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Table of Content

      
    24 October 2007
    Volume 42 Issue 10
    Articles
    Comparison theorem for solution Z of BSDEs
    HE Kun
    J4. 2007, 42(10):  1-04 .  doi:
    Abstract ( 1843 )   PDF (157KB) ( 1442 )   Save
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    Talking about the complete comparison theorem BSDEs brought out by Z J Chen. It's well known that the comparison theorem operate primarily in Backward Stochastic Differential Equations theory, however existing comparison theorem mostly concerns about Y, which was part of the pair solution (Y,Z).Following［1,2］, concerning comparison results on Z.
    Remarks on “Some properties of the induced map”
    LU Juan,LI Sheng-gang*
    J4. 2007, 42(10):  5-08 .  doi:
    Abstract ( 1966 )   PDF (146KB) ( 1335 )   Save
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    （1, t） encryption based on the Weil pairing
    ZHANG Li-jiang,WANG Wei,WEI Pu-wen
    J4. 2007, 42(10):  9-12 .  doi:
    Abstract ( 1643 )   PDF (237KB) ( 1675 )   Save
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    (1, t) encryption scheme is defined and two fully functional (1, t) encryption schemes based on the Weil pairing are proposed. The schemes are based on bilinear maps, of which the Weil pairing on the elliptic curves is an example.
    Conjugate duality and optimal properties of value-type bilevel linear programming problem
    SU Jie,
    J4. 2007, 42(10):  13-17 .  doi:
    Abstract ( 1701 )   PDF (208KB) ( 1694 )   Save
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    The conjugate dual for the value-type bilevel linear programming was formulated based on the Frenchel-Rockafellar duality for DC programming. Strong duality between primal and dual problems was established, and some theorems on the optimal properties of the primal and dual problems were given.
    Minimal and maximal mild solutions of semilinear evolution equations in Banach spaces
    ZHANG Xiao-yan,SUN Jing-xian
    J4. 2007, 42(10):  18-21 .  doi:
    Abstract ( 1577 )   PDF (214KB) ( 1551 )   Save
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    By using the cone theory, the existence of global minimal and maximal mild solutions of initial value problem for a class of semilinear evolution equation with noncompact semigroup in Banach spaces was obtained without demanding the existence of upper and lower solutions. The results improve and generalize many relative results.
    Uniqueness of meromorphic functions with their derivatives
    QU Jing-jing
    J4. 2007, 42(10):  22-26 .  doi:
    Abstract ( 1784 )   PDF (191KB) ( 1388 )   Save
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    The uniqueness problems of meromorphic functions with their derivatives were studied and some results given by Zhang Qingcai were improved. The condition obtained by Rainer Bru¨ck that fand f(k)share 1CM can be replaced by E1)(1,f)=E1)(1,f(k)).
    Two direction variation S-probability rough sets and its attribute probability characters
    ZHAO Jun-kai,CAI Cheng-wen,REN Xue-fang
    J4. 2007, 42(10):  27-30 .  doi:
    Abstract ( 1693 )   PDF (215KB) ( 1582 )   Save
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    Based on attribute's dynamic transfer property of two direction variation S-rough sets and statistical information in knowledge base, the two direction variation S-probability rough sets was put forward. The attribute's probability characters of two direction variation S-probability rough sets were discussed. These properties are the bases of dynamic decision-making. Using the above discussion, a special application example was given.
    One direction S-dual rough decision law and decision law mining
    HUANG Shun-liang,HAO Xiu-mei,SHI Kai-quan,
    J4. 2007, 42(10):  31-36 .  doi:
    Abstract ( 1820 )   PDF (301KB) ( 1608 )   Save
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    By using the dual of one direction S-rough sets, a generation method of one direction S-dual rough decision law is presented and the concepts of upper decision law, lower decision law, one direction S- dual rough decision law kernel and one direction S-dual rough decision law band are proposed. Then by using these concepts, the theorem of lower decision law transfer, the theorem of upper decision law transfer, the theorem of -seperation attribute, the theorem of rough decision law mining and the rough decision law mining criteria are presented.
    Dynamic chromatic number of unicyclic graphs and bicyclic graphs
    QIN Jian,ZHANG Yan
    J4. 2007, 42(10):  37-40 .  doi:
    Abstract ( 2073 )   PDF (198KB) ( 1436 )   Save
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    The dynamic chromatic number of unicyclic graphs is proved to be 3 or 4 based on the analysis of the property of unicyclic graphs. Then the dynamic chromatic number of most bicyclic graphs is proved to be χd(G)=max{χd(H1),χd(H2)} after the subgraphs H1 and H2 of bicyclic graphs are structured. At last, a bicyclic graph, is given whose dynamic chromatic number is not max{χd(H1),χd(H2)}.
