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20 February 2009, Volume 29 Issue 1 Previous Issue    Next Issue

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ON MARKOV CHAINS IN SPACE-TIME RANDOM ENVIRONMENTS Hu Dihe; Hu Xiaoyu Acta mathematica scientia,Series B. 2009, 29 (1):  1-10.  DOI: 10.1016/S0252-9602(09)60001-1 Abstract ( 896 )   RICH HTML PDF (177KB) ( 1552 )   Save In Section 1, the authors establish the models of two kinds of Markov chains in space-time random environments (MCSTRE and MCSTRE(+)) with abstract state space. In Section 2, the authors construct a MCSTRE and a MCSTRE(+) by an initial distribution Φ and a random Markov kernel (RMK) p(γ). In Section 3, the authors establish several equivalence theorems on MCSTRE and MCSTRE(+). Finally, the authors give two very important examples of MCMSTRE, the random walk in spce-time random environment and the Markov branching chain in space-time random environment. Related Articles | Metrics

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BIFURCATIONS OF A CUBIC SYSTEM PERTURBED BY DEGREE FIVE Shang Desheng; Zhang Tonghua Acta mathematica scientia,Series B. 2009, 29 (1):  11-24.  DOI: 10.1016/S0252-9602(09)60002-3 Abstract ( 788 )   RICH HTML PDF (308KB) ( 1282 )   Save In this article, using multi-parameter perturbation theory and qualitative analysis, the authors studied a kind of cubic system perturbed by degree five and obtained the system that can have 17 limit cycles giving their two kinds of distributions (see Fig.5). Related Articles | Metrics

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RIEMANN BOUNDARY VALUE PROBLEMS WITH GIVEN PRINCIPAL PART Li Weifeng; Du Jinyuan Acta mathematica scientia,Series B. 2009, 29 (1):  25-31.  DOI: 10.1016/S0252-9602(09)60003-5 Abstract ( 928 )   RICH HTML PDF (145KB) ( 1037 )   Save In this article, the authors discuss the Riemann boundary value problems with given principal part. First, authors consider a special case and give a classification of the solution class Rn by the way. And then, they consider the general case. The solvable conditions for this problem and its solutions is obtained when it is solvable. Related Articles | Metrics

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CRITERIA FOR AN ANALYTIC FUNCTION BELONGING TO QK SPACES Hasi Wulan Acta mathematica scientia,Series B. 2009, 29 (1):  33-44.  DOI: 10.1016/S0252-9602(09)60004-7 Abstract ( 691 )   RICH HTML PDF (172KB) ( 1148 )   Save The author gives a mild integral condition in a nondecreasing function K: [0, ∞) → [0, ∞), which is sufficient and the best possible to ensure that f is a Bloch function if and only if f belongs to QK , a Möbius-invariant space of functions analytic in the unit disk. Their contributions are slight improvements of known results, and the proofs presented here are independently developed. The corresponding results for meromorphic case are also given. Related Articles | Metrics

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WEIGHTED AVERAGE OF DIRICHLET KERNELS FOR VILENKIN-LIKE SYSTEM Zhang Chuanzhou; Liu Peide Acta mathematica scientia,Series B. 2009, 29 (1):  45-55.  DOI: 10.1016/S0252-9602(09)60005-9 Abstract ( 839 )   RICH HTML PDF (177KB) ( 1347 )   Save For Vilenkin-like system, the authors define a new operator H* f:=supn|Hnf|, where Hnf is the weighted average for partial sums, and prove that H* is of type (H*p(Gm), Lp(Gm)) for all 1/2 < p ≤ ∞ . As a consequence, the authors prove the operator S*f:=supn|Snf| is of type (p, p) for 1<p< ∞, where Snf is the n-partial sum. Related Articles | Metrics

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MATHEMATICAL ANALYSIS OF THE COLLAPSE IN BOSE-EINSTEIN CONDENSATE Li Xiaoguang;Zhang Jian;Wu Yonghong Acta mathematica scientia,Series B. 2009, 29 (1):  56-64.  DOI: 10.1016/S0252-9602(09)60006-0 Abstract ( 772 )   RICH HTML PDF (175KB) ( 1527 )   Save In this article, the authors consider the collapse solutions of Cauchy problem for the nonlinear Schrödinger equation i Ψ t + 1/ 2 △ Ψ- 1 /2 ω2|x|2 ψ+|ψ|2ψ = 0, x ∈ R2, which models the Bose-Einstein condensate with attractive interactions. The authors establish the lower bound of collapse rate as t → T. Furthermore, the L2-concentration property of the radially symmetric collapse solutions is obtained. Related Articles | Metrics

