中国科学院数学与系统科学研究院期刊网

Acta Mathematica Sinica, Chinese Series 2015 Vol.58

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Trajectory Attractor for a Class of Three-Dimensional Incompressible Non-Newtonian Fluids
Cai Di ZHAO, He Ling WU, Chu Jin LI
Acta Mathematica Sinica, Chinese Series    2015, 58 (1): 1-12.   DOI: 10.12386/A2015sxxb0001
Abstract1737)      PDF(pc) (523KB)(913)       Save
This paper studies the trajectory asymptotic behavior of solutions for equations of a class of three-dimensional autonomous and incompressible non-Newtonian fluids. The authors prove the existence of the trajectory attractor for this class of equations in an appropriate topological space.
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Stability of Traveling Wave Fronts for Nonlocal Reaction Diffusion Equations with Delay
Xiao Huan WANG, Guang Ying LV
Acta Mathematica Sinica, Chinese Series    2015, 58 (1): 13-28.   DOI: 10.12386/A2015sxxb0002
Abstract2185)      PDF(pc) (576KB)(958)       Save
This paper is concerned with the stability of traveling wave fronts for reaction diffusion equations with nonlocal delay. We prove that, in the appropriate weighted L spaces, the non-critical traveling wave fronts are globally exponentially stable, and the critical traveling wave fronts are globally algebraically stable. Moreover, we obtain the rates of convergence by weighted energy estimates. We apply these results to a host-vector disease model, the generalized Nicholson blowflies equation, and a modified vector disease model.
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Commutators of Hardy Type Operators on Herz Spaces with Variable Exponents
Li Sheng SHU, Min WANG, Meng QU
Acta Mathematica Sinica, Chinese Series    2015, 58 (1): 29-40.   DOI: 10.12386/A2015sxxb0003
Abstract1878)      PDF(pc) (445KB)(825)       Save
We mainly prove the boundedness of the commutators of Hardy type operators on Herz spaces , where α(·) and p(·) are both variable.
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Transcendental Solutions of Systems of Complex Differential Equations
Ling Yun GAO
Acta Mathematica Sinica, Chinese Series    2015, 58 (1): 41-48.   DOI: 10.12386/A2015sxxb0004
Abstract2606)      PDF(pc) (341KB)(1022)       Save
Using maximum modulus principle, we investigate the problem of the existence of the transcendental meromorphic solutions of system of complex algebraic differential equations, and obtain a result which the system only the algebraic solution under certain conditions. Examples show that our results are sharp.
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Higher Order Schwarzian Derivatives and Quasisymmetric Homeomorphisms
Jian Jun JIN
Acta Mathematica Sinica, Chinese Series    2015, 58 (1): 49-58.   DOI: 10.12386/A2015sxxb0005
Abstract1738)      PDF(pc) (446KB)(877)       Save
We characterize two subclasses of quasisymmetric homeomorphisms of the unit circle in terms of higher order Schwarzian derivatives, which are the strongly symmetric homeomorphisms and the Weil-Petersson class.
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Super O-Operators of Pre-Lie Superalgebras and Super S-Equations
Jun Na NI
Acta Mathematica Sinica, Chinese Series    2015, 58 (1): 59-70.   DOI: 10.12386/A2015sxxb0006
Abstract1556)      PDF(pc) (458KB)(808)       Save
Super O-operators on Pre-Lie superalgebras are introduced. The solutions of super S-equation are discussed by super O-operators. Then the notion of L-dendriform superalgebras is introduced as the algebraic structure behind the super O-operators. Moreover, the relation between L-dendriform superalgebras, dendriform superalgebras and Pre-Lie superalgebra is also established.
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A Characterization of *-Isomorphism on Factor von Neumann Algebras
Mei Li WANG, Guo Xing JI
Acta Mathematica Sinica, Chinese Series    2015, 58 (1): 71-78.   DOI: 10.12386/A2015sxxb0007
Abstract1566)      PDF(pc) (379KB)(811)       Save
Let H and K be complex Hilbert spaces. Let A and B be two factor von Neumann algebras acting on H and K respectively. A characterization of *-isomorphism between A and B is given. Let Φ: AB be a bijection. If Φ(A*B + B*A) = Φ(A)*Φ(B) + Φ(B)*Φ(A) for all A,BA, then Φ is a linear or a conjugate linear *-isomorphism.
