Let {X_i;i≥1} be a strictly stationary sequence of associated random variables with mean zero and let σ2=EX2_1+2∞_~j=2 EX_1X_j with 0<σ2<∞.Set S_n=n_~i=1 X_i,the precise asymptotics for _~n≥1 n^rp-2 P(|S_n...Let {X_i;i≥1} be a strictly stationary sequence of associated random variables with mean zero and let σ2=EX2_1+2∞_~j=2 EX_1X_j with 0<σ2<∞.Set S_n=n_~i=1 X_i,the precise asymptotics for _~n≥1 n^rp-2 P(|S_n|≥εn^1p ),_~n≥1 1nP(|S_n|≥εn^1p ) and _~n≥1 (log n)δnP(|S_n|≥εnlogn) as ε0 are established.展开更多
By extending the concept of asymptotic weakly Pareto-Nash equilibrium point to vector-valued case, Tikhonov well-posedness and Hadamard well-posedness results of the multiobjective generalized games are established in...By extending the concept of asymptotic weakly Pareto-Nash equilibrium point to vector-valued case, Tikhonov well-posedness and Hadamard well-posedness results of the multiobjective generalized games are established in this paper.展开更多
SVM (support vector machines) have become an increasingly popular tool for machine learning tasks involving classification,regression or novelty detection.In particular,they exhibit good generalization performance on ...SVM (support vector machines) have become an increasingly popular tool for machine learning tasks involving classification,regression or novelty detection.In particular,they exhibit good generalization performance on many real issues and the approach is properly motivated theoretically.There are relatively a few free parameters to adjust and the architecture of the learning machine does not need to be found by experimentation.In this paper,survey of the key contents on this subject,focusing on the most well-known models based on kernel substitution,namely SVM,as well as the activated fields at present and the development tendency,is presented.展开更多
This paper considers an SIRS epidemic model that incorporates constant immigrati on rate, a general population size dependent contact rate and proportional tran sfer rate from the infective class to susceptible class...This paper considers an SIRS epidemic model that incorporates constant immigrati on rate, a general population size dependent contact rate and proportional tran sfer rate from the infective class to susceptible class.A threshold parameter σ is identified. If σ≤1, the disease free equilibrium is globally stab le. If σ>1, a unique endemic equilibrium is locally asymptotically stable. For two important special cases of mass action incidence and standard incidence, global stability of the endemic equilibrium is proved provided the threshold is larger than unity. Some previous results are extended and improved.展开更多
Let Mn be a closed spacelike submanifold isometrically immersed in de Sitter space S^n+p _p(c).Denote by R,H and S the normalized scalar curvature,the mean curvature and the square of the length of the second fundamen...Let Mn be a closed spacelike submanifold isometrically immersed in de Sitter space S^n+p _p(c).Denote by R,H and S the normalized scalar curvature,the mean curvature and the square of the length of the second fundamental form of Mn,respectively.Suppose R is constant and R≤c. The pinching problem on S is studied and a rigidity theorem for Mn immersed in ~S^n+p _p(c) with parallel normalized mean curvature vector field is proved.When n≥3, the pinching constant is the best.Thus,the mistake of the paper “Space-like hypersurfaces in de Sitter space with constant scalar curvature”(see Manus Math,1998,95:499-505) is corrected.Moreover,the reduction of the codimension when Mn is a complete submanifold in S^n+p _p(c) with parallel normalized mean curvature vector field is investigated.展开更多
The authors study the singular integral operatorT_~Ω,α f(x)=p.v.∫_~Rn b(｜y｜)Ω(y′)｜y｜^-n-α f(x-y)dy,defined on all test functions f,where b is a bounded function,α>0,Ω(y′) is an integrable function on t...The authors study the singular integral operatorT_~Ω,α f(x)=p.v.∫_~Rn b(｜y｜)Ω(y′)｜y｜^-n-α f(x-y)dy,defined on all test functions f,where b is a bounded function,α>0,Ω(y′) is an integrable function on the unit sphere S^n-1 satisfying certain cancellation conditions.It is proved that,for n/(n+α)<p<∞,T_~Ω,α is a bounded operator from the Hardy-Sobolev space Hp_α to the Hardy space Hp.The results and its applications improve some theorems in a previous paper of the author and they are extensions of the main theorems in Wheeden's paper(1969).The proof is based on a new atomic decomposition of the space Hp_α by Han,Paluszynski and Weiss(1995).By using the same proof,the singluar integral operators with variable kernels are also studied.展开更多
Based on the combination of fractional calculus with fractal functions, a new type of functions is introduced; the definition, graph, property and dimension of this function are discussed.
