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2007年, 第27卷, 第4期　刊出日期：2007-10-20 上一期    下一期

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NONTRIVIAL SOLUTIONS OF HARDY-HENON TYPE ELLIPTIC SYSTEMS 刘芳; 杨健夫 数学物理学报(英文版). 2007 (4):  673-688.  DOI: 10.1016/S0252-9602(07)60067-8 摘要 ( 1125 )   RICH HTML PDF(208KB) ( 1449 )   收藏 In this article, the authors investigate the existence problem for Hardy--Henon type strongly indefinite elliptic systems. Existence results are obtained for such systems with superlinear subcritical nonlinearities. 相关文章 | 计量指标

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COMPLEX POWER OF HERMITE OPERATOR 丁夏畦; 罗佩珠 数学物理学报(英文版). 2007 (4):  689-693.  DOI: 10.1016/S0252-9602(07)60068-X 摘要 ( 985 )   RICH HTML PDF(117KB) ( 1215 )   收藏 In this paper the authors define complex power of Hermite operator and give some applications in Riemann Zeta function. 相关文章 | 计量指标

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EXTENSION OF SOLUTIONS TO RIEMANN BOUNDARY VALUE PROBLEMS AND ITS APPLICATION 路见可 数学物理学报(英文版). 2007 (4):  694-702.  DOI: 10.1016/S0252-9602(07)60069-1 摘要 ( 1126 )   RICH HTML PDF(156KB) ( 1070 )   收藏 In this paper, solutions of Riemann boundary value problems with nodes are extended to the case where they may have singularties of high order at the nodes. Moreover, further extension is discussed when the free term of the problem involved also possesses singularities at the nodes. As an application, certain singular integral equation is discussed. 相关文章 | 计量指标

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BLOW-UP RESULTS AND ASYMPTOTIC BEHAVIOR OF THE EMDEN-FOWLER EQUATION u''=|u|p 李明融 数学物理学报(英文版). 2007 (4):  703-734.  DOI: 10.1016/S0252-9602(07)60070-8 摘要 ( 1284 )   RICH HTML PDF(512KB) ( 1014 )   收藏 In this article the author works with the ordinary differential equation u''=|u|p for some p>0 and obtains some interesting phenomena concerning blow-up, blow-up rate, life-span, stability, instability, zeros and critical points of solutions to this equation. 相关文章 | 计量指标

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DISAPPEARANCE OF INTERFACES FOR DEGENERATE PARABOLIC EQUATIONS WITH VARIABLE DENSITY AND ABSORPTION 胡学刚; 穆春来 数学物理学报(英文版). 2007 (4):  735-742.  DOI: 10.1016/S0252-9602(07)60071-X 摘要 ( 1225 )   RICH HTML PDF(151KB) ( 1246 )   收藏 In this article, the authors deal with the Cauchy problem of a nonlinear parabolic equation with variable density and absorption. By using energy methods, the authors prove that the interfaces can disappear in finite time under some assumptions on the density functions. 相关文章 | 计量指标

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ON THE DEPENDENT PROPERTY OF SOLUTIONS FOR HIGHER ORDER PERIODIC #br# DIFFERENTIAL EQUATIONS 陈宗煊; 高仕安; 孙光镐 数学物理学报(英文版). 2007 (4):  743-752.  DOI: 10.1016/S0252-9602(07)60072-1 摘要 ( 1136 )   RICH HTML PDF(181KB) ( 1477 )   收藏 This article investigates the property of linearly dependence of solutions f(z) and f(z+2πi) for higher order linear differential equations with entire periodic coefficients. 相关文章 | 计量指标

