The SEIR epidemic model studied here includes constant inflows of new susceptibles, exposeds, infectives, and recovereds. This model also incorporates a population size dependent contact rate and a disease-related dea...The SEIR epidemic model studied here includes constant inflows of new susceptibles, exposeds, infectives, and recovereds. This model also incorporates a population size dependent contact rate and a disease-related death. As the infected fraction cannot be eliminated from the population, this kind of model has only the unique endemic equilibrium that is globally asymptotically stable. Under the special case where the new members of immigration are all susceptible, the model considered here shows a threshold phenomenon and a sharp threshold has been obtained. In order to prove the global asymptotical stability of the endemic equilibrium, the authors introduce the change of variable, which can reduce our four-dimensional system to a three-dimensional asymptotical autonomous system with limit equation.展开更多
Let M be a convex Chebyshev subset of a uniformly convex and uniformly smooth Banach space.It is proved that the metric projection P_M of X onto M is uniformly continu- ous on every bounded subset of X.Moreover,a glob...Let M be a convex Chebyshev subset of a uniformly convex and uniformly smooth Banach space.It is proved that the metric projection P_M of X onto M is uniformly continu- ous on every bounded subset of X.Moreover,a global and explicit estimate on the modulus of continuity of the metric projection is obtained.展开更多
In this article the authors propose a new approximate inertial manifold（AIM） to the Navier-Stokes equations. The solutions are in the neighborhoods of this AIM with thickness δ=o（h^2k＋1-ε）. The article aims to ...In this article the authors propose a new approximate inertial manifold（AIM） to the Navier-Stokes equations. The solutions are in the neighborhoods of this AIM with thickness δ=o（h^2k＋1-ε）. The article aims to investigate a two grids finite element approximation based on it and give error estimates of the approximate solution ｜｜｜（u-uh^＊·,p-ph^＊·）｜｜｜≤C（h^2k＋1-ε＋h^＊（m＋1））,where （h, h＊） and （k, m） are co^trse and fine meshes and degree of finite element subspa^es, respectively. These results are much better them Standard G^tlerkin（SG） and nonlinear Galcrkin （NG） methods. For example, for 2D NS eqs and linear element, let uh,u^h, u^＊ be the SG, NG and their approximate solutions respectively, then ｜｜u-uh｜｜1≤Ch,｜｜u-u^h｜｜i≤Ch^2,｜｜u-u^＊｜｜1≤Ch^3,and h^＊ ≈ h^2 for NG, h^＊ ≈ h^3/2 for theirs.展开更多
A kind of direct methods is presented for the solution of optimal control problems with state constraints. These methods are sequential quadratic programming methods. At every iteration a quadratic programming which i...A kind of direct methods is presented for the solution of optimal control problems with state constraints. These methods are sequential quadratic programming methods. At every iteration a quadratic programming which is obtained by quadratic approximation to Lagrangian function and linear approximations to constraints is solved to get a search direction for a merit function. The merit function is formulated by augmenting the Lagrangian function with a penalty term. A line search is carried out along the search direction to determine a step length such that the merit function is decreased. The methods presented in this paper include continuous sequential quadratic programming methods and discreate sequential quadratic programming methods.展开更多
This paper is devoted to discussing the discrete-ordinates method for the monoenergetic neutron transport equation in a slab with generalized boundary conditions. For homogeneous medium with isotropic scattering and f...This paper is devoted to discussing the discrete-ordinates method for the monoenergetic neutron transport equation in a slab with generalized boundary conditions. For homogeneous medium with isotropic scattering and fission, the convergence theorems for discrete-ordinates approximations are given respectively for critical eigenvalue problem and dominant eigenvalue problems: for inhomogeneous medium with anisotropic scattering and fission, a similar discussion and an estimation for the convergence rate are given for critical eigenvalue problems. Finally, some numerical results are given by use of this method.展开更多
In this paper, we present a series of new preconditioners with parameters of strictly diagonally dominant Z-matrix, which contain properly two kinds of known preconditioners as special cases. Moreover, we prove the mo...In this paper, we present a series of new preconditioners with parameters of strictly diagonally dominant Z-matrix, which contain properly two kinds of known preconditioners as special cases. Moreover, we prove the monotonicity of spectral radiuses of iterative matrices with respect to the parameters and some comparison theorems. The results obtained show that the bigger the parameter k is（i.e., we select the more upper right diagonal elements to be the preconditioner）, the less the spectral radius of iterative matrix is. A numerical example generated randomly is provided to illustrate the theoretical results.展开更多
