By using the continuation theorem of coincidence theory,the existence of a positive periodic solution for a two patches competition system with diffusion and time delay and functional response x_(1)(t)=x_(1)(t)a_(1)(t...By using the continuation theorem of coincidence theory,the existence of a positive periodic solution for a two patches competition system with diffusion and time delay and functional response x_(1)(t)=x_(1)(t)a_(1)(t)-b_(1)(t)x_(1)(t)-c_(1)(t)y(t)1+m(t)x_(1)(t)+D_(1)(t)[x_(2)(t)-x_(1)(t)],x_(2)(t)=x_(2)(t)a_(2)(t)-b_(2)(t)x_(2)(t)-c_(2)(t)∫^(0)_(-τ)k(s)x_(2)(t+s)d s+D_(2)(t)[x_(1)(t)-x_(2)(t)],y′(t)=y(t)a_(3)(t)-b_(3)(t)y(t)-c_(3)(t)x_(1)(t)1+m(t)x_(1)(t)is established,where a i(t),b_(i)(t),c_(i)(t)(i=1,2,3),m(t)and D_(i)(t)(i=1,2)are all positive periodic continuous functions with period w>0,τis a nonnegative constant and k(s)is a continuous nonnegative function on[-τ,0].展开更多
This paper deals with the existence of multiple positive solutions for a class of nonlinear singular four-point boundary value problem with p-Laplacian：{（φ（u′））′＋a（t）f（u（t））=0, 0〈t〈1, αφ（u（...This paper deals with the existence of multiple positive solutions for a class of nonlinear singular four-point boundary value problem with p-Laplacian：{（φ（u′））′＋a（t）f（u（t））=0, 0〈t〈1, αφ（u（0））-βφ（u′（ξ））=0,γφ（u（1））＋δφ（u′（η））0,where φ（x） = ｜x｜^p-2x,p 〉 1, a（t） may be singular at t = 0 and/or t = 1. By applying Leggett-Williams fixed point theorem and Schauder fixed point theorem, the sufficient conditions for the existence of multiple （at least three） positive solutions to the above four-point boundary value problem are provided. An example to illustrate the importance of the results obtained is also given.展开更多
This paper is concerned with the boundary value problem of a nonlinear fractional differential equation. By means of Schauder fixed-point theorem, an existence result of solution is obtained.
Let {εt; t ∈ Z^＋} be a strictly stationary sequence of associated random variables with mean zeros, let 0〈Eε1^2〈∞ and σ^2=Eε1^2＋1∑j=2^∞ Eε1εj with 0〈σ^2〈∞.{aj;j∈Z^＋} is a sequence of real numbers s...Let {εt; t ∈ Z^＋} be a strictly stationary sequence of associated random variables with mean zeros, let 0〈Eε1^2〈∞ and σ^2=Eε1^2＋1∑j=2^∞ Eε1εj with 0〈σ^2〈∞.{aj;j∈Z^＋} is a sequence of real numbers satisfying ∑j=0^∞｜aj｜〈∞.Define a linear process Xt=∑j=0^∞ ajεt-j,t≥1,and Sn=∑t=1^n Xt,n≥1.Assume that E｜ε1｜^2＋δ′〈 for some δ′〉0 and μ（n）=O（n^-ρ） for some ρ〉0.This paper achieves a general law of precise asymptotics for {Sn}.展开更多
To solve the nonlinear partial differential equations is changed into solving some algebraic equations by using the function U to be expressed as linear independent functions.The new soliton and periodic solutions of ...To solve the nonlinear partial differential equations is changed into solving some algebraic equations by using the function U to be expressed as linear independent functions.The new soliton and periodic solutions of some fifth\|order nonlinear partial differential equations are obtained.展开更多
In this paper, we first introduce a concept of companion vector, and studythe Jordan canonical forms of quaternion matrices by using the methods of complex representation and companion vector, not only give out a prac...In this paper, we first introduce a concept of companion vector, and studythe Jordan canonical forms of quaternion matrices by using the methods of complex representation and companion vector, not only give out a practical algorithm for Jordancanonical form J of a quaternion matrix A, but also provide a practical algorithm forcorresponding nonsingular matrix P with P- 1 AP = J.展开更多
The concept of quasi-coincidence of a fuzzy interval value with an interval valued fuzzy set is considered. In fact, this is a generalization of quasi-coincidence of a fuzzy point with a fuzzy set. By using this new i...The concept of quasi-coincidence of a fuzzy interval value with an interval valued fuzzy set is considered. In fact, this is a generalization of quasi-coincidence of a fuzzy point with a fuzzy set. By using this new idea, the notion of interval valued （∈,∈ ∨q）-fuzzy filters in BL-algebras which is a generalization of fuzzy filters of BL-algebras, is defined, and related properties are investigated. In particular, the concept of a fuzzy subgroup with thresholds is extended to the concept of an interval valued fuzzy filter with thresholds in BL-algebras.展开更多
In this paper, lower bounds of the topological entropy for nonautonomous dynamical systems are given via the growths of topological complexity in fundamental group and in degree.
