中国科学院数学与系统科学研究院期刊网

15 May 2006, Volume 49 Issue 3
    

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  • The Boundedness of Commutators for the Marcinkiewicz Integrals
    Shan Zhen LU, Hui Xia MO
    Acta Mathematica Sinica, Chinese Series. 2006, 49(3): 481-490. https://doi.org/10.12386/A2006sxxb0061
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    In this paper, the authors consider the boundedness of commutators for the Marcinkiewicz integral μΩb on Lp(Rn) and Hardy spaces, here Ω being a homogeneous function of degree zero on Rn and satisfying a class of Lq-Dini condition. The results in this paper are substantial improvements over some known results.
  • Schur Decomposition for Symmetric Ternary Forms and Readable Proof to Inequalities
    Sheng Li CHEN, Fang Jian HUANG
    Acta Mathematica Sinica, Chinese Series. 2006, 49(3): 491-502. https://doi.org/10.12386/A2006sxxb0062
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    In this paper, we give a means to partition the ternary symmetric forms. Using this method, it's very easy to indicate the positive semidefinition of the polynomial. At the end of the paper, we will show the application of this partition.
  • Algebraic Independence of Values of Power Series with Algebraic Coefficients at Transcendental Numbers
    Yao Chen ZHU
    Acta Mathematica Sinica, Chinese Series. 2006, 49(3): 503-508. https://doi.org/10.12386/A2006sxxb0063
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    In this note the algebraic independence of values of a set of power series with algebraic coefficients at transcendental numbers is given.
  • The Best Approximation Rate of Certain Trigonometric Series Important Applications of a "Two-sided" Monotonicity Condition
    Song Ping ZHOU(1), Rui Jun LE(
    Acta Mathematica Sinica, Chinese Series. 2006, 49(3): 509-518. https://doi.org/10.12386/A2006sxxb0064
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    The main object of the present paper is to give a complete result regarding the best approximation rate of certain trigonometric series in general complex valued continuous function space under a new condition which gives an essential generalization to O-regularly varying quasimonotonicity, An application is presented.
  • Inverse Theorem to the Best Approximation by Polynomials in Bergman Spaces B_q~p(p>0, q>1)
    Fu Chong XING
    Acta Mathematica Sinica, Chinese Series. 2006, 49(3): 519-524. https://doi.org/10.12386/A2006sxxb0065
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    In this paper we obtained the inverse theorem estimating the order of the best approximation error by polynomials in Bergman spaces Bqp(p>0, q>1).
  • Continuity of Multiplication of the Locally Convex Topological Algebra L(E)
    Jun Jun LIAO
    Acta Mathematica Sinica, Chinese Series. 2006, 49(3): 525-528. https://doi.org/10.12386/A2006sxxb0066
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    Let (E, T) be a real locally convex topological vector space and E′ be the dual space of (E, T). Denote by L(E) the algebra of all of the continuous endomorphisms of (E, σ(E, E′)). Some criteria for the continuity of multiplication of L(E) with respect to strong and weak topologies are obtained. Furthermore, if (L(E),ω) has the continuity of multiplication, then E must be a finite dimension space.
  • Weyl's Theorem for 3×3 Upper Triangular Operator Matrices
    Xiao Hong CAO
    Acta Mathematica Sinica, Chinese Series. 2006, 49(3): 529-538. https://doi.org/10.12386/A2006sxxb0067
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    When A∈B(H1), B∈B(H2) and C∈B(H3) are given, we denote by M(D,E,F) an operator, acting on the Hilbert space H1H2H3, of the form M(D, E, F)= . In this paper, we give the necessary and sufficient condition for M(D,E,F) to be upper semi-Fredholm (lower semi-Fredholm) operator for some D∈B(H2,H1), E∈B(H3,H1), F∈B(H3,H2). Weyl type theorems are liable to fail for 2×2 operator matrices. In this paper, we also explore how Weyl's theorem, Browder's theorem, α-Weyl's theorem and α-Browder's theorem survive for 3×3 upper triangular operator matrices on the Hilbert space.
  • Higher Eigenvalue Estimates on Riemannian Manifolds with Ricci Curvature Bounded Below
    He Jun SUN
    Acta Mathematica Sinica, Chinese Series. 2006, 49(3): 539-548. https://doi.org/10.12386/A2006sxxb0068
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    By deriving sharp gradient estimates for the positive solutions of the heat equation and deducing some Harnack type inequalities, we obtain some quantitative estimates of the lower bounds for heat kernels and higher eigenvalues on Riemannian manifold with Ric (M)≥-K (K>0).