In this paper,the time-dependent neutron transport integro-differential equationin a nonuniform slab with generalized boundary conditions and initial value is considered forgeneral cases concerned with an arbitrary no...In this paper,the time-dependent neutron transport integro-differential equationin a nonuniform slab with generalized boundary conditions and initial value is considered forgeneral cases concerned with an arbitrary nonhomogeneous medium possibly with cavity,withthe anisotropic scattering and fission,and with continuous energy varying from null to any finiteconstant or from one positive constant to another positive constant.We prove that the correspon-ding neutron transport operator A has finite Spectrum points in any strip {λ|β<sub>1</sub>≤R（?）λ≤β<sub>2</sub>}whereβ<sub>2</sub>】β1】-λ<sup>*</sup>（λ<sup>*</sup> is the essential infimum of v∑（x,v））,and obtain the asymptotic expansion ofthe time-dependent solution which exists and is unique.Furthermore,we give the existence ofthe dominant eigenvalue and indicate the asymptotic behavior of the neutron density as t→+∞.展开更多
<正> The maximum solution of fuzzy relation equations under max. and min. operations was advanced by E. Sanchez. In this paper, we gave a maximum solution of fuzzy relation equations under T-norm operation. Supp...<正> The maximum solution of fuzzy relation equations under max. and min. operations was advanced by E. Sanchez. In this paper, we gave a maximum solution of fuzzy relation equations under T-norm operation. Suppose that mapping T: [0,1]~2→ [0,1] satisfies the following conditions:展开更多
This paper discusses the neutron transport equation in a slab with generalized reflectingboundary conditions.By means of the positive C<sub>0</sub>-semigroup theory,we have proved that this problemhas a un...This paper discusses the neutron transport equation in a slab with generalized reflectingboundary conditions.By means of the positive C<sub>0</sub>-semigroup theory,we have proved that this problemhas a unique nonnegative solution and found the spectral property of the corresponding transportoperator.Finally we give the asymptotic behavior of the solution for this equation.展开更多
In neutron transport theory, the strict dominance of the dominant eigenvalue associated with the transport operator plays a key role in studying the asymptotic behavior of the time dependent transport system. For boun...In neutron transport theory, the strict dominance of the dominant eigenvalue associated with the transport operator plays a key role in studying the asymptotic behavior of the time dependent transport system. For bounded convex medium surrounded by vacuum, and with energy bounded away from the origin, this problem has been solved. Nevertheless, the result is only obtained under special conditions for nonhomogeneous medium with (0, v_m] energy. The general case will be discussed in this note. By the inequality given in Lemma 3, some hypotheses of [2] are weakened.展开更多
where p is a positive integer, t<sub>i</sub>’s and s<sub>i</sub>’s are distinct points in the complex plane and t<sub>i</sub>≠s<sub>j</sub>, i,j=1, 2,…, n. The follo...where p is a positive integer, t<sub>i</sub>’s and s<sub>i</sub>’s are distinct points in the complex plane and t<sub>i</sub>≠s<sub>j</sub>, i,j=1, 2,…, n. The following question was considered in[1].Given a vector b. Does there exist an algorithm for computing the product B<sub>1</sub>b in less than O（n<sup>2</sup>） operations?'展开更多
In this paper, a new concept of selection operators on hyperspaces (subsets spaces) is introduced, and the existence theorems for several kinds of selection operators are proved. Using the methods of selection operato...In this paper, a new concept of selection operators on hyperspaces (subsets spaces) is introduced, and the existence theorems for several kinds of selection operators are proved. Using the methods of selection operators, we give a selection characterization of identically distributed multivalued random variables and completely solve the vector-valued selection problem for sequences of multivalued random variables converging in distribution. The regular selections and Markov selections for multivalued stochastic processes are studied, and a discretization theorem for multivalued Markov processes is established. A theorem on the asymptotic martingale selections for compact and convex multivalued asymptotic martingale is proved.展开更多
Consider the following integro-differential operator arising from neutron transport in a finite closed convex medium V surrounded by vacuum: A·=-vΩ·grad_r·-v∑(r, v)·+∫_D∫_E k(r, v, Ω, v’, Ω...Consider the following integro-differential operator arising from neutron transport in a finite closed convex medium V surrounded by vacuum: A·=-vΩ·grad_r·-v∑(r, v)·+∫_D∫_E k(r, v, Ω, v’, Ω’)·dv’ dΩ’, D(A)={ψ∈L^P(G)|Aψ∈L^P(G); ψ(r, v, Ω)=0 for r∈V and Ω entering V}, where (r, v, Ω)∈ G=V×E×D, E=(0, v_M], 0【V_M【+∞, D is the surface of the unit sphere in R^3 and 1【p【+∞.展开更多