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THE RELATION OF TWO-DIMENSIONAL VISCOUS CAMASSA-HOLM EQUATIONS AND THE NAVIER-STOKES EQUATIONS Yang Linge; Ji Yanshan; Ji Yanshan Acta mathematica scientia,Series B. 2009, 29 (1):  65-73.  DOI: 10.1016/S0252-9602(09)60007-2 Abstract ( 579 )   RICH HTML PDF (156KB) ( 1410 )   Save In this article, the authors show the existence of global solution of two- dimensional viscous Camassa-Holm (Navier-Stokes-alpha) (NS-α) equations. The authors also prove that the solution of the NS-α equations converges to the solution of the 2D NS equations in the inviscid limit and give the convergence rate of the difference of the solution. Related Articles | Metrics

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HOMOGENIZATION RESULTS FOR ENZYME CATALYZED REACTIONS THROUGH #br# POROUS MEDIA Claudia Timofte Acta mathematica scientia,Series B. 2009, 29 (1):  74-82.  DOI: 10.1016/S0252-9602(09)60008-4 Abstract ( 753 )   RICH HTML PDF (160KB) ( 1237 )   Save The aim of this article is to study the effective behavior of the solution of a nonlinear problem arising in the modelling of enzyme catalyzed reactions through the exterior of a domain containing periodically distributed reactive solid obstacles, with period ε. The asymptotic behavior of the solution of such a problem is governed by a new elliptic boundary-value problem, with an extra zero-order term that captures the effect of the enzymatic reactions. Related Articles | Metrics

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THE PITS PROPERTY OF ENTIRE FUNCTIONS DEFINED BY DIRICHLET SERIES Shang Lina; Gao Zongsheng Acta mathematica scientia,Series B. 2009, 29 (1):  83-93.  DOI: 10.1016/S0252-9602(09)60009-6 Abstract ( 701 )   RICH HTML PDF (165KB) ( 1286 )   Save The value distribution of entire functions defined by Dirichlet series are studied in this present article. It is proved that entire functions defined by Dirichlet series have the pits property, which improve the relative results on lacunary Taylor series obtained by Littlewood J.E. and Offord A.C. Related Articles | Metrics

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REDUCED MINIMAL NUMERICAL RANGES OF OPERATORS ON A HILBERT SPACE Du Hongke; Wang Yueqing; Lu Jianming Acta mathematica scientia,Series B. 2009, 29 (1):  94-100.  DOI: 10.1016/S0252-9602(09)60010-2 Abstract ( 607 )   RICH HTML PDF (141KB) ( 1304 )   Save In this note, the reduced minimal numerical ranges of a bounded linear oper- ators on a Hilbert space are defined and some of its properties are established. Related Articles | Metrics

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A CLASS OF HOMOTOPIC SOLVING METHOD FOR ENSO MODEL Mo Jiaqi; Lin Wantao; Wang Hui Acta mathematica scientia,Series B. 2009, 29 (1):  101-110.  DOI: 10.1016/S0252-9602(09)60011-4 Abstract ( 880 )   RICH HTML PDF (151KB) ( 1372 )   Save The El Niño/La Niña and the Southern Oscillation (ENSO) is an interannual phenomenon involved in the tropical Pacific ocean-atmosphere interactions. In this article, the aim is to create an asymptotic solving method of nonlinear equation for the ENSO models. And on the basis of a class of oscillator of ENSO models, using the method of homotopic mapping, the approximation of solution of corresponding problem is studied. It is proved from the results that homotopic method can be used for analyzing the SST anomaly in the equatorial eastern Pacific and the thermocline depth anomaly of the atmosphere-ocean oscillation for ENSO model. Related Articles | Metrics