In the case of Z＋^d（d ≥ 2）-the positive d-dimensional lattice points with partial ordering ≤, {Xk,k∈ Z＋^d} i.i.d, random variables with mean 0, Sn =∑k≤nXk and Vn^2 = ∑j≤nXj^2, the precise asymptotics for ∑...In the case of Z＋^d（d ≥ 2）-the positive d-dimensional lattice points with partial ordering ≤, {Xk,k∈ Z＋^d} i.i.d, random variables with mean 0, Sn =∑k≤nXk and Vn^2 = ∑j≤nXj^2, the precise asymptotics for ∑n1/｜n｜（log｜n｜dP（｜Sn/Vn｜≥ε√log log｜n｜） and ∑n（logn｜）b/｜n｜（log｜n｜）^d-1P（｜Sn/Vn｜≥ε√log n）,as ε↓0,is established.展开更多
As is known to all, theory of invariant metric is very important inseveral complex analysis.The Bergman, Caratheodory and Kobayashi metrics are important biholomorphic. invariants.They play very important role in stud...As is known to all, theory of invariant metric is very important inseveral complex analysis.The Bergman, Caratheodory and Kobayashi metrics are important biholomorphic. invariants.They play very important role in studying the boundary geometry of the domain and biholo-morphic mappings extending smoothly to the boundaries of the relevant domains.展开更多
S. Y. Cheng and S. T. Yau showed in [CY] that any C2 bounded pseudoconvex domain in C?has a complete Einstein-Kahler metric with constant negative Ricci curvature. N. Mok and S. T. Yau[MY] have extended this result to...S. Y. Cheng and S. T. Yau showed in [CY] that any C2 bounded pseudoconvex domain in C?has a complete Einstein-Kahler metric with constant negative Ricci curvature. N. Mok and S. T. Yau[MY] have extended this result to arbitrary bounded pseudoconvex domain in Cn. Complete Einstein-Kahler metric with Explicit form, however, is only known in the case of homogeneous domain.展开更多
Let Tμ,b,m be the higher order commutator generated by a generalized fractional integral operator Tμ and a BMO function b. In this paper, we will study the boundedness of Tμ,b,m on classical Hardy spaces and Herz-t...Let Tμ,b,m be the higher order commutator generated by a generalized fractional integral operator Tμ and a BMO function b. In this paper, we will study the boundedness of Tμ,b,m on classical Hardy spaces and Herz-type Hardy spaces.展开更多
This paper considers an SEIS epidemic model with infectious force in the latent period and a general population-size dependent contact rate. A threshold parameter R is identified. If R≤1, the disease-free equilibrium...This paper considers an SEIS epidemic model with infectious force in the latent period and a general population-size dependent contact rate. A threshold parameter R is identified. If R≤1, the disease-free equilibrium O is globally stable. If R〉1, there is a unique endemic equilibrium and O is unstable. For two important special cases of bilinear and standard incidence ,sufficient conditions for the global stability of this endemic equilibrium are given. The same qualitative results are obtained provided the threshold is more than unity for the corresponding SEIS model with no infectious force in the latent period. Some existing results are extended and improved.展开更多
The spectrum of a class of fourth order left-definite differential operators is studied. By using the theory of indefinite differential operators in Krein space and the relationship between left-definite and right-def...The spectrum of a class of fourth order left-definite differential operators is studied. By using the theory of indefinite differential operators in Krein space and the relationship between left-definite and right-definite operators, the following conclusions are obtained： if a fourth order differential operator with a self-adjoint boundary condition that is left-definite and right-indefinite, then all its eigenvalues are real, and there exist countably infinitely many positive and negative eigenvalues which are unbounded from below and above, have no finite cluster point and can be indexed to satisfy the inequality …≤λ-2≤λ-1≤λ-0〈0〈λ0≤λ1≤λ2≤…展开更多
