中国科学院数学与系统科学研究院期刊网

15 July 2006, Volume 49 Issue 4
    

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  • Bo Ling GUOGan Shan YANG
    Acta Mathematica Sinica, Chinese Series. 2006, 49(4): 721-736. https://doi.org/10.12386/A2006sxxb0091
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    The purpose of this paper is to introduce the concepts ofδ-viscosity supersolution,δ-viscosity subsolution andδ-viscosity solution, and give their properties, and using these properties prove the existence ofδ-viscosity supersolution andδ-viscosity subsolution of the multidimensional Landau-Lifshitz equation with values in a unit sphere, and indicate that there exist two disjoint open subsets M and N such that theδ-viscosity supersolution andδ-viscosity subsolution tend to (0,1,0) on arbitrary compact sets in M, and tend to (0,-1,0) on arbitrary compact sets in N.
  • Qiu Xian WU
    Acta Mathematica Sinica, Chinese Series. 2006, 49(4): 737-756. https://doi.org/10.12386/A2006sxxb0092
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    In this paper, we define some operators on tubular category, and some properties of these operators have been studied. We give a formula of the structural constants FML,N for Hall algebra of cyclic serial algebra. By using these operators and this formula, we get some centralizers of composition algebra C(T) and the simesimple module [l(?)i=1nSi](l∈Z+) in H(T). In fact, they are the central elements of H(T) and the algebraically independent generators of H(T) over C(T).
  • Hong Ya GAOJian Pu WANG
    Acta Mathematica Sinica, Chinese Series. 2006, 49(4): 757-762. https://doi.org/10.12386/A2006sxxb0093
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    This paper gives a sufficient condition to ensure the integrability of exterior power for the differential of space mappings by using the method of Hodge decomposition.
  • Chun Yan HUANGZu Han LIU
    Acta Mathematica Sinica, Chinese Series. 2006, 49(4): 763-774. https://doi.org/10.12386/A2006sxxb0094
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    In this paper, we study the Ginzburg-Landau energy of superconductors submitted to a possibly non-uniform magnetic field p(x)hex in the limit of a largeκ, for the applied magnetic field varying between the two critical fields Hc1 and Hc2.We obtain the asymptotic behavior of minimal energy for arbitrary fields, which answers a conjecture raised by Sandier and Serfaty.
  • Zong Xin YANGJi Xiu CHEN
    Acta Mathematica Sinica, Chinese Series. 2006, 49(4): 775-778. https://doi.org/10.12386/A2006sxxb0095
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    LetΓbe a parabolic cyclic Fuchsian group acting on H2, and let(?):R2→R2 be a K-quasiconformal mapping that keeps H2. We give some estimates about the exponent of convergence of the quasiconformal Fuchsian group G =(?)Γ(?)-1.
  • Yan Chang HANMing XU
    Acta Mathematica Sinica, Chinese Series. 2006, 49(4): 779-790. https://doi.org/10.12386/A2006sxxb0096
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    In this paper, the authors prove Tl theorem on nonhomogeneous spaces with Dini kernel conditions, obtain weighted version of Fefferman-Stein vector valued maximal inequality and establish Tl theorem for weighted Triebel-Lizorkin spaces on nonhomogeneous spaces.
  • Chang Guo WEI
    Acta Mathematica Sinica, Chinese Series. 2006, 49(4): 791-796. https://doi.org/10.12386/A2006sxxb0097
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    Homomorphisms between the extensions of torus algebra are considered. Suppose that E1 and E2 are two extensions of C(T2) by K., andφ,ψare injective homomorphisms from E1 into E2. We prove that such two homomorphisms are approximately unitarily equivalent when they have the same induced maps on the invariant V(E1) and the quotient algebra, where K is the C*-algebra of all compact operators on a separable infinite dimensional Hilbert space and V(E1) is the commutative semigroup consisting of the Murray-von Neumann equivalence classes of projections in matrices over E1..
  • Hui Zeng QINNi Na SHANG
    Acta Mathematica Sinica, Chinese Series. 2006, 49(4): 797-802. https://doi.org/10.12386/A2006sxxb0098
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    In this paper, using Hadamard fundamental solutions of hyperbolic equations, Huygens' operator problem is converted into a relation that the hyperbolic equation coefficients satisfy, then more Huygens operators are found, and the Stellmacher' result is generalized. Furthermore, we prove that the Huygens operators by Veselov and Berest sre similiar to the Stellmacher'operators.
  • Jiang Min PAN
    Acta Mathematica Sinica, Chinese Series. 2006, 49(4): 803-808. https://doi.org/10.12386/A2006sxxb0099
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    Let Sri(i=1,2,…,n) be free metabelian groups of rank ri,G = Sr1×Sr2×…×Srn be direct product of free metabelian groups. In this paper, we prove that G has test element if and only if ri=2 (i = 1,2,…,n). Meanwhile, we prove that 3 = (g1,g2,…,gn) is a test element of G if and only if gi∈S'2 - 1 (i = 1,2,…,n), and {g1,g2,…,gn} is an independent set.
