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20 April 2006, Volume 26 Issue 2 Previous Issue    Next Issue

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A NEW FAMILY OF FILTRATION s+6 IN THE STABLE HOMOTOPY GROUPS OF SPHERES Liu Xiugui Acta mathematica scientia,Series B. 2006, 26 (2):  193-201.  DOI: 10.1016/S0252-9602(06)60041-6 Abstract ( 1189 )   RICH HTML PDF (157KB) ( 1329 )   Save In the year 2002, Lin detected a nontrivial family in the stable homotopy groups of spheres $\pi_{t-6}S$ which is represented by $h_ng_0\tilde{\gamma}_{3} \in {\rm Ext}_A^{6,t}(Z_p,Z_p)$ in the Adams spectral sequence, where t=2pn(p-1)+6(p2+p+1)(p-1) and p≥7 is a prime number. This article generalizes the result and proves the existence of a new nontrivial family of filtration s+6 in the stable homotopy groups of spheres $\pi_{t_1-s-6}S$ which is represented by $h_ng_0\tilde{\gamma}_{s+3}\in {\rm Ext}_A^{s+6,t_1}(Z_p,Z_p)$ in the Adams spectral sequence, where n≥4, 0≤ s< p-4, t1=2pn(p-1)+2(p-1)((s+3)p2+(s+3)p+(s+3))+s. Related Articles | Metrics

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ON THE BOTTLENECK CAPACITY EXPANSION PROBLEMS ON NETWORKS Yang Chao; Zhang Jianzhong Acta mathematica scientia,Series B. 2006, 26 (2):  202-208.  DOI: 10.1016/S0252-9602(06)60042-8 Abstract ( 1160 )   RICH HTML PDF (142KB) ( 1288 )   Save This article considers a class of bottleneck capacity expansion problems. Such problems aim to enhance bottleneck capacity to a certain level with minimum cost. Given a network $G(V,A,\overline{C})$ consisting of a set of nodes V={v1,v2,... ,vn}, a set of arcs $A \subseteq \{(v_i,v_j)\ |\ i=1,2,\cdots ,n; ~j=1,2,\cdots ,n \}$ and a capacity vector $\overline{C}$. The component $\overline{c}_{ij}$ of $\overline{C}$ is the capacity of arc $(v_i,v_j)$. Define the capacity of a subset $A'$ of $A$ as the minimum capacity of the arcs in $A$, the capacity of a family ${\cal F}$ of subsets of $A$ is the maximum capacity of its members. There are two types of expanding models. In the arc-expanding model, the unit cost to increase the capacity of arc $(v_i,v_j)$ is $w_{ij}$. In the node-expanding model, it is assumed that the capacities of all arcs $(v_i,v_j)$ which start at the same node vi should be increased by the same amount and that the unit cost to make such expansion is wi. This article considers three kinds of bottleneck capacity expansion problems (path, spanning arborescence and maximum flow) in both expanding models. For each kind of expansion problems, this article discusses the characteristics of the problems and presents several results on the complexity of the problems. Related Articles | Metrics

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ON CRITICAL SINGULAR QUASILINEAR ELLIPTIC PROBLEM WHEN n=p Yao Yangxin; Shen Yaotian Acta mathematica scientia,Series B. 2006, 26 (2):  209-219.  DOI: 10.1016/S0252-9602(06)60043-X Abstract ( 1069 )   RICH HTML PDF (168KB) ( 1382 )   Save This article deals with the problem $$ -\Lap_p u=\lambda{|u|^{p-2}u\over\xlnxRt}+f(x,u),\quad x\in\Omega;\qquad u=0,x\in\partial\Om, $$ where $n = p.$ The authors prove that a Hardy inequality and the constant $ (\pp)^p $ is optimal. They also prove the existence of a nontrivial solution of the above mentioned problem by using the Mountain Pass Lemma. Related Articles | Metrics

