JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE)

Phragmén-Lindelof alternative for the heat conduction equations in a binary mixture

LI Yuan-fei， CHEN Xue-jiao， SHI Jin-cheng

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2020, 55(12): 1-12. doi:10.6040/j.issn.1671-9352.0.2020.201

Abstract ( 950 )

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The heat conduction equations in a binary mixture which are defined in a semi-infinite cylinder is considered and the generatrix of the cylinder is parallel to the coordinate axis. Assuming that the equations satisfy the nonhomogeneous Neumann boundary conditions on the lateral surface of the cylinder and the nonlinear conditions on the finite end of the cylinder, the method of energy estimation is used to obtain the Phragmén-Lindelöf alternative results of the equations. In the case of decay, in order to make the results meaningful, the upper bound of total energy is established.

Flatness properties of diagonal acts

QIAO Hu-sheng, QIAO Xing-bin

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2020, 55(12): 13-18. doi:10.6040/j.issn.1671-9352.0.2020.255

Abstract ( 876 )

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Let S be a monoid. Some equivalent descriptions of diagonal acts D(S) satisfying Conditions(PWP),(P'),(P_E)and(GP)are given. Using GP-flat diagonal acts, some structural characterizations of monoids are characterized. Further, some known results are generalized.

Maximal subsemigroups and the maximal regular subsemigroups of the semigroup H ^*_(n,m)(r)

YUAN Yue, ZHAO Ping

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2020, 55(12): 19-24. doi:10.6040/j.issn.1671-9352.0.2020.319

Abstract ( 955 )

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Let T_n be the full transformation semigroup on X_n={1,2,…,n}. For any 1≤m≤n-1, let X_m={1,2,…,m}. Through the subsemigroupsG_(n,m)={α∈T_(n,m):(X_n\X_m)α=X_n\X_m}andH_(n,m)={α∈T_(n,m):(X_n\X_m)α⊆X_n\X_m}of the semigroup T_(n,m)={α∈T_n:X_mα=X_m}, the subsemigroups of the semigroup H ^*_(n,m)(r)={α∈H_(n,m):|im(α)|≤r}∪G_(n,m) are studied for 1≤m<r≤n-1, and it is proved that the maximal subsemigroups of H ^*_(n,m)(r)are the same as the maximal regular subsemigroups.

Number of homomorphisms between two classes of non-abelian finite groups

LI Feng-jiao, GAO Bai-jun

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2020, 55(12): 25-29. doi:10.6040/j.issn.1671-9352.0.2020.030

Abstract ( 922 )

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The number of homomorphisms among a class of non-abelian groups of order 10pⁿ with cyclic Sylow p-subgroups and from the non-abelian finite groups into quaternion group is obtained by using algebraic number theory. As an application, the number of homomorphisms of such groups satisfies the conjecture of Asai and Yoshida is verified.

Number of homomorphisms from a class of non-abelian groups into dihedral groups

LAI Ji-na, GUO Ji-dong

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2020, 55(12): 30-36. doi:10.6040/j.issn.1671-9352.0.2020.007

Abstract ( 1153 )

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The number of homomorphisms from a class of non-abelian groups into dihedral groups is calculated. As an application, it verifies that T. Asai and T. Yoshidas conjecture is satisfied such groups.

On Coleman automorphism groups of generalized dihedral groups

WU Hong-yi, HAI Jin-ke

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2020, 55(12): 37-39. doi:10.6040/j.issn.1671-9352.0.2020.148

Abstract ( 1116 )

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It is proved that Coleman outer automorphism group of a generalized dihedral group is either 1 or an elementary abelian 2-group by using the projection limit property of the group.

Rota-Baxter operators on the Lie superalgebra S(2)

LU Zhi-ying, YUAN Ji-xia

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2020, 55(12): 40-48. doi:10.6040/j.issn.1671-9352.0.2020.228

Abstract ( 927 )

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The Rota-Baxter operators of Lie superalgebra S(2)with weight zero are investigated. According to the property of isomorphism of S(2)_0^- and sl(2,C), using the Rota-Baxter operators of sl(2,C), the even Rota-Baxter operators with weight zero on Lie superalgebra S(2)are given. At the same time, using the definition of the Rota-Baxter operator to calculate the odd Rota-Baxter operators with weight zero on Lie superalgebra S(2).

Some new results of skew triangular matrix rings

YANG Li-na, WANG Yao, REN Yan-li

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2020, 55(12): 49-55. doi:10.6040/j.issn.1671-9352.0.2020.235

Abstract ( 955 )

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Some new ring theoretic properties of the skew triangular matrix rings T(R,n,α) are investigated. It is proved that(1)if α is an endomorphism of a ring R with α(1)=1, then R is a Hermite ring if and only if T(R,n,α) is a Hermite ring;(2)R is right weakly McCoy if and only if T(R,n,α) is right weakly McCoy;(3)if M is a Monoid and α is a rigid endomorphism of R, then R is M-Armendariz if and only if T(R,n,α) is M-Armendariz.