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POINTWISE CONVERGENCE RATE OF VANISHING VISCOSITY APPROXIMATIONS FOR SCALAR CONSERVATION LAWS WITH BOUNDARY Liu Hongxia; Pan Tao Acta mathematica scientia,Series B. 2009, 29 (1):  111-128.  DOI: 10.1016/S0252-9602(09)60012-6 Abstract ( 1003 )   RICH HTML PDF (220KB) ( 1304 )   Save This article is concerned with the pointwise error estimates for vanishing vis- cosity approximations to scalar convex conservation laws with boundary. By the weighted error function and a bootstrap extrapolation technique introduced by Tadmor-Tang, an optimal pointwise convergence rate is derived for the vanishing viscosity approximations to the initial-boundary value problem for scalar convex conservation laws, whose weak entropy solution is piecewise C2-smooth with interaction of elementary waves and the boundary. The analysis method in this article can be used to deal with the case in which the piecewise smooth solutions of inviscid have finitely many waves with possible all kinds of interaction with the boundary. Related Articles | Metrics

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ALGEBROIDAL FUNCTION AND ITS DERIVED #br# FUNCTION IN UNIT CIRCULAR DISC Huo Yingying; Sun Daochun Acta mathematica scientia,Series B. 2009, 29 (1):  129-139.  DOI: 10.1016/S0252-9602(09)60013-8 Abstract ( 808 )   RICH HTML PDF (174KB) ( 1029 )   Save In this article, the authors define the derived function of an algeboidal function in the unit disc, prove it is an algabriodal function, and study the order of algebroidal function and that of its derived function in unit circular disc. Related Articles | Metrics

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TOEPLITZ-TYPE OPERATORS ON LEBESGUE SPACES Lu Shanzhen; Mo Huixia Acta mathematica scientia,Series B. 2009, 29 (1):  140-150.  DOI: 10.1016/S0252-9602(09)60014-X Abstract ( 912 )   RICH HTML PDF (180KB) ( 1192 )   Save Let L be the infinitesimal generator of an analytic semigroup on L2(Rn) with Gaussian kernel bounds, and L-α/2 be the fractional integrals generated by L for 0 < α< n. Let Tj,1 be the singular integral with nonsmooth kernel related to L, or Tj,1 = I, Tj,2, Tj,4 be the linear operators, which are bounded on Lp(Rn) for 1 < p < 1, and Tj,3 = ±I(j = 1, 2, · · · , m), where I is the identity operator. For b ∈ L1loc(Rn), denote the Toeplitz-type operator by Θba f = ∑m j=1 (Tj,1MbIα Tj,2 + Tj,3MbIα Tj,4), where Mb is a multiplication operator. When b ∈Λβ(0 < < 1), the authors consider the boundedness of Θbα. Related Articles | Metrics

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ATOMIC DECOMPOSITION FOR B-VALUED R.V.SEQUENCE SPACES Li Yufan; Liu Peide Acta mathematica scientia,Series B. 2009, 29 (1):  151-159.  DOI: 10.1016/S0252-9602(09)60015-1 Abstract ( 789 )   RICH HTML PDF (165KB) ( 982 )   Save In this article, atomic decompositions and the duals of some B-valued r.v. se- quence spaces are investigated. The results show that it closely depends on the geometrical properties of the sequence that take values in. Related Articles | Metrics

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REMARKS ON JOHN DISKS Chu Yuming; Cheng Jinfa; Wang Gendi Acta mathematica scientia,Series B. 2009, 29 (1):  160-168.  DOI: 10.1016/S0252-9602(09)60016-3 Abstract ( 791 )   RICH HTML PDF (157KB) ( 921 )   Save Let D R2 be a Jordan domain, D* = R2 \ D, the exterior of D. In this article, the authors obtained the following results: (1) If D is a John disk, then D is an outer linearly locally connected domain; (2) If D* is a John disk, then D is an inner linearly locally connected domain; (3) A homeomorphism f : R2→ R2 is a quasiconformal mapping if and only if f(D) is a John disk for any John disk D R2; and (4) If D is a bounded quasidisk, then D is a John disk, and there exists an unbounded quasidisk which is not a John disk. Related Articles | Metrics

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NORMAL CRITERION FOR FAMILIES OF HOLOMORPHIC MAPS OF SEVERAL COMPLEX VARIABLES INTO PN(C) WITH MOVING HYPERSURFACES Tu Zhenhan; Cao Hongzhe Acta mathematica scientia,Series B. 2009, 29 (1):  169-175.  DOI: 10.1016/S0252-9602(09)60017-5 Abstract ( 1004 )   RICH HTML PDF (144KB) ( 1027 )   Save This article gives a normal criterion for families of holomorphic mappings of several complex variables into PN(C) for moving hypersurfaces in pointwise general position, related to an Eremenko’s theorem. Related Articles | Metrics