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EXISTENCE OF SOLUTION FOR A BOUNDARY VALUE PROBLEM OF FRACTIONAL ORDER Zhang Shuqin Acta mathematica scientia,Series B. 2006, 26 (2):  220-228.  DOI: 10.1016/S0252-9602(06)60044-1 Abstract ( 1274 )   RICH HTML PDF (144KB) ( 4864 )   Save This article considers the existence of solution for a boundary value problem of fractional order, involving Caputo's derivative $$ \left\{ \begin {array}{l} _0^{C}D_t^\delta u(t) =g(t,u(t)),\quad 0u(0)=\alpha\neq 0,\quad u(1)=\beta\neq 0. \end{array} \right. $$ Related Articles | Metrics

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EXISTENCE AND ASYMPTOTIC BEHAVIOR OF THE SOLUTIONS FOR A NONLINEAR ELLIPTIC EQUATION ARISING IN ASTROPHYSICS Tang Zhongwei Acta mathematica scientia,Series B. 2006, 26 (2):  229-245.  DOI: 10.1016/S0252-9602(06)60045-3 Abstract ( 1217 )   RICH HTML PDF (215KB) ( 1096 )   Save The author first analyzes the existence of ground state solutions and cylindrically symmetric solutions and then the asymptotic behavior of the ground state solution of the equation -△u=\phi(r) up-1, u>0, in RN, u ∈D1,2(RN), where N≥3, x=(x',z) ∈RK×RN-K,2≤ K≤ N,r=|x'|. It is proved that for 2(N-s)/(N-2)*=2N/(N-2), 0*, the above equation does not have a ground state solution but a cylindrically symmetric solution, and when p close to 2*, the ground state solutions are not cylindrically symmetric. On the other hand, it is proved that as p close to 2*, the ground state solution up has a unique maximum point xp=(x'p,zp) and as p \to 2*,|x'p|→ r0 which attains the maximum of $\phi$ on RN. The asymptotic behavior of ground state solution up is also given, which also deduces that the ground state solution is not cylindrically symmetric as p goes to 2*. Related Articles | Metrics

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ASYMPTOTIC BEHAVIOR FOR COMMUTATIVE SEMIGROUPS OF ALMOST ASYMPTOTICALLY NONEXPANSIVE TYPE MAPPINGS Zeng Luchuan Acta mathematica scientia,Series B. 2006, 26 (2):  246-254.  DOI: 10.1016/S0252-9602(06)60046-5 Abstract ( 1037 )   RICH HTML PDF (142KB) ( 1461 )   Save This article introduces the concept of commutative semigroups of almost asymptotically nonexpansive-type mappings in a Banach space X which has the Opial property and whose norm is UKK, and establishes the weak convergence theorems for almost-orbits of this class of commutative semigroups. The author improves, extends and develops some recent and earlier results. Related Articles | Metrics

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THE FIRST BOUNDARY VALUE PROBLEM FOR STRONGLY DEGENERATE QUASILINEAR PARABOLIC EQUATIONS IN ANISOTROPIC SOBOLEV SPACES Zhao Yanyan; Chen Zuchi Acta mathematica scientia,Series B. 2006, 26 (2):  255-264.  DOI: 10.1016/S0252-9602(06)60047-7 Abstract ( 1164 )   RICH HTML PDF (144KB) ( 910 )   Save This article concerns the existence of weak solutions of the first boundary value problem for a kind of strongly degenerate quasilinear parabolic equation in the anisotropic Sobolev Space. With the theory of anisotropic Sobolev spaces an existence result is proved. Related Articles | Metrics

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A POLYNOMIAL PREDICTOR-CORRECTOR INTERIOR-POINT ALGORITHM FOR CONVEX QUADRATIC PROGRAMMING Yu Qian; Huang Chongchao; Jiang Yan Acta mathematica scientia,Series B. 2006, 26 (2):  265-270.  DOI: 10.1016/S0252-9602(06)60048-9 Abstract ( 1049 )   RICH HTML PDF (135KB) ( 1860 )   Save This article presents a polynomial predictor-corrector interior-point algorithm for convex quadratic programming based on a modified predictor-corrector interior-point algorithm. In this algorithm, there is only one corrector step after each predictor step, where Step 2 is a predictor step and Step 4 is a corrector step in the algorithm. In the algorithm, the predictor step decreases the dual gap as much as possible in a wider neighborhood of the central path and the corrector step draws iteration points back to a narrower neighborhood and make a reduction for the dual gap. It is shown that the algorithm has ${\rm O}(\sqrt n L)$ iteration complexity which is the best result for convex quadratic programming so far. Related Articles | Metrics