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Some Results About the Coming Generation of Subcritical CMJ Processes in Discrete Time
Hong Song GUO, Mei ZHANG
Acta Mathematica Sinica, Chinese Series    2015, 58 (1): 79-90.   DOI: 10.12386/A2015sxxb0008
Abstract1691)      PDF(pc) (544KB)(861)       Save
We consider the count of the coming generation of subcritical CMJ processes in discrete time. With the help of several renewal theorems, we obtain the limit theorems for the conditional processes. Therefore, we show how the coming generation sheds new light on the limit properties of subcritical CMJ processes.
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The Characterization of Wave Packet Parseval Frames and Its Application
Guo Chang WU, Huai Xin CAO, Da Yong LU
Acta Mathematica Sinica, Chinese Series    2015, 58 (1): 91-102.   DOI: 10.12386/A2015sxxb0009
Abstract1813)      PDF(pc) (543KB)(790)       Save
We provide a characterization of wave packet Parseval frames from their Fourier transforms, which deduces some existing results as e corollaries. Furthermore, some properties and a sufficient condition of wave packet frame multipliers are obtained.
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A Estimate of the Volume of Mininimal Hypersurface in Mn×Rm
Shang Ming TAO
Acta Mathematica Sinica, Chinese Series    2015, 58 (1): 103-106.   DOI: 10.12386/A2015sxxb0010
Abstract1745)      PDF(pc) (326KB)(812)       Save
It estimates the volume of an area-bounded minimal graph supported on Ω which is called admissible and it has Euclidean growth. This result generalizes the related results of Elbert and Rosenberg in Mn×R for minimal graphs to in Mn×Rm.
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Estimates of Multilinear Multipliers on Modulation Spaces
Cong Wei SONG
Acta Mathematica Sinica, Chinese Series    2015, 58 (1): 107-114.   DOI: 10.12386/A2015sxxb0011
Abstract1718)      PDF(pc) (456KB)(791)       Save
We show new estimates of multilinear multipliers, improve the known results. We apply the results obtained into the estimates of the nonlinearities of differential equations.
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Gorenstein-Projective Modules in rep(A3, I, A)
Xiu Hua LUO, Teng Xia JU, Mei Yun WU
Acta Mathematica Sinica, Chinese Series    2015, 58 (1): 115-124.   DOI: 10.12386/A2015sxxb0012
Abstract1748)      PDF(pc) (467KB)(728)       Save
Given a finite-dimensional algebra A over a field k, and a quiver with relations (Q,I), let Λ = AkkQ/I. The category Λ-Mod (Resp. Λ-mod) of (Resp. finitely generated) Λ-modules is equivalent to the category Rep(Q, I,A) (Resp. rep(Q, I,A)) of (Resp. finite-dimensional) representations of (Q, I) over A. The main result of this paper explicitly describes the Gorenstein-projective modules in rep(A3,I,A), where (A3, I) = 3 α 21. with relation I = < βα >. As a corollary, we give a necessary and sufficient condition for A being a self-injective algebra.
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Multiplication Operator on the Weighted Bergman Space of the Unit Ball
Kan ZHANG, Xue FENG, Jian Guo DONG, Chi GUAN, Yan YU
Acta Mathematica Sinica, Chinese Series    2015, 58 (1): 125-130.   DOI: 10.12386/A2015sxxb0013
Abstract1809)      PDF(pc) (324KB)(717)       Save
Multiplication operator is an important class of operators in function space. We mainly research the properties of the multiplication operator on the weighted Bergman space of the unit ball.
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On Exponentially Harmonic Maps
Yuan Jen CHIANG, Heng PAN
Acta Mathematica Sinica, Chinese Series    2015, 58 (1): 131-140.   DOI: 10.12386/A2015sxxb0014
Abstract1558)      PDF(pc) (525KB)(758)       Save
We show that both exponential energy and exponentially harmonic map are conformally invariant under a circumstance. We investigate exponentially harmonic Riemannian submersions and exponentially harmonic isometric immersions. We also examine the associated Gauss map of a Riemannian isometric immersion which is exponentially harmonic.
