中国科学院数学与系统科学研究院期刊网

15 January 2009, Volume 52 Issue 01
    

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  • The Existence of Positive Solution of Multi-Point Boundary Value Problem with a p-Laplace Operator
    De Hong JI Department of Mathematics,College of Science,Tianjin University of Technology Tianjin 300384,P.R.China Yu TIAN School of Science,Beijing University of Posts and Telecommunications,Beijing 100876,P.R.China Wei Gao GE Department of Applied Mathem
    Acta Mathematica Sinica, Chinese Series. 2009, (01): 3-10. https://doi.org/10.12386/A2009sxxb0001
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    We get positive solution of the following multi-point boundary value problem with p-Laplace operator: ■ whereφp(s)=|s|~(p-2)s,p>1,λ>0 is a parameter.
  • Subnormal Solutions of Second Order Homogeneous Linear Differential Equations with Periodic Coefficients
    Zhi Bo HUANG Zong Xuan CHEN School of Mathematical Sciences,South China Normal University,Guangzhou 510631,P.R.China
    Acta Mathematica Sinica, Chinese Series. 2009, (01): 11-18. https://doi.org/10.12386/A2009sxxb0002
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    We aim to discuss representations of all subnormal solutions of second order homogeneous linear differential equations f"+[P_1(e~z)+Q_1(e~(-z))]f'+[P_2(e~z)+ Q_2(e~(-z))]f=0,where P_1(z),P_2(z),Q_1(z)and Q_2(z)are polynomials in z such that P_1(z),P_2(z),Q_1(z)and Q_2(z)are not all constants.
  • Non-Commutative Poisson Algebra Structures on Lie Algebra ■
    Jie TONT Department of Mathematics and Physics,Shanghai University of Electric Power Shanghai 200090,P.R.China Quan Qin JIN Department of Mathematics,Tongji University,Shanghai 200092,P.R.China
    Acta Mathematica Sinica, Chinese Series. 2009, (01): 19-34. https://doi.org/10.12386/A2009sxxb0003
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    Non-commutative Poisson algebras are the algebras having both an asso- ciative algebra structure and a Lie algebra structure together with the Leibniz law.In this paper the non-commutative Poisson algebra structures on ■ are determined.
  • Homoclinic Bifurcations with Two Orbit Flips
    Gui Feng DENG Department of Mathematics and Statistics,Shanghai Lixin University of Commerce,Shanghai 201620,P.R.China De Ming ZHU Department of Mathematics,East China Normal University,Shanghai 200062,P.R.China Yan Cong XU Department of Mathematics,Hangz
    Acta Mathematica Sinica, Chinese Series. 2009, (01): 35-48. https://doi.org/10.12386/A2009sxxb0004
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    Bifurcations in a case of homoclinic orbit connecting the strong stable and strong unstable directions are investigated for 4-dimensional system.The existence, numbers,co-existence and incoexistence of 1-homoclinic orbit,2~n-homoclinic orbit,1- periodic orbit and 2~n-periodic orbit are obtained,and bifurcation diagrams are also presented.
  • Inverse Sturm-Liouville Problems with Indefined Weighted Functions
    Shou Zhong FU School of Science,Xi'an Jiaotong University,Xi'an 710049,P.R.China Department of Computer Science,Zhaoqing University,Zhaoqing 526061,P.R.China Zong Ben XU Guang Sheng WEI School of Science,Xi'an Jiaotong University,Xi'an 710049,P.R.China
    Acta Mathematica Sinica, Chinese Series. 2009, (01): 49-62. https://doi.org/10.12386/A2009sxxb0005
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    We discuss undefined string equation problems where the weighted function is of one turning-point.Firstly,making use of Liouville transformation,we transform it into undefined Sturm-Liouville Problems where its weighted function is a piecewise constant function.Then we study the undefined Sturm-Liouville inverse eigenvalue problems,and give some sufficient conditions for the corresponding potential functions are determined uniquely,when the negative part of potential functions is given.
