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20 September 2010, Volume 30 Issue 5 Previous Issue    Next Issue

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TANGENT UNIT-VECTOR FIELDS: NONABELIAN HOMOTOPY INVARIANTS AND THE DIRICHLET ENERGY A. Majumdar, J.M. Robbins, M. Zyskin Acta mathematica scientia,Series B. 2010, 30 (5):  1357-1399.  DOI: 10.1016/S0252-9602(10)60131-2 Abstract ( 697 )   RICH HTML PDF (430KB) ( 1067 )   Save Let O be a closed geodesic polygon in S2.  Maps from O into S2 are said to satisfy tangent boundary conditions if the edges of O are mapped into the geodesics which contain them. Taking O to be an octant of S2, we compute the infimum Dirichlet energy ε(H) for continuous maps satisfying tangent boundary conditions of arbitrary homotopy type H. The expression for ε(H) involves a topological invariant -- the spelling length -- associated with the (non-abelian) fundamental group of the n-times punctured two-sphere, π1(S2 - s1, …, sn}, *). The lower bound for ε(H) is obtained from combinatorial group theory arguments, while the upper bound is obtained by constructing explicit representatives which, on all but an arbitrarily small subset of O, are alternatively locally conformal or anticonformal. For conformal and anticonformal classes (classes containing wholly conformal and anticonformal representatives respectively),  the expression for ε(H) reduces to a previous result involving the degrees of a set of regular values s1, …, sn in the target S2 space.  These degrees may be viewed as invariants associated with the abelianization of π1(S2 -{s1, …, sn}, *). For nonconformal classes, however, ε(H) may be strictly greater than the abelian bound.  This stems from the fact that, for nonconformal maps, the number of preimages of certain regular values may necessarily be strictly greater than the absolute value of their degrees. This work is motivated by the theoretical modelling of nematic liquid crystals in confined polyhedral geometries. The results imply new lower and upper bounds for the Dirichlet energy (one-constant Oseen-Frank energy) of reflection-symmetric tangent unit-vector fields in a rectangular prism. Related Articles | Metrics

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LEVITIN-POYAK WELL-POSEDNESS OF EQUILIBRIUM PROBLEMS GENERALIZED VECTOR WITH FUNCTIONAL CONSTRAINTS WANG Gang, HUANG Xue-Xiang, ZHANG Jie, CHEN Guang-Ya Acta mathematica scientia,Series B. 2010, 30 (5):  1400-1412.  DOI: 10.1016/S0252-9602(10)60132-4 Abstract ( 842 )   RICH HTML PDF (184KB) ( 1291 )   Save In this article, we study Levitin-Polyak type well-posedness for generalized vector equilibrium problems with abstract and functional constraints. Criteria and characterizations for these types of well-posednesses are given. References | Related Articles | Metrics

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REMARK ON THE BLOW-UP CRITERION OF STRONG SOLUTIONS TO THE NAVIER-STOKES EQUATIONS IN MULTIPLIER SPACES Sadek Gala Acta mathematica scientia,Series B. 2010, 30 (5):  1413-1418.  DOI: 10.1016/S0252-9602(10)60133-6 Abstract ( 823 )   RICH HTML PDF (142KB) ( 1055 )   Save In this note, we prove that Xr ( 0<r<1)  norm of the vorticity controls the blow-up phenomena of strong solutions to the Navier-Stokes equations in R3. References | Related Articles | Metrics

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DECOMPOSITION THEOREMS FOR Qp SPACES WITH SMALL SCALE p ON THE UNIT BALL OF Cn PENG Ru, OUYANG-Cai-Heng Acta mathematica scientia,Series B. 2010, 30 (5):  1419-1428.  DOI: 10.1016/S0252-9602(10)60134-8 Abstract ( 740 )   RICH HTML PDF (177KB) ( 1035 )   Save This article is devoted to studying the decomposition of functions of Qp spaces, which unify Bloch space and BMOA space in the scale of p. A decomposition theorem is established for Qp spaces with small scale p, n-1/ n <p ≤1 by means of p-Carleson measure and the Bergman metric on the unit ball of Cn. At the same time, a decomposition theorem for Qp, 0 spaces is given as well. References | Related Articles | Metrics

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OPTIMAL LOGISTICS FOR MULTIPLE JEEPS CHEN Wen-Lei, DING Yi-Ming, FAN Wen-Tao Acta mathematica scientia,Series B. 2010, 30 (5):  1429-1439.  DOI: 10.1016/S0252-9602(10)60135-X Abstract ( 659 )   RICH HTML PDF (172KB) ( 1122 )   Save We consider  variations of the classical jeep problems: the optimal logistics for a caravan of jeeps which travel together in the desert. The main purpose is to arrange the travels for the one-way trip and the round trip of a caravan of jeeps so that   the chief jeep visits  the farthest destination. Based on the dynamic program principle, the maximum distances for the caravan when only  part of the jeeps should return and when all drivers should return are obtained. Some related results such as the efficiency of the abandoned jeeps, and the advantages of more jeeps in the caravan are also presented. References | Related Articles | Metrics