This paper studies the convergence of the sequence defined by x0 ∈ C, xn＋l =αnu＋（1-αn）Txn, n=0, 1,2,..., where 0 ≤αn ≤ 1, limn→∞ αn = 0, ∑n=0^∞ αn = ∞, and T is a nonexpansive mapping from a nonempty...This paper studies the convergence of the sequence defined by x0 ∈ C, xn＋l =αnu＋（1-αn）Txn, n=0, 1,2,..., where 0 ≤αn ≤ 1, limn→∞ αn = 0, ∑n=0^∞ αn = ∞, and T is a nonexpansive mapping from a nonempty closed convex subset C of a Banach space X into itself. The iterative sequence {xn} converges strongly to a fixed point of T in the case when X is a uniformly convex Banach space with a uniformly Gateaux differentiable norm or a uniformly smooth Banach space only. The results presented in this paper extend and improve some recent results.展开更多
0 IntroductionLet L = ab be a non-closed smooth arc oriented from a to b, t∈ L, t≠a,b, be the fixed point, andf(t) ∈H. (L) . The usual Hadamard principal value is defined asAbout properties and applications of sing...0 IntroductionLet L = ab be a non-closed smooth arc oriented from a to b, t∈ L, t≠a,b, be the fixed point, andf(t) ∈H. (L) . The usual Hadamard principal value is defined asAbout properties and applications of singular integals of high order were investigated by many authors([1],[2],[3] etc. ) In 1987, the concepts of Hadamard principal value at one-side for singular integralsof high order and the rules of their differentiation are introduced [4]. In this paper we established the rulesof substitution of variable for one-sided Hadamard principal value of singular integrals of high order, andthen, we gave some applications in evaluation of real definite integrals.展开更多
0 IntroductionThe mathematical problems of fracture of compound materials are very important on practical applica-tions. In this paper, we study the plane welding problems of different anisotropic media with holes,the...0 IntroductionThe mathematical problems of fracture of compound materials are very important on practical applica-tions. In this paper, we study the plane welding problems of different anisotropic media with holes,theshape of holes and the interface are arbitrary smooth contours. At first, we establish mathematical models,change it into searching complex stress functions, next, we reduce the primitive problems into boundaryvalue problems, and construct the form of solution, under some general restrictions it is reduced to certainsingular integral equations, finally, the existence and the uniqueness of the solution of which are estab-lished.1 The Representation Formula of Complex Stress展开更多
The following equations are basic forms of C-K equation (which is simplified in the following as singu-lar integral equations with convolution, that is C-K equations):where a,b,a_j,b_j are known constants or known fun...The following equations are basic forms of C-K equation (which is simplified in the following as singu-lar integral equations with convolution, that is C-K equations):where a,b,a_j,b_j are known constants or known functions, and find its solution f L_P(R), {0} or {α,β}.There were rather complete investigations on the method of solution for equations of Cauchy type aswell as integral equations of convolution type. But there is not investigation to the C-K equations, nodoubt, such that is important.展开更多