1. Introduction In [1], let (E, F)be a probabilistic metric (PM) space, and then (E. F, T_W) be a generalized Menger (GM) space, where T_W(a, b)= It follows that all Menger’s triangle inequalities can be given with G...1. Introduction In [1], let (E, F)be a probabilistic metric (PM) space, and then (E. F, T_W) be a generalized Menger (GM) space, where T_W(a, b)= It follows that all Menger’s triangle inequalities can be given with GM spaces. However, the weak t-norm展开更多
A （δ, g）-cage is a δ-regular graph with girth g and with the least possible number of vertices. In this paper, we show that all （δ, g）-cages with odd girth g ≥ 9 are r-connected, where （r - 1）2 ≤δ ＋ x/δ ...A （δ, g）-cage is a δ-regular graph with girth g and with the least possible number of vertices. In this paper, we show that all （δ, g）-cages with odd girth g ≥ 9 are r-connected, where （r - 1）2 ≤δ ＋ x/δ - 2 〈 r2 and all （δ, g）-cages with even girth g 〉 10 are r-connected, where r is the largest integer satisfying r（r-1）2/4 ＋ 1 ＋ 2r（r - 1） ≤δ. These results support a conjecture of Fkl, Huang and Rodger that all （δ, g）-cages are 6-connected.展开更多
Predicting protein functions is an important issue in the post-genomic era. This paper studies several network-based kernels including local linear embedding （LLE） kernel method, diffusion kernel and laplacian kerne...Predicting protein functions is an important issue in the post-genomic era. This paper studies several network-based kernels including local linear embedding （LLE） kernel method, diffusion kernel and laplacian kernel to uncover the relationship between proteins functions and protein-protein interactions （PPI）. The author first construct kernels based on PPI networks, then apply support vector machine （SVM） techniques to classify proteins into different functional groups. The 5-fold cross validation is then applied to the selected 359 GO terms to compare the performance of different kernels and guilt-by-association methods including neighbor counting methods and Chi-square methods. Finally, the authors conduct predictions of functions of some unknown genes and verify the preciseness of our prediction in part by the information of other data source.展开更多
The Navier-Stokes-α equations subject to the periodic boundary conditions are considered. Analyticity in time for a class of solutions taking values in a Gevrey class of functions is proven. Exponential decay of the ...The Navier-Stokes-α equations subject to the periodic boundary conditions are considered. Analyticity in time for a class of solutions taking values in a Gevrey class of functions is proven. Exponential decay of the spatial Fourier spectrum for the analytic solutions and the lower bounds on the rate defined by the exponential decay are also obtained.展开更多
This paper first applies the fuzzy set theory to multi-objective semi-definite program-ming （MSDP）, and proposes the fuzzy multi-objective semi-definite programming （FMSDP） model whose optimal efficient solution i...This paper first applies the fuzzy set theory to multi-objective semi-definite program-ming （MSDP）, and proposes the fuzzy multi-objective semi-definite programming （FMSDP） model whose optimal efficient solution is defined for the first time, too. By constructing a membership function, the FMSDP is translated to the MSDP. Then we prove that the optimal efficient solution of FMSDP is consistent with the efficient solution of MSDP and present the optimality condition about these programming. At last, we give an algorithm for FMSDP by introducing a new membership function and a series of transformation.展开更多
基金This research is supported by the NNSF of China (19971066)
文摘The SEIR epidemic model studied here includes constant inflows of new susceptibles, exposeds, infectives, and recovereds. This model also incorporates a population size dependent contact rate and a disease-related death. As the infected fraction cannot be eliminated from the population, this kind of model has only the unique endemic equilibrium that is globally asymptotically stable. Under the special case where the new members of immigration are all susceptible, the model considered here shows a threshold phenomenon and a sharp threshold has been obtained. In order to prove the global asymptotical stability of the endemic equilibrium, the authors introduce the change of variable, which can reduce our four-dimensional system to a three-dimensional asymptotical autonomous system with limit equation.
文摘Let M be a convex Chebyshev subset of a uniformly convex and uniformly smooth Banach space.It is proved that the metric projection P_M of X onto M is uniformly continu- ous on every bounded subset of X.Moreover,a global and explicit estimate on the modulus of continuity of the metric projection is obtained.
