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20 July 2006, Volume 26 Issue 3 Previous Issue    Next Issue

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ON A LARGE SAMPLE PROBLEM IN NONLINEAR REGRESSION Liu Chunling Acta mathematica scientia,Series B. 2006, 26 (3):  385-394.  DOI: 10.1016/S0252-9602(06)60061-1 Abstract ( 1164 )   RICH HTML PDF (157KB) ( 1068 )   Save Assume that in the nonlinear regression model, independent variable sequence {xi,i≥1} is a known constant-vector sequence. This article proposes a condition on {xi}, which can be tested and verified easily. The condition is essential for proving the consistency and asymptotic normality of the estimator. Related Articles | Metrics

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ON ALMOST PRECOVERS AND ALMOST PREENVELOPES Mao Lixin; Ding Nanqing; Tong Wenting Acta mathematica scientia,Series B. 2006, 26 (3):  395-400.  DOI: 10.1016/S0252-9602(06)60062-3 Abstract ( 927 )   RICH HTML PDF (276KB) ( 1344 )   Save Let C be a class of R-modules closed under isomorphisms and finite direct sums. It is first shown that the finite direct sum of almost C-precovers is an almost C-precover and the direct sum of an almost C-cover and a weak C-cover is a weak C-cover. Then the notion of almost C-preenvelopes is introduced and studied. Related Articles | Metrics

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SOME RESULTS OF MODULAR LIE SUPERALGEBRAS Chen Liangyun; Meng Daoji Acta mathematica scientia,Series B. 2006, 26 (3):  401-409.  DOI: 10.1016/S0252-9602(06)60063-5 Abstract ( 969 )   RICH HTML PDF (157KB) ( 1200 )   Save In the present article, the authors give some properties on subinvariant subalgebras of modular Lie superalgebras and obtain the derivation tower theorem of modular Lie superalgebras, which is analogous to the automorphism tower theorem of finite groups. Moreover, they announce and prove some results of modular complete Lie superalgebras. Related Articles | Metrics

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SINGULAR INTEGRAL EQUATIONS WITH COSECANT KERNEL IN SOLUTIONS WITH SINGULARITIES OF ORDER ONE Dai Jinjun; Du Jinyuan Acta mathematica scientia,Series B. 2006, 26 (3):  410-414.  DOI: 10.1016/S0252-9602(06)60064-7 Abstract ( 1184 )   RICH HTML PDF (123KB) ( 759 )   Save In this article, periodic Riemann boundary value problem with period 2aπ along closed smooth contours is discussed, and then singular integral equation with kernel csc{(t-t0)/a} along closed smooth contours restricted in the strip 0zis discussed. Finally, the solutions with singularities of order one for the above two problems are discussed. Related Articles | Metrics

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TWO CONDITIONS FOR NONUNIFORM GABOR FRAMES Liu Youming Acta mathematica scientia,Series B. 2006, 26 (3):  415-420.  DOI: 10.1016/S0252-9602(06)60065-9 Abstract ( 995 )   RICH HTML PDF (126KB) ( 984 )   Save A necessary condition is given for general nonuniform Gabor frames, which generalizes Benedetto and Walnut's theorem. A sufficient and necessary condition for a class of nonuniform Gabor frames is proved. Related Articles | Metrics

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THE PARAMETRIC REPRESENTATION FOR SPIRAL-LIKE MAPPINGS OF TYPE α ON BOUNDED BALANCED PSEUDOCONVEX DOMAINS Liu Hao; Zhang Zhiping; Lu Keping Acta mathematica scientia,Series B. 2006, 26 (3):  421-430.  DOI: 10.1016/S0252-9602(06)60066-0 Abstract ( 1137 )   RICH HTML PDF (159KB) ( 1233 )   Save Let $om$ be a bounded balanced pseudoconvex domain in Cn that admits a plurisubhamonic defining function of class C2. The authors prove that if f is a spiral-like mapping of type α on $om$, then f can be expressed as a limiting form concerning a Schwarz mapping. Moreover, the characteristics for star-like mappings and spiral-like mappings of type α are obtained. As a direct application, the growth theorem for spiral-like mappings of type α is set up. Related Articles | Metrics