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ENDPOINT ESTIMATE FOR MAXIMAL COMMUTATORS WITH NON-DOUBLING MEASUES Hu Guoen; Meng Yan; Yang Dachun Acta mathematica scientia,Series B. 2006, 26 (2):  271-280.  DOI: 10.1016/S0252-9602(06)60049-0 Abstract ( 1111 )   RICH HTML PDF (157KB) ( 1090 )   Save The authors establish the weak type endpoint estimate for the maximal commutators generated by Calderon-Zygmund singular integrals and Orlicz type functions with non-doubling measures. Related Articles | Metrics

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ASYMPTOTICALLY ISOMETRIC COPIES OF lp (1≤ p<∞) AND c0 IN BANACH SPACES Chen Dongyang Acta mathematica scientia,Series B. 2006, 26 (2):  281-290.  DOI: 10.1016/S0252-9602(06)60050-7 Abstract ( 1040 )   RICH HTML PDF (167KB) ( 1465 )   Save Let X be a Banach space. If there exists a quotient space of X which is asymptotically isometric to l1, then X contains complemented asymptotically isometric copies of l1. Every infinite dimensional closed subspace of l1 contains a complemented subspace of l1 which is asymptotically isometric to l1. Let X be a separable Banach space such that X* contains asymptotically isometric copies of lp (1q (\frac{1}{p}+\frac{1}{q}=1). Complemented asymptotically isometric copies of c0 in K(X,Y) and W(X,Y) are discussed. Let X be a Gelfand-Phillips space. If X contains asymptotically isometric copies of c0, it has to contain complemented asymptotically isometric copies of c0. Related Articles | Metrics

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GLOBAL STABILITY OF AN SIRS EPIDEMIC MODEL WITH DELAYS Zhen Jin; Ma Zhien; Han Maoan Acta mathematica scientia,Series B. 2006, 26 (2):  291-306.  DOI: 10.1016/S0252-9602(06)60051-9 Abstract ( 1303 )   RICH HTML PDF (186KB) ( 2875 )   Save In this article, an SIRS epidemic model spread by vectors (mosquitoes) which have an incubation time to become infectious is formulated. It is shown that a disease-free equilibrium point is globally stable if no endemic equilibrium point exists. Further, the endemic equilibrium point (if it exists) is globally stable with a respect ``weak delay". Some known results are generalized. Related Articles | Metrics

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PROJECTIVELY FLAT FINSLER METRICS WITH ALMOST ISOTROPIC S-CURVATURE Cheng Xinyue; Shen Zhongmin Acta mathematica scientia,Series B. 2006, 26 (2):  307-313.  DOI: 10.1016/S0252-9602(06)60052-0 Abstract ( 930 )   RICH HTML PDF (127KB) ( 2261 )   Save This article characterizes projectively flat Finsler metrics with almost isotropic S-curvature. Related Articles | Metrics

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CIRCULAR CHROMATIC NUMBER AND MYCIELSKI GRAPHS Liu Hongmei Acta mathematica scientia,Series B. 2006, 26 (2):  314-320.  DOI: 10.1016/S0252-9602(06)60053-2 Abstract ( 965 )   RICH HTML PDF (138KB) ( 1529 )   Save For a general graph G, M(G) denotes its Mycielski graph. This article gives a number of new sufficient conditions for G to have the circular chromatic number $\chi_c(M(G))$ equals to the chromatic number $\chi(M(G))$, which have improved some best sufficient conditions published up to date. Related Articles | Metrics

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ON THE RUIN FUNCTIONS FOR A CORRELATED AGGREGATE CLAIMS MODEL WITH POISSON AND ERLANG RISK PROCESSES Liu Yan; Yang Wenquan; Hu Yijun Acta mathematica scientia,Series B. 2006, 26 (2):  321-330.  DOI: 10.1016/S0252-9602(06)60054-4 Abstract ( 1164 )   RICH HTML PDF (140KB) ( 1418 )   Save This article considers a risk model as in Yuen et al. (2002). Under this model the two claim number processes are correlated. Claim occurrence of both classes relate to Poisson and Erlang processes. The formulae is derived for the distribution of the surplus immediately before ruin, for the distribution of the surplus immediately after ruin and the joint distribution of the surplus immediately before and after ruin. The asymptotic property of these ruin functions is also investigated. Related Articles | Metrics

