JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE)

τ_q-PF Rings

ZHANG Xiao-lei, QI Wei, XIA Wei-heng

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2023, 58(3): 1-6. doi:10.6040/j.issn.1671-9352.0.2022.227

Abstract ( 677 )

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The notion of τ_q-P-flat modules is introduced and studied. Specially, a ring R is τ_q-PF if and only if any(principal)ideal of R is τ_q-P-flat. Finally, τ_q-PF rings are also studied in terms of finite direct products of rings and amalgamation algebras. By the way, some examples are given to distinguish τ_q-PF rings and PF rings.

The number of homomorphisms between a class of finite 2-groups and dihedral groups

ZHANG Wei, LAI Ji-na, GUO Ji-dong, ZHANG Liang

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2023, 58(3): 7-13. doi:10.6040/j.issn.1671-9352.0.2022.209

Abstract ( 571 )

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Based on the group structure and element properties of G₂ and dihedral groups, the number of homomorphisms between G₂ and dihedral groups is calculated. As an application, it verifies that T.Asai and T.Yoshidas conjecture is satisfied such groups.

The structure of proper glrac semigroups

LIU Hai-jun, GUO Xiao-jiang

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2023, 58(3): 14-18. doi:10.6040/j.issn.1671-9352.0.2022.223

Abstract ( 486 )

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The concept of glrac semigroupoids is introduced and a structure theorem of proper glrac semigroups is established by means of the action of a monoid upon a proper glrac semigroupoid on the left. As an application, the construction of proper left GC-lpp semigroups is also considered.

Weak core inverse of core-EP decomposition

CHENG Yang, CUI Yu-ru

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2023, 58(3): 19-24. doi:10.6040/j.issn.1671-9352.0.2022.167

Abstract ( 469 )

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Based on core-EP decomposition of a matrix, the weak core inverse of a complex matrix is studied. For a complex matrix A, a new representation of the weak core inverse A^,+ of A is given, and some equivalent characterizations of AA^,+=A^,+A are presented, as well as the relation between(A^m)^,+ and(A^,+)^m is investigated.

Jacobsons lemma and Clines formula for core-EP inverse in a ring with involution

HUO Hui-min, SONG Xian-mei, LI Ming-zhu

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2023, 58(3): 25-32. doi:10.6040/j.issn.1671-9352.0.2022.262

Abstract ( 483 )

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The Jacobsons lemma and Clines formula of core-EP inverse are studied, and the equivalent conditions for the establishment of generalized Jacobsons lemma and generalized Clines formula under the conditions acd=dbd and dba=aca are given, which enrich partial results of core-EP reversible elements.

Strongly V W -Gorenstein complexes

JIA Hong-hui, ZHAO Ren-yu

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2023, 58(3): 33-38. doi:10.6040/j.issn.1671-9352.0.2022.285

Abstract ( 478 )

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Let V, W be two classes of R-modules. A notion of strongly V W -Gorenstein complexes is introduced. It is shown that if V, W are closed under extensions and finite direct sums, V ⊥V, W ⊥W, V ⊥W and V,W ⊆G(V W ), a complex M is strongly V W -Gorenstein if and only if M is exact and Z_n(M)is V W -Gorenstein for all n∈Z. In addition, some interesting corollaries are obtained, which unify and genelize some known results.

Weighted hesitation fuzzy preference relation and its application in group decision making

FENG Xue, GENG Sheng-ling, LI Yong-ming

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2023, 58(3): 39-47. doi:10.6040/j.issn.1671-9352.2.2022.2045

Abstract ( 521 )

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Considering that the hesitant fuzzy preference relationship can more comprehensively represent the preference information of decision makers, by putting the hesitation fuzzy preference relationship in the sense of weight, the weighted hesitation fuzzy preference relation and multiplicative consistent weighted hesitation fuzzy preference relation are defined. At the same time, a convergent local consistency improvement process is designed to detect and improve the consistency level of weighted hesitant fuzzy preference relationship. It is more suitable to sovle the group decision-making problem, because the weighted hesitation fuzzy preference relation can fully reflect the preference information of decision makers and clearly reflect the importance of different preference degrees. Finally, a group decision-making is applied to the specific case, which shows that the proposed method is practical and feasible.

L-valued modules based on L-valued universal algebras

ZHOU Xin, LIU Miao

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2023, 58(3): 48-54. doi:10.6040/j.issn.1671-9352.0.2022.461

Abstract ( 439 )

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L-valued modules are lattice-valued algebraic structures, defined on universal algebras of the same type as modules, but which are not necessary modules. First, the classical equality is replaced by a fuzzy identity, and the concept of L-valued modules are given based on L-valued universal algebras. Next, the necessary and sufficient conditions for L-valued universal algebras to be L-valued modules are given by using quotient structure of fuzzy algebras. Furthermore, this gives some basic properties of L-valued modules. Finally, we shows the structure of L-valued submodules.