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THE CONSTRUCTION OF MULTITYPE CANONICAL MARKOV BRANCHING CHAINS IN RANDOM ENVIRONMENTS Hu Dihe Acta mathematica scientia,Series B. 2006, 26 (3):  431-442.  DOI: 10.1016/S0252-9602(06)60067-2 Abstract ( 1106 )   RICH HTML PDF (165KB) ( 1132 )   Save The investigation for branching processes has a long history by their strong physics background, but only a few authors have investigated the branching processes in random environments. First of all, the author introduces the concepts of the multitype canonical Markov branching chain in random environment (CMBCRE) and multitype Markov branching chain in random environment (MBCRE) and proved that CMBCRE must be MBCRE, and any MBCRE must be equivalent to another CMBCRE in distribution. The main results of this article are the construction of CMBCRE and some of its probability properties. Related Articles | Metrics

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FULLY COUPLED FORWARD-BACKWARD STOCHASTIC DIFFERENTIAL EQUATIONS WITH GENERAL MARTINGALE Li Juan Acta mathematica scientia,Series B. 2006, 26 (3):  443-450.  DOI: 10.1016/S0252-9602(06)60068-4 Abstract ( 1260 )   RICH HTML PDF (139KB) ( 2260 )   Save The article first studies the fully coupled Forward-Backward Stochastic Differential Equations (FBSDEs) with the continuous local martingale. The article is mainly divided into two parts. In the first part, it considers Backward Stochastic Differential Equations (BSDEs) with the continuous local martingale. Then, on the basis of it, in the second part it considers the fully coupled FBSDEs with the continuous local martingale. It is proved that their solutions exist and are unique under the monotonicity conditions. Related Articles | Metrics

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CONSTRUCTING UNIFORM DESIGNS WITH TWO- OR THREE-LEVEL Qin Hong; Zhang Shangli; Fang Kaitai Acta mathematica scientia,Series B. 2006, 26 (3):  451-459.  DOI: 10.1016/S0252-9602(06)60069-6 Abstract ( 1182 )   RICH HTML PDF (150KB) ( 1303 )   Save When the number of runs is large, to search for uniform designs in the sense of low-discrepancy is an NP hard problem. The number of runs of most of the available uniform designs is small (≤ 50). In this article, the authors employ a kind of the so-called Hamming distance method to construct uniform designs with two- or three-level such that some resulting uniform designs have a large number of runs. Several infinite classes for the existence of uniform designs with the same Hamming distances between any distinct rows are also obtained simultaneously. Two measures of uniformity, the centered L2-discrepancy (CD, for short) and wrap-around L2-discrepancy (WD, for short), are employed. Related Articles | Metrics

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EXISTENCE OF A NONTRIVIAL SOLUTION FOR CHOQUARD'S EQUATION Zhang Zhengjie; Tassilo Kupper; Hu Ailian; Xia Hongqiang Acta mathematica scientia,Series B. 2006, 26 (3):  460-468.  DOI: 10.1016/S0252-9602(06)60070-2 Abstract ( 1001 )   RICH HTML PDF (154KB) ( 1642 )   Save In this article, the authors consider the existence of a nontrivial solution for the following equation: -△ u + u =q(x)(|u|2*{1/|x|})u, x∈ R3, where q(x) satisfies some conditions. Using a Min-Max method, the authors prove that there is at least one nontrivial solution for the above equation. Related Articles | Metrics

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VARIABLE SELECTION BY PSEUDO WAVELETS IN HETEROSCEDASTIC REGRESSION MODELS INVOLVING TIME SERIES Wang Qinghe; Zhou Yong Acta mathematica scientia,Series B. 2006, 26 (3):  469-476.  DOI: 10.1016/S0252-9602(06)60071-4 Abstract ( 1065 )   RICH HTML PDF (148KB) ( 1009 )   Save A simple but efficient method has been proposed to select variables in heteroscedastic regression models. It is shown that the pseudo empirical wavelet coefficients corresponding to the significant explanatory variables in the regression models are clearly larger than those nonsignificant ones, on the basis of which a procedure is developed to select variables in regression models. The coefficients of the models are also estimated. All estimators are proved to be consistent. Related Articles | Metrics

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EDGE-FACE CHROMATIC NUMBER OF 2-CONNECTED PLANE GRAPHS WITH HIGH MAXIMUM DEGREE Zhang Zhongfu; Wang Weifan; Li Jingwen; Yao Bing; Bu Yuehua Acta mathematica scientia,Series B. 2006, 26 (3):  477-482.  DOI: 10.1016/S0252-9602(06)60072-6 Abstract ( 1138 )   RICH HTML PDF (129KB) ( 1040 )   Save The edge-face chromatic number χef(G)$ of a plane graph G is the least number of colors assigned to the edges and faces such that every adjacent or incident pair of them receives different colors. In this article, the authors prove that every 2-connected plane graph G with △(G)≥ |G|-2≥ 9 has χef(G)=△(G). Related Articles | Metrics

