The drive system is assumed to have only one state variable available. By constructing proper observers, some novel criteria for PC synchronization are proposed via event-triggered control scheme. The Lii system and Chen system are taken as examples to demonstrate the efficiency of the proposed approach.展开更多
By means of the classical method, we investigate the （3＋1）-dimensional Zakharov-Kuznetsov equation. The symmetry group of the （3＋1）-dimensional Zakharov-Kuznetsov equation is studied first and the theorem of gro...By means of the classical method, we investigate the （3＋1）-dimensional Zakharov-Kuznetsov equation. The symmetry group of the （3＋1）-dimensional Zakharov-Kuznetsov equation is studied first and the theorem of group invariant solutions is constructed. Then using the associated vector fields of the obtained symmetry, we give the one-, two-, and three-parameter optimal systems of group-invariant solutions. Based on the optimal system, we derive the reductions and some new solutions of the （3＋1）-dimensional Zakharov-Kuznetsov equation.展开更多
In this article, we focus on discussing the degree distribution of the DMS model from the perspective of probability. On the basis of the concept and technique of first-passage probability in Markov theory, we provide...In this article, we focus on discussing the degree distribution of the DMS model from the perspective of probability. On the basis of the concept and technique of first-passage probability in Markov theory, we provide a rigorous proof for existence of the steady-state degree distribution, mathematically re-deriving the exact formula of the distribution. The approach based on Markov chain theory is universal and performs well in a large class of growing networks.展开更多
文摘We build a computer program to reconstruct convex bodies using even L_(p)surface area measures for p≥1.Firstly,we transform the minimization problem Pi,which is equivalent to solving the even L_(p)Minkowski problem,into a convex optimization problem P4 with a finite number of constraints.This transformation makes it suitable for computational resolution.Then,we prove that the approximate solutions obtained by solving the problem P4 converge to the theoretical solution when N and k are sufficiently large.Finally,based on the convex optimization problem P_(4),we provide an algorithm for reconstructing convex bodies from even L_(p)surface area measures,and present several examples implemented using MATLAB.
文摘The mid-facet of a simplex in n-dimensional Euclidean space which was introduced quite recently is an important geometric element. An analytic expression for the mid-facet area of a simplex is firstly given. In order to obtain the expression,the exterior differential method was presented. Furthermore, the properties of the mid-facets of a simplex analogous to median lines of a triangle (such as for all mid-facets of a simplex,there exists another simplex such that its edge-lengths equal to these mid-facets area respectively, and all of the mid-facets of a simplex have a common point) were proved. Finally, by applying the analytic expression, a number of inequalities which combine edge-lengths, circumradius, median line, bisection area and facet area with the mid-facet area for a simplex were established.
基金Project supported by the Natural Science Foundation of Shanghai (Grant No. 09ZR1410800)the Science Foundation of Key Laboratory of Mathematics Mechanization (Grant No. KLMM0806)+2 种基金the Shanghai Leading Academic Discipline Project (Grant No. J50101)the Key Disciplines of Shanghai Municipality (Grant No. S30104)the National Natural Science Foundation of China (Grant Nos. 61072147 and 11071159)
文摘A kind of integrable coupling of soliton equations hierarchy with self-consistent sources associated with s/（4） has been presented （Yu F J and Li L 2009 Appl. Math. Comput. 207 171; Yu F J 2008 Phys. Lett. A 372 6613）. Based on this method, we construct two integrable couplings of the soliton hierarchy with self-consistent sources by using the loop algebra sl（4）. In this paper, we also point out that there are some errors in these references and we have corrected these errors and set up new formula. The method can be generalized to other soliton hierarchy with self-consistent sources.
基金This work is supported by the National Sciences Foundation of China (10471040)the Youth Science Foundations of Shanxi Province (20021003).
文摘In this article, an SIRS epidemic model spread by vectors （mosquitoes） which have an incubation time to become infectious is formulated. It is shown that a disease-free equilibrium point is globally stable if no endemic equilibrium point exists. Further, the endemic equilibrium point （if it exists） is globally stable with a respect ＂weak delay＂. Some known results are generalized.
文摘The authors establish some inequalities about the dual mixed volumes of star bodies in Rn. These inequalities are the analogue in the Brunn-Minkowski theory of the inequalities of Marcus-Lopes and Bergstrom about symmetric functions of positive reals.