Quasi-likelihood nonlinear models （QLNM） include generalized linear models as a special case. Under some regularity conditions, the rate of the strong consistency of the maximum quasi-likelihood estimation （MQLE） ...Quasi-likelihood nonlinear models （QLNM） include generalized linear models as a special case. Under some regularity conditions, the rate of the strong consistency of the maximum quasi-likelihood estimation （MQLE） is obtained in QLNM. In an important case, this rate is O（n-^1/2（loglogn）^1/2）, which is just the rate of LIL of partial sums for i.i.d variables, and thus cannot be improved anymore.展开更多
The boundedness on Triebel-Lizorkin spaces of oscillatory singular integral operator T in the form e^i｜x｜^aΩ（x）｜x｜^-n is studied,where a∈R,a≠0,1 and Ω∈L^1（S^n-1） is homogeneous of degree zero and satisfie...The boundedness on Triebel-Lizorkin spaces of oscillatory singular integral operator T in the form e^i｜x｜^aΩ（x）｜x｜^-n is studied,where a∈R,a≠0,1 and Ω∈L^1（S^n-1） is homogeneous of degree zero and satisfies certain cancellation condition. When kernel Ω（x＇ ）∈Llog＋L（S^n-1 ）, the Fp^a,q（R^n） boundedness of the above operator is obtained. Meanwhile ,when Ω（x） satisfies L^1- Dini condition,the above operator T is bounded on F1^0,1 （R^n）.展开更多
基金Supported by the National Natural Science Foundation of China(19531070)the Major and Youth Project Foundation of Hubei Province Education Department(2001Z06003)(2002B00002).
文摘By using the continuation theorem of coincidence theory,the existence of a positive periodic solution for a two patches competition system with diffusion and time delay and functional response x_(1)(t)=x_(1)(t)a_(1)(t)-b_(1)(t)x_(1)(t)-c_(1)(t)y(t)1+m(t)x_(1)(t)+D_(1)(t)[x_(2)(t)-x_(1)(t)],x_(2)(t)=x_(2)(t)a_(2)(t)-b_(2)(t)x_(2)(t)-c_(2)(t)∫^(0)_(-τ)k(s)x_(2)(t+s)d s+D_(2)(t)[x_(1)(t)-x_(2)(t)],y′(t)=y(t)a_(3)(t)-b_(3)(t)y(t)-c_(3)(t)x_(1)(t)1+m(t)x_(1)(t)is established,where a i(t),b_(i)(t),c_(i)(t)(i=1,2,3),m(t)and D_(i)(t)(i=1,2)are all positive periodic continuous functions with period w>0,τis a nonnegative constant and k(s)is a continuous nonnegative function on[-τ,0].
基金Tutorial Scientific Research Program Foundation of Education Department of Gansu Province(0710-04).
文摘This paper deals with the existence of multiple positive solutions for a class of nonlinear singular four-point boundary value problem with p-Laplacian：{（φ（u′））′＋a（t）f（u（t））=0, 0〈t〈1, αφ（u（0））-βφ（u′（ξ））=0,γφ（u（1））＋δφ（u′（η））0,where φ（x） = ｜x｜^p-2x,p 〉 1, a（t） may be singular at t = 0 and/or t = 1. By applying Leggett-Williams fixed point theorem and Schauder fixed point theorem, the sufficient conditions for the existence of multiple （at least three） positive solutions to the above four-point boundary value problem are provided. An example to illustrate the importance of the results obtained is also given.
文摘This paper is concerned with the boundary value problem of a nonlinear fractional differential equation. By means of Schauder fixed-point theorem, an existence result of solution is obtained.
基金National Natural Science Foundation of China(10571073).
文摘Let {εt; t ∈ Z^＋} be a strictly stationary sequence of associated random variables with mean zeros, let 0〈Eε1^2〈∞ and σ^2=Eε1^2＋1∑j=2^∞ Eε1εj with 0〈σ^2〈∞.{aj;j∈Z^＋} is a sequence of real numbers satisfying ∑j=0^∞｜aj｜〈∞.Define a linear process Xt=∑j=0^∞ ajεt-j,t≥1,and Sn=∑t=1^n Xt,n≥1.Assume that E｜ε1｜^2＋δ′〈 for some δ′〉0 and μ（n）=O（n^-ρ） for some ρ〉0.This paper achieves a general law of precise asymptotics for {Sn}.