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WEAK REGULARIZATION FOR A CLASS OF ILL-POSED CAUCHY PROBLEMS Huang Yongzhong; Zheng Quan Acta mathematica scientia,Series B. 2006, 26 (3):  483-490.  DOI: 10.1016/S0252-9602(06)60073-8 Abstract ( 1265 )   RICH HTML PDF (149KB) ( 1171 )   Save This article is concerned with the ill-posed Cauchy problem associated with a densely defined linear operator A in a Banach space. A family of weak regularizing operators is introduced. If the spectrum of A is contained in a sector of right-half complex plane and its resolvent is polynomially bounded, the weak regularization for such ill-posed Cauchy problem can be shown by using the quasi-reversibility method and regularized semigroups. Finally, an example is given. Related Articles | Metrics

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GLOBAL CLASSICAL SOLUTIONS OF THE BOLTZMANN EQUATION NEAR MAXWELLIANS Yu Hongjun Acta mathematica scientia,Series B. 2006, 26 (3):  491-501.  DOI: 10.1016/S0252-9602(06)60074-X Abstract ( 1240 )   RICH HTML PDF (159KB) ( 1294 )   Save Global classical solutions near Maxwellians are constructed for the Boltzmann equation in a periodic box with angular soft cutoff, that is, -3<γ<0. The construction of global solution is based on an energy method used in [9]. Related Articles | Metrics

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ISOMETRIES ON THE SPACE s Fu Xiaohong Acta mathematica scientia,Series B. 2006, 26 (3):  502-508.  DOI: 10.1016/S0252-9602(06)60075-1 Abstract ( 1215 )   RICH HTML PDF (132KB) ( 1455 )   Save In this article, the author presents some results of the isometric linear extension from some spheres in the finite dimensional space s(n). Moreover, the author presents the representation for the onto isometric mappings in the space s. It is obtained that if V is a surjective isometry from the space s onto s with V(0)={0}, then V must be real linear. Related Articles | Metrics

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THE RISK MODEL OF THE EXPECTED DISCOUNTED PENALTY FUNCTION WITH CONSTANT INTEREST FORCE Liu Li; Mao Shisong Acta mathematica scientia,Series B. 2006, 26 (3):  509-518.  DOI: 10.1016/S0252-9602(06)60076-3 Abstract ( 1279 )   RICH HTML PDF (146KB) ( 1163 )   Save In this article, the expected discounted penalty function $\Phi_{\delta,\alpha}(u)$ with constant interest δ and ``discounted factor" exp(-αTδ) is considered. As a result, the integral equation of $\Phi_{\delta,\alpha}(u)$ is derived and an exact solution for $\Phi_{\delta,\alpha}(0)$ is found. The relation between the joint density of the surplus immediately prior to ruin, and the deficit at ruin and the density of the surplus immediately prior to ruin is then obtained based on analytical methods. Related Articles | Metrics

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THE CAUCHY PROBLEM FOR A CLASS OF DOUBLY DEGENERATE NONLINEAR #br# PARABOLIC EQUATION Liu Zhaoxia Acta mathematica scientia,Series B. 2006, 26 (3):  519-524.  DOI: 10.1016/S0252-9602(06)60077-5 Abstract ( 1283 )   RICH HTML PDF (128KB) ( 1003 )   Save This article studies the Cauchy problem for a class of doubly nonlinear degenerate parabolic equations $\frac{\partial u}{\partial t}={\rm div}(A(|\nabla{B}(u)|)\nabla{B}(u)).$ Under certain conditions, the author considers its regularized problem and establishes some estimates. On the basis of the estimates, the existence and uniqueness of the generalized solutions in BV space are proved. Related Articles | Metrics