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Asymptotic Estimates of Unimodular Modifiers on α Modulation Space
Guo Ping ZHAO, Wei Chao GUO
Acta Mathematica Sinica, Chinese Series    2015, 58 (1): 141-152.   DOI: 10.12386/A2015sxxb0015
Abstract1757)      PDF(pc) (495KB)(732)       Save
We study the asymptotic estimates of unimodular multipliers on α modulation spaces. We make a unified study about different types of function spaces, including modulation spaces and Besov spaces. The upper bound estimates of our results generalize many known results of modulation spaces. Moreover, under a partial non-degenerate assumptions on the symbol, we get the sharp asymptotic estimates of the unimodular Fourier multipliers.
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Sharp Bounds for Multilinear Hausdorff Operators
Gui Lian GAO, Yun FAN
Acta Mathematica Sinica, Chinese Series    2015, 58 (1): 153-160.   DOI: 10.12386/A2015sxxb0016
Abstract1715)      PDF(pc) (377KB)(688)       Save
We give the necessary conditions of boundedness of multilinear Hausdorff operators on Lebesgue spaces and λ-central Morrey spaces, respectively, when the kernel functions are nonnegative. Meanwhile, the corresponding operator norms are worked out.
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Strongly Damped Wave Equations with Critical Nonlinearities
Qing Hua ZHANG, Yue Ping ZHU
Acta Mathematica Sinica, Chinese Series    2015, 58 (1): 161-168.   DOI: 10.12386/A2015sxxb0017
Abstract1302)      PDF(pc) (499KB)(604)       Save
We study the strongly damped wave equations with critical nonlinearities. By choosing suitable state spaces, we prove sectorial properties of the operator matrix , analysis the criticality of the nonlinearities with critical growth, and investigate the local and global existence of weak solutions together with their higher regularity.
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Complex Convexity of Musielak-Orlicz Sequence Spaces Equipped with the p-Amemiya Norm
Li Li CHEN, Yu Nan CUI, Yan Feng ZHAO, Jin Ling NIU
Acta Mathematica Sinica, Chinese Series    2015, 58 (1): 169-176.   DOI: 10.12386/A2015sxxb0018
Abstract1481)      PDF(pc) (434KB)(501)       Save
We mainly discuss the complex convexity of Musielak-Orlicz sequence spaces equipped with the p-Amemiya norm. It is obtained that for any Musielak- Orlicz sequence space equipped with the p-Amemiya norm when 1 ≤ p < ∞, complex strongly extreme points of the unit ball coincide with complex extreme points of the unit ball. Moreover, criteria for them in above spaces are given. Criteria for complex rotundity and complex mid-point locally uniform convexity of above spaces are also deduced.
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The Crossing Number of Link in Thickened Surface
Xin Ming YAN
Acta Mathematica Sinica, Chinese Series    2015, 58 (2): 177-182.   DOI: 10.12386/A2015sxxb0019
Abstract1831)      PDF(pc) (446KB)(903)       Save
We estimate the crossing number of framed link in thickened surface, we define the span of framed link in Kauffman bracket skein module, which may give a lower bound of the crossing number.
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The Construction of Modified Green Function in a Cone and Its Application
Lei QIAO, Guo Shuang PAN, Yan Hui ZHANG
Acta Mathematica Sinica, Chinese Series    2015, 58 (2): 183-194.   DOI: 10.12386/A2015sxxb0020
Abstract1594)      PDF(pc) (470KB)(844)       Save
Our first aim in this paper is to construct a modified Green function in a cone and give the growth property of it. As an application, we next give the general solutions of the Dirichlet problem. Finally, we prove that this solution is unique.
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Laguerre Isoparametric Hypersurface in Rn with Three Distinct Principal Curvatures
Ding Xing ZHONG, Xian Hua XIE, Hai Lian CHEN
Acta Mathematica Sinica, Chinese Series    2015, 58 (2): 195-212.   DOI: 10.12386/A2015sxxb0021
Abstract1969)      PDF(pc) (589KB)(855)       Save
An umbilical free oriented hypersurface x:MRn with nonzero princi-pal curvatures is called Laguerre isoparametric hypersurface if its Laguerre form C=∑i Ciwi =∑iρ-1(Ei(logρ)(r-ri)-Ei(r))wi vanishes and Laguerre shape operator S=ρ-1(S-rid has constant eigenvalues. Here ρ2=∑i(r-ri)2,r=r1+r2+…+rn-1/n-1 is the mean curvature radius and S is the shape operator of x, Ei is local orthogonal basis for Laguerre metric g with dual basis wi. In this paper, we classify all Laguerre isoprametric hypersurfaces in Rn with three distinct Laguerre principal curvatures up to Laguerre transformation.