  • On w-Radicals of Submodules
    You Hua CHEN College of Mathematics and Software Science,Sichuan Normal University,Chengdu 610068,P.R.China Hua Yu YIN Department of Mathematics,Nanjing University,Nanjing 210093,P.R.China Fang Gui WANG College of Mathematics and Software Science,Sichuan
    Acta Mathematica Sinica, Chinese Series. 2009, (01): 63-74. https://doi.org/10.12386/A2009sxxb0006
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    We introduce the notion of the w-radical of a submodule and study the properties of w-radicals.As applications of the obtained results,we study the w- radicals of multiplication modules and finitely generated free modules respectively. In particular,we prove that if F=R~((n)),N=sum from i=1 to m Rα_i ■ andα∈F,thenα∈w-rad_F N if and only if[α,α_1,...,α_m]_t■ w-rad_R[0,α_1,...,α_m]_t for all 1≤t≤min{m+1,n}.
  • Weyl Type Theorem and Perturbations
    Chen Hui SUN Xiao Hong CAO Lei DAI College of Mathematics and Information Science,Shaanxi Normal University,Xi'an 710062,P.R.China
    Acta Mathematica Sinica, Chinese Series. 2009, (01): 75-82. https://doi.org/10.12386/A2009sxxb0007
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    Using the analytic core and the quasi-nilpotent part of an operator A, we study Weyl type theorem for A.In additional,we study the stability of Weyl's theorem under perturbations by operators in some known classes.Weyl type theorem in an important class of Banach space operators is also studied.

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  • Global PoincaréInequalities for Sublaplacians and Other Subelliptic Operators
    Hua Ying WEI Wuhan Institute of Physics and Mathematics,Chinese Academy of Sciences,Wuhan 430071,P.R.China Qiao Hua YANG School of Mathematics and Statistics,Wuhan University,Wuhan 430072,P.R.China
    Acta Mathematica Sinica, Chinese Series. 2009, (01): 83-92. https://doi.org/10.12386/A2009sxxb0008
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    Let f be in the localized Sobolev space W_(loc)~(1,p)(N)on the Heisenberg type group N.Suppose that the subelliptic gradient is globally L~p integrable.We prove a Poincaréinequality for f on the entire space N.We also show analogous results for Grushin operators like L=Δ_x+(α+1)~2|x|~(2α)Δyy,α>0.
  • Heat Flow of Higher-Dimensional H-Systems with Small Initial Data
    Tao HUANG Zhong TAN School of Mathematical Sciences Xiamen University,Xiarnen,Fujian 361005,P.R.China
    Acta Mathematica Sinica, Chinese Series. 2009, (01): 93-106. https://doi.org/10.12386/A2009sxxb0009
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    We study the heat flow of higher-dimensional H-systems with small initial data.We find that there exists a unique global weak solution u satisfying u_t∈L~2(Ω×[0,∞))and u,▽u∈C~β(Ω×[0,∞),R~(n+1)) for someβ∈(0,1).We also consider the convergence of the solution as time converging to infinite and find that for some time sequence t_k→∞,u(·,t_k)→u_∞in C~(1+β'),0<β'<β.u_∞satisfies the equations of H-systems.
  • Lie Derivable Mappings at Zero Point on Nest Algebras
    Lin CHEN Jian Hua ZHANG College of Mathematics and Information Science,Shaanxi Normal University,Xi'an 710062,P.R.China
    Acta Mathematica Sinica, Chinese Series. 2009, (01): 107-112. https://doi.org/10.12386/A2009sxxb0010
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    Let N be a nest on a separable Hilbert space H with dim H>2 and r(N)be the associated nest algebra.We prove that every Lie derivable mapping at zero point from r(N)into itself is of the form A→AT-TA+λA+h(A),where T∈r(N),λ∈C and h:r(N)→CI is a linear mapping.
  • Additive Relative Perturbation Bounds of Singular Subspaces
    Xiao Shah CHEN Wen LI School of Mathematical Sciences,South China Normal University,Guangzhou 510631,P.R.China
    Acta Mathematica Sinica, Chinese Series. 2009, (01): 113-118. https://doi.org/10.12386/A2009sxxb0011
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    We present a relative perturbation bound of singular subspaces for the Wedin's sin θ type bound.On the other hand,perturbation bounds for both right and left singular subspaces are also given by using different relative gaps,respectively.Our results are better than the existing bounds in some sense.