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SOLUTIONS FOR A NONHOMOGENEOUS ELLIPTIC PROBLEM INVOLVING CRITICAL SOBOLEV-HARDY EXPONENT IN RN Wang Zhengping; Zhou Huansong Acta mathematica scientia,Series B. 2006, 26 (3):  525-536.  DOI: 10.1016/S0252-9602(06)60078-7 Abstract ( 1327 )   RICH HTML PDF (190KB) ( 1638 )   Save For the following elliptic problem -△ u - μu/|x|2={|u|2*(s)-2u}/|x|s+h(x), on RN u ∈ D1,2(RN), N≥3, 0≤μ<\bar\mu=(N-2)2 /4, 0≤ s<2, where 2*(s)=2(N-s)/(N-2) is the critical Sobolev-Hardy exponent, h(x)∈ D1,2(RN))* , the dual space of (D1,2(RN)), with h(x)≥(≠) 0. By Ekeland's variational principle, subsuper solutions and a Mountain Pass theorem, the authors prove that the above problem has at least two distinct solutions if ||h||*<CN,s As (n-s)/(4-2s)(1-μ/{\bar\mu})1/2, CN,s=(4-2s)/(N-2) ((N-2)/(N+2-2s)(N+2-2s)/(4-2s) and As=inf u∈ D1,2(RN)\{0} {∫RN(|▽u|2-μu2/|x|2) dx}/{(∫RN|u|2*(s)/|x|s dx)2/2*(s)}. Related Articles | Metrics

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A NOTE ON THE EXISTENCE AND NONEXISTENCE OF GLOBALLY BOUNDED CLASSICAL SOLUTIONS FOR NONISENTROPIC GAS DYNAMICS Lin Longwei; Vong Seakweng Acta mathematica scientia,Series B. 2006, 26 (3):  537-540.  DOI: 10.1016/S0252-9602(06)60079-9 Abstract ( 1354 )   RICH HTML PDF (106KB) ( 1190 )   Save Existence of globally bounded classical solution for nonisentropic gas dynamics system has long been studied, especially in the case of polytropic gas. In [4], Liu claimed that sufficient condition has been established. However, the authors find that the argument he used is not true in general. In this article, the authors give a counter example of his argument. Hence, his claim is not valid. The authors believe that it is difficult to impose general conditions on the initial data to obtain globally bounded classical solution. Related Articles | Metrics

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AN ITERATIVE EQUATION ON THE UNIT CIRCLE Li Xiaopei; Deng Shengfu Acta mathematica scientia,Series B. 2006, 26 (3):  541-550.  DOI: 10.1016/S0252-9602(06)60080-5 Abstract ( 1002 )   RICH HTML PDF (164KB) ( 1076 )   Save A functional equation of nonlinear iterates is discussed on the circle S1 for its continuous solutions and differentiable solutions. By lifting to R, the existence, uniqueness and stability of those solutions are obtained. Techniques of continuation are used to guarantee the preservation of continuity and differentiability in lifting. Related Articles | Metrics

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GLOBAL DYNAMICS OF AN SEIR EPIDEMIC MODEL WITH IMMIGRATION OF DIFFERENT COMPARTMENTS Zhang Juan; Li Jianquan; Ma Zhien Acta mathematica scientia,Series B. 2006, 26 (3):  551-567.  DOI: 10.1016/S0252-9602(06)60081-7 Abstract ( 1187 )   RICH HTML PDF (210KB) ( 3670 )   Save The SEIR epidemic model studied here includes constant inflows of new susceptibles, exposeds, infectives, and recovereds. This model also incorporates a population size dependent contact rate and a disease-related death. As the infected fraction cannot be eliminated from the population, this kind of model has only the unique endemic equilibrium that is globally asymptotically stable. Under the special case where the new members of immigration are all susceptible, the model considered here shows a threshold phenomenon and a sharp threshold has been obtained. In order to prove the global asymptotical stability of the endemic equilibrium, the authors introduce the change of variable, which can reduce our four-dimensional system to a three-dimensional asymptotical autonomous system with limit equation. Related Articles | Metrics

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SOME PROPERTIES OF MULTIPLE TAYLOR SERIES AND RANDOM TAYLOR SERIES Yu Jiarong Acta mathematica scientia,Series B. 2006, 26 (3):  568-576.  DOI: 10.1016/S0252-9602(06)60082-9 Abstract ( 1098 )   RICH HTML PDF (143KB) ( 1246 )   Save Some polar coordinates are used to determine the domain and the ball of convergence of a multiple Taylor series. In this domain and in this ball the series converges, converges absolutely and converges uniformly on any compact set. Growth and other properties of the series may also be studied. For some random multiple Taylor series there are some corresponding properties. Related Articles | Metrics