Table of Content

    16 August 2009
    Volume 44 Issue 8
    Roth’s theorem and abc-conjecture
    Pei-Chu HU, Chong-Jun YANG
    J4. 2009, 44(8):  1-12. 
    Abstract ( 1520 )   PDF (263KB) ( 499 )   Save
    Related Articles | Metrics

    In this survey, we compare Roth’s theorem with abc-conjecture, and introdu ce an approach routine for the abc-conjecture.

    Degree conditions for bipartite graphs to contain 6-cycles
    JU Jing-Song, LI Shuo, YANG Xin-Gang
    J4. 2009, 44(8):  13-15. 
    Abstract ( 964 )   Save
    Related Articles | Metrics

    Let G=(V1,V2;E) be a balanced bipartite  graph with |V1|=|V2|=3k and k≥1. If the minimum degree δ≥2k,  then G either contains k  vertices d isjoint 6-cycles or contains k-1 vertices disjoint 6-cycles and a 4-cycle.

    On the extremal Merrifield-Simmons index with  respect to trees having given number of endvertices
    GAO Yu-Fen, WEI Xiao-Li
    J4. 2009, 44(8):  16-20. 
    Abstract ( 872 )   Save
    Related Articles | Metrics

    The Merrifield-Simmons index for a 5-leaf tree of order n  is investiga ted, and the minimal Merrifield-Simmons index for a 5-leaf tree is characteri zed.

    Signed edge total domination numbers of graphs
    YUAN Xiu-Hua
    J4. 2009, 44(8):  21-24. 
    Abstract ( 832 )   Save
    Related Articles | Metrics

    Let γ′ws(G) be the signed edge  total domination number of a grap h G. The low bound of the signed edge total domination number of a graph G   is given,and the signed edge total domination number of Kn is determined.

    Graham's conjecture on the product of the thorn graph
    LIU Hai-Yang, MA Cheng-Gang, WANG Zhi-Beng
    J4. 2009, 44(8):  25-30. 
    Abstract ( 1058 )   Save
    Related Articles | Metrics

    It is proved that Graham’s conjecture holds for a thorn graph  of the  complete graph by a graph with the two-pebbling property. As a corollary, Graham's conjecture is true when G and H are a thorn graph of the complete graphs.


    L(2,1,1)-Labeling of simple graphs
    DUAN Ci-Meng, LV Ping-Li, MIAO Lian-Yang, MIAO Zheng-Ke
    J4. 2009, 44(8):  31-34. 
    Abstract ( 1409 )   Save
    Related Articles | Metrics

    The L(2,1,1)-labeling numbers for comp lete graphs, complete bipartite   graphs, paths and cycles are given. An arithmetic method for L(2,1,1)-labeling  to a graph G with maximum degree Δ is given. It is proved that λ2,1,1(G)≤Δ3-Δ2+2Δ.

    Some conditions for finite groups to be solvable
    WANG Dun-Xin
    J4. 2009, 44(8):  35-38. 
    Abstract ( 894 )   Save
    Related Articles | Metrics

    The relationships between the semi cover-avoiding property of subgroups  and the solvability of groups are investigated. As an application, some sufficient and necessary conditions for finite groups to be solvable are obtained. It is proved that a finite group G is solvable if and only if for every maximal subgroup M of  G, either M is semi cover-avoiding in G, or M has a solvable m aximal completion C such that C is semi cover-avoiding in G.

    Tensor product of left quasinormal bands
    BI Xiao-Dong
    J4. 2009, 44(8):  39-41. 
    Abstract ( 1022 )   Save
    Related Articles | Metrics

    The existence of a tensor product is proved  in the left quasi-normal ban d category, and the relationship with the tensor product in the semi-group          category  is provided. Furthermore, the relationship between the tensor product of semi-lattices in the left quasi-normal band category and in the semi-lattice category is  given.


    Some properties and simple application of a generalized kind of  generalized matrix functions
    LI Cong-Hui
    J4. 2009, 44(8):  42-45. 
    Abstract ( 775 )   Save
    Related Articles | Metrics

    A new kind of generalized matrix function  is defined, which is with classical generalized matrix functions for exceptions .  Some  properties of this function are obtained, and some application are investigated. 


    Lower bounds for the rank and estimation for eigenvalues
    HU Xin-Kai, WU Dun-Liang
    J4. 2009, 44(8):  46-50. 
    Abstract ( 1061 )   Save
    Related Articles | Metrics

     Lower bounds for the rank and  the estimation for eigenvalues of matrices are discussed. Two lower bounds for the rank and estimation for the real part and imaginary part of eigenvalues are obtained. Also, we prove that all the eigenvalues of any complex matrix are located in one disk. Some numerical examples show the effectiveness of our results.


    Resarches on some properties of a strong FS-Poset
    LIANG Shao-Hui, DIAO Ban
    J4. 2009, 44(8):  51-55. 
    Abstract ( 711 )   Save
    Related Articles | Metrics

    The definition of strong FS-Posets is given. Some properties of strong FS-Posets are discussed, and it is proved that strong FS -Posets not only are continuous, but also are Scott. Based on strong FS-Poset s, the concept of strong FS-Lattices is given. Some properties of strong FS-La tt ices are studied. Strong FS-Lattices are characteristic of the function space. The sufficient and necessary conditions for a continuous lattice to be a s trong FS-Lattice are obtained.