  • Stability of Weak Solutions of a Class of Non-Variational Quasi-Linear Elliptic Systems with Respect to Boundary Data
    Ye Xin HU Applied Mathematics Department,Shanghai University of Finance and Economics,Shanghai 200433,P.R.China
    Acta Mathematica Sinica, Chinese Series. 2009, (01): 119-126. https://doi.org/10.12386/A2009sxxb0012
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    We prove that the weak solutions to a class of non-variational elliptic systems governed by two p-Laplacian operators continuously depend on boundary data in the sense of set convergence under some conditions ■ where ΩR~N,(N≥3)is bounded smooth domain,(u,v)∈W~(1,p)(Ω)×W~(1,q)(Ω),p and q are real numbers satisfying 2≤p≤q
  • A Note on Conjugacy Class Sizes in Finite Groups
    Guo Hua QIAN Department of Mathematics,Changshu Institute of Technology,Changshu 215500,P.R.China;School of Mathematics,Zhongshan University,Guangzhou 510275,P.R.China Yan Ming WANG Lingnan College and School of Mathematics,Zhongshan University,Guangzhou
    Acta Mathematica Sinica, Chinese Series. 2009, (01): 127-132. https://doi.org/10.12386/A2009sxxb0013
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    Let G be a finite group and p be a prime.It is shown that if p~2 does not divide|x~G|for every p-regular element x∈G,then|M/N|_p=1 or p for any chief factor M/N of G.And then some interesting known results are generalized or strengthened.
  • Regularity of the Inelastic Kac Equation
    Xian Wen ZHANG Department of Mathematics,Huazhong University of Science and Technology,Wuhan 430074,P.R.China Zi Qing WEI Department of Common Education,Jiangxi Blue Sky University,Nanehang 330098,P.R.China
    Acta Mathematica Sinica, Chinese Series. 2009, (01): 133-142. https://doi.org/10.12386/A2009sxxb0014
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    We study the Kac-Boltzmann equation.Firstly,the Povzner inequality for the collision kernel and the L~p estimates for the collision operator are established. Secondly,we obtain some weighted L~p estimates for positive solutions to the equation. With these estimates,the smoothness of the solutions is proved.
  • Coexistence States of the Unstirred Chemostat Model
    Yan Ling LI Hai Xia LI Jian Hua WU College of Mathematics and Information Science,Shaanxi Normal University,Xi'an 710062,P.R.China
    Acta Mathematica Sinica, Chinese Series. 2009, (01): 143-154. https://doi.org/10.12386/A2009sxxb0015
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    The existence and stability of the positive steady-state solutions and the asymptotic behavior to the unstirred food-chain chemostat model with Beddington- DeAngelis functional response are discussed.First,by applying the maximum principle, monotone method and bifurcation theory,we discuss the global structure of the coex- istence solutions to the steady-state system.The necessary and sufficient conditions for the existence of the coexistence solutions are established.Second,some results of local stability for the coexistence solutions are obtained by the perturbation theorem for linear operators and the stability theorem for bifurcation solutions.Finally,by ap- plying the maximum principle and theory of permanence in semi-dynamical systems, we discuss the asymptotic behavior of solutions to the system,the conditions for the permanence of the system are obtained.
  • Weighted Composition Operators of Weighted Bergman Spaces intoβ-Bloch Spaces on the Unit Ball
    Min Zhu ZHANG Department of Mathematics,Southeast University,Nanjing 210096,P.R.China
    Acta Mathematica Sinica, Chinese Series. 2009, (01): 155-164. https://doi.org/10.12386/A2009sxxb0016
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    We characterize the boundedness and compactness of weighted composition operators of weighted Bergman spaces intoβ-Bloch spaces on the unit ball in C~n.
  • The Derivations and Central Extensions of a Class of Lie Algebras over Quantum Torus
    Bo ZENG School of Mathematical Science,Xiangtan University,Xiangtan 411105,P.R.China School of Mathematical Science,Xiamen University,Xiamen 361005,P.R.China
    Acta Mathematica Sinica, Chinese Series. 2009, (01): 165-172. https://doi.org/10.12386/A2009sxxb0017
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    Let(q):=C_q[x_1~(±1),x=_2~(±1)]Der_(skew)(C_q),where C_q:=C_q[x_1~(±1),x_2~(±1)]is the quantum torus in two variables,Der_(skew)(C_q)is the skew derivation Lie algebra over C_q, and q is any nonzero complex number.Denote L(q)the derived subalgebra[■(q),■(q)] of L(q).In this paper,we determine the derivations and central extensions of L(q) with q a p-th primitive root of unity when p>1.