    The degree-constrained k-arboricity of outerplanar graphs
    MA Qin
    J4. 2007, 42(10):  41-43 .  doi:
    Abstract ( 2138 )   PDF (179KB) ( 1134 )   Save
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    Let ak(G) be the least number of forests of maximum degree not exceeding k which cover the edges of a graph G. Then ak(G)=「Δ(G)/k for any outerplanar graph G having 2≤k＜Δ(G).
    On some properties of strongly KC space
    SUN Wei-hua,XU Yu-ming,FAN Ling-ling
    J4. 2007, 42(10):  44-46 .  doi:
    Abstract ( 2101 )   PDF (181KB) ( 1636 )   Save
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    The properties of strongly KC spaces were further studied and a sufficient condition for a space to be Katetov-strongly KC was given.
    Linear two-step stationary iteration for solving Ill-posed problems
    ZHU Guang-jun,ZHANG Yu-hai,ZHANG Chao
    J4. 2007, 42(10):  47-53 .  doi:
    Abstract ( 2222 )   PDF (239KB) ( 1484 )   Save
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    The approximate solutions of equation Kx=y was solved by linear two-step stationary iterative methods. Filter function is a regularizing filter function by restricting α,β. Finally, the stopping criteria and the order of convergence were given.
    Knowledge filter and attribute f-transfer dependence
    FU Hai-yan,SHI Kai-quan
    J4. 2007, 42(10):  54-58 .  doi:
    Abstract ( 1775 )   PDF (210KB) ( 1648 )   Save
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    Based on S-rough sets, the concepts of f-transfer knowledge, F-transfer knowledge, knowledge filter degree and knowledge filter attribute f-transfer dependence were given. Then knowledge filter attribute f-transfer dependence theorems were proposed. Finally, an example was given to illustrate the application of knowledge filter attribute f-transfer dependence and reveal the essence of knowledge filter.
    The 3-choosability of plane graphs without3-， 6-,9- and 10-cycles
    ZHU Xiao-ying,XU Yang,SHI Hong-jun
    J4. 2007, 42(10):  59-62 .  doi:
    Abstract ( 1777 )   PDF (189KB) ( 1500 )   Save
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    Lam proved that every planar graph with girth at least 4 and without 5-and 6- cycle is 3-choosable. It is shown that if G is of girth 4 and contains no 6-, 9-, and 10-cycles,then G is 3-choosable.
    Converse comparison theorems for reflected BSDEs with double obstacles
    ZHENG Shi-qiu,ZHOU Sheng-wu,XU Feng
    J4. 2007, 42(10):  63-68 .  doi:
    Abstract ( 1995 )   PDF (238KB) ( 1100 )   Save
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    The converse comparison problem of reflected backward stochastic differential equations (RBSDEs) with double obstacles was explored, and some converse comparison theorems for the generators under some suitable conditions were established.
    Lie ideas of the nest subalgebras in hyperfinite factors
    BU Mei-hua,JI Pei-sheng,QI Wei-qing
    J4. 2007, 42(10):  69-75 .  doi:
    Abstract ( 1953 )   PDF (259KB) ( 1700 )   Save
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    Let B be a hyperfinite factor and let T(N) be a regular nest subalgebra of B. It is proved that a σ weakly closed subspace L of T(N) is a Lie ideal in T(N) if there exist a σ weakly closed associative ideal J of T(N)and a subspace Eof the center of the diagonal part of T(N), such that J0L J+E，where J0 is the set of trace-zero elements in J.
    A practical method for the least common multiple of polynomials
    WANG Xin-min,SUN Xia
    J4. 2007, 42(10):  76-79 .  doi:
    Abstract ( 2332 )   PDF (164KB) ( 1852 )   Save
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    Based on the elementary row transformation and the technique of matrix, a practical method was given for the least common multiple of polynomials. The least common multiple of polynomials can be found only through the elementary transformations on a matrix.
    Convexity-preserving piecewise rational cubic interpolation
    TIAN Meng,LI Shi-long
    J4. 2007, 42(10):  80-83 .  doi:
    Abstract ( 2075 )   PDF (216KB) ( 1826 )   Save
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    An explicit representation of a C1 piecewise rational cubicspline was developed, which can produce a convex interpolant to given convex data. The explicit representation was easily constructed, and no additional restriction on data was needed. Numerical experiments indicate that the method produces visually pleasing curves. Furthermore, an error analysis of the interpolant was given.
    Empirical study about value at risk model based on the realized volatility
    MA Yu-lin.WANG Xi-quan
    J4. 2007, 42(10):  84-89 .  doi:
    Abstract ( 1965 )   PDF (593KB) ( 1770 )   Save
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    The forecast method of realized volatility instead of methods previously used was used to study the value at risk model. Five stocks were chosen at random for empirical research. For forecasting performance of a GARCH type model with the forecasting performance of a model based on the daily realized volatility, the results show that the later is evidently better than the former.