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MARKOV SKELETON PROCESS IN PERT NETWORKS KONG Xiang-Xing, ZHANG Xuan, HOU Zhen-Ting Acta mathematica scientia,Series B. 2010, 30 (5):  1440-1448.  DOI: 10.1016/S0252-9602(10)60136-1 Abstract ( 705 )   RICH HTML PDF (161KB) ( 1108 )   Save In this article, we investigate Programming Evaluation and Review Technique networks with independently and generally distributed activity durations. For any path in this network, we select all the activities related to this path such that the completion time of the sub-network (only consisting of all the related activities) is equal to the completion time of this path. We use the elapsed time as the supplementary variables and model this sub-network as a Markov skeleton process, the state space is related to the sub-network structure. Then use the backward equation to compute the distribution of the sub-network's completion time, which is an important rule in project management and scheduling. References | Related Articles | Metrics

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ON A SUBCLASS OF CLOSE TO CONVEX FUNCTIONS PENG Zhi-Gang Acta mathematica scientia,Series B. 2010, 30 (5):  1449-1456.  DOI: 10.1016/S0252-9602(10)60137-3 Abstract ( 786 )   RICH HTML PDF (145KB) ( 1788 )   Save Let C'(α，β) be the class of functions f(z)=z+Σ∞n=2anzn analytic in D={z: |z|<1}, satisfying for some convex function g(z) with g(0)=g'(0)-1=0 and for all z in D the condition |{zf'(z)/{g(z) -1/zf'(z)/{g(z)}+(1-2α)|<β for some α，β(0≤α<1, 0<β≤1). A sharp coefficient estimate, distortion theorems and radius of convexity are determined for the class C'(α, β). The results extend the work of C. Selvaraj. References | Related Articles | Metrics

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GENERIC WARPED PRODUCT SUBMANIFOLDS %OF LOCALLY CONFORMAL KEAHLER MANIFOLDS Nargis Jamal??20Khalid Ali Khan, Viqar Azam Khan Acta mathematica scientia,Series B. 2010, 30 (5):  1457-1468.  DOI: S0252-9602(10)60138-5 Abstract ( 635 )   RICH HTML PDF (175KB) ( 1365 )   Save Warped product manifolds are known to have applications in physics. For instance, they provide an excellent setting to model space-time near a black hole or a massive star (cf. [9]). The studies on warped product manifolds with extrinsic geometric point of view were intensified after the B.Y. Chen's work on CR-warped product submanifolds of Kaehler manifolds (cf. [6], [7]). Later on, similar studies were carried out in the setting of l.c.K. manifolds and nearly Kaehler manifolds (cf. [3], [11]). In the present article, we investigate a larger class of warped product submanifolds of l.c.K. manifolds, ensure their existence by constructing an example of such manifolds and   obtain some important properties of these submanifolds. With regard to the CR-warped product submanifold, a special case of generic warped product submanifolds, we  obtain  a characterization under which a CR-submanifold is reducesd to a CR-warped product submanifold. References | Related Articles | Metrics

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REGULARITY OF WEAK SOLUTIONS TO MAGNETO-MICROPOLAR FLUID EQUATIONS YUAN Bao-Quan Acta mathematica scientia,Series B. 2010, 30 (5):  1469-1480.  DOI: 10.1016/S0252-9602(10)60139-7 Abstract ( 867 )   RICH HTML PDF (192KB) ( 1528 )   Save In this article, we study the regularity of weak solutions and the blow-up criteria for smooth solutions to the magneto-micropolar fluid equations in R3. We obtain the classical blow-up criteria for smooth solutions (u, ω,b), i.e., Lq(0,T; Lp(R3) )for 2/q+3/p≤1 with 3<p≤∞, u ∈ C([0, T); L3(R3)) or $\nabla u\in Lq(0, T; Lp) for 3/2< p ≤∞ satisfying 2/q+3/p≤2. Moreover, our results indicate that the regularity of weak solutions is dominated by the velocity u of the fluid. In the end-point case p=∞, the blow-up criteria can be extended to more general spaces $\nabla u\in L1(0, T;  B0∞, ∞ (R3)). References | Related Articles | Metrics