This note studies the existence of positive homoclinic orbits of the second order equation-u″+α(x)u=β(x)u q+γ(x)u p, x∈R,where 1<q<p.Assume that the coefficient functions α(x),β(x) and γ(x) are asympt...This note studies the existence of positive homoclinic orbits of the second order equation-u″+α(x)u=β(x)u q+γ(x)u p, x∈R,where 1<q<p.Assume that the coefficient functions α(x),β(x) and γ(x) are asymptotically periodic and satisfy0<a≤α(x), 0<γ(x)≤B, -M≤β(x)≤M.A positive homoclinic orbit of the equation is obtained by means of variational methods.展开更多
Let (X 1,X 2,...,X n) and (Y 1,Y 2,...,Y n) be real random vectors with the same marginal distributions,if (X 1,X 2,...,X n)≤ c(Y 1,Y 2,...,Y n), it is showed in this paper that ∑ n i=1 X i≤ c...Let (X 1,X 2,...,X n) and (Y 1,Y 2,...,Y n) be real random vectors with the same marginal distributions,if (X 1,X 2,...,X n)≤ c(Y 1,Y 2,...,Y n), it is showed in this paper that ∑ n i=1 X i≤ cx ∑ n i=1 Y i and max 1≤k≤n ∑ k i=1 X i≤ icx max 1≤k≤n ∑ k i=1 Y i hold.Based on this fact,a more general comparison theorem is obtained.展开更多
In a dot productspace with the reproducing kernel (r.k.S.) ,a fuzzy system with the estimation approximation errors is proposed,which overcomes the defect thatthe existing fuzzy control system is difficult to estima...In a dot productspace with the reproducing kernel (r.k.S.) ,a fuzzy system with the estimation approximation errors is proposed,which overcomes the defect thatthe existing fuzzy control system is difficult to estimate the errors of approximation for a desired function,and keeps the characteristics of fuzzy system as an inference approach.The structure of the new fuzzy approximator benefits a course got by other means展开更多
Based on the modified Jocobi elliptic function expansion method and the modified extended tanh function method,a new algebraic method is presented to obtain mu ltiple travelling wave solutions for nonlinear wave equ...Based on the modified Jocobi elliptic function expansion method and the modified extended tanh function method,a new algebraic method is presented to obtain mu ltiple travelling wave solutions for nonlinear wave equations.By using the metho d,Ito's 5th order and 7th order mKdV equations are studied in detail and more new exact Jocobi elliptic function periodic solutions are found.With modulus m→1 or m→0,these solutions degenerate into corresponding solitary wave s olutions,shock wave solutions and trigonometric function solutions.展开更多
In this paper,the L2-boundedness of a class of parametric Marcinkiewicz integral μρ Ω,h with kernel function Ω in B 0,0 q(S n-1) for some q>1,and the radial function h(x)∈l∞(Ls)(R +) for 1<s≤∞ are...In this paper,the L2-boundedness of a class of parametric Marcinkiewicz integral μρ Ω,h with kernel function Ω in B 0,0 q(S n-1) for some q>1,and the radial function h(x)∈l∞(Ls)(R +) for 1<s≤∞ are given.The Lp(Rn)(2≤p<∞) boundedness of μ *,ρ Ω,h,λ and μ ρ Ω,h,S with Ω in B 0,0 q(S n-1) and h(|x|)∈l∞(Ls)(R +) in application are obtained.Here μ *,ρ Ω,h,λ and μ ρ Ω,h,S are parametric Marcinkiewicz integrals corresponding to the Littlewood-Paley g* λ function and the Lusin area function S,respectively.展开更多
The axioms of A ∞ algebras can be written as Maurer Cartan equation.Infi nitesimal multiplication of a graded associative algebra is defined and the integrability of infinitesimal multiplication is discussed throu...The axioms of A ∞ algebras can be written as Maurer Cartan equation.Infi nitesimal multiplication of a graded associative algebra is defined and the integrability of infinitesimal multiplication is discussed through the Massey F product.展开更多
A new smoothing method is proposed. The smoothing process adapts to image characteristics and is good at preserving local image structures. More importantly, in the theory under the conditions weaker than those in the...A new smoothing method is proposed. The smoothing process adapts to image characteristics and is good at preserving local image structures. More importantly, in the theory under the conditions weaker than those in the original Kaanov method an approximal sequence of solutions to the variational problems can be constructed and the global convergence can be proved. And the conditions in the papers of Schno¨rr(1994) and Heers, et al (2001) are discussed. Numerical solutions of the model are given.展开更多
In the present paper the transformation of symmetric Markov processes by symmetric martingale multiplicative functionals is studied and the corresponding Dirichlet form is formulated.