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A COMPREHENSIVE PROOF OF THE GREENBERGER-HORNE-ZEILINGER THEOREM FOR THE FOUR-QUBIT SYSTEM 唐莉; 陈泽乾; 钟杰; 任耀峰; 詹明生 数学物理学报(英文版). 2007 (4):  753-776.  DOI: 10.1016/S0252-9602(07)60073-3 摘要 ( 1070 )   RICH HTML PDF(228KB) ( 1110 )   收藏 Greenberger--Horne--Zeilinger (GHZ) theorem asserts that there is a set of mutually commuting nonlocal observables with a common eigenstate on which those observables assume values that refute the attempt to assign values only required to have them by the local realism of Einstein, Podolsky, and Rosen (EPR). It is known that for a three-qubit system, there is only one form of the GHZ-Mermin-like argument with equivalence up to a local unitary transformation, which is exactly Mermin's version of the GHZ theorem. This article for a four-qubit system, which was originally studied by GHZ, the authors show that there are nine distinct forms of the GHZ-Mermin-like argument. The proof is obtained using certain geometric invariants to characterize the sets of mutually commuting nonlocal spin observables on the four-qubit system. It is proved that there are at most nine elements (except for a different sign) in a set of mutually commuting nonlocal spin observables in the four-qubit system, and each GHZ-Mermin-like argument involves a set of at least five mutually commuting four-qubit nonlocal spin observables with a GHZ state as a common eigenstate in GHZ's theorem. Therefore, we present a complete construction of the GHZ theorem for the four-qubit system. 相关文章 | 计量指标

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ASYMPTOTIC METHOD OF TRAVELLING WAVE SOLUTIONS FOR A CLASS OF #br# NONLINEAR REACTION DIFFUSION EQUATION 莫嘉琪; 张伟江; 何铭 数学物理学报(英文版). 2007 (4):  777-780.  DOI: 10.1016/S0252-9602(07)60074-5 摘要 ( 1139 )   RICH HTML PDF(116KB) ( 1492 )   收藏 In this article the travelling wave solution for a class of nonlinear reaction diffusion problems are considered. Using the homotopic method and the theory of travelling wave transform, the approximate solution for the corresponding problem is obtained. 相关文章 | 计量指标

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PROJECTIVELY FLAT MATSUMOTO METRIC AND ITS APPROXIMATION 李本伶 数学物理学报(英文版). 2007 (4):  781-789.  DOI: 10.1016/S0252-9602(07)60075-7 摘要 ( 1163 )   RICH HTML PDF(152KB) ( 2251 )   收藏 In this article, the author studies the projectively flat Matsumoto metric F=α2/(α-β), where α=\sqrt{a_{ij}y^{i}y^{j}} is a Riemannian metric and β=biyi is a 1-form. They conclude that α is locally projectively flat and β is paralled with respect to α. And get the same result for the higher order approximate Matsumoto metric. 相关文章 | 计量指标

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TRACTABILITY OF MULTIVARIATE INTEGRATION PROBLEM FOR PERIODIC CONTINUOUS FUNCTIONS 房艮孙; 龙晶凡 数学物理学报(英文版). 2007 (4):  790-802.  DOI: 10.1016/S0252-9602(07)60076-9 摘要 ( 1163 )   RICH HTML PDF(195KB) ( 1057 )   收藏 The authors study the tractability and strong tractability of a multivariate integration problem in the worst case setting for weighted 1-periodic continuous functions spaces of d coordinates with absolutely convergent Fourier series. The authors reduce the initial error by a factor ε for functions from the unit ball of the weighted periodic continuous functions spaces. Tractability is the minimal number of function samples required to solve the problem in polynomial in ε-1 and d, and the strong tractability is the presence of only a polynomial dependence in ε-1. This problem has been recently studied for quasi-Monte Carlo quadrature rules, quadrature rules with non-negative coefficients, and rules for which all quadrature weights are arbitrary for weighted Korobov spaces of smooth periodic functions of d variables. The authors show that the tractability and strong tractability of a multivariate integration problem in worst case setting hold for the weighted periodic continuous functions spaces with absolutely convergent Fourier series under the same assumptions as in Ref.[14] on the weights of the Korobov space for quasi-Monte Carlo rules and rules for which all quadrature weights are non-negative. The arguments are not constructive. 相关文章 | 计量指标

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ON THE SHARP GROWTH, COVERING THEOREMS FOR NORMALIZED BIHOLOMORPHIC MAPPINGS IN Cn 刘小松; 刘太顺 数学物理学报(英文版). 2007 (4):  803-812.  DOI: 10.1016/S0252-9602(07)60077-0 摘要 ( 1231 )   RICH HTML PDF(176KB) ( 1194 )   收藏 In this article, a normalized biholomorphic mapping f defined on bounded starlike circular domain in Cn is considered, where z=0 is a zero of order k+1 of f(z)-z. The sharp growth, covering theorems for almost starlike mappings of order α and starlike mappings of order α are established. Meanwhile, the construction of the above mappings on bounded starlike circular domain in Cn is also discussed, it provides the extremal mappings for the growth, covering theorems of the above mappings. 相关文章 | 计量指标