  • On Existence of the Generalized Moore-Penrose Inverses of Matrices over Ring
    Jian Miao CEN
    Acta Mathematica Sinica, Chinese Series. 2006, 49(3): 549-558. https://doi.org/10.12386/A2006sxxb0069
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    The generalized Moore-Penrose inverses of matrices over a ring with an involution * and unitary are discussed. Some necessary and sufficient conditions for existence of the generalized Moore-Penrose inverse of matrices over a ring are given. In particular, it is obtained that a necessary and sufficient condition for existence of the generalized Moore-Penrose inverse with relation to M and N of a matrix A over a ring is that A = GDH, where D2 = D, (MD)* = MD, (GD)*MGD + M(I-D) and DHN-1(DH)* + (I-D)M-1 are invertible.
  • On a Relation Between Hardy-Hilbert's Inequality and Mulholland's Inequality
    Bi Cheng YANG
    Acta Mathematica Sinica, Chinese Series. 2006, 49(3): 559-566. https://doi.org/10.12386/A2006sxxb0070
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    This paper deals with a relation between Hardy-Hilbert's inequality and Mulholland's inequality with a best constant factor by introducing a parameter A and using the β function. As applications, the equivalent form and some particular results are considered.
  • The Refining Growth, Covering Theorems and the Refining Estimation of Expansion Coefficients for Spirallike Mappings of Type a
    Xiao Song LIU, Tai Shun LIU
    Acta Mathematica Sinica, Chinese Series. 2006, 49(3): 567-576. https://doi.org/10.12386/A2006sxxb0071
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    In this paper, we consider a normalized biholomorphic spirallike mapping of type α(-π/2 <α<π/2) f defined on the unit ball in a complex Banach space and the unit polydisk of Cn, where x=0 is a zero of order k+1 of f(x)-x, we investigate its construction, and the refining growth and covering theorems for f(x) and the refining estimation of the homogeneous expansion for f(x) is obtained. Our result includes many known conclusions.
  • On Quantitative Romanoff's Theorem
    Xue Gong SUN(2), Yong Gao CHEN
    Acta Mathematica Sinica, Chinese Series. 2006, 49(3): 577-582. https://doi.org/10.12386/A2006sxxb0072
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    In 1934, Romanoff proved that there are positive proportion natural numbers which can be expressed as a sum of a prime and a power of 2. Recently, the authors proved that for all sufficiently larger x, the proportion is large than 0.0868. In this paper,a quantitative version of Romanoff's Theorem is given. The following result is proved: For all x≥5, the proportion of natural numbers which can be expressed as a sum of a prime and a power of 2 is larger than 0.005.
  • Existence and Multiplicity of Positive Solutions for Two-point Boundary Value Problem of Nonhomogeneous Differential Equations
    Li Ping LUO; Yong Geng GU; Qiu
    Acta Mathematica Sinica, Chinese Series. 2006, 49(3): 583-594. https://doi.org/10.12386/A2006sxxb0073
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    A class of two-point boundary value problems of nonhomogeneous differential equations are investigated in this paper. Some exact conditions for the existence or multiplicity of positive solutions for the problem are given.
  • Optimal Structure of the Covariance Matrix of Errors for F-Tests in Linear Models
    Mi Xia WU,Song Gui WANG
    Acta Mathematica Sinica, Chinese Series. 2006, 49(3): 595-604. https://doi.org/10.12386/A2006sxxb0074
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    In the literature, F-statistics used in testing linear restrictions mainly include F(θ) based on the general least squares estimate, FLSE based on the least squares estimate, and the adjusted F-statistic FA(θ) given by C. F. J. Wu, et al. in 1988. Due to their simple forms, the latter two are more commonly employed in practice. In this paper, we mainly consider the optimality of FA(θ) and FLSE, and obtain the necessary and sufficient conditions for FA(θ)=F(θ) and FLSE=F(θ), respectively. Lastly, we apply the results obtained to two important models in the field of pharmacology.