基金Project supported by the National Natural Science Foundation of China (Grant Nos 10672043 and 10272032)
文摘A numerical method for simulating the motion and deformation of an axisymmetric bubble or drop rising or falling in another infinite and initially stationary fluid is developed based on the volume of fluid （VOF） method in the frame of two incompressible and immiscible viscous fluids under the action of gravity, taking into consideration of surface tension effects. A comparison of the numerical results by this method with those by other works indicates the validity of the method. In the frame of inviseid and incompressible fluids without taking into consideration of surface tension effects, the mechanisms of the generation of the liquid jet and the transition from spherical shape to toroidal shape during the bubble or drop deformation, the increase of the ring diameter of the toroidal bubble or drop and the decrease of its cross-section area during its motion, and the effects of the density ratio of the two fluids on the deformation of the bubble or drop are analysed both theoretically and numerically.
基金Supported by the National Natural Science Foundation of China under Grant Nos 60744003, 10635040 and 10532060, the Specialized Research Fund for the Doctoral Program of Higher Education of China （20060358065）, the National Science Fund for Fostering Talents in Basic Science （J0630319）, the Foundation of Anhui Education Bureau under Grant No KJ2007A003, and the Natural Science Foundation of Anhui Province under Grant No 070416225.
文摘We present a novel and effective method for controlling epidemic spreading on complex networks, especially on scale-free networks. The proposed strategy is performed by deleting edges according to their significances （the significance of an edge is defined as the product of the degrees of two nodes of this edge）. In contrast to other methods, e.g., random immunization, proportional immunization, targeted immunization, acquaintance immunization and so on, which mainly focus on how to delete nodes to realize the control of epidemic spreading on complex networks, our method is more effective in realizing the control of epidemic spreading on complex networks, moreover, such a method can better retain the integrity of complex networks.
基金Supported by the National Natural Science Foundation of China under Grant Nos 10371070 and 10671121, the Foundation of Shanghai Education Committee for Shanghai Prospective Excellent Young Teachers, and Magnolia Grant of Shanghai Sciences and Technology Committee. The author is grateful to the anonymous referees for their invaluable comments. The author is also grateful to Professor Li Yi-shen for his kind visit to Shanghai University and invaluable discussions on variable coefficient evolution equations.
文摘By a transformation between a Painlevé integrable variable coefficient KdV equation and the standard KdV equation, we derive the Lax pair and infinitely many conservation laws of the variable coefficient KdV equation from the counterparts of the KdV equation.
基金supported by the National Natural Science Foundation of China(1127100861072147+1 种基金11071159)the First-Class Discipline of Universities in Shanghai and the Shanghai University Leading Academic Discipline Project(A13-0101-12-004)
文摘Based on fractional isospectral problems and general bilinear forms, the gener-alized fractional trace identity is presented. Then, a new explicit Lie algebra is introduced for which the new fractional integrable couplings of a fractional soliton hierarchy are derived from a fractional zero-curvature equation. Finally, we obtain the fractional Hamiltonian structures of the fractional integrable couplings of the soliton hierarchy.
基金Project supported by the National Natural Science Foundation of China (Grant Nos.61072147 and 11071159)the Natural Science Foundation of Shanghai,China (Grant No.09ZR1410800)+2 种基金the Science Foundation of the Key Laboratory of Mathematics Mechanization,China (Grant No.KLMM0806)the Shanghai Leading Academic Discipline Project,China (Grant No.J50101)the Key Disciplines of Shanghai Municipality of China (Grant No.S30104)
文摘The symmetry constraint and binary nonlinearization of Lax pairs for the super classical-Boussinesq hierarchy is obtained. Under the obtained symmetry constraint, the n-th flow of the super classical-Boussinesq hierarchy is decomposed into two super finite-dimensional integrable Hamiltonian systems, defined over the super-symmetry manifold with the corresponding dynamical variables x and tn. The integrals of motion required for Liouville integrability are explicitly given.
基金Sponsored by the Natural Science Foundation of China (10671117)Academic Mainstay Foundation of Hubei Province of China (D200729002)Science Foundation of China Three Gorges University
文摘Associated with the concepts of the Lp-mixed quermassintegrals, the Lp-mixed volume, and the Lp-dual mixed volume, we establish inequalities for the quermassintegrals of the Lp-projection body and the Lp-centroid body. Further, the general results for the Shephard problem of the Lp-projection body and the Lp-centroid body are obtained.
基金Supported by the National Natural Science Foundation of China under Grant Nos 11975145,11271008 and 61072147
文摘This work aims to study the N-coupled Hirota equations in an optical fiber under the zero boundary condition at infinity. By analyzing the spectral problem, a matrix Riemann–Hilbert problem on the real axis is strictly established. Then, by solving the presented matrix Riemann–Hilbert problem under the constraint of no reflection,the bright multi-soliton solutions to the N-coupled Hirota equations are explicitly gained.
