JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE)

A local characterization of centralizers on B(H)

YANG Yuan, ZHANG Jian-hua

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2015, 50(12): 1-4. doi:10.6040/j.issn.1671-9352.0.2014.460

Abstract ( 1330 )

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Let H be a Hilbert space over the real or complex field F. Suppose Ф:B(H)→B(H) is a linear map such that 2Ф(P)=PФ(P)+Ф(P)P holds for all idempotent operators P∈B(H), then there exists a λ∈F such that Ф(A)=λA for all A∈B(H).

The perturbation of the single valued extension property for bounded linear operators

WU Xue-li, CAO Xiao-hong, ZHANG Min

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2015, 50(12): 5-9. doi:10.6040/j.issn.1671-9352.0.2014.516

Abstract ( 1294 )

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Let H be an infinite dimensional separable complex Hilbert space and B(H) the algebra of all bounded linear operators on H. An operator T∈B(H) is said to have the single-valued extension property(SVEP for brevity, write T∈ (SVEP)), if for every open set U∈C, the only analytic solution f:U→X of the equation (T-λI)f(λ)=0 for all λ∈U is zero function on U, where C denotes the complex number set. T∈B(H) is said to have the perturbations of the single valued extension property if T+K have the single-valued extension property for every compact operator K∈K(H). The perturbations of the single valued extension property for bounded linear operators are discussed, and the sufficient necessary condition for is given 2×2 upper triangular operator matrices for which the single valued extension property is stable under compact perturbations.

Nonlinear Lie centralizers of generalized matrix algebras

ZHANG Fang-juan

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2015, 50(12): 10-14. doi:10.6040/j.issn.1671-9352.0.2014.501

Abstract ( 1440 )

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Let G be a generalized matrix algebra. Assume that Ф:G→Gis a nonlinear Lie centralizer. It is shown that, under some mild conditions, Ф can be expressed as Ф=φ+τ, where φ:G→Gis an additive centralizer and τ:G→Z(G) is a mapping that vanishes at commutators. Based on the above results, the characterizations of nonlinear Lie centralizers on factor von Neumann algebras, triangular algebras are obtained.

Extremal eigenvalues of a class of tridiagonal interval matrices

JIAN Yuan, LIU Ding-you

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2015, 50(12): 15-22. doi:10.6040/j.issn.1671-9352.0.2014.549

Abstract ( 1364 )

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A class of tridiagonal interval matrices is studied by the recursive characteristic polynomials and Chebyshev polynomials where some results on eigenvalues are involved. The sharp (lower and upper) bound for the eigenvalues of this class of tridiagonal interval matrices is presended, and the realization matrices whose smallest (largest) eigenvalues reach the lower(upper) bound is characterized.

(λ, μ)-anti-fuzzy rough subgroup

BO Chun-xin, YAO Bing-xue

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2015, 50(12): 23-27. doi:10.6040/j.issn.1671-9352.0.2014.506

Abstract ( 1685 )

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The definitions of (λ, μ) anti-fuzzy subgroup and (λ, μ) anti-fuzzy normal subgroup were introduced first and their properties were discussed. Then based on the new congruence relation defined from (λ, μ) anti-fuzzy normal subgroup, the concepts of (λ, μ) anti-fuzzy rough subgroup and (λ, μ) anti-fuzzy rough normal subgroup were defined, and some properties were researched.

A schematic extension of IMTL logic system

ZHOU Jian-ren, WU Hong-bo

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2015, 50(12): 28-34. doi:10.6040/j.issn.1671-9352.0.2014.458

Abstract ( 1267 )

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A new fuzzy logic system IMTL^* logic is introduced. The feature of this logic system is only one logic connective concerned. It is proved that IMTL^* logic is a schematic extension of IMTL logic and ?ukasiewicz logic and logic system ℵ^* are both schematic extension of IMTL^* Logic. Finally the pure implication representation of ?ukasiewicz logic and logic ℵ^* are obtained. The fuzzy logic systems which is only one logic connective implication concerned will bring convenience to use of fuzzy logic.

Superconvergence and extrapolation of a lower order mixed finite method for nonlinear fourth-order hyperbolic equation

ZHANG Hou-chao, ZHU Wei-jun, WANG Jun-jun

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2015, 50(12): 35-46. doi:10.6040/j.issn.1671-9352.0.2014.424

Abstract ( 1445 )

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With the help of the bilinear element Q₁₁ and the Q₀₁×Q₁₀ element, a lower order conforming mixed finite element approximation scheme is proposed for nonlinear fourth-order hyperbolic equation. Firstly, the existence and uniqueness of approximation solution are proved. Secondly, Based on the known high accuracy results of the about two elements, by use of derivative delivery techniques, the superclose with order O(h²) for both scalar unknown u and the diffusion term v=-Δu in H¹-norm and the flux p=-∇u in L²-norm are derived, respectively. Moreover, the global superconvergence is obtained through interpolation post-processing technique. Finally, throught constructing a new asymptotic expansion formula of Q₀₁×Q₁₀ element and a suitable extrapolation scheme, the extrapolation solutions with order O(h³) are derived. Here, h is the subdivision parameter for the space.