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ON THE EXPECTED DISCOUNTED PENALTY FUNCTION IN A MARKOV-DEPENDENT RISK MODEL WITH CONSTANT DIVIDEND BARRIER LIU Juan, XU Jian-Cheng, HU Yi-Jun Acta mathematica scientia,Series B. 2010, 30 (5):  1481-1491.  DOI: 10.1016/S0252-9602(10)60140-3 Abstract ( 799 )   RICH HTML PDF (181KB) ( 1552 )   Save This article considers a Markov-dependent risk model with a constant dividend barrier. A system of integro-differential equations with boundary conditions satisfied by the expected discounted penalty function, with given initial environment state, is derived and solved. Explicit formulas for the discounted penalty function are obtained when the initial surplus is zero or when all the claim amount distributions are from rational family. In two state model, numerical illustrations with exponential claim amounts are given. References | Related Articles | Metrics

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WEAK ORLICZ SPACE AND ITS CONVERGENCE THEOREMS LIU Ning, XIE Yong-Gang Acta mathematica scientia,Series B. 2010, 30 (5):  1492-1500.  DOI: 10.1016/S0252-9602(10)60141-5 Abstract ( 746 )   RICH HTML PDF (165KB) ( 1506 )   Save In this article, a class of weak Orlicz function spaces is defined and their basic properties are discused. In particular, for the sequences in weak Orlicz space, we establish several basic convergence theorems including bounded convergence theorem, control convergence theorem and Vitali-type convergence theorem and so on. Moreover, the conditional compactness of its subsets is also discussed. References | Related Articles | Metrics

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THE SCHUR HARMONIC CONVEXITY FOR A CLASS OF SYMMETRIC FUNCTIONS CHU Yu-Ming, SUN Tian-Chuan Acta mathematica scientia,Series B. 2010, 30 (5):  1501-1506.  DOI: 10.1016/S0252-9602(10)60142-7 Abstract ( 726 )   RICH HTML PDF (143KB) ( 1436 )   Save In this article, we prove that the symmetric function  Fn*(x, r)=∑i1+i2+…+in=r(x1i1x2i2…xnin )1/r is Schur harmonic convex for x ∈R+n and r ∈ N={1, 2, 3, …}. As its applications, some analytic inequalities are established. References | Related Articles | Metrics

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A RESULT OF SYSTEMS OF NONLINEAR COMPLEX ALGEBRAIC DIFFERENTIAL EQUATIONS GAO Ling-Yun Acta mathematica scientia,Series B. 2010, 30 (5):  1507-1513.  DOI: 10.1016/S0252-9602(10)60143-9 Abstract ( 750 )   RICH HTML PDF (142KB) ( 1219 )   Save In this article, we mainly investigate the behavior of systems of complex differential equations when we add some condition to the quality of the solutions, and obtain an interesting result, which  extends Gackstatter and Laine's result concerning complex differential equations to the systems of algebraic differential equations. References | Related Articles | Metrics

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IFS ON BOUNDARIES OF HOMOGENEOUS TREES: WQB CONDITION AND MULTIFRACTAC ANALYSIS LIU Hao, WEN Zhi-Xiong Acta mathematica scientia,Series B. 2010, 30 (5):  1514-1522.  DOI: 10.1016/S0252-9602(10)60144-0 Abstract ( 626 )   RICH HTML PDF (171KB) ( 980 )   Save We study, from the point of view of the multifractal analysis, iterated function systems on totally disconnected spaces, namely, the boundaries of homogeneous trees. In particular, we study in this setting the "weak quasi-Bernoulli'' property introduced by Testud [3, 4]. After projection on R or R2, we get new examples of self-similar measures which, being WQB, obey the multifractal formalism for positive q's. References | Related Articles | Metrics

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SOLUTIONS FOR THE QUASILINEAR ELLIPTIC PROBLEMS INVOLVING CRITICAL HARDY--SOBOLEV EXPONENTS KANG Dong-Sheng Acta mathematica scientia,Series B. 2010, 30 (5):  1529-1540.  DOI: 10.1016/S0252-9602(10)60146-4 Abstract ( 1358 )   RICH HTML PDF (187KB) ( 1232 )   Save In this article,  we study  the quasilinear  elliptic problem involving critical Hardy--Sobolev exponents and Hardy  terms. By  variational methods and analytic techniques, we obtain  the existence of sign--changing solutions to the problem. References | Related Articles | Metrics

