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- Jordan multiplicative isomorphisms on Spin factors
- JI Pei-sheng, SUN Lin, CHEN Jian-hui
- J4. 2011, 46(8): 1-3.
- Abstract ( 604 ) PDF (261KB) ( 971 ) Save
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- Conservative scheme for the general improved KdV equation
- ZHANG Tian-de1, ZUO Jin-ming2, DUAN Ling-ji1
- J4. 2011, 46(8): 4-7.
- Abstract ( 612 ) PDF (829KB) ( 1189 ) Save
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- A subspace accelerated truncated Newton algorithm for solving the extreme eigenvalue of large-scale sparse symmetric matrix
- QIAN Xiao-yan
- J4. 2011, 46(8): 8-12.
- Abstract ( 633 ) PDF (313KB) ( 1483 ) Save
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- An implicit difference scheme for solving the neutral delay parabolic differential equation
- JIN Cheng-ri, YU Zhan-hua, QU Rong-ning
- J4. 2011, 46(8): 13-16.
- Abstract ( 541 ) PDF (311KB) ( 1422 ) Save
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- Structure of eigenvalues of multi-point boundary value problems
- GAO Jie
- J4. 2011, 46(8): 17-22.
- Abstract ( 610 ) PDF (312KB) ( 1066 ) Save
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- Fundamental solutions of fractional-in-space diffusion equation with Riesz fractional derivative in two and three dimensions
- WANG Xue-bin
- J4. 2011, 46(8): 23-30.
- Abstract ( 695 ) PDF (300KB) ( 742 ) Save
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- Higher accuracy analysis for the bilinear element solution of nonlinear viscoelasticity type equations
- NIU Yu-qi1, WANG Fen-ling1, SHI Dong-wei2
- J4. 2011, 46(8): 31-37.
- Abstract ( 590 ) PDF (343KB) ( 760 ) Save
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- Approximation method for two-point boundary value problem of differential game based on ridge basis function
- TIAN Shuang-liang1, FANG Bao-yan1*, WANG Zhi-gang2
- J4. 2011, 46(8): 38-41.
- Abstract ( 565 ) PDF (589KB) ( 1091 ) Save
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- Super-convergence analysis of Adini′s finite element for a kind of nonlinear generalized nerve conductive equations
- QIAO Bao-min, LIANG Hong-liang
- J4. 2011, 46(8): 42-46.
- Abstract ( 646 ) PDF (357KB) ( 747 ) Save
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- Existence of periodic solutions for higher order nonlinear neutral delay equations
- CHEN Xin-yi
- J4. 2011, 46(8): 47-51.
- Abstract ( 547 ) PDF (294KB) ( 1195 ) Save
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- Some new integral inequalities in two independent variables and their applications
- ZHANG Hong-xia1, KONG Xiang-zhi2
- J4. 2011, 46(8): 52-58.
- Abstract ( 637 ) PDF (297KB) ( 983 ) Save
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- Oscillation of second order difference equations with positive and negative coefficients
- YANG Jia-shan, SUN Wen-bing
- J4. 2011, 46(8): 59-62.
- Abstract ( 732 ) PDF (326KB) ( 906 ) Save
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- A note normal criterion about share values
- QI Jian-ming1, DING Jie2, ZHU Tai-ying1
- J4. 2011, 46(8): 63-67.
- Abstract ( 616 ) PDF (278KB) ( 1048 ) Save
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- Stabilizer of N(2,2,0) algebras
- LI Xu-dong
- J4. 2011, 46(8): 68-72.
- Abstract ( 679 ) PDF (308KB) ( 696 ) Save
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- The lattice of fuzzy ⊙-ideals in regular residuated lattices
- QIN Xue-cheng, LIU Chun-hui*
- J4. 2011, 46(8): 73-76.
- Abstract ( 647 ) PDF (304KB) ( 1274 ) Save
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- Quasi-elastic spaces
- MIAO Cheng-dong, XU Yu-ming, CAO Zhen-bo
- J4. 2011, 46(8): 77-79.
- Abstract ( 627 ) PDF (253KB) ( 1589 ) Save
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- Quasi-uniformities and topologies on a finite set
- WANG Yi-rui1, LI Sheng-gang2
- J4. 2011, 46(8): 80-83.
- Abstract ( 517 ) PDF (306KB) ( 1255 ) Save
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- Star edge coloring of tree
- DENG Kai1, LIU Xin-sheng2, TIAN Shuang-liang1
- J4. 2011, 46(8): 84-88.
- Abstract ( 667 ) PDF (288KB) ( 1231 ) Save
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- Adjacent vertex distinguishing incidence coloring of the join of some special graphs
- WANG Qian, TIAN Shuang-liang
- J4. 2011, 46(8): 89-91.
- Abstract ( 575 ) PDF (379KB) ( 1047 ) Save
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- The application of some special hyper-graphs in the perfect graphs
- SUN Lin
- J4. 2011, 46(8): 92-94.
- Abstract ( 676 ) PDF (275KB) ( 870 ) Save
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- The L(p,q)-labeling of planar graphs with girth g(G)≥5
- ZHU Hai-yang1, HOU Li-feng1, CHEN Wei1, Lü Xin-zhong2
- J4. 2011, 46(8): 95-103.
- Abstract ( 580 ) PDF (362KB) ( 1433 ) Save
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- Properties of interval-valued intuitionistic fuzzy rough sets with implicators
- LIN Meng-lei1, YANG Wei-ping2
- J4. 2011, 46(8): 104-109.
- Abstract ( 601 ) PDF (339KB) ( 1179 ) Save
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- A one-direction S-fuzzy rough set and its application
- LU Xiao-yun1, YANG Yong 2
- J4. 2011, 46(8): 110-113.
- Abstract ( 639 ) PDF (300KB) ( 1256 ) Save
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- Remarks on axiomatizations of generalized rough sets theory
- MA Zhou-ming1,2, LI Jin-jin1,2*
- J4. 2011, 46(8): 114-117.
- Abstract ( 588 ) PDF (294KB) ( 1260 ) Save
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- P-sets and dynamic data outer access-applications
- XIE Wei-qi1,2, LIU Dao-guang1
- J4. 2011, 46(8): 118-121.
- Abstract ( 593 ) PDF (294KB) ( 1229 ) Save
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- P-set and it′s measure space
- ZHAO Zhan-ping, ZHOU Hou-yong, XIE Li-ming
- J4. 2011, 46(8): 122-126.
- Abstract ( 621 ) PDF (314KB) ( 1194 ) Save
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Let R be the field of real numbers and H be a real Hilbert space of dimension at least 2. Let A=H十R be the Spin factor corresponding to H. In this note, we prove that if a bijective map Ø from A onto itself satisfies Ø(x。y)=Ø(x)。Ø(y) for all x,y∈A, and Ø(α+β)=Ø(α)+Ø(β) for all α,β∈R, then there is a unitary operator U on H such that Ø(a+α)=Ua+α for every a∈H, α∈R.