基金Supported by National Basic Research Program of China(973 Program No.2007CBS14903)National Science Foundation of China(70671069)
文摘Some strong laws of large numbers for the frequencies of occurrence of states and ordered couples of states for nonsymmetric Markov chain fields （NSMC） on Cayley trees are studied. In the proof, a new technique for the study of strong limit theorems of Markov chains is extended to the case of Markov chain fields, The asymptotic equipartition properties with almost everywhere （a,e.） convergence for NSMC on Cayley trees are obtained,
基金supported by National Natural Science Foundation of China (Grant Nos 60744003,10635040,10532060 and 10672146)the Specialized Research Fund for the Doctoral Program of Higher Education of China (Grant No 20060358065)+2 种基金National Science Fund for Fostering Talents in Basic Science (Grant No J0630319)A grant from the Health,Welfare and Food Bureau of the Hong Kong SAR GovernmentShanghai Leading Academic Discipline Project (Project Number:J50101)
文摘In this paper, we study the dynamical behaviour of an epidemic on complex networks with population mobility. In our model, the number of people on each node is unrestricted as the nodes of the network are considered as cities, communities, and so on. Because people can travel between different cities, we study the effect of a population＇s mobility on the epidemic spreading. In view of the population＇s mobility, we suppose that the susceptible individual can be infected by an infected individual in the same city or other connected cities. Simulations are presented to verify our analysis.
基金The study is supported by National Natural Science Foundation of China (10131050)the Educational Ministry of Chinathe Shanghai Science and Technology Committee foundation (03QMH1407)
文摘This article discusses spherical pulse like solutions of the system of semilinear wave equations with the pulses focusing at a point and emerging outgoing in three space variables. In small initial data case, it shows that the nonlinearities have a strong effect at the focal point. Scattering operator is introduced to describe the caustic crossing. With the aid of the L^∞ norms, it analyzes the relative errors in approximate solutions.
基金the National Natural Science Foundation of China(Grant Nos.11601312,11631007,and 11875040)
文摘Dynamics of three nonisospectral nonlinear Schrdinger equations(NNLSEs), following different time dependencies of the spectral parameter, are investigated. First, we discuss the gauge transformations between the standard nonlinear Schrdinger equation(NLSE) and its first two nonisospectral counterparts, for which we derive solutions and infinitely many conserved quantities. Then, exact solutions of the three NNLSEs are derived in double Wronskian terms. Moreover,we analyze the dynamics of the solitons in the presence of the nonisospectral effects by demonstrating how the shapes,velocities, and wave energies change in time. In particular, we obtain a rogue wave type of soliton solutions to the third NNLSE.
基金Project supported by the Teaching and Research Award Fund for Outstanding Young Teachers in Higher Education Institutions of MOE,P.R.C., by the Dawn Program Foundation in Shanghai, and by Shanghai Leading Academic Discipline Project Fund (T0401).
文摘This article introduces the concept of commutative semigroups of almost asymptotically nonexpansive-type mappings in a Banach space X which has the Opial property and whose norm is UKK, and establishes the weak convergence theorems for almostorbits of this class of commutative semigroups. The author improves, extends and develops some recent and earlier results.
基金supported by the National Natural Science Foundation of China(Grant Nos.11361043 and 61304161)the Natural Science Foundation of Jiangxi Province,China(Grant No.20122BAB201005)
文摘The PC synchronization of a class of chaotic systems is investigated in this paper. The drive system is assumed to have only one state variable available. By constructing proper observers, some novel criteria for PC synchronization are proposed via event-triggered control scheme. The Lii system and Chen system are taken as examples to demonstrate the efficiency of the proposed approach.
基金supported by the National Natural Science Foundation of China (Grant Nos.10735030 and 90718041)Shanghai Leading Academic Discipline Project,China (Grant No.B412)Program for Changjiang Scholars and Innovative Research Team in University,China (Grant No.IRT0734)
文摘By means of the classical method, we investigate the （3＋1）-dimensional Zakharov-Kuznetsov equation. The symmetry group of the （3＋1）-dimensional Zakharov-Kuznetsov equation is studied first and the theorem of group invariant solutions is constructed. Then using the associated vector fields of the obtained symmetry, we give the one-, two-, and three-parameter optimal systems of group-invariant solutions. Based on the optimal system, we derive the reductions and some new solutions of the （3＋1）-dimensional Zakharov-Kuznetsov equation.
基金supported by the National Natural Science Foundation (11071258, 60874083, 10872119, 10901164)
文摘In this article, we focus on discussing the degree distribution of the DMS model from the perspective of probability. On the basis of the concept and technique of first-passage probability in Markov theory, we provide a rigorous proof for existence of the steady-state degree distribution, mathematically re-deriving the exact formula of the distribution. The approach based on Markov chain theory is universal and performs well in a large class of growing networks.