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OPTIMAL INTERIOR PARTIAL REGULARITY FOR NONLINEAR ELLIPTIC SYSTEMS WITH DINI CONTINUOUS COEFFICIENTS QIU Ya-Lin, TAN Zhong Acta mathematica scientia,Series B. 2010, 30 (5):  1541-1554.  DOI: 10.1016/S0252-9602(10)60147-6 Abstract ( 877 )   RICH HTML PDF (202KB) ( 1137 )   Save In this article, we consider nonlinear elliptic systems of divergence type with Dini continuous coefficients. The authors use a new method introduced by Duzaar and Grotowski, to prove partial regularity for weak solutions, based on a generalization of the technique of harmonic approximation and directly establish the optimal H\"{o}lder exponent for the derivative of a weak solution on its regular set. References | Related Articles | Metrics

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ELLIPTIC GRADIENT ESTIMATES FOR DIFFUSION OPERATORS ON COMPLETE RIEMANNIAN MANIFOLDS JIAN Bin Acta mathematica scientia,Series B. 2010, 30 (5):  1555-1560.  DOI: 10.1016/S0252-9602(10)60148-8 Abstract ( 761 )   RICH HTML PDF (139KB) ( 1231 )   Save In this note, we obtain the elliptic estimate for diffusion operator L = Δ + \nabla\phi\cdot\nabla$ on complete, noncompact Riemannian manifolds, under the curvature condition CD(K, m), which generalizes B. L. Kotschwar's work [5].  As an application, we get estimate on the heat kernel. The Bernstein-type gradient estimate for Schr\"odinger-type gradient is also derived. References | Related Articles | Metrics

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REMARK ON CRITICAL SPEED OF TRAVELING WAVEFRONTS FOR NICHOLSON'S BLOWFLIES EQUATION WITH DIFFUSION WEI De, WU Jiao-Yu, MEI Ming Acta mathematica scientia,Series B. 2010, 30 (5):  1561-1566.  DOI: 10.1016/S0252-9602(10)60149-X Abstract ( 667 )   RICH HTML PDF (140KB) ( 1057 )   Save This note is devoted to the study on the traveling wavefronts to the Nicholson's blowflies equation with diffusion, a time-delayed reaction-diffusion equation. For the critical speed of traveling waves, we give a detailed analysis on its location and asymptotic behavior with respect to the mature age. References | Related Articles | Metrics

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SOLUTIONS TO |A SECOND-ORDER MULTI-POINT |BOUNDARY VALUE PROBLEM |AT RESONANCE DU Zeng-Ji, MENG Fan-Chao Acta mathematica scientia,Series B. 2010, 30 (5):  1567-1576.  DOI: 10.1016/S0252-9602(10)60150-6 Abstract ( 641 )   RICH HTML PDF (169KB) ( 1229 )   Save This article deals with the following second-order multi-point boundary value problem $$x''(t)=f(t, x(t), x'(t))+e(t), \ \ \ t\in (0,1), $$ $$x'(0)=\sum\limits_{i=1}^{m}\alpha_{i}x'(\xi_{i}), \ \ \ x(1)=\sum\limits_{j=1}^{n}\beta_{j}x(\eta_{j}). $$ Under the resonance conditions $\sum\limits_{i=1}^{m}\alpha_{i}=1, sum\limits_{j=1}^{n}\beta_{j}=1, \sum\limits_{j=1}^{n}\beta_{j}\eta_{j}=1$ , by applying the coincidence degree theory, some existence results of the problem are established. The emphasis here is that the dimension of the linear operator is two. In this paper, we extend and improve some previously known results like the ones in the references. References | Related Articles | Metrics

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POSITIVE SOLUTIONS FOR WEAKLY COUPLED NONLINEAR ELLIPTIC SYSTEMS LONG Jing, YANG Jian-Fu Acta mathematica scientia,Series B. 2010, 30 (5):  1577-1592.  DOI: 10.1016/S0252-9602(10)60151-8 Abstract ( 715 )   RICH HTML Save In this article, we consider the existence of positive solutions for weakly coupled nonlinear elliptic systems $$\left\{ \begin{array}{ll}-\Delta u+u=(1+a(x))|u|^{p-1}u+\mu|u|^{\alpha-2}u|v|^\beta+\lambda v \quad & \rm{in}\ {\Bbb R}^N,\\ -\Delta v+v=(1+b(x))|v|^{p-1}v+\mu|u|^\alpha|v|^{\beta-2}v+\lambda u & \rm{in} \ {\Bbb R}^N. \end{array} \right.\eqno(0.1)$$ To find nontrivial solutions, we first investigate autonomous systems. In this case, results of bifurcation from semi-trivial solutions are obtained by the implicit function theorem. Next, the existence of positive solutions of problem (0.1) is obtained by variational methods. References | Related Articles | Metrics