Structure of Poisson algebras on Sweedler 4-dimensional Hopf algebras

QIAO Ning, FANG Ying, ZHANG Liang-yun

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2020, 55(12): 56-62. doi:10.6040/j.issn.1671-9352.0.2020.064

Abstract ( 950 )

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Constructing the relations among L-dendriform algebras, Rota-Baxter systems and Poisson algebras, and applying the theory of Poisson algebras to construct Poisson algebras and Poisson Hopf algebras on Sweedler 4-dimensional Hopf algebra are of significance to the research and application of Rota-Baxter algebras and Hopf algebras.

General symmetric rings

QIN Lan-lan, WANG Yao, REN Yan-li

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2020, 55(12): 63-68. doi:10.6040/j.issn.1671-9352.0.2020.233

Abstract ( 1064 )

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In the general ring(not necessarily with 1)category, the concepts of left and right symmetric rings are different. The concept of general symmetric rings in general ring category is introduced and give its characterization, discuss the relationship between general symmetric rings and related rings as well as their ring extensions.

Higher rigid subcategories and t-structures

YANG Ting, XIE Yun-li

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2020, 55(12): 69-75. doi:10.6040/j.issn.1671-9352.0.2020.294

Abstract ( 954 )

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Let D be a triangulated category and A a D -admissible abelian subcategory of D. This paper shows that under some conditions a higher rigid subcategory of A induces a t-structure on D whose heart is just A.

Gorenstein(m,n)-injective modules

YANG Qiang, ZHAO Ren-yu

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2020, 55(12): 76-80. doi:10.6040/j.issn.1671-9352.0.2020.156

Abstract ( 857 )

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The notion of Gorenstein (m,n)-injective left R-modules is introduced as a generalization of (m,n)-injective left R-modules. Some properties of such modules are investigated over strongly left (m,n)-coherent rings, and some equivalent characterizations of left(m,n)-injective rings are given over strongly left (m,n)-coherent rings by using Gorenstein (m,n)-injective left R-modules.

Absolutely clean modules and Gorenstein AC flat modules over formal triangular matrix rings

DI Zhen-xing, LI Xiao-man

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2020, 55(12): 81-88. doi:10.6040/j.issn.1671-9352.0.2020.200

Abstract ( 966 )

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Let T=(A 0U B) be a formal triangular matrix ring, where A and B are rings and U is a (B,A)-bimodule. In this article, we investigate absolutely clean T-modules and Gorenstein AC-flat T-modules. More specifically, under some mild conditions, we prove that L=(L1, L2) is absolutely clean right T-module then L1 is absolutely clean right A-module and L₂ is absolutely clean right B-module. As an application of this result, under some conditions, we show that M=(M1M2)_φ^M is Gorenstein AC flat left T-module if and only if M1 is a Gorenstein AC flat left A-module, M2/Im φ^M is a Gorenstein AC flat left B-module and the morphism φ^M is a monomorphism.

Flat bimodules and Gorenstein modules

ZHAO Zhuang, LIANG Li

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2020, 55(12): 89-92. doi:10.6040/j.issn.1671-9352.0.2020.155

Abstract ( 736 )

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The notion of flat bimodules and get some results of ascent properties of Gorenstein modules under flat ring extensions by flat bimodules are introduced.

Z₂-extensions of a pointed fusion category and applications

DAI Li

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2020, 55(12): 93-96. doi:10.6040/j.issn.1671-9352.0.2020.366

Abstract ( 768 )

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Using the decomposition of the tensor product of a non-invertible simple object and its dual, the Z₂-extensions of a pointed fusion category is studied. Then the universal grading structure of this class of fusion categories is given and their applications in the classification of semisimple Hopf algebras are discussed.

A new construction method of triangulated model structures

ZHANG Ping-er, YANG Xiao-yan

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2020, 55(12): 97-102. doi:10.6040/j.issn.1671-9352.0.2020.194

Abstract ( 1072 )

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Let T be a triangulated category and ξ denote some proper class of triangles, and suppose that we have two complete hereditary cotorsion pairs(Q,R)and(Q,R)with respect to ξ in T satisfying R⊆R and Q ∩R=Q∩R. We show how to construct an unique triangulated model structures with respect to ξ on T with Q(resp.Q)as the class of cofibrant(resp. trivially cofibrant)objects and R(resp. R)as the class of fibrant(resp. trivially fibrant)objects.

Supply chain optimization considering add-on pricing under distribution contract

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2020, 55(12): 103-110. doi:10.6040/j.issn.1671-9352.0.2019.029

Abstract ( 729 )

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Aiming at the problem of additional sales of additional products or bundled sales with core products under distribution contract, the demand function is established by using the theory of consumer utility. Using the principle of master-slave strategy, the equilibrium solutions under different situations are obtained, and the win-win conditions of supply chain members are compared and analyzed when the consumer utility maximizes. The results show that: when the acceptance degree of online products is low, but the perceived value of core products is high, the company and online platform can achieve win-win situation by adopting “additional+bundling” pricing under wholesale price contract; when the revenue sharing factor is low enough, but the perceived value of the core product is high, or the revenue sharing factor is low, the company and the online platform can achieve a win-win situation by adopting “additional+bundling” pricing under the consignment contract. Finally, when comparing contracts, we find that when the revenue sharing factor is low, the company gains more under the wholesale price contract, while the online platform gains more under the consignment contract.

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