A new conservative finite difference scheme is presented for an initial-boundary value problem of the general improved KdV(GIKdV) equation. It is proved by the discrete energy method that the scheme is unconditionally stable and second-order convergent. Numerical experiments demonstrate that the scheme is accurate efficient.

Based on the classic truncated Newton algorithm for nonlinear optimization, a new subspace accelerated truncated Newton algorithm is presented for large-scale symmetric sparse extreme eigenvalue problems. The convergence properties are proved and numerical experiments are done. The numerical results match the convergence analysis,which showing the new algorithm is effective.

An implicit difference scheme for solving the neutral delay parabolic differential equation is presented. This scheme is unconditional stable in the sense of discrete L2norm. The local truncation error of this scheme is O(Δt^{2}+Δx^{2}). This scheme leads to a tridiagonal linear system to be solved at each time-step. The Crout factorization algorithm is used to solve this linear system. The numerical results show that the presented implicit difference scheme is effective.

The fundamental solutions of fractional-in-space diffusion equation is considered with Riesz fractional derivative (RFDE) in two and three dimensions. The existing definitions of the fractional Laplacian (two dimensions and three dimensions) are investigated and discussed by using eigenfunction expansion, and the relations between fractional Laplacian and Riesz fractional derivative are given. Finally, the fundamental solutions of homogeneous and non-homogeneous RFDE with an initial and boundary condition is derived on a finite domain using a spectral representation.

In this paper, by use of the integral identities and the mean value technique, approximation of bilinear finite element for the nonlinear viscoelasticity type equations with superclose property of order O(h^{2}) in H^{1}-norm is obtained. A global superconvergence result is yielded by interpolated post-processing method. Then higher accuracy of order O(h^{3}) for approximation solution is derived through constructing a proper extrapolation scheme.

The study of differential game has yielded a number of substantial results. However, numerical method for saddle point strategy is still open question. In this paper, a new method with ridge basis function for twopoint boundary value problem of differential game is developed, where the existence and uniqueness of the solution of twopoint boundary value problem is established and discussed.Also, the method is applied to numerical examples to examine its appropriateness. It will be a useful way to solving the numerical solutions of saddle point strategy.

