JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE)

Separated monic representations of quivers of type A4and RSS equivalences

ZHU Lin

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2018, 53(2): 1-8. doi:10.6040/j.issn.1671-9352.0.2017.574

Abstract ( 1298 )

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Ringel-Schmidmeier-Simson equivalences between separated monomorphism categories and separated epimorphism categories when the quiver is the of type of A₄ with nonlinear order is studied. Using combinatorial methods and representation tools, the equivalence and its quasi inverse are given explicitly, and also the Auslander-Reiten quiver when A is the path algebra of A₂ is given.

Interval algorithm for mixed integer nonlinear two-level programming problems

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2018, 53(2): 9-17. doi:10.6040/j.issn.1671-9352.0.2017.135

Abstract ( 1445 )

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The interval algorithm for a class of constrained mixed integer nonlinear two-level programming problems is discussed, in which the objective functions and constrained functions are in C¹. Based on the penalty function method and constructing the interval extensions of two-level objective functions and introducing the test rules of region deletion, an interval algorithm for solving mixed integer nonlinear two-level programming problems is established. Experimentation upon numerical examples is performed. Both theoretical proof and numerical experiments show that the algorithm is reliable and effective.

A posteriori choice rule for the mollification regularization parameter for the Cauchy problem of an elliptic equation

DING Feng-xia, CHENG Hao

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2018, 53(2): 18-24. doi:10.6040/j.issn.1671-9352.0.2017.292

Abstract ( 1571 )

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We transform the ill-posed problem into a well-posed problem by convolutioning the Gaussian function with parameters and the measurement data. A posteriori parameter choice rule is given which is based on Morozovs discrepancy principle and the error estimates between the exact solution and its approximation are also given. Numerical experiments show the validity of mollification regularization posteriori parameter choice rule.

Existence results of a resonance problem with derivative terms

YE Fu-mei

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2018, 53(2): 25-31. doi:10.6040/j.issn.1671-9352.0.2017.266

Abstract ( 1265 )

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This paper shows the existence results of a resonance problem with derivative terms{u″(t)=f(t,u(t),u'(t)), t∈［0,1］,u(0)=εu'(0), u(1)=αu(η).under the condition of α(η+ε)=1+ε at resonance, where ε∈［0,+∞), α∈(0,∞), η∈(0,1)are given constants, and αη<21. f:［0,1］×R²→R is continuous and satisfies the Nagumo condition. The proof of the main results is based on the method of upper and lower solutions and the connectivity theory of the solution set.

Multiple solutions of Navier boundary value problem for fourth-order elliptic equation with variable exponents

ZHANG Shen-gui

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2018, 53(2): 32-37. doi:10.6040/j.issn.1671-9352.0.2017.359

Abstract ( 1436 )

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A class of Navier boundary value problem for fourth-order elliptic equation with variable exponents is investigated. When the nonlinear term is growing superlinearly, some sufficient conditions for the existence of multiplicity of solutions are obtained by using the fountain theorem in critical point theory.

Modified subgradient extragradient method for solving monotone variational inequality problems

YANG Yan-tao

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2018, 53(2): 38-45. doi:10.6040/j.issn.1671-9352.0.2017.310

Abstract ( 1412 )

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A modified subgradient extragradient method for solving variational inequality problems is proposed in Hilbert space. It is shown that the sequence generated by the proposed algorithm converges weakly to a common element in the intersection of fixed points sets for nonexpansive mappings and of solution sets for monotone variational inequalities. The results presented in this paper improve and generalize the known results.

Endpoint theorem on existence of solutions for Hadamard-type fractional differential inclusions with nonlocal integral boundary value conditions

YANG Dan-dan

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2018, 53(2): 46-51. doi:10.6040/j.issn.1671-9352.0.2017.222

Abstract ( 1214 )

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Based on fixed-point theorem for multi-value maps, the endpoint theorem on the existence of solutions for the following Hadamard fractional order differential inclusions with nonlocal integral boundary value problems is given:{D^αx(t)∈F(t,x(t)), 1<t<e, 1<α≤2, x(1)=x(0), A/(Γ(γ))∫^η₁(logη/s)^γ-1(x(s))/sds+Bx(e)=c, γ>0, 1<η<e, where D^α is Hadamard type fractional derivative, F:［1,e］×R→P(R)is a multi-valued map, A,B,c are constants. The aim of this paper is to extend known single value result to multi-valued framework.