  • Jin Ru WANG
    Acta Mathematica Sinica, Chinese Series. 2006, 49(4): 809-818. https://doi.org/10.12386/A2006sxxb0100
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    We consider the problem uxx= ut,0≤x<1, t≥0. The solution on the boundary x = 1 is a known function g(t). This is an ill-posed problem in the sense that a small disturbance on the boundary g(t) can produce a big alternation on its solution (if it exists). We shall define a wavelet solution with the Meyer multi-resolution analysis to obtain well-posed approximating problem in the scaling space Vj. We shall also give an estimate for the difference between the exact solution of the problem and the defined wavelet solution.
  • Min Bo YANGZi Fei SHEN
    Acta Mathematica Sinica, Chinese Series. 2006, 49(4): 819-826. https://doi.org/10.12386/A2006sxxb0101
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    We investigate a class of semilinear elliptic equations with Hardy-Sobolev critical exponent. With the aids of pseudoindex theory, multiple nontrivial solutions are obtained by proving local (P.S.) conditon and estimating energy carefully (see [1-13]).
  • Ling ZHOU
    Acta Mathematica Sinica, Chinese Series. 2006, 49(4): 827-834. https://doi.org/10.12386/A2006sxxb0102
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    strongly coupled elliptic system with homogeneous Dirichlet boundary conditions is considered. It is shown that there is no coexistence state if diffusion rates are strong, or if the intrinsic growth rates are slow. Making use of the Schauder fixed point theory, we derive some sufficient conditions to have a coexistence state for the strongly coupled elliptic problem. Moreover, our results reveal that this problem possesses at least one coexistence state if the intra-specific competition of predator is strong and cross-diffusions are relatively weak, or if the capturing rate is slow and cross-diffusions are relatively weak.
  • Wei WANG
    Acta Mathematica Sinica, Chinese Series. 2006, 49(4): 835-846. https://doi.org/10.12386/A2006sxxb0103
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    In 1966, Leo Moser published a set of open geometry questions, one of which is Worm Problem. It was described as follows: "What is the (convex) region of smallest area which will accommodate every planar arc of length one?" When the region is convex, this paper reduces the smallest known upper bound for the area from 0.2738086 to 0.270911861.
  • Xin Feng HEZhen HE
    Acta Mathematica Sinica, Chinese Series. 2006, 49(4): 847-852. https://doi.org/10.12386/A2006sxxb0104
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    By topological degree theory of type (S+), the topological degree for compact perturbations of pseudo-monotone map is induced, and we discuss the applications in ranges.
  • Luo LUOJi Huai SHI
    Acta Mathematica Sinica, Chinese Series. 2006, 49(4): 853-856. https://doi.org/10.12386/A2006sxxb0105
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    In this paper, we study composition operators between weighted Bergman spaces on a bounded symmetric domainΩin Cn. We get the characterization of the bounded and the compact composition operator C(?):Lαp(Ω,dvα)→Lαq(Ω,dvβ)(0
  • Hai Tao YANG
    Acta Mathematica Sinica, Chinese Series. 2006, 49(4): 857-860. https://doi.org/10.12386/A2006sxxb0106
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    The main purpose of this paper is to study that problem, it is equivalent conditions of weakly and uniformly closed on the generate operator algebra in Pontrja-gin space. We prove the following theorem: Suppose that C0(U),C1(U,L,R,D,V),C2a(U),C2b(U,R),C3a(U),C3b(U,R) are, respectively, classes 0,Ⅰ,Ⅱa,Ⅱb,Ⅲa andⅢb of general symmetric operator algebras on spaceⅡk. Then (1)C0(U), C2a(U) or C3a(U) is uniformly (weakly) closed if and only if u is C*-algebra (W*-algebra) on the Hilbert space H; (2) C1(U,L,R,D,V) is uniformly (weakly) closed if and only if U is C*-algebra (W*-algebra) on the Hilbert space H, and R is closed subspace, V is a closed operator, L is symmetrically closed; (3) C2b(U,R) or C3B(U,R) is uniformly (weakly) closed if and only if U is C*-algebra (W*-algebra) on the Hilbert space H, and R is a closed subspace.
  • Qing Nian ZHANGWei DONGChang
    Acta Mathematica Sinica, Chinese Series. 2006, 49(4): 861-868. https://doi.org/10.12386/A2006sxxb0107
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    In this paper, we consider positive solutions of the degenerate logistic type p-Laplacian equation -△pu =a(x)|u|p-2u-b(x)|u|q-1u,x∈RN (N≥2). We show that under rather general conditions on a(x) and b(x) for large |x|, there exists a unique positive solution. Our results improve the corresponding ones in [1] and [2].
  • Qi Lin LIUYu Xiang LIHong Ju
    Acta Mathematica Sinica, Chinese Series. 2006, 49(4): 869-882. https://doi.org/10.12386/A2006sxxb0108
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    This paper deals with the blow-up property of positive solution for a reaction diffusion system ut(x,t) =△u(x,t) + vκ(x,t)up(0,t), vt(x,t) =△v(x,t) + uβ(x,t)vq(0,t), with null Dirichlet boundary conditions. The blow up set and blowup rates are obtained.
