中国科学院数学与系统科学研究院期刊网

Acta Mathematica Sinica, Chinese Series 2009 Vol.52

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Real Operator Algebras on a Complex Hilbert Space
Bing Ren LI
Acta Mathematica Sinica, Chinese Series    2009, 52 (6): 1041-1046.   DOI: 10.12386/A2009sxxb0131
Abstract3226)      PDF(pc) (401KB)(1151)       Save
We study real operator algebras on a complex Hilbert space H. From H, we can get a real Hilbert space Hr. Further, we have a complex Hilbert space Hrc=Hr iHr. Through this process, we prove the following. If A and M are uniformly closed and weakly closed real * operator algebras on H respectively, then their complex span A+iA and M+iM are (complex) C*-algebra and (complex) von Neumann algebra on H, respectively. Here, we don't need the condition: A∩iA={0}, M∩iM={0}. So our result is a generalization of Stormer's result.  
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Automorphism Groups of Infinite Metacyclic Groups
He Guo LIU, Ji Ping ZHANG, Jun LIAO
Acta Mathematica Sinica, Chinese Series    2009, 52 (6): 1047-1054.   DOI: 10.12386/A2009sxxb0132
Abstract3662)      PDF(pc) (407KB)(805)       Save
We discuss automorphisms of infinite metacyclic groups and present their automorphism groups, and then we prove the following result: All automorphisms of an infinite metacyclic group G are inner automorphisms if and only if G is isomorphism to one of following groups: (i) Z∝ξ Zpl. where p is an odd prime, l is an integer, ξ maps the generator 1 of Z to ξ(1) = m, p m, and Zpl=Zpl*=Zp(l-1)(p-1)=<m>; (ii) The infinite dihedral group D∞.

 

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The Existence of an Intermediate Phase for the Contact Process on Some Product Graphs
Qiang YAO
Acta Mathematica Sinica, Chinese Series    2009, 52 (6): 1055-1066.   DOI: 10.12386/A2009sxxb0133
Abstract2501)      PDF(pc) (611KB)(743)       Save
In this article the author considers the contact process on the product graph of a homogeneous tree with degree d≥q3 and an arbitrary finite connected simple graph, showing that an intermediate phase for weak survival exists.

 