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A NEGATIVE ANSWER TO A PROBLEM OF FREMLIN AND MENDOZA 叶国菊; Stefan Schwabik 数学物理学报(英文版). 2007 (4):  813-820.  DOI: 10.1016/S0252-9602(07)60078-2 摘要 ( 1056 )   RICH HTML PDF(154KB) ( 1030 )   收藏 This article studies some convergence results for the McShane integral of functions mapping the interval [0, 1] into a Banach space X from the point of view of an open problem proposed by D.H.Fremlin and J. Mendoza in [2], also the anthors give a negative answer to this open problem. 相关文章 | 计量指标

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LARGE DEVIATION FOR THE EMPIRICAL CORRELATION COEFFICIENT OF TWO GAUSSIAN RANDOM VARIABLES 沈思 数学物理学报(英文版). 2007 (4):  821-828.  DOI: 10.1016/S0252-9602(07)60079-4 摘要 ( 1223 )   RICH HTML PDF(166KB) ( 1653 )   收藏 In this article, the author obtains the large deviation principles for the empirical correlation coefficient of two Gaussian random variables X and Y. Especially, when considering two independent Gaussian random variables X, Y with the means EX, EY (both known), wherein the author gives two kinds of different proofs and gets the same results. 相关文章 | 计量指标

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STRONG LAW OF LARGE NUMBERS AND ASYMPTOTIC EQUIPARTITION PROPERTY FOR NONSYMMETRIC MARKOV CHAIN FIELDS ON CAYLEY TREES 包振华; 叶中行 数学物理学报(英文版). 2007 (4):  829-837.  DOI: 10.1016/S0252-9602(07)60080-0 摘要 ( 1214 )   RICH HTML PDF(156KB) ( 1323 )   收藏 Some strong laws of large numbers for the frequencies of occurrence of states and ordered couples of states for nonsymmetric Markov chain fields (NSMC) on Cayley trees are studied. In the proof, a new technique for the study of strong limit theorems of Markov chains is extended to the case of Markov chain fields. The asymptotic equipartition properties with almost everywhere (a.e.) convergence for NSMC on Cayley trees are obtained. 相关文章 | 计量指标

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ON A GENERALIZED MODULUS OF CONVEXITY AND UNIFORM NORMAL STRUCTURE 杨长森; 王丰辉 数学物理学报(英文版). 2007 (4):  838-844.  DOI: 10.1016/S0252-9602(07)60081-2 摘要 ( 1076 )   RICH HTML PDF(147KB) ( 1799 )   收藏 In this article, the authors study a generalized modulus of convexity, δα(ε). Certain related geometrical properties of this modulus are analyzed. Their main result is that Banach space X has uniform normal structure if there exists ε, 0≤ε≤1, such that δα(1+ε)>(1-α)ε. 相关文章 | 计量指标

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MEROMORPHIC FUNCTIONS SHARING TWO FINITE SETS 林伟川; 仪洪勋 数学物理学报(英文版). 2007 (4):  845-851.  DOI: 10.1016/S0252-9602(07)60082-4 摘要 ( 1254 )   RICH HTML PDF(144KB) ( 1450 )   收藏 Let S1={∞} and S2={w: Ps(w)=0}, Ps(w) being a uniqueness polynomial under some restricted conditions. Then, for any given nonconstant meromorphic function f, there exist at most finitely many nonconstant meromorphic functions g such that f-1(Si)=g-1(Si), (i=1,2), where f-1(Si) and g-1(Si)$ denote the pull-backs of Si considered as a divisor, namely, the inverse images of Si counted with multiplicities, by f and g respectively. 相关文章 | 计量指标