By introducing a kind of maximal operator of fractional order associated with the mean Luxemburg norm and using the technique of Sharp function,multilinear commutators of fractional integral operator with vector symbo...By introducing a kind of maximal operator of fractional order associated with the mean Luxemburg norm and using the technique of Sharp function,multilinear commutators of fractional integral operator with vector symbol b=(b 1,...,b m)defined byI b αf(x)=∫ R∏mj=1(b j(x)-b j(y))1｜x-y｜ n-αf(y)dyare considered.The following priori estimates are proved.For 1<p<∞,there exists a constant c such that‖I b αf‖ Lp(Rn)≤c‖b‖‖M L(logL) 1r,α(f)‖ Lp(Rn),So‖I b αf‖ Lq(Rn)≤c‖b‖‖f‖ Lp(Rn),where 1<p<nα,1q=1p-αn,0<α<n,and supt>01Φ1t｜｛y∈Rn:｜I b αf(y)｜>t｝｜ 1q≤ c supt>01Φ1t｜｛y∈Rn:M L(logL) 1r,α(‖b‖f)(y)>t｝｜ 1q,where ‖b‖=∏ m j=1‖b j‖ Osc expL r j,Φ(t)=t(1+log+t) 1r,1r=1r 1+...+1r m, M L(logL) 1r,α is an Orlicz type maximal operator.展开更多
文摘Let {X_i;i≥1} be a strictly stationary sequence of associated random variables with mean zero and let σ2=EX2_1+2∞_~j=2 EX_1X_j with 0<σ2<∞.Set S_n=n_~i=1 X_i,the precise asymptotics for _~n≥1 n^rp-2 P(|S_n|≥εn^1p ),_~n≥1 1nP(|S_n|≥εn^1p ) and _~n≥1 (log n)δnP(|S_n|≥εnlogn) as ε0 are established.
基金Supported by Natural Science Foundation of Guizhou Province
文摘By extending the concept of asymptotic weakly Pareto-Nash equilibrium point to vector-valued case, Tikhonov well-posedness and Hadamard well-posedness results of the multiobjective generalized games are established in this paper.
基金Supported by the National863Plan Foundation of China( 2 0 0 2 AA41 2 0 1 0 )
文摘SVM (support vector machines) have become an increasingly popular tool for machine learning tasks involving classification,regression or novelty detection.In particular,they exhibit good generalization performance on many real issues and the approach is properly motivated theoretically.There are relatively a few free parameters to adjust and the architecture of the learning machine does not need to be found by experimentation.In this paper,survey of the key contents on this subject,focusing on the most well-known models based on kernel substitution,namely SVM,as well as the activated fields at present and the development tendency,is presented.
基金Supported by the Science and Technology Foundation of Zhejiang University(1 0 70 0 0 - 54430 1 )
文摘This paper considers an SIRS epidemic model that incorporates constant immigrati on rate, a general population size dependent contact rate and proportional tran sfer rate from the infective class to susceptible class.A threshold parameter σ is identified. If σ≤1, the disease free equilibrium is globally stab le. If σ>1, a unique endemic equilibrium is locally asymptotically stable. For two important special cases of mass action incidence and standard incidence, global stability of the endemic equilibrium is proved provided the threshold is larger than unity. Some previous results are extended and improved.
文摘Let Mn be a closed spacelike submanifold isometrically immersed in de Sitter space S^n+p _p(c).Denote by R,H and S the normalized scalar curvature,the mean curvature and the square of the length of the second fundamental form of Mn,respectively.Suppose R is constant and R≤c. The pinching problem on S is studied and a rigidity theorem for Mn immersed in ~S^n+p _p(c) with parallel normalized mean curvature vector field is proved.When n≥3, the pinching constant is the best.Thus,the mistake of the paper “Space-like hypersurfaces in de Sitter space with constant scalar curvature”(see Manus Math,1998,95:499-505) is corrected.Moreover,the reduction of the codimension when Mn is a complete submanifold in S^n+p _p(c) with parallel normalized mean curvature vector field is investigated.
文摘The authors study the singular integral operatorT_~Ω,α f(x)=p.v.∫_~Rn b(｜y｜)Ω(y′)｜y｜^-n-α f(x-y)dy,defined on all test functions f,where b is a bounded function,α>0,Ω(y′) is an integrable function on the unit sphere S^n-1 satisfying certain cancellation conditions.It is proved that,for n/(n+α)<p<∞,T_~Ω,α is a bounded operator from the Hardy-Sobolev space Hp_α to the Hardy space Hp.The results and its applications improve some theorems in a previous paper of the author and they are extensions of the main theorems in Wheeden's paper(1969).The proof is based on a new atomic decomposition of the space Hp_α by Han,Paluszynski and Weiss(1995).By using the same proof,the singluar integral operators with variable kernels are also studied.
基金National Natural Science Foundation of Zhejiang Province
文摘Based on the combination of fractional calculus with fractal functions, a new type of functions is introduced; the definition, graph, property and dimension of this function are discussed.
