数学物理学报(英文版)

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TANGENT UNIT-VECTOR FIELDS: NONABELIAN HOMOTOPY INVARIANTS AND THE DIRICHLET ENERGY

A. Majumdar, J.M. Robbins, M. Zyskin

数学物理学报(英文版). 2010 (5): 1357-1399. DOI: 10.1016/S0252-9602(10)60131-2

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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, …, s_n}, *). 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, …, s_n in the target S² space. These degrees may be viewed as invariants associated with the abelianization of π₁(S² -{s₁, …, s_n}, *). 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.

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LEVITIN-POYAK WELL-POSEDNESS OF EQUILIBRIUM PROBLEMS GENERALIZED VECTOR WITH FUNCTIONAL CONSTRAINTS

王刚, 黄学祥, 张杰, 陈光亚

数学物理学报(英文版). 2010 (5): 1400-1412. DOI: 10.1016/S0252-9602(10)60132-4

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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.

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REMARK ON THE BLOW-UP CRITERION OF STRONG SOLUTIONS TO THE NAVIER-STOKES EQUATIONS IN MULTIPLIER SPACES

Sadek Gala

数学物理学报(英文版). 2010 (5): 1413-1418. DOI: 10.1016/S0252-9602(10)60133-6

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In this note, we prove that X_r ( 0<r<1) norm of the vorticity controls the blow-up phenomena of strong solutions to the Navier-Stokes equations in R³.

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DECOMPOSITION THEOREMS FOR Q_p SPACES WITH SMALL SCALE p ON THE UNIT BALL OF Cⁿ

彭茹, 欧阳才衡

数学物理学报(英文版). 2010 (5): 1419-1428. DOI: 10.1016/S0252-9602(10)60134-8

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This article is devoted to studying the decomposition of functions of Q_p spaces, which unify Bloch space and BMOA space in the scale of p. A decomposition theorem is established for Q_pspaces 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 Q_p_{, 0} spaces is given as well.

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OPTIMAL LOGISTICS FOR MULTIPLE JEEPS

陈文磊, 丁义明, 范文涛

数学物理学报(英文版). 2010 (5): 1429-1439. DOI: 10.1016/S0252-9602(10)60135-X

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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.

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MARKOV SKELETON PROCESS IN PERT NETWORKS

孔祥星, 张玄, 侯振挺

数学物理学报(英文版). 2010 (5): 1440-1448. DOI: 10.1016/S0252-9602(10)60136-1

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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.

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ON A SUBCLASS OF CLOSE TO CONVEX FUNCTIONS

彭志刚

数学物理学报(英文版). 2010 (5): 1449-1456. DOI: 10.1016/S0252-9602(10)60137-3

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Let C'(α，β) be the class of functions f(z)=z+Σ^∞_n=2a_nz_n 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.

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GENERIC WARPED PRODUCT SUBMANIFOLDS %OF LOCALLY CONFORMAL KEAHLER MANIFOLDS

Nargis Jamal??20Khalid Ali Khan, Viqar Azam Khan

数学物理学报(英文版). 2010 (5): 1457-1468. DOI: S0252-9602(10)60138-5

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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.

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REGULARITY OF WEAK SOLUTIONS TO MAGNETO-MICROPOLAR FLUID EQUATIONS

原保全

数学物理学报(英文版). 2010 (5): 1469-1480. DOI: 10.1016/S0252-9602(10)60139-7

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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., L^q(0,T; L^p(R³) )for 2/q+3/p≤1 with 3<p≤∞, u ∈ C([0, T); L³(R³)) or $\nabla u\in L^q(0, T; L^p) 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)).

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ON THE EXPECTED DISCOUNTED PENALTY FUNCTION IN A MARKOV-DEPENDENT RISK MODEL WITH CONSTANT DIVIDEND BARRIER

刘娟, 徐建成, 胡亦钧

数学物理学报(英文版). 2010 (5): 1481-1491. DOI: 10.1016/S0252-9602(10)60140-3

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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.

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WEAK ORLICZ SPACE AND ITS CONVERGENCE THEOREMS

刘宁, 叶永刚

数学物理学报(英文版). 2010 (5): 1492-1500. DOI: 10.1016/S0252-9602(10)60141-5

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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.