  • Zheng Xin CHEN
    Acta Mathematica Sinica, Chinese Series. 2006, 49(4): 883-892. https://doi.org/10.12386/A2006sxxb0109
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    Let A be a tubular algebra of type T(2,2,2,2) over a finite field k. It is the one-point extension of a tame hereditary algebra A0 and also the one-point coextension of a tame hereditary algebra A∞. Let P0 be the set of preprojective A0-modules and =L∞be the set of preinjective A∞-modules. Then we have P0,L∞(?)mod A. We denote T=mod A4\(P0∪L∞). In this paper, we get a triangular decomposition structure P0·J·L∞for the composition algebra C(A) of A.
  • Xiao Feng WANGZheng An YAO
    Acta Mathematica Sinica, Chinese Series. 2006, 49(4): 893-898. https://doi.org/10.12386/A2006sxxb0110
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    In this paper, the Fredholm properties of some Toeplitz operators on Dirichlet space are discussed, and the essential spectra of Toeplitz operators with symbols in C1 are computed.
  • Xian Hua TANGYing Gao ZHOU
    Acta Mathematica Sinica, Chinese Series. 2006, 49(4): 899-908. https://doi.org/10.12386/A2006sxxb0111
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    In this paper, we consider the existence, uniqueness and global attractivity of the periodic solutions of the higher dimensional nonlinear functional differential equation x(t) = A(t,x(t+·))x(t) + f(t,x(t+·)). The obtained results extend and improve the related known ones in the literature.
  • Xiao Guang LIJian ZHANG
    Acta Mathematica Sinica, Chinese Series. 2006, 49(4): 909-914. https://doi.org/10.12386/A2006sxxb0112
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    We consider the Cauchy problem for the critical nonlinear Schrodinger equation with a harmonic potential, and get the rate of L2-concentration of the radially symmetric blow-up solutions.
  • Qi Hua RUANZhi Hua CHEN
    Acta Mathematica Sinica, Chinese Series. 2006, 49(4): 915-918. https://doi.org/10.12386/A2006sxxb0113
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    In this paper, we study the property of Riemannian manifold satisfying Nash inequality, and prove that for any complete n-dimensional Riemannian manifold with nonnegative Ricci curvature, if the Nash inequality is satisfied and the Nash constant is more than the best Nash constant, then the manifold is diffeomorphic to Rn.
  • Zhi Wei ZHUZuo Ling ZHOU
    Acta Mathematica Sinica, Chinese Series. 2006, 49(4): 919-926. https://doi.org/10.12386/A2006sxxb0114
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    Let Cλbe the symmetric Cantor set generated by the iterated function system (IFS){f1,f2}, where f1(x) = Ax, f2(x) = 1 -λ+λx,0 <λ<1/2, x∈[0,1]. In this paper, we determine the exact Hausdorff centered measure of Cλ×Cλunder some conditions.
  • Yao Jun YE
    Acta Mathematica Sinica, Chinese Series. 2006, 49(4): 927-940. https://doi.org/10.12386/A2006sxxb0115
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    In this paper we prove the existence and uniqueness for the global solutions of the Cauchy problem of the coupled system of semilinear wave equations. In particular, we show the existence and uniqueness of self-similar solutions. Also, we build some asymptotically self-similar solutions.
  • Xiang Yang PENGXi Yan HULei
    Acta Mathematica Sinica, Chinese Series. 2006, 49(4): 941-948. https://doi.org/10.12386/A2006sxxb0116
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    This paper gives the definition of the set GSRn×n(M) and the necessary and sufficient conditions for the solvability of and the solution's general forms of ATXA= B. Let SE denote the set of solutions. Given an arbitrary X*,find a matrix X∈SE which is nearest to X* in Probenius norm. The matrix is unique and its expression is gives.
  • Xi Yan YAO
    Acta Mathematica Sinica, Chinese Series. 2006, 49(4): 949-954. https://doi.org/10.12386/A2006sxxb0117
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    Let H and K be separable complex infinite-dimensional Hilbert spaces. In this note, we primarily study inverses of 2×2 operator matrices on H(?)K by utilizing the method of geometrical structure of operators, and obtain some meaningful results.
  • Li Juan WANGGong Fu LIAO
    Acta Mathematica Sinica, Chinese Series. 2006, 49(4): 955-960. https://doi.org/10.12386/A2006sxxb0118
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    In this paper, we consider the topological conjugacy on 3-order Feigenbaum's maps which limited their nonwandering sets. 3-order Feigenbaum's maps must bring on chaos, and the nonwandering sets become complication for chaos. In addition, 3-order Feigenbaum's maps can be divided into two types-single-valley Feigenbaum's map and nonsingle-valley Feigenbaum's map. We make use of finite subshifting to proof that: for any two 3-order Feigenbaum's maps with some given conditions, they are topological conjugacy limited to their non-wandering sets.