文摘This note studies the existence of positive homoclinic orbits of the second order equation-u″+α(x)u=β(x)u q+γ(x)u p, x∈R,where 1<q<p.Assume that the coefficient functions α(x),β(x) and γ(x) are asymptotically periodic and satisfy0<a≤α(x), 0<γ(x)≤B, -M≤β(x)≤M.A positive homoclinic orbit of the equation is obtained by means of variational methods.
基金the National Natural Science Foundation of China( 1 0 371 1 0 9)
文摘Let (X 1,X 2,...,X n) and (Y 1,Y 2,...,Y n) be real random vectors with the same marginal distributions,if (X 1,X 2,...,X n)≤ c(Y 1,Y 2,...,Y n), it is showed in this paper that ∑ n i=1 X i≤ cx ∑ n i=1 Y i and max 1≤k≤n ∑ k i=1 X i≤ icx max 1≤k≤n ∑ k i=1 Y i hold.Based on this fact,a more general comparison theorem is obtained.
文摘In a dot productspace with the reproducing kernel (r.k.S.) ,a fuzzy system with the estimation approximation errors is proposed,which overcomes the defect thatthe existing fuzzy control system is difficult to estimate the errors of approximation for a desired function,and keeps the characteristics of fuzzy system as an inference approach.The structure of the new fuzzy approximator benefits a course got by other means
基金Supported by the Natural Science Foundation of Zhejiang Province (1 0 2 0 37)
文摘Based on the modified Jocobi elliptic function expansion method and the modified extended tanh function method,a new algebraic method is presented to obtain mu ltiple travelling wave solutions for nonlinear wave equations.By using the metho d,Ito's 5th order and 7th order mKdV equations are studied in detail and more new exact Jocobi elliptic function periodic solutions are found.With modulus m→1 or m→0,these solutions degenerate into corresponding solitary wave s olutions,shock wave solutions and trigonometric function solutions.
文摘In this paper,the L2-boundedness of a class of parametric Marcinkiewicz integral μρ Ω,h with kernel function Ω in B 0,0 q(S n-1) for some q>1,and the radial function h(x)∈l∞(Ls)(R +) for 1<s≤∞ are given.The Lp(Rn)(2≤p<∞) boundedness of μ *,ρ Ω,h,λ and μ ρ Ω,h,S with Ω in B 0,0 q(S n-1) and h(|x|)∈l∞(Ls)(R +) in application are obtained.Here μ *,ρ Ω,h,λ and μ ρ Ω,h,S are parametric Marcinkiewicz integrals corresponding to the Littlewood-Paley g* λ function and the Lusin area function S,respectively.
文摘The axioms of A ∞ algebras can be written as Maurer Cartan equation.Infi nitesimal multiplication of a graded associative algebra is defined and the integrability of infinitesimal multiplication is discussed through the Massey F product.
基金the National Natural Science Foundation of China( 1 9871 0 77)
文摘A new smoothing method is proposed. The smoothing process adapts to image characteristics and is good at preserving local image structures. More importantly, in the theory under the conditions weaker than those in the original Kaanov method an approximal sequence of solutions to the variational problems can be constructed and the global convergence can be proved. And the conditions in the papers of Schno¨rr(1994) and Heers, et al (2001) are discussed. Numerical solutions of the model are given.
基金in partby the National Natural Science Founda-tion of China(1 950 1 0 36)
文摘In the present paper the transformation of symmetric Markov processes by symmetric martingale multiplicative functionals is studied and the corresponding Dirichlet form is formulated.
文摘By introducing a kind of maximal operator of fractional order associated with the mean Luxemburg norm and using the technique of Sharp function,multilinear commutators of fractional integral operator with vector symbol b=(b 1,...,b m)defined byI b αf(x)=∫ R∏mj=1(b j(x)-b j(y))1｜x-y｜ n-αf(y)dyare considered.The following priori estimates are proved.For 1<p<∞,there exists a constant c such that‖I b αf‖ Lp(Rn)≤c‖b‖‖M L(logL) 1r,α(f)‖ Lp(Rn),So‖I b αf‖ Lq(Rn)≤c‖b‖‖f‖ Lp(Rn),where 1<p<nα,1q=1p-αn,0<α<n,and supt>01Φ1t｜｛y∈Rn:｜I b αf(y)｜>t｝｜ 1q≤ c supt>01Φ1t｜｛y∈Rn:M L(logL) 1r,α(‖b‖f)(y)>t｝｜ 1q,where ‖b‖=∏ m j=1‖b j‖ Osc expL r j,Φ(t)=t(1+log+t) 1r,1r=1r 1+...+1r m, M L(logL) 1r,α is an Orlicz type maximal operator.