基金Subsidized by the Special Funds for Major State Basic Research Projects (G1999 03 2801)NFS of China (10001028 and 40375010)
文摘In this article the authors propose a new approximate inertial manifold（AIM） to the Navier-Stokes equations. The solutions are in the neighborhoods of this AIM with thickness δ=o（h^2k＋1-ε）. The article aims to investigate a two grids finite element approximation based on it and give error estimates of the approximate solution ｜｜｜（u-uh^＊·,p-ph^＊·）｜｜｜≤C（h^2k＋1-ε＋h^＊（m＋1））,where （h, h＊） and （k, m） are co^trse and fine meshes and degree of finite element subspa^es, respectively. These results are much better them Standard G^tlerkin（SG） and nonlinear Galcrkin （NG） methods. For example, for 2D NS eqs and linear element, let uh,u^h, u^＊ be the SG, NG and their approximate solutions respectively, then ｜｜u-uh｜｜1≤Ch,｜｜u-u^h｜｜i≤Ch^2,｜｜u-u^＊｜｜1≤Ch^3,and h^＊ ≈ h^2 for NG, h^＊ ≈ h^3/2 for theirs.
文摘A kind of direct methods is presented for the solution of optimal control problems with state constraints. These methods are sequential quadratic programming methods. At every iteration a quadratic programming which is obtained by quadratic approximation to Lagrangian function and linear approximations to constraints is solved to get a search direction for a merit function. The merit function is formulated by augmenting the Lagrangian function with a penalty term. A line search is carried out along the search direction to determine a step length such that the merit function is decreased. The methods presented in this paper include continuous sequential quadratic programming methods and discreate sequential quadratic programming methods.
基金This work is supported by the National Natural Science Foundation of China
文摘This paper is devoted to discussing the discrete-ordinates method for the monoenergetic neutron transport equation in a slab with generalized boundary conditions. For homogeneous medium with isotropic scattering and fission, the convergence theorems for discrete-ordinates approximations are given respectively for critical eigenvalue problem and dominant eigenvalue problems: for inhomogeneous medium with anisotropic scattering and fission, a similar discussion and an estimation for the convergence rate are given for critical eigenvalue problems. Finally, some numerical results are given by use of this method.
基金Shaanxi Province Natural Science Foundation,2007A16,China
文摘In this paper, we present a series of new preconditioners with parameters of strictly diagonally dominant Z-matrix, which contain properly two kinds of known preconditioners as special cases. Moreover, we prove the monotonicity of spectral radiuses of iterative matrices with respect to the parameters and some comparison theorems. The results obtained show that the bigger the parameter k is（i.e., we select the more upper right diagonal elements to be the preconditioner）, the less the spectral radius of iterative matrix is. A numerical example generated randomly is provided to illustrate the theoretical results.
基金This work is supported by the National Natural Science Foundation of China
文摘In this paper,the time-dependent neutron transport integro-differential equationin a nonuniform slab with generalized boundary conditions and initial value is considered forgeneral cases concerned with an arbitrary nonhomogeneous medium possibly with cavity,withthe anisotropic scattering and fission,and with continuous energy varying from null to any finiteconstant or from one positive constant to another positive constant.We prove that the correspon-ding neutron transport operator A has finite Spectrum points in any strip {λ|β<sub>1</sub>≤R（?）λ≤β<sub>2</sub>}whereβ<sub>2</sub>】β1】-λ<sup>*</sup>（λ<sup>*</sup> is the essential infimum of v∑（x,v））,and obtain the asymptotic expansion ofthe time-dependent solution which exists and is unique.Furthermore,we give the existence ofthe dominant eigenvalue and indicate the asymptotic behavior of the neutron density as t→+∞.
文摘<正> The maximum solution of fuzzy relation equations under max. and min. operations was advanced by E. Sanchez. In this paper, we gave a maximum solution of fuzzy relation equations under T-norm operation. Suppose that mapping T: [0,1]~2→ [0,1] satisfies the following conditions:
基金Project supported by the science Fund of the Chinese Academy of Sciences
文摘This paper discusses the neutron transport equation in a slab with generalized reflectingboundary conditions.By means of the positive C<sub>0</sub>-semigroup theory,we have proved that this problemhas a unique nonnegative solution and found the spectral property of the corresponding transportoperator.Finally we give the asymptotic behavior of the solution for this equation.
基金Project supported by the National Natural Science Foundation of China.
文摘In neutron transport theory, the strict dominance of the dominant eigenvalue associated with the transport operator plays a key role in studying the asymptotic behavior of the time dependent transport system. For bounded convex medium surrounded by vacuum, and with energy bounded away from the origin, this problem has been solved. Nevertheless, the result is only obtained under special conditions for nonhomogeneous medium with (0, v_m] energy. The general case will be discussed in this note. By the inequality given in Lemma 3, some hypotheses of [2] are weakened.
