Table of Content

    24 February 2008
    Volume 43 Issue 2
    Continuous-time hedging under complete market by BSDEs
    HE Kun
    J4. 2008, 43(2):  1-07 .  doi:
    Abstract ( 1017 )   PDF (275KB) ( 1176 )   Save
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    Applying backward stochastic differential equations, the hedging under complete market were considered. Based on the generalized Feynman-Kac formula related with forward and backward equations, proposed by El. Karoui, Peng, Quenez(1997),a particular formula about the portfolio strategy for hedging one contingent claim was given.
    A high order parallel iterative scheme for the dispersive equation
    ZHANG Qing-jie,WANG Wen-qia
    J4. 2008, 43(2):  8-11 .  doi:
    Abstract ( 1204 )   PDF (413KB) ( 938 )   Save
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    A high order implicit scheme was presented for the dispersive equation and a corresponding alternating group iterative scheme was derived, which has high accuracy and quick ratio of convergence. The unconditional stability for the implicit scheme and the convergence for the alternating group iterative scheme were also proved. A numerical experiment conformed to theoretical results. A numerical comparison between the scheme mentioned in this paper (NAGI) and a similar known method (AGI) was also presented.
    The number of quadrilaterals in a graph satisfying the given degree condition
    LI Feng,LI Shuo,LIANG Feng
    J4. 2008, 43(2):  12-15 .  doi:
    Abstract ( 1315 )   PDF (181KB) ( 1053 )   Save
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    It was proved that if G is a graph of order 4k,and the minimum sum of degree of any two nonadjacent vertices in G is no less than 4k-2,then G contains k-1 disjoint quadrilaterals.
    Ruin probability for a compound Poisson-Geometric process of multi-risk model with interference
    YU Wen-guang,HUANG Yu-juan
    J4. 2008, 43(2):  16-18 .  doi:
    Abstract ( 1470 )   PDF (198KB) ( 944 )   Save
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    A risk model, which the compensation arrives to the compound Poisson-Geometric process, was generalized. The arrival of term policies with interference, which was a Poisson process with intensity α, was studied. Applying the martingle theory, the Lundberg inequality and the formula for the ruin probability were concluded.
    A two-direction S-rough fuzzy set and its application
    LIU Ji-qin,PEI Hai-feng
    J4. 2008, 43(2):  19-22 .  doi:
    Abstract ( 1103 )   PDF (223KB) ( 971 )   Save
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    Using the concept of fuzzy elementary transfers, a static fuzzy set was generalized to a dynamic fuzzy set, then a two-direction S-fuzzy set was obtained. Based on this, a two-direction S-rough fuzzy set was proposed, and its general structure was given. The relationships between a two-direction S-rough fuzzy set and Z.Pawlak rough sets, between a two-direction S-rough fuzzy set and a Dubois rough fuzzy set, between a two-direction S-rough fuzzy set and a two-direction S-rough set were analyzed. The application of the two-direction S-rough fuzzy set was given. A two-direction S-rough fuzzy set is a dynamic rough fuzzy set.
    Function one-direction S-rough sets and system state detection-recognition
    DU Ying-ling,REN Xue-fang
    J4. 2008, 43(2):  23-28 .  doi:
    Abstract ( 1042 )   PDF (268KB) ( 1227 )   Save
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    Function S-rough sets which have dynamic characteristic and law characteristic have three forms: function one-direction S-rough sets, function two-direction S-rough sets, and dual of function one-direction S-rough sets. Introducing the concept of function one-direction S-rough sets into system state detection-recognition, the concepts of state departure and the distance of state departure were presented, and criterion of system state recognition and its applications were given. Using function one-direction S-rough sets to detect the system state is a new trend of system state recognition and detection research.
    F-rough integrals generated by function one-direction S-rough sets
    YU Xiu-qing,SHI Kai-quan
    J4. 2008, 43(2):  29-34 .  doi:
    Abstract ( 1107 )   PDF (236KB) ( 1115 )   Save
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    The upper approximation and the lower approximation in function onedirection S-rough sets are both seen as R-function equivalence classes which can generate two functions. If the two generated functions are continuous in closed interval [a,b], the pair of the integrals generated by the two functions are called F-rough integrals based on function one-direction S-rough sets. F-rough integrals are ordinary integral promotion, and they have dynamic characteristics with some good nature, and they provides a convenient and effective tool to resolve some factual problems.