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Multipliers and Cyclic Vectors in the Logarithmic α-Bloch Spaces
Shan Li YE
Acta Mathematica Sinica, Chinese Series    2009, 52 (6): 1067-1074.   DOI: 10.12386/A2009sxxb0134
Abstract2690)      PDF(pc) (401KB)(1039)       Save
We study the pointwise multipliers in the logarithmic α-Bloch Spaces
 and cyclic vectors in the little logarithmic α-Bloch Spaces . We obtain as follows. (i) A characterization of multipliers on and  is obtained. (ii) If |f(z)|≥q |g(z)| in the open unit disk and g is cyclic in , then f is cyclic in . (iii) If 0<α<1, then f is cyclic in  if and only if f has no zeros in the closed unit disc.  
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On Ros' Theorem for Hypersurfaces
Jia Zu ZHOU, De Shuo JIANG, Ming LI, Fang Wei CHEN
Acta Mathematica Sinica, Chinese Series    2009, 52 (6): 1075-1084.   DOI: 10.12386/A2009sxxb0135
Abstract3469)      PDF(pc) (501KB)(1022)       Save
We first investigate the convex hypersurfaces in the Euclidean spaces . We obtain some geometric inequalities that generalize and refine the known Ros' theorem for all dimensions n. We also give a fundamental geometric proof of Ros' theorem for higher dimensions.  
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The Necessary and Sufficient Condition for [D, φ(x), λ]=0
Jian Quan LIAO, Xing Min LI
Acta Mathematica Sinica, Chinese Series    2009, 52 (6): 1085-1090.   DOI: 10.12386/A2009sxxb0136
Abstract2813)      PDF(pc) (359KB)(985)       Save
Let be the Dirac operator, . If , then is called a left -analytic function. In this paper, we prove that if , then for all if and only if is the Stein--Weiss conjugate harmonic system.  
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Weighted Lp Boundedness of Commutators of Schõdinger Type Operators
Liu YU
Acta Mathematica Sinica, Chinese Series    2009, 52 (6): 1091-1100.   DOI: 10.12386/A2009sxxb0137
Abstract3444)      PDF(pc) (453KB)(1078)       Save
We consider the Schrõdinger operators -Δ +V, where Δ is the Laplacian on and the nonnegative potential V belongs to the reverse Hõlder class Bq1 for q1 . The weighted Lp boundedness of the commutators of the Schrõdinger type operators (-Δ+V)Vα and (-Δ+V)∇ Vα  is obtained.  
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Space of BLO Type Associated with Schrõdinger Operator
Wen Hua GAO, Yin Sheng JIANG, Lin TANG
Acta Mathematica Sinica, Chinese Series    2009, 52 (6): 1101-1110.   DOI: 10.12386/A2009sxxb0138
Abstract2589)      PDF(pc) (503KB)(1114)       Save
Let =-Δ+V be a Schrõdinger operator on  with n≥3, where the non-zero, non-negative potential V belongs to the reverse Hõlder class Bq for some q≥. A BLO-type space () associated with Schrõdinger operators is defined and a characterization of it is obtained. () estimates for maximal Riesz transforms associated with Schrõdinger operators, Hardy--Littlewood maximal operator and natural maximal operator are obtained.  
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The Blow-up of Solution for Generalized Hyperelastic-rod Equation
Dan Ping DING Min SHIYun Rui BI
Acta Mathematica Sinica, Chinese Series    2009, 52 (6): 1111-1118.   DOI: 10.12386/A2009sxxb0139
Abstract3345)      PDF(pc) (421KB)(677)       Save
We will study the condition of blow-up for the generalized hyperelastic-rod equation. The solution blowing up in finite time lies in the scope of minimal initial velocity and the maximal variation of intial date and generalized functional G(μ).

 

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Involutions Fixing ∪mi=1 RPi(3)×HPi(k)
Su Qian ZHAO, Yan Ying WANG, Jing Yan LI
Acta Mathematica Sinica, Chinese Series    2009, 52 (6): 1119-1134.   DOI: 10.12386/A2009sxxb0140
Abstract3312)      PDF(pc) (500KB)(750)       Save
Let (M,T) be a closed and smooth manifold with an involution T. The fixed point set of T is F. In this paper, we determine bordism classes of the involutions with fixed point set F=∪mi=1 RPi(3)×HPi(k), where HP(k) is the k-dimensional quaternionic projective space, and k=2λ-2 or k=2λ-1 (λ>1).

 

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On Generalized Mõbius Inversion Formulae
Ping XI, Yuan YI
Acta Mathematica Sinica, Chinese Series    2009, 52 (6): 1135-1140.   DOI: 10.12386/A2009sxxb0141
Abstract2851)      PDF(pc) (523KB)(1092)       Save
In this paper,    a general Mõbius transform on  is discussed, and a pair of dual Mõbius inversion formulae are given, based on which some properties of the Mõbius transforms involving the k-th order divisor function and central binomial coefficients are obtained. A directly simplified proof of a known result, as a special case of our theorem, is also given.  
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A Spectral Representation of Infimum of Self-Adjoint Operators in the Logic Order
Hong Ke DU, Yan Ni DOU
Acta Mathematica Sinica, Chinese Series    2009, 52 (6): 1141-1146.   DOI: 10.12386/A2009sxxb0142
Abstract2379)      PDF(pc) (323KB)(754)       Save
In this note, using the spectral theory of linear operators, a spectral representation of infimum of two self-adjoint operators with respect to the logic order is established.