文摘where p is a positive integer, t<sub>i</sub>’s and s<sub>i</sub>’s are distinct points in the complex plane and t<sub>i</sub>≠s<sub>j</sub>, i,j=1, 2,…, n. The following question was considered in[1].Given a vector b. Does there exist an algorithm for computing the product B<sub>1</sub>b in less than O（n<sup>2</sup>） operations?'
基金Project supported by the National Natural Science Foundation of China.
文摘In this paper, a new concept of selection operators on hyperspaces (subsets spaces) is introduced, and the existence theorems for several kinds of selection operators are proved. Using the methods of selection operators, we give a selection characterization of identically distributed multivalued random variables and completely solve the vector-valued selection problem for sequences of multivalued random variables converging in distribution. The regular selections and Markov selections for multivalued stochastic processes are studied, and a discretization theorem for multivalued Markov processes is established. A theorem on the asymptotic martingale selections for compact and convex multivalued asymptotic martingale is proved.
基金Project supported by the Natural Science Foundation of Xi'an Jiaotong University.
文摘Consider the following integro-differential operator arising from neutron transport in a finite closed convex medium V surrounded by vacuum: A·=-vΩ·grad_r·-v∑(r, v)·+∫_D∫_E k(r, v, Ω, v’, Ω’)·dv’ dΩ’, D(A)={ψ∈L^P(G)|Aψ∈L^P(G); ψ(r, v, Ω)=0 for r∈V and Ω entering V}, where (r, v, Ω)∈ G=V×E×D, E=(0, v_M], 0【V_M【+∞, D is the surface of the unit sphere in R^3 and 1【p【+∞.
文摘1. Introduction In [1], let (E, F)be a probabilistic metric (PM) space, and then (E. F, T_W) be a generalized Menger (GM) space, where T_W(a, b)= It follows that all Menger’s triangle inequalities can be given with GM spaces. However, the weak t-norm
文摘A （δ, g）-cage is a δ-regular graph with girth g and with the least possible number of vertices. In this paper, we show that all （δ, g）-cages with odd girth g ≥ 9 are r-connected, where （r - 1）2 ≤δ ＋ x/δ - 2 〈 r2 and all （δ, g）-cages with even girth g 〉 10 are r-connected, where r is the largest integer satisfying r（r-1）2/4 ＋ 1 ＋ 2r（r - 1） ≤δ. These results support a conjecture of Fkl, Huang and Rodger that all （δ, g）-cages are 6-connected.
基金This research is supported in part by HKRGC Grant 7017/07P, HKU CRCG Grants, HKU strategic theme grant on computational sciences, HKU Hung Hing Ying Physical Science Research Grant, National Natural Science Foundation of China Grant No. 10971075 and Guangdong Provincial Natural Science Grant No. 9151063101000021. The preliminary version of this paper has been presented in the OSB2009 conference and published in the corresponding conference proceedings[25]. The authors would like to thank the anonymous referees for their helpful comments and suggestions.
文摘Predicting protein functions is an important issue in the post-genomic era. This paper studies several network-based kernels including local linear embedding （LLE） kernel method, diffusion kernel and laplacian kernel to uncover the relationship between proteins functions and protein-protein interactions （PPI）. The author first construct kernels based on PPI networks, then apply support vector machine （SVM） techniques to classify proteins into different functional groups. The 5-fold cross validation is then applied to the selected 359 GO terms to compare the performance of different kernels and guilt-by-association methods including neighbor counting methods and Chi-square methods. Finally, the authors conduct predictions of functions of some unknown genes and verify the preciseness of our prediction in part by the information of other data source.
文摘The Navier-Stokes-α equations subject to the periodic boundary conditions are considered. Analyticity in time for a class of solutions taking values in a Gevrey class of functions is proven. Exponential decay of the spatial Fourier spectrum for the analytic solutions and the lower bounds on the rate defined by the exponential decay are also obtained.
基金Supported by the National Natural Science Foundation of China (Grant No.10671057)
文摘This paper first applies the fuzzy set theory to multi-objective semi-definite program-ming （MSDP）, and proposes the fuzzy multi-objective semi-definite programming （FMSDP） model whose optimal efficient solution is defined for the first time, too. By constructing a membership function, the FMSDP is translated to the MSDP. Then we prove that the optimal efficient solution of FMSDP is consistent with the efficient solution of MSDP and present the optimality condition about these programming. At last, we give an algorithm for FMSDP by introducing a new membership function and a series of transformation.