The category of E-quantales

LIANG Shao-hui

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2015, 50(12): 47-53. doi:10.6040/j.issn.1671-9352.0.2014.559

Abstract ( 1156 )

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The definition of an E-quantale is introduced, and some properies of E-quantale is obtained. It is proved that the power set of Quantale and the product of E-quantales are E-quantales. Finally, an embedding functor K from the subcategory of Quantales to the category of E-quantale is introducted, and a natural transformation from functor K and forgotten functor U is constructed. Moreover, under some conditions an E-quantale is isomorphic to the power set of a unital Quantale.

An equivalent characterization of the choice axiom in a Topos

LU Tao, WANG Xi-juan, HE Wei

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2015, 50(12): 54-57. doi:10.6040/j.issn.1671-9352.0.2015.396

Abstract ( 1350 )

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We give the new definition of complete lattice object and the equivalent characterization of the choice axiom based on the partially ordered object in a Topos: the choice axiom is equivalent to that L is a continuous lattice object if and only if L is a constructive continuous lattice object.

Concept lattice based knowledge discovery and its application to analysis of employment data in universities

QIN Li-zhen, LI Jin-hai, WANG Yang-yang

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2015, 50(12): 58-64. doi:10.6040/j.issn.1671-9352.1.2015.051

Abstract ( 1386 )

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Formal concept analysis is an effective tool in data analysis and knowledge discovery, and it has been applied in various fields. Formal decision context is one of the key relational datasets in formal concept analysis and rule acquisition based knowledge discovery is its main research topic. In this paper, Wille's concept lattice and object-oriented concept lattice are used to study rule acquisition in formal decision context, the corresponding rule acquisition algorithm is explored, and employment data from universities is employed to illustrate the feasibility of the proposed algorithm.

Strongly Cartan-Eilenberg Gorenstein projective and injective complexes

ZHAI Xiao-rui, ZHANG Chun-xia

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2015, 50(12): 65-72. doi:10.6040/j.issn.1671-9352.0.2014.588

Abstract ( 1147 )

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The subclasses of Cartan-Eilenberg (CE) Gorenstein projective and CE Gorenstein injective complexes, which are called strongly CE Gorenstein projective and injective complexes, are defined and investigated. The relationships between them and CE complexes are illustrated by some examples. It is proved that a complex G is a CE Gorenstein projective if and only if it is a direct summand of strongly CE Gorenstein projective complex. Some equivalent conditions of which CE Gorenstein projective complex is strongly CE Gorenstein projective complex are given.

An exponential upper tail bound for the deviation of induced degrees

GUAN Ai-xia, LI Fang, LI Guo-quan

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2015, 50(12): 73-75. doi:10.6040/j.issn.1671-9352.0.2014.555

Abstract ( 956 )

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An exponential upper tail bound for the deviation of induced degrees is given. It improved results which was proved by Friedgut, Rödl and Schacht.

Diagonal crossed products over monoidal Hom-Hopf algebras

YOU Mi-man, ZHAO Xiao-fan

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2015, 50(12): 76-80. doi:10.6040/j.issn.1671-9352.0.2014.512

Abstract ( 1405 )

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The diagonal crossed products over ordinary Hopf algebras to monoidal Hom-Hopf algebras is generalized. Furthermore, it is proved that the category of Yetter-Drinfeld Hom-modules is isomorphic to the category of left modules over the diagonal crossed products.

Admissible congruence pairs on C-quasiregular semigroups

SUN Yan, REN Xue-ming

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2015, 50(12): 81-84. doi:10.6040/j.issn.1671-9352.0.2014.493

Abstract ( 1310 )

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Let S be a nil-extension of a Clifford semigroup K by a nil semigroup Q=S/K. By introducing a concept of admissible congruence pairs (δ,ω), where δ is a congruence on a nil semigroup Q and ω is a congruence on a Clifford semigroup K respectively, it is proved that every congruence σ on S can be uniquely represented by an admissible congruence pair on S. In addition, for any congruence σ on S, suppose that σ_K is a restriction of σ on a Clifford semigroup K, that is, σ_K=σ|_K and σ_Q=(σ∨ρ_K)/ρ_K, where ρ_K is a Rees congruence on S induced by a ideal K of S, it is proved that there is an order-preserving bijection Γ:σ→(σ_Q,σ_k) from the set of all congruences on S onto the set of all admissible congruence pairs on S. Finally, a condition has been given for a congruence which is a regular congruence on S.

Gorenstein projective modules and dimensions over triangular matrix ring of order n

ZHU Rong-min, WANG Zhan-ping

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2015, 50(12): 85-92. doi:10.6040/j.issn.1671-9352.0.2014.537

Abstract ( 1375 )

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It is investigated that when the triangular matrix ring T of order n is left Gorenstein, and when a left T-module is Gorenstein projective, and Gorenstein projective dimensions of left T-modules are characterized.