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CONTROLLABILITY FOR A PARABOLIC EQUATION WITH A NONLINEAR TERM INVOLVING THE STATE AND THE GRADIENT XU You-Jun, LIU Zhen-Hai Acta mathematica scientia,Series B. 2010, 30 (5):  1593-1604.  DOI: 10.1016/S0252-9602(10)60152-X Abstract ( 709 )   RICH HTML PDF (191KB) ( 1142 )   Save In this article, we consider the controllability of a quasi-linear heat equation involving gradient terms with Dirichlet boundary conditions in a bounded domain of RN. The results are established by using the variational methods, the related duality theory and Kakutani Fixed-point Theorem. References | Related Articles | Metrics

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MODERATE DEVIATIONS FOR THE BESSEL CLOCK WANG Yan-Qing, JIANG Hui Acta mathematica scientia,Series B. 2010, 30 (5):  1605-1613.  DOI: 10.1016/S0252-9602(10)60153-1 Abstract ( 788 )   RICH HTML PDF (178KB) ( 1033 )   Save By the method of change measures, the moderate deviations for the Bessel clock ∫t0ds/Xs(ν) is studied, where (Xt(ν), t ≥ 0) is a squared Bessel process with index ν>0. The rate function can be given explicitly. Furthermore, the functional moderate deviations for the Bessel clock are obtained. References | Related Articles | Metrics

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GRADIENT ESTIMATES FOR POSITIVE SMOOTH f-HARMONIC FUNCTIONS CHEN Li, CHEN Wen-Yi Acta mathematica scientia,Series B. 2010, 30 (5):  1614-1618.  DOI: 10.1016/S0252-9602(10)60154-3 Abstract ( 722 )   RICH HTML PDF (124KB) ( 1587 )   Save For Riemannian manifolds with a measure, we study the gradient estimates for positive smooth f-harmonic functions when the ∞-Bakry-Emery Ricci tensor and Ricci tensor are bounded from below, generalizing the classical ones of Yau (i.e., when f is constant). References | Related Articles | Metrics

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BOUNDEDNESS FROM BELOW OF MULTIPLICATION OPERATORS BETWEEN α-BLOCH SPACES ON THE UNIT BALL ZHANG Min-Zhu Acta mathematica scientia,Series B. 2010, 30 (5):  1619-1630.  DOI: 10.1016/S0252-9602(10)60155-5 Abstract ( 702 )   RICH HTML PDF (188KB) ( 1060 )   Save In this article,  we characterize the boundedness from below of multiplication operators between α-Bloch spaces on the unit ball. References | Related Articles | Metrics

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ON THE EXISTENCE OF SINGULAR DIRECTIONS OF HOLOMORPHIC MAPS FROM THE UNIT DISK INTO Pn(C) TU Zhen-Han, ZHANG Sha-Sha Acta mathematica scientia,Series B. 2010, 30 (5):  1631-1639.  DOI: 10.1016/S0252-9602(10)60156-7 Abstract ( 992 )   RICH HTML PDF (177KB) ( 900 )   Save This article proves the existence of Julia directions of value distribution of holomorphic mapping f from the unit disk into the n-dimensional complex projective space Pn(C) under the assumption limits_{r\rightarrow 1^{-}} T(r, f)/ log 1/1-r= +∞ for hypersurfaces in general position. A heuristic principle concerning the existence of Julia directions of holomorphic mappings from the unit disk into Pn(C) is given also. References | Related Articles | Metrics

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CONVERGENCE AND GROWTH OF MULTIPLE DIRICHLET SERIES LIANG Mei-Li, GAO Zong-Sheng Acta mathematica scientia,Series B. 2010, 30 (5):  1640-1648.  DOI: 10.1016/S0252-9602(10)60157-9 Abstract ( 719 )   RICH HTML PDF (162KB) ( 1215 )   Save This article investigates the convergence and growth of multiple Dirichlet series. The Valiron formula of Dirichlet series is extended to n-tuple Dirichlet series and an equivalence relation between the order of n-tuple Dirichlet series and its coefficients and exponents is obtained. References | Related Articles | Metrics

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ON SOME RESULTS OF YI AND THEIR APPLICATIONS IN THE FUNCTIONAL EQUATIONS YANG Lian-Zhong, ZHANG Ji-Long Acta mathematica scientia,Series B. 2010, 30 (5):  1649-1660.  DOI: 10.1016/S0252-9602(10)60158-0 Abstract ( 886 )   RICH HTML PDF (171KB) ( 1362 )   Save In this article, we  establish some uniqueness theorems  that improves some results of H. X. Yi for a family of meromorphic functions, and as applications, we give some results about the non-existence of meromorphic solutions of Fermat type functional equations. References | Related Articles | Metrics