    The eventually regularity on a class subsemirings of a semiring
    JIAO Tie-Ke
    J4. 2009, 44(8):  56-57. 
    Abstract ( 731 )   Save
    Related Articles | Metrics

    We give the regular condition for the congruence class of an idempotent in  some semirings, and prove that the congruence class of an idempotent in a completely regular semiring and an inverse semiring is regular.  At the  same time,we discuss the eventually regularity on the congruence class of an idem potent in an eventually regular semiring.

    S-Noetherianess of A+xB[[x]]
    JIAO Yu-Juan, ZHANG Shen-Gui
    J4. 2009, 44(8):  58-61. 
    Abstract ( 840 )   Save
    Related Articles | Metrics

    Let ABbe an extension  of commutative rings with identity, x an indeterminate over B, R:=A+xB[[ x]] and SA a given multiplicative set . It is shown that if ,(∩snA,n1)∩SФfor each  s∈S  where  Scons ists of nonzerodivisors, then Ris SNoetherian if and only if  A is S-Noetherian and B is an  S -finite A-module. 



    On a generalization of α-reversible rings
    DONG Jun, WEI Jie
    J4. 2009, 44(8):  62-67. 
    Abstract ( 801 )   Save
    Related Articles | Metrics

    Let α be a ring endomorphism α. Weak α-reversible rings are introduced whi ch generalized  α-reversible rings, some extension of weak α-reversible rings and their properties are investigated. The relations between weak α-reversible rings and weak α-skew Armendariz rings are
    obtained. 


    The M/M/1/N queuing system with negative customers and a single working vacation
    FAN Jian-Wu, DIAO Xiao-Hua, TIAN Ai-Shuo, YUAN Xiao-Jing
    J4. 2009, 44(8):  68-73. 
    Abstract ( 883 )   Save
    Related Articles | Metrics

    An M/M/1/N queuing system was considered with negative  customers and a single working vacation. The server works at a lower rate rather  than completel y stops service during the vacation period. Negative customers remove positive customers only one by one at the head (if present). When a negative customer arrives, if the system is empty, it will disappear. Negative customers need no services.  The matrix form solution of the steadystate probability is derive d  by the Markfov process method and the matrix solution method. Some performance  measures of the system such as the expected number of customers the system or  in the queue and the loss probability of the customer are also presented. Finally the effects of the parameters of the system are investigated, such as the va cati on service rate μvand the vacation rate θon the expected waiting  queue length and the loss probability of customers by numerical examples.


    Existence of a positive solution for first order nonlinear impulsive singular differential equations of mixed type in Banach spaces
    LOU Guo-Jiu, ZHANG Xin-Qiu, WANG Jian-Guo
    J4. 2009, 44(8):  74-79. 
    Abstract ( 894 )   Save
    Related Articles | Metrics

    By constructing a closed convex set and using the fixed point theory of completely continuous operators, the existence of positive solutions for an initial value problems of first order nonlinear impulsive singular integro-differential equations in a Banach space are obtained.

    Exact generalized tautologies in fuzzy modal logic system M?uk
    JU Chang-Tian, WANG Guo-Dun
    J4. 2009, 44(8):  80-85. 
    Abstract ( 940 )   Save
    Related Articles | Metrics

    The fuzzy modal logic system M?uk is introduced, where the evaluation lattice is taken to be the unite interval and the binary relation R is fuzzif ied, then it is discretized to be the multi-valued fuzzy modal logic system M? n. It is proved that for any possible value α in M?n there exists an exact  α-tautology; and in M?uk, for any rational α∈[0,1], there exists  an exac t α-tautology. It is pointed out that the lift-algorithm which plays a key role in R0 systems is not suitable for the system M?n, and the reasons are  analyzed.

    A method for ranking fuzzy numbers based on the ideal points
    GAO Shan-Lin, LI Jian, RUAN Xiao-Jia
    J4. 2009, 44(8):  86-89. 
    Abstract ( 798 )   Save
    Related Articles | Metrics

    Under the integrated considerations about  the possibilistic mean and the ideal points, the fuzzy numbers are mapped to the possibilistic interval by a  αcut. In order to form a synthesized index for ranking fuzzy numbers, the  distances between the possibilistic mean and the ideal point are calculated.


    The dynamic finite element method with characteristics for convectiondominated diffusion problems
    LI Zhi-Chao, FU Gong-Fei
    J4. 2009, 44(8):  90-96. 
    Abstract ( 813 )   Save
    Related Articles | Metrics

    The method of characteristics is combined with dynamic  finite element spaces based on the moving grids method to create a fully discrete characteristic dynamic finite element procedure for the solution of  second order linear convectiondominated diffusion problems. The procedure is proved to be stable. Convergence analysis and error estimates are established, which  show that the error estimate in the energy norm is optimal when Mh4/Δt is bounded. Both the L2-norm and the energy norm error  estimate are optimal when  Mh2/Δt is bounded, where M is the total number of gridschanging. h and Δt are the spatial and temporal mesh parameters respectively. 