    Provable degree of formula on theories in the propositional fuzzy logic system God
    GAO Qin,ZHANG Xing-fang,WANG Qing-ping
    J4. 2007, 42(10):  90-95 .  doi:
    Abstract ( 2436 )   PDF (240KB) ( 1473 )   Save
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    Based on the concept of provable degree of formula on theories in propositional fuzzy logic systems， the calculating formula provable degree of formula on theories was given in the propositional fuzzy logic system， and its properties were shown.
    Comparision theorem of comodules over rings
    WEN Chuan-bao
    J4. 2007, 42(10):  96-99 .  doi:
    Abstract ( 1825 )   PDF (180KB) ( 1191 )   Save
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    A sufficient condition of comparision theorem of comodule over rings is set up. The content includes comudules over commutative rings with 1, projective comodules, injective comodules, injective resolution, projective resolution, homotopies and comparision theorem.
    Jordan(α,β)-derivations and generalized Jordan(α,β)-derivations on upper triangular matrix algebras
    SUN Liang-ji,JI Guo-xing
    J4. 2007, 42(10):  100-105 .  doi:
    Abstract ( 2077 )   PDF (226KB) ( 1543 )   Save
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    Let R be a commutative ring with identity and let Tn(R) be an upper triangular matrix algebra over R, it is proved that every generalized Jordan (α,β)-derivation from upper triangular matrices over a commutative ringinto its bimodule is the sum of a generalized (α,β)-derivation and (α,β)-antiderivation.
    Error analysis of the rational interpolation based on arithmetic average difference quotient
    LI Shi-long,ZHANG Yun-feng
    J4. 2007, 42(10):  106-110 .  doi:
    Abstract ( 1911 )   PDF (205KB) ( 1586 )   Save
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    The definition of the arithmetic average difference quotient is introduced. A kind of the rational cubic spline interpolation with linear denominator based on arithmetic average difference quotient is also given. A new method based on the Peano-kernel theory is proposed. The approximation properties of the function value and the derivative of the rational interpolation are studied, and the data analysis is given.
    Properties of a quasi-claw-free graph
    WANG Bing
    J4. 2007, 42(10):  111-113 .  doi:
    Abstract ( 1931 )   PDF (173KB) ( 1644 )   Save
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    The properties of quasi-claw-free graphs were discussed, which are larger than claw-free graphs. and the following two results were obtained: if G is a quasi-claw-free graph, then (ⅰ) 2t(G)=κ(G), where ω(G-S)≤t(G).(ⅱ) For every dominating set D and each t∈D, there are at most three vetices u1,u2,u3∈(V-D) satisfying,　N(ui)∩D={t}(i=1,2,3), then γ(G)=i(G). This result is the best possible. These results extend the corresponding results in claw-free graph.
    Embedding hypergraph in trees of rings
    WANG Qi,ZHAO Xiu-heng,LI Guo-jun
    J4. 2007, 42(10):  114-117 .  doi:
    Abstract ( 1985 )   PDF (214KB) ( 1386 )   Save
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    Given a hypergraph H on trees of rings G, the problem of embedding hypergraph in trees of rings(EHTR) was given to embe each hyperedge of H as a tree in G such that the maximal times that these trees using any edge of G is minimal. This problem was initiated from the problem of minimum-congestion hypergraph embedding in a cyle(MCHEC). The EHTR problem can be solved as a PTAS by the abbreviative algorithm of the MCHEC problem, and can be proved that it is NP-complete.
    Function S-rough sets and integral metric of laws
    XIE Yun-long,DU Ying-ling
    J4. 2007, 42(10):  118-122 .  doi:
    Abstract ( 1939 )   PDF (207KB) ( 1402 )   Save
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    Using function one direction singular rough sets and dual of function one direction singular rough sets, the concepts of f-law knowledge, law knowledge, f-law and -law were given. With these concepts, the relation of laws generated by law knowledge, and the integral metric were both discussed.
    Schur factorization and normal matrices factorization of row (column) symmetric matrices
    YUAN Hun-ping
    J4. 2007, 42(10):  123-126 .  doi:
    Abstract ( 2665 )   PDF (186KB) ( 3706 )   Save
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    The concept of row (column) transposed matrix and row (column) symmetric matrix are given, and their basic properties are also studied. The formula for the Schur factorization and normal matrix factorization of row (column) symmetric matrix are obtained, which all can dramatically reduce the amount of calculation and Schur factorization and normal matrix factorization of row (column) symmetric matrix can save dramatically the CPU time and memory without losing any numerical precision.
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