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ISOTROPIC WEYL MANIFOLD WITH A SEMI-SYMMETRIC CONNECTION Elif Özkara Canfes Acta mathematica scientia,Series B. 2009, 29 (1):  176-180.  DOI: 10.1016/S0252-9602(09)60018-7 Abstract ( 849 )   RICH HTML PDF (113KB) ( 1581 )   Save In this work, it is proved that every isotropic Weyl manifold with a semi- symmetric connection is locally conformal to an Einstein manifold with a semi-symmetric connection. Related Articles | Metrics

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RAZUMIKHIN-TYPE THEOREMS OF NEUTRAL STOCHASTIC FUNCTIONAL DIFFERENTIAL EQUATIONS Zhou Shaobo; Hu Shigeng Acta mathematica scientia,Series B. 2009, 29 (1):  181-190.  DOI: 10.1016/S0252-9602(09)60019-9 Abstract ( 949 )   RICH HTML PDF (164KB) ( 1579 )   Save The stability of stochastic functional differential equation with Markovian switching was studied by several authors, but there was almost no work on the stability of the neutral stochastic functional differential equations with Markovian switching. The aim of this article is to close this gap. The authors establish Razumikhin-type theorem of the neutral stochastic functional differential equations with Markovian switching, and those without Markovian switching. Related Articles | Metrics

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GENERALIZED HILBERT OPERATOR AND FEJÉR-RIESZ TYPE INEQUALITIES ON THE#br# POLYDISC Li Songxiao; Stevo Stevic Acta mathematica scientia,Series B. 2009, 29 (1):  191-200.  DOI: 10.1016/S0252-9602(09)60020-5 Abstract ( 781 )   RICH HTML PDF (185KB) ( 1136 )   Save Let f be a holomorphic function on the unit polydisc Dn, with Taylor expan- sion f(z) = ∑∞|k|=0 akzk ≡ ∑∞k1+···+kn=0 ak1,···, knzk11· · · zknn where k = (k1, · · · , kn) ∈ Zn+. The authors define generalized Hilbert operator on Dn by Hγ,n(f)(z) =∑∞|k|=0 i1,···,in≥0 ai1,···,in Πnj=1Γ( γj + kj + 1)Γ(kj + ij + 1) /Γ(kj + 1)Γ(kj + ij +γj + 2)zk, where γ ∈ Cn, such that Rγj > -1, j = 1, 2, · · · , n. An upper bound for the norm of the operator on Hardy spaces Hp(Dn) is found. The authors also present a Fejér-Riesz type inequality on the weighted Bergman space on Dn and find an invariant space for the generalized Hilbert operator. Related Articles | Metrics

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AN INEQUALITY OF HOMOGENEOUS EXPANSION FOR BIHOLOMORPHIC QUASI-CONVEX MAPPINGS ON THE UNIT POLYDISK AND ITS APPLICATION Liu Xiaosong; Liu Taishun Acta mathematica scientia,Series B. 2009, 29 (1):  201-209.  DOI: 10.1016/S0252-9602(09)60021-7 Abstract ( 726 )   RICH HTML PDF (163KB) ( 1254 )   Save In this article, the authors obtain an inequality of homogeneous expansion for f, where f is a quasi-convex mapping (including quasi-convex mapping of type A and quasi-convex mapping of type B) defined on the open unit polydisk in Cn. Meanwhile, the authors also investigate its application. Related Articles | Metrics

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BOUNDARY BEHAVIOR OF CAUCHY-TYPE INTEGRALS IN CLIFFORD ANALYSIS Du Jinyuan; Xu Na; Zhang Zhongxiang Acta mathematica scientia,Series B. 2009, 29 (1):  210-224.  DOI: 10.1016/S0252-9602(09)60022-9 Abstract ( 802 )   RICH HTML PDF (209KB) ( 1553 )   Save In this article, the authors discussed the boundary behavior for the Cauchy- type integrals with values in a Clifford algebra, obtained some Sochocki–Plemelj formulae and Privalov–Muskhelishvili theorems for the Cauchy-type integral taken over a smooth surface by rather simple method. Related Articles | Metrics