基金Project supported by the National Natural Science Foundation of China(69577009).
文摘To solve the nonlinear partial differential equations is changed into solving some algebraic equations by using the function U to be expressed as linear independent functions.The new soliton and periodic solutions of some fifth\|order nonlinear partial differential equations are obtained.
基金Supported by the National Natural Science Foudnation of China and Shanghai Priority Academic Discipline Foundation,Shanghai,China.
文摘In this paper, we first introduce a concept of companion vector, and studythe Jordan canonical forms of quaternion matrices by using the methods of complex representation and companion vector, not only give out a practical algorithm for Jordancanonical form J of a quaternion matrix A, but also provide a practical algorithm forcorresponding nonsingular matrix P with P- 1 AP = J.
基金Supported by the National Natural Science Foundation of China(60474022)a grant of the Key Science Foundation of Education Committee of Hubei Province(D200729003)
文摘The concept of quasi-coincidence of a fuzzy interval value with an interval valued fuzzy set is considered. In fact, this is a generalization of quasi-coincidence of a fuzzy point with a fuzzy set. By using this new idea, the notion of interval valued （∈,∈ ∨q）-fuzzy filters in BL-algebras which is a generalization of fuzzy filters of BL-algebras, is defined, and related properties are investigated. In particular, the concept of a fuzzy subgroup with thresholds is extended to the concept of an interval valued fuzzy filter with thresholds in BL-algebras.
基金Supported by the National Natural Science Foundation of China (10701032)Natural Science Foundation of Hebei Province (A2008000132)the Doctoral Foundation of Hebei Normal University (L2005B02)
文摘In this paper, lower bounds of the topological entropy for nonautonomous dynamical systems are given via the growths of topological complexity in fundamental group and in degree.
文摘In the case of Z＋^d（d ≥ 2）-the positive d-dimensional lattice points with partial ordering ≤, {Xk,k∈ Z＋^d} i.i.d, random variables with mean 0, Sn =∑k≤nXk and Vn^2 = ∑j≤nXj^2, the precise asymptotics for ∑n1/｜n｜（log｜n｜dP（｜Sn/Vn｜≥ε√log log｜n｜） and ∑n（logn｜）b/｜n｜（log｜n｜）^d-1P（｜Sn/Vn｜≥ε√log n）,as ε↓0,is established.
基金Supported by NSFC(No.10171068,No.10071051),NSF of Beijing(No.1012004)and Planned Project for the Development of Science and Technology,Beijing Eduction Committee.
文摘As is known to all, theory of invariant metric is very important inseveral complex analysis.The Bergman, Caratheodory and Kobayashi metrics are important biholomorphic. invariants.They play very important role in studying the boundary geometry of the domain and biholo-morphic mappings extending smoothly to the boundaries of the relevant domains.
基金Supported in part by NSFC(Grant No.:10171068,10171051)and NSF of Bejing(Grant No. 1012004).
文摘S. Y. Cheng and S. T. Yau showed in [CY] that any C2 bounded pseudoconvex domain in C?has a complete Einstein-Kahler metric with constant negative Ricci curvature. N. Mok and S. T. Yau[MY] have extended this result to arbitrary bounded pseudoconvex domain in Cn. Complete Einstein-Kahler metric with Explicit form, however, is only known in the case of homogeneous domain.
基金Supported Partially by NSF of China (10371087) Education Committee of Anhui Province (2003kj034zd).
文摘Let Tμ,b,m be the higher order commutator generated by a generalized fractional integral operator Tμ and a BMO function b. In this paper, we will study the boundedness of Tμ,b,m on classical Hardy spaces and Herz-type Hardy spaces.
文摘This paper considers an SEIS epidemic model with infectious force in the latent period and a general population-size dependent contact rate. A threshold parameter R is identified. If R≤1, the disease-free equilibrium O is globally stable. If R〉1, there is a unique endemic equilibrium and O is unstable. For two important special cases of bilinear and standard incidence ,sufficient conditions for the global stability of this endemic equilibrium are given. The same qualitative results are obtained provided the threshold is more than unity for the corresponding SEIS model with no infectious force in the latent period. Some existing results are extended and improved.
