JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE)

FR-injective and FR-flat dimensions of complexes

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2018, 53(6): 1-6. doi:10.6040/j.issn.1671-9352.0.2017.524

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The notion of FR-injective and FR-flat dimensions of complexes is introduced and investigated. Two new Quillen model structures are also obtained by means of corresponding cotorsion pairs.

Linear 2-arboricity of graphs with maximum average degree at most 4

ZHANG Jiang-yue, XU Chang-qing

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2018, 53(6): 7-10. doi:10.6040/j.issn.1671-9352.0.2017.286

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A linear 2-forest is a graph whose components are paths of length at most 2. The linear 2-arboricity of a graph G is the least integer m such that G can be partitioned into m linear 2-forests, denoted by la2(G). The upper bound of the linear 2-arboricity of graph G with mad(G)≤4 is determined and if G is a graph with mad(G)≤4, then la₂(G)≤「Δ(G)/2+5 if Δ(G)≡1,2(mod 4)and la₂(G)≤「Δ(G)/2+4 if Δ(G)≡0,3(mod 4).

(*,~)-good congruences on completely J ^*,~-simple semigroups

GONG Chun-mei, FENG Li-xia, REN Xue-ming

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2018, 53(6): 11-16. doi:10.6040/j.issn.1671-9352.0.2017.284

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It is characterized that the(*,~)-good congruences on completely J ^*,~-simple semigroups by means of(*,~)-good congruences pairs. Some results about congruences on completely simple semigroups in regular semigroups are generalized to r-wide semigroups, and this establishes the foundation to investigate good congruences over super r-wide semigroups.

The number of homomorphisms from metacyclic groups to metacyclic groups

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2018, 53(6): 17-22. doi:10.6040/j.issn.1671-9352.0.2017.562

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The number of homomorphisms between a class of metacyclic groups, which are normal cyclic groups of the order m extended by cyclic groups of the order 2p, is calculated, and the number of endomorphisms of such groups is obtained. As an application, the number of homomorphisms of such groups satisfies the conjecture of T.Asai and T.Yohsdia is varified.

Further results on the growth of solutions of linear complex differential equations

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2018, 53(6): 23-29. doi:10.6040/j.issn.1671-9352.0.2017.575

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The growth of solutions of complex linear differential equations is discussed by using Nevanlinna theory. Some results concerning a problem of Gundersen are obtained in this paper, which are improvement of predecessors.

Estimates of multilinear fractional integrals and maximal operators on weighted Morrey spaces

TAO Shuang-ping, GAO Rong

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2018, 53(6): 30-37. doi:10.6040/j.issn.1671-9352.0.2017.629

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By using the function decompositions and the inequalities of A_{((→overp),q)} weights, the boundedness and weak estimates of the multilinear fractional integrals and multilinear fractional maximal operators are established on the weighted Morrey spaces.

Boundedness of Marcinkiewicz integrals operators with variable kernels on Herz-type Hardy spaces with variable exponent

XIN Yin-ping, TAO Shuang-ping

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2018, 53(6): 38-43. doi:10.6040/j.issn.1671-9352.0.2017.646

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Based on the boundedness of Marcinkiewicz integrals on variable Lebesgue spaces and the atomic decomposition of Herz-type Hardy spaces with variable exponent, we obtain the boundedness of Marcinkiewicz integrals with variable kernels on the homogeneous and non-homogeneous Herz-type Hardy spaces with variable exponent.

O-convexity of Orlicz-Bochner spaces with the Luxemburg norm

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2018, 53(6): 44-52. doi:10.6040/j.issn.1671-9352.0.2017.507

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Some characterizations of O-convexity in Banach space are given. Using these characterizations, the criteria is obtained for O-convex of Orlicz-Bochner spaces endowed with the Luxemburg norm.

Solvability of nonlinear second-order boundary value problems with nonlinearities which cross the resonance points

WANG Su-yun, LI Yong-jun

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2018, 53(6): 53-56. doi:10.6040/j.issn.1671-9352.0.2017.647

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We study the existence and uniqueness of solutions of the boundary value problem for nonlinear second-order ordinary equations:{u″+f(t,u)=h(t), t∈(0,1),u(0)=u(1)=0,under the conditions that (f(t,s))/s may exceeds the eigenvalue interval ［λ_k0, λ_k0+1］ in some “smaller sets”. The existence and uniqueness of solutions of this equation are obtained.

Regularity for solutions of elliptic obstacle problems with subcritical growth

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2018, 53(6): 57-63. doi:10.6040/j.issn.1671-9352.0.2018.003

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Based on a modification of p-harmonic approximation argument, the gradients of solutions to the quasilinear elliptic p-Laplace type obstacle problems with subcritical growth enjoy the Morrey regularity are proved. Then the Hölder continuity of solutions is obtained by using the integral characterization of Hölder continuous functions. Making use of this method, one can simplify the proof avoiding the proof of a suitable reverse Hölder inequality for the gradient.

Existence of positive solutions for a class of nonlinear second-order Dirichlet problem

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2018, 53(6): 64-69. doi:10.6040/j.issn.1671-9352.0.2017.178

Abstract ( 1380 )

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The existence of positive solutions for a class of second-order Dirichlet problem{u″(t)+a(t)u(t)+f(t,u(t))=0, t∈(0,1),u(0)=u(1)=0is studied by using the fixed-point theorem in cones, where a∈C(［0,1］, ［0,∞))and a(t)≢0 on any subinterval of(0,1), f∈C(［0,1］×［0,∞), ［0,∞)). The results generalize and improve the related results of the existingwork.

Freeness of arrangements between the Weyl arrangements of types A_n-1 and B_n

GAO Rui-mei, CHU Ying

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2018, 53(6): 70-75. doi:10.6040/j.issn.1671-9352.0.2017.644

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The set of reflecting hyperplanes of a Weyl group is called Weyl arrangement. Assume the notations A_n-1 and B_n denote the Weyl arrangements of types A_n-1 and B_n respectively. The arrangement A which satisfies A_n-1⊂A⊂B_n is called the arrangement between A_n-1 and B_n. Firstly, we study threshold graphs, and give a construction for threshold graphs. Secondly, we study the freeness of the arrangements between A_n-1 and B_n by using threshold graphs. And we conclude: for any integer k satisfying |A_n-1|<k<|B_n|, there exists a free arrangement between A_n-1 and B_n with cardinality k. A similar conclusion for the non-freeness arrangements between A_n-1 and B_n is given.

Rules acquisition on three-way weakly consistent formal decision contexts

REN Rui-si, WEI Ling, QI Jian-jun

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2018, 53(6): 76-85. doi:10.6040/j.issn.1671-9352.0.2017.500

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Rules acquisition is an important problem in three-way concept analysis. Based on the finer relation on attribute-induced three-way concept lattices, the three-way weakly consistent formal decision context is defined. And the way to acquire rules on three-way weakly consistent formal decision context is presented. Then, the relationship between two-way rules and three-way rules is studied. Finally, the weakly closed label of attribute-induced three-way concept is given, and the weakly closed label is used to extract three-way rules, which can remove the redundant rules.

Representative forms of commutative BR₀-algebras on a set by implication operator

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2018, 53(6): 86-94. doi:10.6040/j.issn.1671-9352.0.2018.035

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By the further study of the definition and properties of commutative BR₀-algebras, some equivalent forms of commutative BR₀-algebras are obtained on a set by using implication operator. This work not only further simplifies the definition of commutative BR₀-algebras, but also conforms commutative BR₀-algebras to the features of logical algebras in definition. It provides a basis for studying the relations between commutative BR₀-algebras and other logical algebras.

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