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SAMPLING INSPECTION OF RELIABILITY IN (LOG)NORMAL CASE#br# WITH TYPE I CENSORING Wu Qiguang; Lu Jianhua Acta mathematica scientia,Series B. 2006, 26 (2):  331-343.  DOI: 10.1016/S0252-9602(06)60055-6 Abstract ( 1136 )   RICH HTML PDF (170KB) ( 1505 )   Save This article proposes a statistical method for working out reliability sampling plans under Type I censored sample for items whose failure times have either normal or lognormal distributions. The quality statistic is a method of moments estimator of a monotonous function of the unreliability. An approach of choosing a truncation time is recommended. The sample size and acceptability constant are approximately determined by using the Cornish-Fisher expansion for quantiles of distribution. Simulation results show that the method given in this article is feasible. Related Articles | Metrics

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KERNEL IDEALS AND CONGRUENCES ON MS-ALGEBRAS Luo Congwen; Zeng Yanlu Acta mathematica scientia,Series B. 2006, 26 (2):  344-348.  DOI: 10.1016/S0252-9602(06)60056-8 Abstract ( 1046 )   RICH HTML PDF (111KB) ( 1618 )   Save In this article, the authors describe the largest congruence induced by a kernel ideal of an MS-algebra and characterize those MS-algebras on which all the congruences are in a one-to-one correspondence with the kernel ideals. Related Articles | Metrics

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ON STATIONARY HYPERSURFACES IN EUCLIDEAN SPACES Zhao Peibiao; Yang Xiaoping Acta mathematica scientia,Series B. 2006, 26 (2):  349-357.  DOI: 10.1016/S0252-9602(06)60057-X Abstract ( 1138 )   RICH HTML PDF (155KB) ( 1365 )   Save Some techniques in the Geometric Measure Theory are used to study the hypersurfaces in Euclidean spaces and some fundamental properties with this subject are discussed in this article. Related Articles | Metrics

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ABSOLUTE CONTINUITIES OF EXIT MEASURES AND TOTAL WEIGHTED OCCUPATION TIME MEASURES FOR SUPER-α-STABLE PROCESSES Zhang Jing; Ren Yanxia Acta mathematica scientia,Series B. 2006, 26 (2):  358-370.  DOI: 10.1016/S0252-9602(06)60058-1 Abstract ( 1222 )   RICH HTML PDF (174KB) ( 897 )   Save Suppose X is a super-α-stable process in Rd, (0<α<2), whose branching rate function is dt, and branching mechanism is of the form ψ(z)=z1+β (0<β≤1). Let Xτ and Yτ denote the exit measure and the total weighted occupation time measure of X in a bounded smooth domain D, respectively. The absolute continuities of Xτ and Yτ are discussed. Related Articles | Metrics

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ON THE LASOTA-WAZEWSKA MODEL WITH PIECEWISE CONSTANT ARGUMENT Feng Qiuxiang; Yuan Rong Acta mathematica scientia,Series B. 2006, 26 (2):  371-378.  DOI: 10.1016/S0252-9602(06)60059-3 Abstract ( 1091 )   RICH HTML PDF (141KB) ( 2125 )   Save In this article, a delay differential equation with piecewise constant argument is considered; the existence and global attractivity condition of almost periodic solution and quasi-periodic solution are obtained. Related Articles | Metrics

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WEAK UNCORRELATEDNESS OF RANDOM VARIABLES Sofiya Ostrovska Acta mathematica scientia,Series B. 2006, 26 (2):  379-384.  DOI: 10.1016/S0252-9602(06)60060-X Abstract ( 1091 )   RICH HTML PDF (115KB) ( 1012 )   Save New measures of independence for n random variables, based on their moments, are studied. A scale of degrees of independence for random variables which starts with uncorrelatedness (for n=2) and finishes at independence is constructed. The scale provides a countable linearly ordered set of measures of independence. Related Articles | Metrics