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DISTORTION THEOREMS FOR BLOCH MAPPINGS ON THE UNIT POLYDISC Dn WANG Jian-Fei, LIU Ta-Shun, TANG Xiao-Min Acta mathematica scientia,Series B. 2010, 30 (5):  1661-1668.  DOI: 10.1016/S0252-9602(10)60159-2 Abstract ( 730 )   RICH HTML PDF (164KB) ( 1032 )   Save In this article, we establish distortion theorems for some various subfamilies of Bloch mappings defined in the unit polydisc Dn with critical points, which extend the results of Liu and Minda to higher dimensions. We obtain lower bounds of |det (f'(z))| and R det (f'(z)) for Bloch mapping f. As an application, some lower and upper bounds of Bloch constants for the subfamilies of holomorphic mappings are given. References | Related Articles | Metrics

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THE BRANCHING CHAIN WITH DRIFT IN SPACE-TIME RANDOM ENVIRONMENT (I): MODEL, MARKOV PROPERTY, MOMENTS HU Di-He, HU Xiao-Yu Acta mathematica scientia,Series B. 2010, 30 (5):  1669-1678.  DOI: 10.1016/S0252-9602(10)60160-9 Abstract ( 641 )   RICH HTML PDF (175KB) ( 966 )   Save There are three parts in this article. In Section 1, we establish the model of branching chain with drift in space-time random environment (BCDSTRE),  i.e.,  the coupling of branching chain and random walk. In Section 2,  we prove that any BCDSTRE must be a Markov chain in time random environment when we consider the distribution of the particles in space as a random element. In Section 3,  we calculate the first-order moments and the second-order moments of BCDSTRE. References | Related Articles | Metrics

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CAUCHY PROBLEM FOR A |PARABOLIC EQUATION WITH NON-DIVERGENCE FORM ZHOU Wen-Shu, YAO Zheng-An Acta mathematica scientia,Series B. 2010, 30 (5):  1679-1686.  DOI: 10.1016/S0252-9602(10)60161-0 Abstract ( 912 )   RICH HTML PDF (151KB) ( 1282 )   Save In this article, it is shown that there exists a unique viscosity solution of the Cauchy problem for a degenerate parabolic equation with non-divergence form. References | Related Articles | Metrics

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SHARED VALUE IN A FINITE-DIMENSIONAL BANACH MANIFOLD J.M. Soriano Acta mathematica scientia,Series B. 2010, 30 (5):  1687-1695.  DOI: 10.1016/S0252-9602(10)60162-2 Abstract ( 779 )   RICH HTML PDF (155KB) ( 834 )   Save Sufficient conditions are given to assert that two C1-mappings share only one value in a connected compact Banach manifold modelled over  Rn. The proof of the result, which is based upon continuation methods, is constructive. References | Related Articles | Metrics

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ASYMPTOTIC BEHAVIOR FOR RANDOM WALK IN RANDOM |ENVIRONMENT WITH HOLDING TIMES MAO Ming-Zhi, LI Zhi-Min Acta mathematica scientia,Series B. 2010, 30 (5):  1696-1708.  DOI: 10.1016/S0252-9602(10)60163-4 Abstract ( 614 )   RICH HTML PDF (197KB) ( 1121 )   Save In this article, we mainly discuss the asymptotic behavior for multi-dimensional continuous-time random walk in random environment with holding times. By constructing a renewal structure and using the point "environment viewed from the particle'', under General Kalikow's Condition, we show the law of large numbers (LLN) and central limit theorem (CLT) for the escape speed of random walk. References | Related Articles | Metrics

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HYPERCYCLIC OPERATORS ON QUASI-MAZUR SPACES QIU Jing-Hui Acta mathematica scientia,Series B. 2010, 30 (5):  1709-1720.  DOI: 10.1016/S0252-9602(10)60164-6 Abstract ( 668 )   RICH HTML PDF (191KB) ( 1057 )   Save Modifying the method of Ansari, we give some criteria for hypercyclicity of quasi-Mazur spaces. They can be applied to judging hypercyclicity of non-complete and non-metrizable locally convex spaces. For some special locally convex spaces, for example, K\"{o}the (LF)-sequence spaces and countable inductive limits of quasi-Mazur spaces, we investigate their hypercyclicity. As we see, bounded biorthogonal systems play an important role in the construction of Ansari. Moreover, we obtain characteristic conditions respectively for locally convex spaces having  bounded sequences with dense linear spans and for locally convex spaces  having bounded absorbing sets, which are useful in judging the existence of bounded biorthogonal systems. References | Related Articles | Metrics