基金Supported by the National Natural Science Foundation of China(10561005)the Doctor's Discipline Fund of the Ministry of Education of China(20040126008)
文摘The spectrum of a class of fourth order left-definite differential operators is studied. By using the theory of indefinite differential operators in Krein space and the relationship between left-definite and right-definite operators, the following conclusions are obtained： if a fourth order differential operator with a self-adjoint boundary condition that is left-definite and right-indefinite, then all its eigenvalues are real, and there exist countably infinitely many positive and negative eigenvalues which are unbounded from below and above, have no finite cluster point and can be indexed to satisfy the inequality …≤λ-2≤λ-1≤λ-0〈0〈λ0≤λ1≤λ2≤…
基金Supported by the Natural Science Foundation of the Educational Dept.of Zhejiang Province(20020868).
文摘This paper studies the convergence of the sequence defined by x0 ∈ C, xn＋l =αnu＋（1-αn）Txn, n=0, 1,2,..., where 0 ≤αn ≤ 1, limn→∞ αn = 0, ∑n=0^∞ αn = ∞, and T is a nonexpansive mapping from a nonempty closed convex subset C of a Banach space X into itself. The iterative sequence {xn} converges strongly to a fixed point of T in the case when X is a uniformly convex Banach space with a uniformly Gateaux differentiable norm or a uniformly smooth Banach space only. The results presented in this paper extend and improve some recent results.
文摘0 IntroductionLet L = ab be a non-closed smooth arc oriented from a to b, t∈ L, t≠a,b, be the fixed point, andf(t) ∈H. (L) . The usual Hadamard principal value is defined asAbout properties and applications of singular integals of high order were investigated by many authors([1],[2],[3] etc. ) In 1987, the concepts of Hadamard principal value at one-side for singular integralsof high order and the rules of their differentiation are introduced [4]. In this paper we established the rulesof substitution of variable for one-sided Hadamard principal value of singular integrals of high order, andthen, we gave some applications in evaluation of real definite integrals.
文摘0 IntroductionThe mathematical problems of fracture of compound materials are very important on practical applica-tions. In this paper, we study the plane welding problems of different anisotropic media with holes,theshape of holes and the interface are arbitrary smooth contours. At first, we establish mathematical models,change it into searching complex stress functions, next, we reduce the primitive problems into boundaryvalue problems, and construct the form of solution, under some general restrictions it is reduced to certainsingular integral equations, finally, the existence and the uniqueness of the solution of which are estab-lished.1 The Representation Formula of Complex Stress
文摘The following equations are basic forms of C-K equation (which is simplified in the following as singu-lar integral equations with convolution, that is C-K equations):where a,b,a_j,b_j are known constants or known functions, and find its solution f L_P(R), {0} or {α,β}.There were rather complete investigations on the method of solution for equations of Cauchy type aswell as integral equations of convolution type. But there is not investigation to the C-K equations, nodoubt, such that is important.
基金Supported by the National Natural Sciences Foundation of China (10761011)Mathematical Tianyuan Fund of National Natural Science Fundation of China(10626048)
文摘Quasi-likelihood nonlinear models （QLNM） include generalized linear models as a special case. Under some regularity conditions, the rate of the strong consistency of the maximum quasi-likelihood estimation （MQLE） is obtained in QLNM. In an important case, this rate is O（n-^1/2（loglogn）^1/2）, which is just the rate of LIL of partial sums for i.i.d variables, and thus cannot be improved anymore.
文摘The boundedness on Triebel-Lizorkin spaces of oscillatory singular integral operator T in the form e^i｜x｜^aΩ（x）｜x｜^-n is studied,where a∈R,a≠0,1 and Ω∈L^1（S^n-1） is homogeneous of degree zero and satisfies certain cancellation condition. When kernel Ω（x＇ ）∈Llog＋L（S^n-1 ）, the Fp^a,q（R^n） boundedness of the above operator is obtained. Meanwhile ,when Ω（x） satisfies L^1- Dini condition,the above operator T is bounded on F1^0,1 （R^n）.