    The theory of ∑Γ-fuzzy truth degree being relative to finite theory in logic system L
    WANG Zhao-hai,WU Hong-bo*
    J4. 2008, 43(2):  35-39 .  doi:
    Abstract ( 1187 )   PDF (228KB) ( 1266 )   Save
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    Having combination of the theory of truth degree in metrology of logic with the theory of ∑-α-tautologies in fuzzy logic, which have been introduced by professor G.J.Wang, the theory of ∑Γ-truth degree was introduced, and its properties which induce a pseudometric on F(S) were investigated. The results gained have complemented and enhanced the original theory, and the work delivers a new frame for fuzzy reasoning.
    Fuzzy good congruences on type-A semigroups
    LI Chun-hua
    J4. 2008, 43(2):  40-43 .  doi:
    Abstract ( 958 )   PDF (201KB) ( 857 )   Save
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    The notions of a fuzzy good congruence relation and a fuzzy cancellative congruence relation on abundant semigroups were introduced, and some properties and characterizations of fuzzy good congruences on such semigroups were given. Some properties of fuzzy good congruences on type-A semigroups were given. Finally, sufficient and necessary conditions for a fuzzy good congruence on a type-A semigroup to be cancellative were proved.
    A note on ultra separation axioms of L-topological spaces
    YU Yue,MENG Guang-wu
    J4. 2008, 43(2):  44-47 .  doi:
    Abstract ( 870 )   PDF (183KB) ( 1114 )   Save
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    In L-fuzzy topological spaces, ultra separation axioms were defined, some characterization of them were gvien, and their properties were discussed.
    The least-squares solutions of inverse problems for generalized(R,S)-symmetric matrices
    SONG Jun-ling,TIAN Jin-ting,ZHAO Jian-li
    J4. 2008, 43(2):  48-51 .  doi:
    Abstract ( 1083 )   PDF (201KB) ( 686 )   Save
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    The least-squares solutions of inverse problems for generalized(R,S)-symmetric matrices were discussed.The necessary and sufficient conditions were presented, and the general form was given.The optimal approximation was discussed, and the precise expression of the solution was provided.
    The two-grid algorithm of the finite volume element method for second-order indefinite elliptic problems
    DAI Zhen-xiang
    J4. 2008, 43(2):  52-57 .  doi:
    Abstract ( 1160 )   PDF (240KB) ( 844 )   Save
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    The two-grid algorithm of the finite volume element method for second-order indefinite elliptic problems in R2 was presented ,based on the P1 nonconforming element.The following error estimated in the H1-norm between the solution of the two-grid and the finite volume element appoximation of the elliptic problem were derived::‖uh-uh‖1,h≤CH2‖f‖1,‖u-uh‖1,h≤C(h+H2)‖f‖1.
    Relation between constancy of g-expectations and g(y,0,t)=0
    LIU Jie
    J4. 2008, 43(2):  58-61 .  doi:
    Abstract ( 1097 )   PDF (199KB) ( 920 )   Save
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    A risk measure usually needs the constancy property. By investigating the constancy property of g and g-expectations, a necessary and sufficient condition on the constancy of g-expectations can be gained. Furthermore, it strengthens the relationship between the space of function g and the space of nonlinear expectation.
    Armendariz and semicommutative properties of a class of upper triangular matrix rings
    WANG Wen-kang
    J4. 2008, 43(2):  62-65 .  doi:
    Abstract ( 1566 )   PDF (161KB) ( 963 )   Save
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    A ring R is called Armendariz,if (∑mi=0aixi)(∑nj=0bjxj)=0∈R[x],then aibj=0,where 0≤i≤m, 0≤j≤n .A ring R is called semicommutative if for ant a,b∈R,ab=0 implies aRb=0.
    The property of some special n-Coherent functor
    XING Jian-min
    J4. 2008, 43(2):  66-69 .  doi:
    Abstract ( 942 )   PDF (162KB) ( 948 )   Save
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    A small n-Coherent functor is defined, and the co-kernel and kernel of some special n-Coherent functors were studied. Some properties of n-Coherent functor were described.