  • Multiple Positive Solutions for a Class of Weighted Nonlinear Elliptic Equations
    Lin Mei LIN Department of Mathematics,Putian University,Putian 351100,P.R.China
    Acta Mathematica Sinica, Chinese Series. 2009, (01): 173-182. https://doi.org/10.12386/A2009sxxb0018
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    Let 0 E∈ΩR~N(N≥3)be a bounded domain with smooth boundary.We characterize an exact growth order near zero for positive solutions of a class of weighted nonlinear elliptic equations -div(|x|~(-2a)▽u)-u/(|x|~(2(a+1)))u=|x|~(-bp)|u|~(p-2)u+λ|u|~(q-2)u with Dirichlet boundary condition.Then we obtain multiple positive solutions for equations involving critical weighted Sobolev-Hardy exponents.
  • Existence of Positive Solutions to a Singular p-Laplacian Dynamic Equation with Sign Changing Nonlinearity
    You Hui SU Mathematics and Physical Sciences Technology,Xuzhou Institute of Technology,Xuzhou 221008,P.R.China School of Mathematics and Statistics,Lanzhou University,Lanzhou 730000,P.R.China Wan Tong LI School of Mathematics and Statistics,Lanzhou Univer
    Acta Mathematica Sinica, Chinese Series. 2009, (01): 183-198. https://doi.org/10.12386/A2009sxxb0019
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    This paper is concerned with the following m-point singular p-Laplacian dy- namic equation(_p(u~Δ(t)))~▽+q(t)f(t,u(t))=0,t∈(0,T)_T,u(0)=0,_p(u~Δ(T))= sum from i=1 to m-2_i(u~Δ(ξ_i)),where _p(s)=|s|~(p-2)with p>1,_i:R→R is continuous and nondecreasing,0<ξ_1<ξ_2<…<ξ_(m-2)<ρ(T).The nonlinearity term is allowed to change sign.By using the Schauder fixed point theorem together with upper and lower solutions method,some existence criteria are established for positive solutions of the boundary value problem.These results are new even for the corresponding differential (T=R)and difference equation(T=Z),as well as general time scales setting.In particular,if the nonlinear term is allowed to change sign,then the problem of Sun and Li[Appl.Math.Comput.,2006,182:478-491]is only a special case of our problem for the corresponding differential equation(T=R).As an application,an example is given to illustrate these results.
  • A Mixed-Type Reverse Order Law for Generalized Inverse of a Triple Matrix Product
    Yong Hui LIU Department of Applied Mathematics,Shanghai Finance University,Shanghai 201209,P.R.China Yong Ge TIAN China Economics and Management Academy,Central University of Finance and Economics,Beijing 100081,P.R.China
    Acta Mathematica Sinica, Chinese Series. 2009, (01): 199-206. https://doi.org/10.12386/A2009sxxb0020
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    For the triple matrix product ABC,we show through the product-product singular value decomposition of matrix triplets(A,B,C)that there exist three general- ized inverses A~((1,2,3)),B~((1,2))and C~((1,2,4))such that the Moore-Penrose inverse of ABC can be expressed as (ABC)~+=C~((1,2,4)) B~((1,2))A~((1,2,3)).The results are the generalization of results obtained by Wibker,Howe and Gilbert.
  • Convergence of Einstein 4-Orbifolds
    Hong HUANG School of Mathematical Sciences,Key Laboratory of Mathematics and Complex Systems,Beijing Normal University,Beijing 100875,P.R.China
    Acta Mathematica Sinica, Chinese Series. 2009, (01): 207-210. https://doi.org/10.12386/A2009sxxb0021
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    We prove a compactness theorem for Einstein 4-orbifolds,which general- izes a theorem of Sesum on convergence of(complex)2-dimensional Khler-Einstein orbifolds.This also generalizes a theorem of Anderson,Bando,Kasue,Nakajima and Tian on convergence of Einstein 4-manifolds.
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