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THE SCHUR HARMONIC CONVEXITY FOR A CLASS OF SYMMETRIC FUNCTIONS

褚玉明, 孙天川

数学物理学报(英文版). 2010 (5): 1501-1506. DOI: 10.1016/S0252-9602(10)60142-7

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In this article, we prove that the symmetric function
F_n*(x, r)=∑_{i1+i2+…+in=}_r(x₁^i₁x₂^i₂…x_n^i_n )^1/r is Schur harmonic convex for x ∈R₊ⁿ and r ∈ N={1, 2, 3, …}. As its applications, some analytic inequalities are established.

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A RESULT OF SYSTEMS OF NONLINEAR COMPLEX ALGEBRAIC DIFFERENTIAL EQUATIONS

高凌云

数学物理学报(英文版). 2010 (5): 1507-1513. DOI: 10.1016/S0252-9602(10)60143-9

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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.

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IFS ON BOUNDARIES OF HOMOGENEOUS TREES: WQB CONDITION AND MULTIFRACTAC ANALYSIS

刘浩, 文志雄

数学物理学报(英文版). 2010 (5): 1514-1522. DOI: 10.1016/S0252-9602(10)60144-0

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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.

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STABILITY OF THE LCD MODEL

侯振挺, 谭利, 史定华

数学物理学报(英文版). 2010 (5): 1523-1528. DOI: 10.1016/S0252-9602(10)60145-2

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The growing network model with loops and multiple edges proposed by Bollobás et al. (Random Structures and Algorithms 18(2001))
is restudied from another perspective. Based on the first-passage probability of Markov chains, we prove that the degree distribution of the LCD model is power-law with degree exponent 3 as the network size grows to infinity.

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SOLUTIONS FOR THE QUASILINEAR ELLIPTIC PROBLEMS INVOLVING CRITICAL HARDY--SOBOLEV EXPONENTS

康东升

数学物理学报(英文版). 2010 (5): 1529-1540. DOI: 10.1016/S0252-9602(10)60146-4

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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.

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OPTIMAL INTERIOR PARTIAL REGULARITY FOR NONLINEAR ELLIPTIC SYSTEMS WITH DINI CONTINUOUS COEFFICIENTS

邱亚林, 谭忠

数学物理学报(英文版). 2010 (5): 1541-1554. DOI: 10.1016/S0252-9602(10)60147-6

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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.

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ELLIPTIC GRADIENT ESTIMATES FOR DIFFUSION OPERATORS ON COMPLETE RIEMANNIAN MANIFOLDS

钱斌

数学物理学报(英文版). 2010 (5): 1555-1560. DOI: 10.1016/S0252-9602(10)60148-8

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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.

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REMARK ON CRITICAL SPEED OF TRAVELING WAVEFRONTS FOR NICHOLSON'S BLOWFLIES EQUATION WITH DIFFUSION

危地, 吴教育, 梅茗

数学物理学报(英文版). 2010 (5): 1561-1566. DOI: 10.1016/S0252-9602(10)60149-X

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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.

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SOLUTIONS TO |A SECOND-ORDER MULTI-POINT |BOUNDARY VALUE PROBLEM |AT RESONANCE

杜增吉, 孟凡超

数学物理学报(英文版). 2010 (5): 1567-1576. DOI: 10.1016/S0252-9602(10)60150-6

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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.

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POSITIVE SOLUTIONS FOR WEAKLY COUPLED NONLINEAR ELLIPTIC SYSTEMS

龙静, 杨健夫

数学物理学报(英文版). 2010 (5): 1577-1592. DOI: 10.1016/S0252-9602(10)60151-8

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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.

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CONTROLLABILITY FOR A PARABOLIC EQUATION WITH A NONLINEAR TERM INVOLVING THE STATE AND THE GRADIENT

许友军, 刘振海

数学物理学报(英文版). 2010 (5): 1593-1604. DOI: 10.1016/S0252-9602(10)60152-X

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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 R^N. The results are established by using the variational methods, the related duality theory and Kakutani
Fixed-point Theorem.