  • The Number of 2-Connected Cubic Rooted Planar Maps
    Jun Liang CAI,Xiao Li LIU,Yan
    Acta Mathematica Sinica, Chinese Series. 2006, 49(3): 605-612. https://doi.org/10.12386/A2006sxxb0075
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    In this paper the explicit expressions for enumerating 2-connected cubic rooted planar maps with two variables are obtained indirectly by using a constructive method via nonseparable cubic rooted palnar maps.
  • Generalized Schwarz-Pick Lemma
    Min Zhu ZHANG
    Acta Mathematica Sinica, Chinese Series. 2006, 49(3): 613-616. https://doi.org/10.12386/A2006sxxb0076
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    In this paper, we obtain a higher derivative generalization of the Schwarz-Pick lemma for analytic self-maps of the unit disk and a precise estimate of |f"(z)|.
  • Eigenvalue of Discrete Lidstone Boundary Value Problems
    Xue Yan LIU,Bing Gen ZHANG
    Acta Mathematica Sinica, Chinese Series. 2006, 49(3): 617-624. https://doi.org/10.12386/A2006sxxb0077
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    By applying some fixed point theorems and cone theory, we, respectively, obtain some sufficient and necessary conditions for the bounded and unbounded existence intervals of eigenvalues for certain 2mth discrete Lidstone boundary value problem under different assumptions on the nonlinear term.
  • Positive Solutions and Multiplicity of Fourth-Order Boundary Value Problems with Two Parameters
    Chang Ci PANG,Zhong Li WEI
    Acta Mathematica Sinica, Chinese Series. 2006, 49(3): 625-632. https://doi.org/10.12386/A2006sxxb0078
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    By means of calculation of the fixed point index in cone, we study the existence of one or two positive solutions of the fourth-order two point boundary value problems with two parameters.
  • Results of Virasoro Subalgebra
    De Min YU,Cai Hui LU
    Acta Mathematica Sinica, Chinese Series. 2006, 49(3): 633-638. https://doi.org/10.12386/A2006sxxb0079
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    Centerless Virasoro algebra, first appearing in 1909, was defined by Cartan. By introducing the notion of coefficient matrix, we prove that the Virasoro algebra does not have any 2-dimensional commutative subalgebra. We find some interesting 2-dimensional subalgebras of the Virasoro algebra, apart from the obvious ones Cd0+Cdi, and we also discuss some properties of such 2-dimensional subalgebra.
  • On Higher-Power Moments of Δ(x)(Ⅳ)
    Wen Guang ZHAI
    Acta Mathematica Sinica, Chinese Series. 2006, 49(3): 639-646. https://doi.org/10.12386/A2006sxxb0080
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    Suppose Δ(x) is the error term of the Dirichlet divisor problem. In this paper we study the κth power moment of Δ(x) in short intervals for k≥3 and obtain its asymptotic formula. Especially when k=3 and k=4, we improve further the previous results of Ivic and Sargos.
  • Divisibility of Determinant of Power Matrices on Gcd-Closed Sets
    Cong HE
    Acta Mathematica Sinica, Chinese Series. 2006, 49(3): 647-650. https://doi.org/10.12386/A2006sxxb0081
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    Let S={x1,...,xn} be a gcd-closed set of n distinct positive integers, let ε∈Z+. We prove the following results: (1) If n≤3, then det(S)nε|det[S]nε; (2) If maxxi∈S{xi}<12, then det(S)nε|det[S]nε; (3) If maxx∈S {R(x)}≤1, where R(x) is the set of greatest-type divisors of x in S, then det(S)nε|det[S]nε.
  • Adjoint Action for Quantum Algebra wsl_q(2)
    Bo HOU,Zhi Xi WANG
    Acta Mathematica Sinica, Chinese Series. 2006, 49(3): 651-656. https://doi.org/10.12386/A2006sxxb0082
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    We prove that wslq(2) is a left quasi-module algebra over itself and study the structure of the submodules of (?)(wslq(2)), which is the locally finite submodule of the quantum algebra wslq(2).
  • Primitive Normal Element and Its Inverse in Finite Fields
    Tian TIAN,Wen Feng QI
    Acta Mathematica Sinica, Chinese Series. 2006, 49(3): 657-668. https://doi.org/10.12386/A2006sxxb0083
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    Let q be a prime power, n be a positive integer, Fqn denote a finite field with qn elements. We prove that if n≥32, then there exists a primitive element ξ of Fqn satisfying that ξ and ξ-1 are normal elements of Fqn over Fq, i.e., both {ξ,ξq,...,ξqn-1} and {ξ-1,ξ-q,...,ξ-qn-1} are primitive normal bases over Fq.