 

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On Randers Metrics of Isotropic S-Curvature
Guo Jun YANG
Acta Mathematica Sinica, Chinese Series    2009, 52 (6): 1147-1156.   DOI: 10.12386/A2009sxxb0143
Abstract2070)      PDF(pc) (440KB)(830)       Save
We classify a class of Randers metrics of isotropic S-curvature by navigation problem. This class includes all Randers metrics of isotropic S-curvature and scalar flag curvature. In particular, all 2-dimensional Randers metrics of isotropic S-curvature are classified. Besides, we construct for the first time many Randers metrics of constant S-curvature with other special curvature properties.

 

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A Modified Filter Trust Region Method for Nonlinear Programming
Ke SU, Ying LIU
Acta Mathematica Sinica, Chinese Series    2009, 52 (6): 1157-1164.   DOI: 10.12386/A2009sxxb0144
Abstract2729)      PDF(pc) (554KB)(838)       Save
Sequential quadratic programming (SQP) type method is one of the most effective methods for solving nonlinear programming. Recently, filter method, for its good numerical results, are extensively studied to handle nonlinear programming problems. In this paper, a new modified approach combined the filter technique and SQP trust region method is proposed to tackle the original problem, which ensures that every trail point will not be far away from the feasible region. Global convergence results of the proposed algorithm are established under suitable conditions. Some numerical results are reported in this paper.

 

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On Some q-Orders and q-Types of Dirichlet--Hadamard Product Function
Yin Ying KONG
Acta Mathematica Sinica, Chinese Series    2009, 52 (6): 1165-1172.   DOI: 10.12386/A2009sxxb0145
Abstract2662)      PDF(pc) (412KB)(800)       Save
The present paper give an estimation of the upper and lower bounds of the (lower) q-order and the (lower) q-type of a new product function defined by two Dirichlet series, named Dirichlet--Hadamard product function. It is of ρ[q]-regular growth or perfectly ρ[q]-regular growth, when two constituent Dirichlet series satisfy some special conditions. Finally we give an example and generalize a result concerning the subject of linear substitution.

 

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Weighted Inequalities for Iterated Maximal Operators in Martingale Space
Yan Ming JIN, Pei De LIU
Acta Mathematica Sinica, Chinese Series    2009, 52 (6): 1173-1180.   DOI: 10.12386/A2009sxxb0146
Abstract2740)      PDF(pc) (351KB)(714)       Save
We introduced the iterated maximal operators on martingale space and established some weighted Kolmogorov inequality and weighted double Φ-inequality for this kind of operators.

 

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Solvability Theorems with Applications of an Operator Equation in Partial Order Space
Zhan LIU, Chuan Xi ZHU
Acta Mathematica Sinica, Chinese Series    2009, 52 (6): 1181-1188.   DOI: 10.12386/A2009sxxb0147
Abstract3402)      PDF(pc) (433KB)(688)       Save
In this paper, the theorem of cone and the techniques of partial order theory are used to discuss the existence of coupled quasi-solutions and solutions for a mixed monotone operator equation Lx = N(x,y) in complete metric space and Banach space, where neither L nor N need to be continuous. We also construct some new non-symmetric iterative sequences and study their approximation, then we get some new theorems. Finally, we apply the new results presented in this paper to Hammerstain integral equations.

 

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The Study for Estimation of Homogeneous Expansion of Subclasses of Biholomorphic Mappings by a Unified Method
Qing Hua XU, Tai Shun LIU
Acta Mathematica Sinica, Chinese Series    2009, 52 (6): 1189-1198.   DOI: 10.12386/A2009sxxb0148
Abstract2701)      PDF(pc) (535KB)(892)       Save
We introduce a class of holomorphic mappings on the unit polydisc in or the unit ball in a complex Banach space. Let f(x) be a normalized locally biholomorphic mapping on B such that and f(x)-x has a zero of order k+1 at x=0. The estimation of homogeneous expansion for f(x) is obtained. Especially, we unify and generalize many known results. Moreover, in view of proofs of corollaries, the essential relations among the subclasses of biholomorphic mappings are shown.  
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Twist Property and the Second Order Differential Equations Without a Priori Bounds
Xi Ying SUN, Ding Bian QIAN
Acta Mathematica Sinica, Chinese Series    2009, 52 (6): 1199-1206.   DOI: 10.12386/A2009sxxb0149
Abstract3537)      PDF(pc) (533KB)(580)       Save
We study some twist second order differential equations. We prove that in some cases, the geometric property of angle function implies the existence of periodic solutions. As the applications, we obtain some new results for the existence of periodic solutions for some second order equations or reversible systems without a priori bounds, such as superlinear second order equations or reversible systems with time-dependent potential.