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Strong Convergence of Multi-Valued Bregman Totally Quasi-Asymptotically Nonexpansive Mappings
Shi Sheng ZHANG, Lin WANG, Yun He ZHAO, Gang WANG
Acta Mathematica Sinica, Chinese Series    2015, 58 (2): 213-226.   DOI: 10.12386/A2015sxxb0022
Abstract1803)      PDF(pc) (569KB)(843)       Save
We propose an algorithms for finding a common fixed point of a finite family of multi-valued Bregman total quasi-φ-asymptotically nonexpansive mappings in reflexive Banach spaces. The results presented in the paper improve and extend the corresponding new results announced by many authors. The algorithms are based on the Bregman distance related to a well-chosen convex function. As applications, we apply our results to a system of equilibrium problems and zero point problem of maximal monotone mappings in reflexive Banach spaces.
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Global Attractor for a Class of Semi-Discrete System of Nonlinear Schrödinger-BBM Equations
Ming Hao ZHAO, Chao Sheng ZHU, Yang Rong LI
Acta Mathematica Sinica, Chinese Series    2015, 58 (2): 227-242.   DOI: 10.12386/A2015sxxb0023
Abstract1633)      PDF(pc) (524KB)(738)       Save
This paper is devoted to the large time behavior and especially to the regularity of the global attractor for the semi-discrete in time Crank-Nicolson scheme to discretize a class of system of nonlinear Schrödinger-BBM equations on R × R. We first prove that such a semi-discrete system provides a discrete infinite-dimensional dynamical system in H1 × H1 that possesses a global attractor Aτ in H1 × H1. We also show that the global attractor Aτ is regular, i.e. Aτ is actually included, bounded and compact in H(3/2)-ε×H2.
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Algebraic Extensions of nth Root of Class A Operators are Subscalar
Jun Li SHEN, Alatancang
Acta Mathematica Sinica, Chinese Series    2015, 58 (2): 243-250.   DOI: 10.12386/A2015sxxb0024
Abstract2052)      PDF(pc) (439KB)(701)       Save
Algebraic extension of nth root of class A operator is studied. Specifically, we obtain that every algebraic extension of nth root of class A operator is subscalar. The proof uses the space decomposition technique. As a consequence, we consider the Weyl type theorems and the hyperinvariant subspace for such operator.
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On a Jensen-quadratic Functional Equation and Its Hyers-Ulam Stability
Pei Sheng JI, Ying Zi ZHAO
Acta Mathematica Sinica, Chinese Series    2015, 58 (2): 251-260.   DOI: 10.12386/A2015sxxb0025
Abstract1694)      PDF(pc) (304KB)(732)       Save
We obtain the general solution and stability of the Jensen-quadratic functional equation f((x1+x2)/2,y1+y2)+f((x1+x2)/2,y1-y2)=f(x1,y1)+f(x1,y2)+f(x2,y1)+f(x2,y2).
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The Solutions for Semipositone (k,n-k) Conjugate Boundary Value Problems
Hua SU, Li Shan LIU
Acta Mathematica Sinica, Chinese Series    2015, 58 (2): 261-270.   DOI: 10.12386/A2015sxxb0026
Abstract2042)      PDF(pc) (414KB)(775)       Save
We consider the existence of positive solutions to the following semiposi-tone (k,n-k) conjugate boundary value problems (SCBVP): 

where n≥2, 1<k<n-1. The nonlinear function f may change sign for 0 < t < 1, i.e., we allow that the nonlinear term f is both semipositone and lower unbounded. Without making any monotone-type assumption, by using the fixed-point index theory, the existence of positive solution and many positive solutions are obtained.