  • One-Regularity of 4-Valent and Normal Cayley Graphs of Dihedral Groups
    Chang Qun WANG,Zhi Yong ZHOU
    Acta Mathematica Sinica, Chinese Series. 2006, 49(3): 669-678. https://doi.org/10.12386/A2006sxxb0084
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    Let G be a finite group. A Cayley graph Cay(G, S) is said to be normal if R(G) is normal in its full automorphism group. We call a graph X one-regular if its full automorphism group acts regularly on its arcs. In this paper we classify the 4-valent, one-regular and normal Cayley graphs of dihedral groups D2n with vertex-stabilizer Z22.
  • On Polars of Projection Bodies and Centroid Bodies
    Chang Jian ZHAO,Bin Wu HE,Gang
    Acta Mathematica Sinica, Chinese Series. 2006, 49(3): 679-686. https://doi.org/10.12386/A2006sxxb0085
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    In this paper, we first establish several Brunn-Minkowski inequalities of polars of projection bodies, for the Blaschke linear combination and the harmonic Blaschke linear combination. Then, we prove Brunn-Minkowski inequalities of polars of centroid bodies, and similar resuets for the harmonic Blaschke linear combination.
  • On the Existence of m-Point Boundary Value Problem at Resonance
    Shi Ping LU,Wei Gao GE
    Acta Mathematica Sinica, Chinese Series. 2006, 49(3): 687-692. https://doi.org/10.12386/A2006sxxb0086
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    By means of Mawhin's continuation theorem, we study m-point boundary value problem at resonance in the following form where m≥3 is an integer, ai≥0, ξi∈(0,1) (i=1,2,...,m-2) are constants satisfying ∑i=1m-2 ai=1 and 0<ξ1<ξ2 <... <ξm-2. A new result on the existence of solutions is obtained. The significance is that we allow the degree of power with respect to the second variable x and the third variable y of f(t, x, y) to be greater than 1, especially, the degree of variable x may be grater then the degree of variable y, which is different from corresponding ones of the past work.
  • Estimation of Exponential Sums over Primes in Short Intervals
    Guang Shi LV
    Acta Mathematica Sinica, Chinese Series. 2006, 49(3): 693-698. https://doi.org/10.12386/A2006sxxb0087
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    Let ∧(n) be the von Mangoldt function and θ=95-83~(1/2)/121. This paper gives a non-trivial estimate of the sum S2(x,y;α)=∑x0, and in the same range of y.
  • On Jordan Structure of Real Banach* Algebras with Continuous Involution
    Min Li LI,Zhong Yan LI
    Acta Mathematica Sinica, Chinese Series. 2006, 49(3): 699-702. https://doi.org/10.12386/A2006sxxb0088
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    In this paper, the Jordan structure of real Banach* algebras is discussed. In part one, the results are that the continuity of a Jordan* homomorphism T of A1 onto A2, where A2 is * semi-simple, is automatic, the kernel is a closed * ideal ,and if A2 is commutative, then the factor algebra A1/ker (T) is also commutative. In part two, two different cones of a real Banach* algebra are introduced, and their relation is studied. Moreover, we obtain a new characterization of the *-radical of a real Banach* algebra. This paper is thereal counterpart of Satish Shirali's work in the complex case.
  • D(β)-Vertex-Distinguishing Proper Edge-Coloring of Graphs
    Zhong Fu ZHANG,Jing Wen LI,Xia
    Acta Mathematica Sinica, Chinese Series. 2006, 49(3): 703-708. https://doi.org/10.12386/A2006sxxb0089
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    In this paper, we present a new concept of the D(β)-vertex-distinguishing proper edge-coloring of graphs (briefly, D(β)-VDPEC of graphs) and, meanwhile, have obtained the D(β)-VDPEC chromatic number on some families of graphs such as cycles, complete graphs, complete bipartite graphs, fans, wheels, trees conjecture is proposed.
  • Local W~(2,p) Regularity for Some Elliptic Equations in Nondivergence Form
    Yue Shan WANG
    Acta Mathematica Sinica, Chinese Series. 2006, 49(3): 709-720. https://doi.org/10.12386/A2006sxxb0090
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    In this note, we will prove a result of local W2,p(p≥2) regularity for some elliptic equations in nondivergence form with coefficients in small BMO, and give an application of the result.
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