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THE REGULARITY OF THE FREE BOUNDARY FOR |STRIKE RESET OPTION YANG Zhou Acta mathematica scientia,Series B. 2010, 30 (5):  1721-1729.  DOI: 10.1016/S0252-9602(10)60165-8 Abstract ( 653 )   RICH HTML PDF (164KB) ( 920 )   Save A strike reset option is an option that allows its holder to reset the strike price to the prevailing underlying asset price at a moment chosen by the holder. The pricing model of the option can be formulated as a parabolic variational inequality and the optimal reset strategy is the free boundary. The smoothness of the free boundary in some cases was  showed in our article published in JDE. We would prove its smoothness in the other case in this paper by a generalized comparison principle for the variational inequality. References | Related Articles | Metrics

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ON THE RENEWAL RISK MODEL WITH INTEREST AND DIVIDEND FANG Ying, WU Rong Acta mathematica scientia,Series B. 2010, 30 (5):  1730-1738.  DOI: 10.1016/S0252-9602(10)60166-X Abstract ( 667 )   RICH HTML PDF (164KB) ( 1141 )   Save We consider that the reserve of an insurance company follows a renewal risk process with interest and dividend. For this risk process, we derive integral equations and exact infinite series expressions for the Gerber-Shiu discounted penalty function. Then we give lower and upper bounds for the ruin probability. Finally, we present exact expressions for the ruin probability in a special case of renewal risk processes. References | Related Articles | Metrics

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CONFORMAL AND GENERALIZED CONCIRCULAR MAPPINGS OF EINSTEIN-WEYL MANIFOLDS Abdulkadir ?zdeger Acta mathematica scientia,Series B. 2010, 30 (5):  1739-1745.  DOI: 10.1016/S0252-9602(10)60167-1 Abstract ( 816 )   RICH HTML PDF (139KB) ( 2104 )   Save In this article, after giving a necessary and sufficient condition for two Einstein-Weyl manifolds to be in conformal correspondence, we prove that any conformal mapping between such manifolds is generalized concircular if and only if the covector  field of the conformal mapping is locally a gradient. Using this fact we deduce that any conformal mapping between two isotropic Weyl manifolds is a generalized concircular mapping. Moreover, it is shown that a generalized concircularly flat Weyl manifold is generalized concircular to an Einstein manifold and that its scalar curvature is prolonged covariant constant. References | Related Articles | Metrics

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THE JUMPING PHENOMENON OF THE DIMENSIONS OF COHOMOLOGY GROUPS OF TANGENT SHEAF YE Xuan-Ming Acta mathematica scientia,Series B. 2010, 30 (5):  1746-1758.  DOI: 10.1016/S0252-9602(10)60168-3 Abstract ( 645 )   RICH HTML PDF (206KB) ( 1314 )   Save Let X be a compact complex manifold. Consider a small deformation π: χ→ B of X, the dimensions of the cohomology groups of tangent sheaf H q(Xt, TXt) may vary under this deformation. This article  studies such phenomena by studying the obstructions to deform a class in H q(X, TX) with parameter t and gets a formula for the obstructions. References | Related Articles | Metrics

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HAZARD REGRESSION WITH PENALIZED SPLINE: THE SMOOTHING PARAMETER CHOICE AND ASYMPTOTICS TONG Xing-Wei, HU Tao, CUI Heng-Jian Acta mathematica scientia,Series B. 2010, 30 (5):  1759-1768.  DOI: 10.1016/S0252-9602(10)60169-5 Abstract ( 756 )   RICH HTML PDF (185KB) ( 1589 )   Save In this article,  we  use penalized spline to estimate  the hazard function from a set of censored failure time data. A new approach to estimate the amount of smoothing is provided. Under regularity conditions we establish the consistency and the asymptotic normality of  the penalized likelihood estimators. Numerical studies and an  example are conducted to evaluate the performances of the new procedure. References | Related Articles | Metrics

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TOWERS OF DERIVATION FOR LIE RINGS AND SOME RESULTS ON COMPLETE LIE RINGS LIAO Jun, ZHENG Da-Bin, LIU He-Guo Acta mathematica scientia,Series B. 2010, 30 (5):  1769-1775.  DOI: 10.1016/S0252-9602(10)60170-1 Abstract ( 616 )   RICH HTML PDF (156KB) ( 937 )   Save The well-known tower theorem of groups (resp. Lie algebras) shows that the tower of automorphism groups (resp. derivation algebras) of a finite group (resp. a finite dimensional Lie algebra) with trivial center terminates after finitely many steps. We generalize these results for Lie rings, and present some necessary and sufficient conditions for Lie rings to be complete. References | Related Articles | Metrics