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Estimates on Higher Order Damped Wave Equation
Wei Liang XIAO, Xu Huan ZHOU, Tao Tao ZHENG
Acta Mathematica Sinica, Chinese Series    2015, 58 (2): 271-286.   DOI: 10.12386/A2015sxxb0027
Abstract1484)      PDF(pc) (604KB)(762)       Save
This paper focus on the Lp estimates of the higher order damped wave equation. Using tools from harmonic analysis, especially the method of oscillatory integral, we calculated the point-wise estimates for the kernel related to the solution of the homogeneous equation. Also we apply these estimates to study the space-time estimates and the global solution to the Cauchy problem of the nonlinear equation.
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C-Filters in Enriched Union Semi-Lattice with Its Applications
Hong Bo WU, Hai Yan KOU
Acta Mathematica Sinica, Chinese Series    2015, 58 (2): 287-300.   DOI: 10.12386/A2015sxxb0028
Abstract1648)      PDF(pc) (398KB)(700)       Save
Firstly, the concept of upper covering relation in a union semi-lattice and upper coverage defined by the forme in an enriched union semi-lattice are introduced, the basic properties of them are discussed in enriched union semi-lattices. Secondly, the concept of C-filters is introduced in enriched union semi-lattices through upper coverage, it is proved that C-filters are usual filters, but usual filters are not C-filters in an enriched union semi-lattice. Thirdly, the relationships between morphisms of enriched union semi-lattice and co-Frames are investigated. At last, the isomorphism theorem between co-Frames and its CS-filter co-Frames is proved.
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Filtrations and Classifications for the Non-Simple Lie Superalgebras of Type W or S
Xiu Qiang ZHANG, Wen De LIU
Acta Mathematica Sinica, Chinese Series    2015, 58 (2): 301-308.   DOI: 10.12386/A2015sxxb0029
Abstract1998)      PDF(pc) (477KB)(754)       Save
Let F be a field and char F = p > 3. Let g denote the Lie superalgebra which is the tensor product of an exterior superalgebra and a finite-dimensional generalized Witt algebra or special Lie algebra over F. In this paper it is proved that the standard filtration of the non-simple Lie superalgebra g is invariant under the automorphism group of g by means of investigating the ad nilpotent elements. Finally, the superalgebras of type W or S are classified by means of the parameters defining them.
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Some Boundedness of Homogeneous Fractional Integrals onVariable Exponent Function Spaces
Jian TAN, Zong Guang LIU
Acta Mathematica Sinica, Chinese Series    2015, 58 (2): 309-320.   DOI: 10.12386/A2015sxxb0030
Abstract2140)      PDF(pc) (480KB)(785)       Save
In this paper, the authors establish some boundedness of homogeneous fractional integrals on some variable exponent function spaces, such as variable Lebesgue spaces, variable Hardy spaces and variable Herz-type Hardy spaces.
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On Non-Commuting Sets in a Finite p-Group with a Cyclic Center
Yu Lei WANG, He Guo LIU
Acta Mathematica Sinica, Chinese Series    2015, 58 (2): 321-328.   DOI: 10.12386/A2015sxxb0031
Abstract1957)      PDF(pc) (351KB)(669)       Save
Let G be a group. A subset X in G is said to be non-commuting if xyyx for any x, yX with xy. Furthermore, if |X| ≥ |Y| for any other non-commuting subset Y in G, then X is said to be a maximal non-commuting set. In this paper, the bound for the cardinality of a maximal non-commuting set in a finite p-group with a cyclic center is determined.
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Affine Factorable Surfaces in Three-Dimensional Euclidean Space
Peng ZONG, Lin XIAO, Hui Li LIU
Acta Mathematica Sinica, Chinese Series    2015, 58 (2): 329-336.   DOI: 10.12386/A2015sxxb0032
Abstract2131)      PDF(pc) (355KB)(772)       Save
Affine factorable surfaces in Euclidean 3-space were defined. The classification of surfaces with zero Gauss curvature and nonzero constant mean curvature and minimal affine factorable surfaces was given.
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A Reconsideration on the Ptolemy Constant of Absolute Normalized Norms
Zhan Fei ZUO
Acta Mathematica Sinica, Chinese Series    2015, 58 (2): 337-344.   DOI: 10.12386/A2015sxxb0033
Abstract1699)      PDF(pc) (381KB)(639)       Save
We determine and estimate the Ptolemy constant of absolute normalized norms on some new conditions. The new results which not only contain the previous results, but also give some new results in some concrete Banach spaces.