    Oscillation of second order nonlinear neutral delay difference equations with continuous arguments
    LI Tong-xing,HAN Zhen-lai,ZHANG Meng,CAO Feng-juan
    J4. 2008, 43(2):  70-71 .  doi:
    Abstract ( 1251 )   PDF (163KB) ( 1148 )   Save
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    By analytic method, the oscillation for a class of second order nonlinear neutral delay difference equations with continuous arguments was studied. Some sufficient conditions were obtained for oscillation of all bound solutions of the equations and oscillation of the equations.
    Some generalizations of Ou-Iang's inequality and its applications
    GAO Qing-ling,WANG Jian-guo
    J4. 2008, 43(2):  72-76 .  doi:
    Abstract ( 1026 )   PDF (177KB) ( 1117 )   Save
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    Some new Ou-Iang's inequalities for the nonlinear integral type were established,which can generalize and improve some eatablished results,and the character of the solutions of differential equations was discussed by using the conclusions.
    The model of supply chains in part information sharing
    ZHANG Yun,CUI Yu-quan*,LIU Lei
    J4. 2008, 43(2):  77-81 .  doi:
    Abstract ( 1153 )   PDF (307KB) ( 1067 )   Save
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    The problem of twolayer supply chains in part information sharing was studied. At the base of simple introduction in twolayer supply chains in whole information sharing, it set up the model of part information sharing by using the method of a dynamic program. Some factors influencing part information sharing which including market waving, and waiting time of replenishing the goods were discussed. Finally, an example was given and computed by MATLB.
    Two types of decomposition algorithms for stochastic programming
    ZHANG Xia,FU Hai-ying,SUN Jin-ling
    J4. 2008, 43(2):  82-86 .  doi:
    Abstract ( 1238 )   PDF (235KB) ( 1333 )   Save
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    Based on stochastic programming theory, two types of decomposition algorithms, primal-dual decomposition algorithm and Benders decomposition, were given; both of which can partition the variables into two sets-x and y.Rather than attempting to solve the programming, a collection of smaller sub-problems can be iteratively solved, and a solution to the entire problem was obtained.
    On the D(2)-vertex-distinguishing proper edge-coloring of cones over paths and cycles
    LIU Li-qun,CHEN Xiang-en*
    J4. 2008, 43(2):  87-97 .  doi:
    Abstract ( 901 )   PDF (349KB) ( 1111 )   Save
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    It is studied that the D(2)-vertex distinguishing proper edgecolosings of cones over paths and cycles, and it is obtained thatthe D(2)-vertex distinguishing proper edge chromatic numbers ofcones over paths and cycles in this paper.
    On the BQ property of linear ordered transformation semigroups
    CAO Yong
    J4. 2008, 43(2):  98-100 .  doi:
    Abstract ( 896 )   PDF (163KB) ( 1232 )   Save
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    BQ property is studied in linear ordered regular transformation semigroups, and some results of Y.Kemprasit on BQ property in linear ordered regular transformation semigroups were developed.
    Stochastic study in the ternary logic system G3
    WANG Qing-ping,ZHANG Xing-fang,WANG Da-quan
    J4. 2008, 43(2):  101-108 .  doi:
    Abstract ( 1293 )   PDF (266KB) ( 790 )   Save
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    DG3-stochastic truth degree of formulae in the ternary logic G3 was presented by using stochastic method on evaluation sets. It was proved that the set of stochastic truth degree of all formulae has no isolated point. The conceptions of DG3-similarity degree and pseudo-metric on two formulae were given. DG3-logic metric space was built. It was proved that this space has no isolated point.
    The total labelling number of some bipartite graphs
    MA Qiao-ling,ZHANG Su-mei
    J4. 2008, 43(2):  109-112 .  doi:
    Abstract ( 1098 )   PDF (208KB) ( 1106 )   Save
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    The (d,1)-total labelling number of a graph G is the width of the smallest range of integers that suffices to label the vertices and edges of G such that: (1) any two adjacent vertices of G receive distinct integers; (2) any two adjacent edges of G receive distinct integers; (3) each vertex and its incident edges receive integers which differ as at least d(d≥2) in absolute value. Some results of the (d,1)-total labelling number for some bipartite graphs were given.