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BOUNDEDNESS OF GENERALIZED HIGHER COMMUTATORS OF MARCINKIEWICZ INTEGRALS 默会霞; 陆善镇 数学物理学报(英文版). 2007 (4):  852-866.  DOI: 10.1016/S0252-9602(07)60083-6 摘要 ( 1306 )   RICH HTML PDF(219KB) ( 1613 )   收藏 Let $\vec{b}=(b_{1},\cdots ,b_{m})$ be a finite family of locally integrable functions. Then, we introduce generalized higher commutator of Marcinkiwicz integral as follows: $$\mu_{\Omega}^{\vec{b}}(f)(x)=\Bigl(\int_{0}^{\infty} |F_{\Omega,t}^{\vec{b}}(f)(x)|^{2}\frac{{\rm d}t}{t}\Bigr)^{1/2},$$ where $$F_{\Omega,t}^{\vec{b}}(f)(x)=\frac{1}{t}\int_{|x-y|\leq t} \frac{\Omega(x-y)}{|x-y|^{n-1}}\prod\limits_{j=1}^{m}(b_{j}(x)-b_{j}(y))f(y){\rm d}y.$$ When $b_{j}\in\dot{\Lambda}_{\beta_{j}}, 1\leq j\leq m,$ $0<\beta_{j}<1, \sum\limits_{j=1}^{m}\beta_{j}=\betais homogeneous of degree zero and satisfies the cancelation condition, we prove that$\mu_{\Omega}^{\vec{b}}$is bounded from$L^{p}({\Bbb R}^{n})$to$L^{s}({\Bbb R}^{n}),$where$1Moreover, if $\Omega$ also satisfies some Lq-Dini condition, then $\mu_{\Omega}^{\vec{b}}$ is bounded from $L^{p}({\Bbb R}^{n})$ to $\dot{F}^{\beta,\infty}_{p}({\Bbb R}^{n})$ and on certain Hardy spaces. The article extends some known results. 相关文章 | 计量指标

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THE SPHERICAL FUNCTIONS AND THE CENTRAL LIMIT THEOREM ON SU(2,2)/S(U(2)×U(2)) 杨乔华; 张钦 数学物理学报(英文版). 2007 (4):  867-874.  DOI: 10.1016/S0252-9602(07)60084-8 摘要 ( 1190 )   RICH HTML PDF(179KB) ( 986 )   收藏 Let G=SU(2,2), K=S(U(2)×U(2)), and for l∈Z, let {τl}l∈Z be a one-dimensional K-type and let El be the line bundle over G/K associated to τl. It is shown that the τl-spherical function on G is given by the hypergeometric functions of several variables. By applying this result, a central limit theorem for the space G/K is obtained. 相关文章 | 计量指标

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A FINITE ELEMENT COLLOCATION METHOD FOR TWO-PHASE INCOMPRESSIBLE#br# IMMISCIBLE PROBLEMS 马宁 数学物理学报(英文版). 2007 (4):  875-885.  DOI: 10.1016/S0252-9602(07)60085-X 摘要 ( 1178 )   RICH HTML PDF(176KB) ( 2062 )   收藏 Two-phase, incompressible, immiscible flow in porous media is governed by a coupled system of nonlinear partial differential equations. The pressure equation is elliptic, whereas the concentration equation is parabolic, and both are treated by the collocation scheme. Existence and uniqueness of solutions of the algorithm are proved. A optimal convergence analysis is given for the method. 相关文章 | 计量指标

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LARGE DEVIATIONS AND MODERATE DEVIATIONS FOR m-NEGATIVELY ASSOCIATED RANDOM VARIABLES 胡亦钧; 明瑞星; 杨文权 数学物理学报(英文版). 2007 (4):  886-896.  DOI: 10.1016/S0252-9602(07)60086-1 摘要 ( 1294 )   RICH HTML PDF(184KB) ( 1324 )   收藏 M-negatively associated random variables, which generalizes the classical one of negatively associated random variables and includes m-dependent sequences as its particular case, are introduced and studied. Large deviation principles and moderate deviation upper bounds for stationary m-negatively associated random variables are proved. Kolmogorov-type and Marcinkiewicz-type strong laws of large numbers as well as the three series theorem for m-negatively associated random variables are also given. 相关文章 | 计量指标

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ANOTHER TYPE OF GENERALIZED BALL CURVES AND SURFACES 余丹; 陈莘萌 数学物理学报(英文版). 2007 (4):  897-907.  DOI: 10.1016/S0252-9602(07)60087-3 摘要 ( 1169 )   RICH HTML PDF(169KB) ( 1234 )   收藏 In 2000, Wu presented two new types of generalized Ball curves, one of which is called an NB1 curve located between the Wang--Ball curve and the Said--Ball curve. In this article, the authors aim to discuss properties of NB1 curves and surfaces, including the recursive algorithms, conversion algorithms between NB1 and Bezier curves and surfaces, etc. In addition the authors compare the computation efficiency of recursive algorithms for the NB1 and above mentioned two generalized Ball curves and surfaces. 相关文章 | 计量指标