The convergence analysis is studied for a kind of nonlinear generalized nerve conductive equations by Adini′s finite element. Error estimates and result of superclose are obtained by using some novel approaches and techniques. Finally, the corresponding global superconvergence is obtained by taking the advantage of the post-processing technique.

The following nonlinear neutral delay equations ［x(t)+cx(t-τ)］^{(n)} +g(t,x(t-σ))=p(t) is discussed. By using the coincidence degree theory, a sufficient condition for the existence of periodic solution of the equation is given, which generalizes the known results.

Some new nonlinear delay integral inequalities in two independent variables are established. The boundedness of the solution of more general delay integral equations of two variables are carried out.

The oscillation of a class of second order nonlinear neutral variable delay difference equation with positive and negative coefficients is discussed. Using the fixed point theorem in Banach space, a new nonoscillation criteria for the equation is obtained by introducing parameter function and the generalized Riccati transformation. Also, a sufficient condition for oscillation of the equation is proposed. These criteria can improve the restriction of the conditions for the equation, which promote some existed results.

By the ideas of sharing values, and using the Zaclman lemma, a generaliztiona of the original result is improved.

The stabilizer of N(2,2,0) algebras is studied. By using the stabilizer, congruence decomposition on N(2,2,0) algebras is given. The algebraic structure of the quotient algebra is obtained and also algebraic structure and some properties of a class of converse images under the natural homomorphism are obtained.

The lattice operations and the adjoint pair on the set of all fuzzy ⊙-ideals in regular residuated lattices are defined. It is obtained that the fuzzy ⊙-ideals lattice defined in our sense is a distributive residuated lattice.

The definition of quasi-elastic spaces and network-elastic spaces are defined. Quasi-elastic spaces are well-ordered (F) spaces and network-elastic spaces are equivalent to T1 spaces.

The star edge coloring of tree is studied, the star chromatic index of two kinds of special trees are obtained, and an attainable upper bound of star chromatic index of tree is proved.

An adjacent vertex distinguishing incidence coloring of graph G is an incidence coloring of G such that no pair of adjacent vertices meets the same set of colors. The adjacent vertex distinguishing incidence chromatic number of G∨C_{m}, G∨S_{m} and G∨T_{m} are obtained, where G is a star, wheel, or fan of order n+1 and C_{m} is a cycle of order m, S_{m} is a star of order m+1, T_{m} is a tree of order m.

It is proved that the representative graphs of unimodular hyper-graph, balanced hypergraph and tree hypergraph are perfect. The definition of the kperfect hypergraph is given, which is an extention of the perfect graph. Finally, the properties of normal hyper-graph and quasi-regularizable hypergraph are discussed, and some results are obtained.

Let p and q be two positive integers with p≥q, and let λ_{p,q}(G) be the L(p,q)-labeling number of a planar graph G. It is proved that λ_{p,q}(G)≤(2q-1)Δ(G)+6p+10q-8 if G is a planar graphs with girth g(G)≥5, which implies Wegner’s conjecture holds for a planar graph G with girth g(G)≥5 and Δ(G)≥16.

By employing two interval-valued intuitionistic fuzzy implicators I and J, interval-valued intuitionistic fuzzy rough sets with implicators are first defined in the intervalvalued intuitionistic fuzzy approximation space. Properties of interval-valued intuitionistic fuzzy rough sets with implicators are proved. Finally, the reflexivity, symmetry and transitivity of interval-valued intuitionistic fuzzy relations are characterized.

A one-direction fuzzy rough set is proposed, and its general structure and the concept are given by the theory of Dubois fuzzy rough set and the concept of the dynamic fuzzy set. Then, the relationships between a one-direction S-fuzzy rough set and fuzzy rough set are analyzed, and properties and its application of one-direction S-fuzzy rough set are presented.

Generalized rough sets theory is a development of rough sets theory based on equivalence relation. The axiomatizations of generalized rough sets is discussed based on binary relations, and the necessary axiom condition of a binary relations are analyzed by the actual examples.The sufficient conditions of every axiom set are given.

P-sets can be obtained from the improved finite general sets based on the dynamic characteristics. P-sets are a pair of set. Using outer P-sets, the process and characteristic of dynamic data outer access are given, and the metric and dependence relation of dynamic data outer access are obtained. Then, the iterative algorithm and criterion of dynamic data outer access are proposed. Finally the applications are given.

The P-set is generalized from finite sets to arbitrary set. The dynamic σ-algebra of P-set and P-measure space are proposed according to the knowledge about measure theory based on the given measure space. The P-set based on the arbitrary ordinary sets is studied,which is provided reliable theory support for the information safety.