On the structures of groups of order p²q³ with non-Abelian Sylow subgroups

CHEN Song-liang

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2015, 50(12): 93-97. doi:10.6040/j.issn.1671-9352.0.2014.502

Abstract ( 1322 )

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Let p, q be odd primes such that p>q, and G be groups of order p²q³ with non-Abelian Sylow q-subgroups. The isomorphic classification of G and their structures are determined with the help of local analysis of finite groups.

A duality theorem for a Yetter-Drinfeld Hopf algebra

JIA Ling, CHEN Xiao-yuan

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2015, 50(12): 98-101. doi:10.6040/j.issn.1671-9352.0.2014.480

Abstract ( 1213 )

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A dual theorem for a Yetter-Drinfeld Hopf algebra is given, and it is proved that L#L^* is a semisimple algebra for a cocommutative Yetter-Drinfeld Hopf algebra, which generalizing the classical Blatter-Montgomery dual theorem for Hopf algebras.

The Omega result of coefficients of automorphic L-functions over different sparse sequences

WEI Hong-bin

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2015, 50(12): 102-105. doi:10.6040/j.issn.1671-9352.0.2014.570

Abstract ( 1313 )

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Let k be a positive even integer, and H^_*_k be the set of all normalized Hecke primitive eigencuspforms of weight k for Γ=SL₂(Z). The Fourier expansion of f∈H^_*_k at the cusp ∞ is defined by f(z)=

λ_f(n)n^(k-1)/2e^2πinz, where λ_f(n) is the eigenvalue of the (normalized) Hecke operator T_n. The Omega result for the summatory function

λ_f(nⁱ)λ_f(n^j) is investigated. Set
E_1,2(f,x)=

λ_f(nⁱ)λ_f(n^j)-c_j-1x, i=1, j=2,3,
where c₁, c₂ is a suitable constant. Then it is proved that
E_1,2(f,x)=Ω(x^5/12),E_1,3(f,x)=Ω(x^7/16).

A Maschke theorem of Hom-crossed products

GUO Shuang-jian, LI Yi-zheng

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2015, 50(12): 106-108. doi:10.6040/j.issn.1671-9352.0.2014.560

Abstract ( 1289 )

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A Maschke theorem for Hom-crossed products is obtained by Integrals of monoidal Hom-Hopf algebras.

On a generalizations of principally weakly po-flat posets

QIAO Hu-sheng, WEN Hai-cun

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2015, 50(12): 109-113. doi:10.6040/j.issn.1671-9352.0.2014.526

Abstract ( 1096 )

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A general form of partially ordered principally weakly flat S-posets are presented, and the homological classification problems of S-posets on this new property are investigated. As applications, some known results are generalized.

Projective resolution in triangulated categories

WANG Wen-kang

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2015, 50(12): 114-120. doi:10.6040/j.issn.1671-9352.0.2014.456

Abstract ( 1323 )

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Descriptions of distinguished triangles and ξ-projective resolution of objects being exact are given. A property on ξ-projective resolution of distinguished triangles is described.

Cleft extensions of weak Hopf group coalgebras

WANG Zheng-ping, YANG Ren-ming

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2015, 50(12): 121-126. doi:10.6040/j.issn.1671-9352.0.2014.518

Abstract ( 1152 )

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Weak group crossed products are generalization of the weak group smash products, in which the action of the weak Hopf group coalgebras is twisted by a cocycle. The notion of cleft extensions of weak Hopf group coalgebras is introduced, and the relation between crossed products and cleft extensions of weak Hopf group coalgebras is established.

The complete coloring of 3-regular Halin graphs

MENG Xian-yong, GUO Jian-hua, SU Ben-tang

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2015, 50(12): 127-129. doi:10.6040/j.issn.1671-9352.0.2014.479

Abstract ( 1594 )

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The complete coloring of 3-regular Halin graphs is studied. A procedure, for completely coloring an 3-regular Halin graph which is not a wheel graph, is proposed. By this procedure, the conclusion that χ_C(G)=6, where G(≠W₄) is a 3-regular Halin graph, can be easily obtained. Furthermore, this implies that the complete coloring of a 3-regular Halin graph can be solved by computer.

Solving the algebraic model of k-dominating sets of graph by Grbner basis

YIN Jie-jie

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2015, 50(12): 130-136. doi:10.6040/j.issn.1671-9352.0.2014.567

Abstract ( 1353 )

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Let G be a simple connected graph of n vertices. It is shown that finding all dominating sets of G is equivalent to finding all 0-1 solutions of a system of multivariate polynomial equations; furthermore, it is shown that this polynomial equation model can be modified to give a polynomial equation model for finding dominating sets of k vertices (i.e. k-dominating sets) of G, and that such a model can be solved by using the Grbner basis method. Consequently, a feasible way of finding minimal dominating sets and the dominating number of G is obtained. The numerical example is presented to illustrate the effectiveness of this algebraic computational method.

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