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ON UNIQUE CONTINUATION PROPERTIES FOR THE SUB-LAPLACIAN ON |CARNOT GROUPS NIU Peng-Cheng, WANG Jia-Lin Acta mathematica scientia,Series B. 2010, 30 (5):  1776-1784.  DOI: 10.1016/S0252-9602(10)60171-3 Abstract ( 681 )   RICH HTML PDF (164KB) ( 1233 )   Save In this article, authors begin with establishing representation formulas and properties for functions on Carnot groups. Then, some unique continuation results to solutions of sub-Laplace equations with potentials are proved. References | Related Articles | Metrics

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HIGHER ORDER SINGULAR INTEGRAL EQUATIONS ON COMPLEX HYPERSPHERE CHEN Lv-Ping, ZHONG Tong-De Acta mathematica scientia,Series B. 2010, 30 (5):  1785-1792.  DOI: 10.1016/S0252-9602(10)60172-5 Abstract ( 666 )   RICH HTML PDF (156KB) ( 989 )   Save A theory of a class of higher order singular integral under the operator (Lf)(u)=1/u1[u1 ∂f}/ ∂u1 (u)-u1 ∂f/ ∂u1 (u)+f(u)] is given. We transform the higher order singular integral to a usual Cauchy integral, extend the permutation formula of the higher order singular integral deduced by Qian and Zhong in [4] to a general case, and discuss the regularization problem of the higher order singular integral equations with Cauchy kernel and variable coefficients on complex hypersphere. References | Related Articles | Metrics

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GLOBAL EXISTENCE AND BLOW-UP OF SOLUTIONS FOR GENERALIZED POCHHAMMER-CHREE EQUATIONS XU Run-Zhang, LIU YA-Cheng Acta mathematica scientia,Series B. 2010, 30 (5):  1793-1807.  DOI: 10.1016/S0252-9602(10)60173-7 Abstract ( 860 )   RICH HTML PDF (200KB) ( 1383 )   Save In this article, we study the initial boundary value problem of generalized Pochhammer-Chree equation utt-uxx-uxxt-uxxtt=f(u)xx, x ∈Ω, t >0, u(x, 0)=u0(x), ut(x, 0)=u1(x), x ∈Ω, u(0, t)=u(1, t)=0, t ≥0, where Ω =(0, 1). First, we obtain the existence of local Wk, p solutions. Then, we prove that, if f(s) ∈ in Ck+1(R) is ondecreasing, f(0)=0 and |f(u)| ≤ C1|u| ∫0uf(s)ds + C2, u0(x), u1(x) ∈Wk, p(Ω) ∩ W0{1, p}(Ω), k ≥1, 1< p ≤∞, then for any T>0 the problem admits a unique solution u(x, t) ∈ W2, ∞ (0, T; Wk, p(Ω)∩W01, p(Ω) ). Finally, the finite time blow-up of solutions and global Wk, p solution of generalized IMBq equations are discussed. References | Related Articles | Metrics

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QUANTUM COMPLEXITY OF THE APPROXIMATION FOR THE CLASSES Β(Wpr([0, 1]d)) AND Β(Hpr([0, 1]d)) YE Pei-Xin, HU Xiao-Fei Acta mathematica scientia,Series B. 2010, 30 (5):  1808-1818.  DOI: 10.1016/S0252-9602(10)60174-9 Abstract ( 670 )   RICH HTML PDF (195KB) ( 1006 )   Save We study the approximation of functions from anisotropic Sobolev classes B(Wpr}([0, 1]d)) and H\"{o}lder-Nikolskii classes B(Hpr}([0, 1]d)) in the Lq([0, 1]d) norm with q ≤ p in the quantum  model of computation. We determine the quantum query complexity of this problem up to logarithmic factors. It shows that the quantum algorithms are  significantly better  than the classical deterministic or randomized algorithms. References | Related Articles | Metrics

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MULTI-DIMENSIONAL REFLECTED BACKWARD STOCHASTIC DIFFERENTIAL EQUATIONS AND THE COMPARISON THEOREM WU Zhen, XIAO Hua Acta mathematica scientia,Series B. 2010, 30 (5):  1819-1836.  DOI: 10.1016/S0252-9602(10)60175-0 Abstract ( 875 )   RICH HTML PDF (216KB) ( 1739 )   Save In this article, we study the multi-dimensional reflected backward stochastic differential equations. The existence and uniqueness result of the solution for this kind of equation is proved by the fixed point argument where  every element of the solution is forced to stay above the  given stochastic process, i.e., multi-dimensional obstacle, respectively. We also give a kind of multi-dimensional comparison theorem for the reflected BSDE and then use it  as the tool to prove an existence result for the multi-dimensional reflected BSDE where the coefficient is continuous and has linear growth. References | Related Articles | Metrics