Falling fuzzy filters on residuated lattices

PENG Jia-yin

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2018, 53(2): 52-64. doi:10.6040/j.issn.1671-9352.0.2017.403

Abstract ( 1235 )

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Using the theory of falling shadows, the fuzzy filter theory of residuated lattices is reestablished. The concepts of falling fuzzy filters, falling fuzzy implicative filters, falling fuzzy Boolean filters, falling fuzzy positive implicative filters and falling fuzzy G-filters on residuated lattices are introduced and their properties are investigated. The relations among them are discussed, and some equivalent characterizations of these filters are obtained. Conditions for a falling shadow to be a falling fuzzy filter, and for a falling fuzzy filter to be a falling fuzzy(positive)implicative filter are given. The relations between a falling fuzzy(implicative, positive implicative, Boolean, G-)filter and fuzzy(implicative, positive implicative, Boolean, G-)filter are studied. It is proved that falling fuzzy(G-)Boolean filter is equivalent to falling fuzzy(positive)implicative filter under certain conditions.

On(∈,∈∨q_{(λ, μ)})-fuzzy LI-ideals in lattice implication algebras

LIU Chun-hui

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2018, 53(2): 65-72. doi:10.6040/j.issn.1671-9352.0.2017.508

Abstract ( 1323 )

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Firstly, the notion of (∈,∈∨q_{(λ, μ)})-fuzzy LI-ideals in lattice implication algebras is further studied, and some new properties and equivalent characterizations of (∈,∈∨q_{(λ, μ)})-fuzzy LI-ideals are given. Secondly, a partial order is defined on the set of all fuzzy sets in a given lattice implication algebra L, the definition of (∈,∈∨q_{(λ, μ)})-fuzzy LI-ideal which is generated by a fuzzy set is given and its representation theorem is established by using. Finally, It is proved that the set consisting of all (∈,∈∨q_{(λ, μ)})-fuzzy LI-ideals with respect to a fixed pair(λ, μ)in a given lattice implication algebra, under the partial order, forms a complete distributive lattice.

The projective objects in the category of Q-sup-algebras

WANG Hai-wei, ZHAO Bin

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2018, 53(2): 73-82. doi:10.6040/j.issn.1671-9352.0.2017.313

Abstract ( 1168 )

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The concept of K-flat projective objects in the category of Q-sup-algebras is introduced, and we give some equivalent characterizations on the object. We prove that Q is a K-flat projective Q-sup-algebra if and only if Q has a coalgebra structure.

Intelligent dynamic fusion of packet information and the intelligent state recognition of information law

CHEN Bao-hui, ZHANG Ling, SHI Kai-quan

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2018, 53(2): 83-87. doi:10.6040/j.issn.1671-9352.0.2017.540

Abstract ( 1356 )

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Based on function packet sets, the concept of the fusion of packet information law and the research on intelligent dynamic fusion is given. The concept of fusion of information law generated by function packet sets is put forward. Under the condition of packet information law reasoning, the intelligent fusion theorems and the generating of intelligent dynamic fusion are obtained. Using these results, a simple application of intelligent dynamic fusion in intelligent recognition of information law state is given.

Multidimensional zero-correlation linear cryptanalysis on Midori

CHENG Lu, WEI Yue-chuan, LI An-hui, PAN Xiao-zhong

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2018, 53(2): 88-94. doi:10.6040/j.issn.1671-9352.2.2017.110

Abstract ( 1370 )

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The security of Midori64 against zero-correlation linear cryptanalysis is evaluated. By using the “miss-in-the-middle” technique, 6-round zero-correlation linear approximations are constructed. Based on the 6-round distinguisher, key-recovery attack on 10-round Midori is performed. The data complexity is 2^62.4 plaintexts and the time complexity is 2^79.35 10-round encryptions. The testing result shows that the Midori reduced to 10-round is not immune to multidimensional zero-correlation linear analysis.

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