 

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Dimension and Measure of Admissible Kneading Sequences with Product Metric
Ai Hua ZHANG, Er Cai CHEN
Acta Mathematica Sinica, Chinese Series    2009, 52 (6): 1207-1210.   DOI: 10.12386/A2009sxxb0150
Abstract2755)      PDF(pc) (402KB)(671)       Save
Using the tools of Hausdorff dimension and Hausdorff measure, we give quantitative version for the set of admission kneading sequences with product metric. It is proved for the set that the Hausdorff dimension is s and the s-dimension Hausdorff measure is zero in Σ2, which are more profound than those obtained by traditional qualitative analysis.

 

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A Differentiable Sphere Theorem with Positive Ricci Curvature
Pei He WANG, Chun Li SHEN
Acta Mathematica Sinica, Chinese Series    2009, 52 (6): 1211-1218.   DOI: 10.12386/A2009sxxb0151
Abstract2847)      PDF(pc) (524KB)(694)       Save
In the paper stated here, Hausdorff convergence is introduced to discuss the differentiable sphere theorem with positive Ricci curvature. Finally, a type of rigidity phenomenon on Riemannian manifolds will be derived.

 

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Invertible Completions for a Classes of Operator Partial Matrices
Guo Jun HAI, Alatancang
Acta Mathematica Sinica, Chinese Series    2009, 52 (6): 1219-1224.   DOI: 10.12386/A2009sxxb0152
Abstract5504)      PDF(pc) (380KB)(886)       Save
Let  and  be separable Hilbert spaces. For given operators and , a necessary and sufficient condition is given for to be an invertible operator for some  and .  
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Topological Characterizations of Properties of Logic Theories in Three-Valued Propositional Logic System L*3
Yan Hong SHE, Guo Jun WANG
Acta Mathematica Sinica, Chinese Series    2009, 52 (6): 1225-1234.   DOI: 10.12386/A2009sxxb0153
Abstract2493)      PDF(pc) (543KB)(625)       Save
Let (F(S),ρ3) be the three-valued logic metric space. The present paper characterizes consistency, full divergency and logical closedness of theories in propositional logic system L*3 by means of topological concepts in the three-valued logic metric space. It is proved that a closed theory Γ is consistent iff it contains no interior points, iff it possesses the truth-forget property, iff it contains no non-empty regular sphere. It is also proved that a theory Γ is fully divergent iff its logic closure is dense in (F(S),ρ3). Finally, it is proved that the logic closure of finite theory is closed in (F(S),ρ3).

 

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Commutators of the Fractional Maximal Functions
Pu ZHANG, Jiang Long WU
Acta Mathematica Sinica, Chinese Series    2009, 52 (6): 1235-1238.   DOI: 10.12386/A2009sxxb0154
Abstract3517)      PDF(pc) (305KB)(897)       Save
In this paper, the boundedness property on Lebesgue spaces for commutators generated by fractional maximal functions with BMO() functions are characterized.  
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Path Algebras and Finite Automata
Fei Dan HUANG, Pei Min DENG , Zhong YI
Acta Mathematica Sinica, Chinese Series    2009, 52 (6): 1239-1248.   DOI: 10.12386/A2009sxxb0155
Abstract3556)      PDF(pc) (504KB)(736)       Save
In this paper, the definition of path algebras of finite automata is given, the relations of characteristics of finite automata and algebraic properties of their path algebra are studied, and some results are given.

 

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