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MODERATE DEVIATIONS FOR THE BESSEL CLOCK

王艳清, 蒋辉

数学物理学报(英文版). 2010 (5): 1605-1613. DOI: 10.1016/S0252-9602(10)60153-1

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By the method of change measures, the moderate deviations for the Bessel clock ∫^t₀ds/X_s^(ν) is studied, where (X_t^(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.

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GRADIENT ESTIMATES FOR POSITIVE SMOOTH f-HARMONIC FUNCTIONS

陈立, 陈文艺

数学物理学报(英文版). 2010 (5): 1614-1618. DOI: 10.1016/S0252-9602(10)60154-3

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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).

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BOUNDEDNESS FROM BELOW OF MULTIPLICATION OPERATORS BETWEEN α-BLOCH SPACES ON THE UNIT BALL

张敏珠

数学物理学报(英文版). 2010 (5): 1619-1630. DOI: 10.1016/S0252-9602(10)60155-5

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In this article, we characterize the boundedness from below of multiplication operators between α-Bloch spaces on the unit ball.

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ON THE EXISTENCE OF SINGULAR DIRECTIONS OF HOLOMORPHIC MAPS FROM THE UNIT DISK INTO Pⁿ(C)

涂振汉, 张莎莎

数学物理学报(英文版). 2010 (5): 1631-1639. DOI: 10.1016/S0252-9602(10)60156-7

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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.

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CONVERGENCE AND GROWTH OF MULTIPLE DIRICHLET SERIES

梁美丽, 高宗升

数学物理学报(英文版). 2010 (5): 1640-1648. DOI: 10.1016/S0252-9602(10)60157-9

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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.

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ON SOME RESULTS OF YI AND THEIR APPLICATIONS IN THE FUNCTIONAL EQUATIONS

杨连中, 张继龙

数学物理学报(英文版). 2010 (5): 1649-1660. DOI: 10.1016/S0252-9602(10)60158-0

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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.

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DISTORTION THEOREMS FOR BLOCH MAPPINGS ON THE UNIT POLYDISC Dⁿ

王建飞, 刘太顺, 唐笑敏

数学物理学报(英文版). 2010 (5): 1661-1668. DOI: 10.1016/S0252-9602(10)60159-2

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In this article, we establish distortion theorems for some various subfamilies of Bloch mappings defined in the unit polydisc Dⁿwith 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.

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THE BRANCHING CHAIN WITH DRIFT IN SPACE-TIME RANDOM ENVIRONMENT (I): MODEL, MARKOV PROPERTY, MOMENTS

胡迪鹤, 胡晓予

数学物理学报(英文版). 2010 (5): 1669-1678. DOI: 10.1016/S0252-9602(10)60160-9

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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.

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CAUCHY PROBLEM FOR A |PARABOLIC EQUATION WITH NON-DIVERGENCE FORM

周文书, 姚正安

数学物理学报(英文版). 2010 (5): 1679-1686. DOI: 10.1016/S0252-9602(10)60161-0

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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.

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SHARED VALUE IN A FINITE-DIMENSIONAL BANACH MANIFOLD

J.M. Soriano

数学物理学报(英文版). 2010 (5): 1687-1695. DOI: 10.1016/S0252-9602(10)60162-2

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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.

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ASYMPTOTIC BEHAVIOR FOR RANDOM WALK IN RANDOM |ENVIRONMENT WITH HOLDING TIMES

毛明志, 李志民

数学物理学报(英文版). 2010 (5): 1696-1708. DOI: 10.1016/S0252-9602(10)60163-4

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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.

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HYPERCYCLIC OPERATORS ON QUASI-MAZUR SPACES

丘京辉

数学物理学报(英文版). 2010 (5): 1709-1720. DOI: 10.1016/S0252-9602(10)60164-6

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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.

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THE REGULARITY OF THE FREE BOUNDARY FOR |STRIKE RESET OPTION

杨舟

数学物理学报(英文版). 2010 (5): 1721-1729. DOI: 10.1016/S0252-9602(10)60165-8

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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.