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Normal Families Concerning Exceptional Functions and Shared Functions
Hui Ling QIU, Cai Yun FANG, Ming Liang FANG
Acta Mathematica Sinica, Chinese Series    2015, 58 (2): 345-352.   DOI: 10.12386/A2015sxxb0034
Abstract2200)      PDF(pc) (412KB)(644)       Save
Let F be a family of meromorphic functions in a domain D, let a(z), b(z), c(z) be three distinct meromorphic functions in D, one may be ∞, and for any zD, a(z)= b(z), a(z) = c(z), b(z) = c(z), and let S = {a(z), b(z), c(z)}. If for any two functions f, gF, f and g share the set S in D, then F is normal in D. This extends the famous Montel's criterion.
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Highest Weight Representations of the Completed Witt Algebra
Jun Ping LIANG, Guang Zhe FAN
Acta Mathematica Sinica, Chinese Series    2015, 58 (3): 353-358.   DOI: 10.12386/A2015sxxb0035
Abstract1997)      PDF(pc) (426KB)(1052)       Save
We investigate the irreducibility of Verma modules over the completed Witt algebra. By embedding the Virasoro algebra into the completed Witt algebra, we give realizations of two classes of irreducible non-weight Virasoro-modules. We also obtain some interesting combinatorial identities.
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Quasirecognition of the Simple Group 2G2(32n+1)
Li Li LI
Acta Mathematica Sinica, Chinese Series    2015, 58 (3): 359-364.   DOI: 10.12386/A2015sxxb0036
Abstract1896)      PDF(pc) (305KB)(788)       Save
Let G be finite group such that M(G) = M(2G2(32n+1)). Then G has a normal subgroup isomorphic to 2G2(32n+1). Especially, if |G| = |2G2(32n+1)|, then G2G2(32n+1).
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Multiplicative Hom-Structures on Finite Dimensional Modular Lie Superalgebras of Cartan Type
Xiu Ying HUA, Li Ming TANG, Wen De LIU
Acta Mathematica Sinica, Chinese Series    2015, 58 (3): 365-372.   DOI: 10.12386/A2015sxxb0037
Abstract1892)      PDF(pc) (435KB)(828)       Save
Let F be an algebraically closed field of characteristic p > 3. Using the invariance of the natural filtration and calculating the actions on the -1 components for the Hom-structures of the modular Lie superalgebras under consideration, we prove that there exists only the trivial multiplicative Hom-structures on the finite dimensional Z-graded modular Lie superalgebras of Cartan type.
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A Note on the Bound of Castelnuovo's Inequality
Zheng Jun ZHAO
Acta Mathematica Sinica, Chinese Series    2015, 58 (3): 373-378.   DOI: 10.12386/A2015sxxb0038
Abstract1708)      PDF(pc) (411KB)(852)       Save
We present some explicit formulae for genus of the composite field of Kummer and Artin-Schreier function fields in some specific cases. Meanwhile, we point out in this note that the genus of function field we addressed reaches the upper bound of Castelnuovo's inequality.
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On the Infinite-Dimensional Modular Lie Superalgebras of L-Type
Jing ZHAO, Jin WANG, Xiao Ning XU
Acta Mathematica Sinica, Chinese Series    2015, 58 (3): 379-400.   DOI: 10.12386/A2015sxxb0039
Abstract1862)      PDF(pc) (598KB)(746)       Save
The infinite-dimensional Lie superalgebras of L-type over a field of positive characteristic are studied. The simplicity is proved and the natural filtration of Lie superalgebras of L-type is proved to be invariant under automorphism group by using ad-nilpotent elements. We are thereby able to obtain a property of Lie superalgebras of L-type.
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Classification and General Forms of Operator Algebras on Pontrjagin Space
Hai Tao YANG
Acta Mathematica Sinica, Chinese Series    2015, 58 (3): 401-418.   DOI: 10.12386/A2015sxxb0040
Abstract1607)      PDF(pc) (498KB)(752)       Save
We classify the general symmetric operator algebras on Pontrjagin space into six classes by using of symmetric ideals, and give the general forms for all the SM operator algebras in each class.
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