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ON THE RENEWAL RISK MODEL WITH INTEREST AND DIVIDEND

房莹, 吴荣

数学物理学报(英文版). 2010 (5): 1730-1738. DOI: 10.1016/S0252-9602(10)60166-X

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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.

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CONFORMAL AND GENERALIZED CONCIRCULAR MAPPINGS OF EINSTEIN-WEYL MANIFOLDS

Abdulkadir ?zdeger

数学物理学报(英文版). 2010 (5): 1739-1745. DOI: 10.1016/S0252-9602(10)60167-1

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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.

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THE JUMPING PHENOMENON OF THE DIMENSIONS OF COHOMOLOGY GROUPS OF TANGENT SHEAF

叶轩明

数学物理学报(英文版). 2010 (5): 1746-1758. DOI: 10.1016/S0252-9602(10)60168-3

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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(X_t, TX_t) may vary under this deformation. This article studies such phenomena by studying the obstructions to deform a class in H ^q(X, T_X) with parameter t and gets a formula for the obstructions.

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HAZARD REGRESSION WITH PENALIZED SPLINE: THE SMOOTHING PARAMETER CHOICE AND ASYMPTOTICS

童行伟, 胡涛, 崔恒建

数学物理学报(英文版). 2010 (5): 1759-1768. DOI: 10.1016/S0252-9602(10)60169-5

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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.

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TOWERS OF DERIVATION FOR LIE RINGS AND SOME RESULTS ON COMPLETE LIE RINGS

廖军, 郑大彬, 刘合国

数学物理学报(英文版). 2010 (5): 1769-1775. DOI: 10.1016/S0252-9602(10)60170-1

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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.

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ON UNIQUE CONTINUATION PROPERTIES FOR THE SUB-LAPLACIAN ON |CARNOT GROUPS

钮鹏程, 王家林

数学物理学报(英文版). 2010 (5): 1776-1784. DOI: 10.1016/S0252-9602(10)60171-3

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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.

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HIGHER ORDER SINGULAR INTEGRAL EQUATIONS ON COMPLEX HYPERSPHERE

陈吕萍, 钟同德

数学物理学报(英文版). 2010 (5): 1785-1792. DOI: 10.1016/S0252-9602(10)60172-5

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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.

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GLOBAL EXISTENCE AND BLOW-UP OF SOLUTIONS FOR GENERALIZED POCHHAMMER-CHREE EQUATIONS

徐润章, 刘亚成

数学物理学报(英文版). 2010 (5): 1793-1807. DOI: 10.1016/S0252-9602(10)60173-7

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In this article, we study the initial boundary value problem of generalized Pochhammer-Chree equation
ut_t-u_xx-u_xxt-u_xxtt=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 W_{k, p} solutions. Then, we prove that, if f(s) ∈ in C^k⁺¹(R) is ondecreasing, f(0)=0 and |f(u)| ≤ C₁|u| ∫₀^uf(s)ds + C₂, u₀(x), u₁(x) ∈W^{k, p}(Ω) ∩ W₀{^1, ^p}(Ω), k ≥1, 1< p ≤∞, then for any T>0 the problem admits a unique solution u(x, t) ∈ W^2, ∞ (0, T; W^k, ^p(Ω)∩W₀^1, ^p(Ω) ). Finally, the finite time blow-up of solutions and global W^{k, p} solution of generalized IMBq equations are discussed.

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QUANTUM COMPLEXITY OF THE APPROXIMATION FOR THE CLASSES Β(W_p^r([0, 1]^d)) AND Β(H_p^r([0, 1]^d))

叶培新, 胡晓菲

数学物理学报(英文版). 2010 (5): 1808-1818. DOI: 10.1016/S0252-9602(10)60174-9

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We study the approximation of functions from anisotropic Sobolev classes B(W_p^r}([0, 1]^d)) and H\"{o}lder-Nikolskii classes B(H_p^r}([0, 1]^d)) in the L_q([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.

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MULTI-DIMENSIONAL REFLECTED BACKWARD STOCHASTIC DIFFERENTIAL EQUATIONS AND THE COMPARISON THEOREM

吴臻, 肖华

数学物理学报(英文版). 2010 (5): 1819-1836. DOI: 10.1016/S0252-9602(10)60175-0

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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.

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