Eigenvalue problem of a coupled system of singular k-Hessian equations

DING Huan-huan, HE Xing-yue

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2023, 58(3): 55-63. doi:10.6040/j.issn.1671-9352.0.2022.133

Abstract ( 624 )

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This paper focuses on the existence of radial solutions for the eigenvalue problem of a coupled system of singular k-Hessian equations. By constructing the suitable upper and lower solutions and using the Schauder fixed point theorem, it is proved that at least one radial solution exists in this problem and some asymptotic properties of the radial solution are obtained.

Modified inertial projection algorithm for solving variational inequality and fixed point problems

CHEN Jing-jing, YANG Yan-tao

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2023, 58(3): 64-76. doi:10.6040/j.issn.1671-9352.0.2022.431

Abstract ( 607 )

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A modified inertial projection algorithm is proposed to find the common element of the set of pseudomonotone variational inequality problems and the fixed point set with a demicontractive mapping, and it is proved that the iterative sequence generated by the algorithm is strongly converged on a common element under the condition that the algorithm is implemented with a self-adaptive step size rule and the Lipschitz continuity. Finally, we implement some computational tests to show the efficiency and advantages of the proposed method.

A mollification method with a posteriori parameter selection for solving the Cauchy problem of the Helmholtz equation

LI Zhen-ping, YU Ya-hui

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2023, 58(3): 77-84. doi:10.6040/j.issn.1671-9352.0.2022.304

Abstract ( 528 )

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In order to restore the stability of the solution, a mollification regularization method with a posteriori selection of regularization parameter based on Gaussian kernel function is proposed. The stability error estimate between the exact solution and its approximation solution is obtained. Numerical experiments are carried out to verify the effectiveness of the proposed method.

Block cipher algorithm Eslice based on Feistel structure

LIANG Li-fang, DU Xiao-ni, LI Kai-bin, XIE Xin, LI Xiao-dan

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2023, 58(3): 85-92. doi:10.6040/j.issn.1671-9352.0.2022.283

Abstract ( 783 )

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A family of highly secure block cipher algorithms Eslice, including three versions: Eslice-64-64, the block length and key length are both 64 bits; Eslice-64-128, the block length is 64 bits, and the key length is 128 bits; Eslice-128-128, the block length and key length are both 128 bits. Eslices design was inspired by LBlock. The Feistel structure is adopted as a whole, and the SP structure is used for the round function. The selected S-box have all the optimal cryptographic properties. The linear transformation has only two operations: cyclic shift and XOR, and the key generation algorithm and the encryption algorithm use the same S-box. Furthermore, the security of Eslice for differential, linear, integral and other cryptanalysis methods is analyzed. The search model based on Mixed Integer Linear Programming(MILP)are used, and the number of minimum active boxes in 20 rounds is 41, which is 3 less than that of LBlock in 20 rounds. The differential probability and linear deviation are estimated by the number of active boxes, and the security of the algorithm is evaluated. The results show that Eslice can effectively resist differential attack and linear attack.

Design and realization of a chaotic system based on multiplier

WANG Zhong-lin, LIU Shu-tang

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2023, 58(3): 93-100. doi:10.6040/j.issn.1671-9352.0.2022.405

Abstract ( 528 )

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This paper makes use of the characteristics of resistance and capacitance in series and parallel to propose a method of using the multiplier to realize chaotic system. Using this method, two Lorenz type chaotic systems are realized with one circuit, and Qi chaotic system with three product terms is realized. By changing the resistance value of one of the resistors, different dynamic behaviors can be transformed from single period, double period, four period, multi period, quasi period and single scroll chaos to double scroll chaos. The circuit experiment results and the simulation results of Multism14 software are consistent with the theoretical analysis results. Compared with the original method, the number of components is greatly reduced.

Low-rank matrix factorization with double Gaussian prior model

WEI Fang, WANG Chang-peng

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2023, 58(3): 101-108. doi:10.6040/j.issn.1671-9352.0.2022.059

Abstract ( 603 )

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In order to fit the complex noise better and enhance the robustness of the low-rank matrix factorization model, the dual Gaussian priors are introduced into the traditional Gaussian mixture model, and the model of low-rank matrix factorization with double Gaussian prior(DGP-LRMF)is proposed, it is assumed that two matrices obtained by model decomposition obey Gaussian priori to realize the effective modeling for noise, and the EM algorithm is used to deduce the model parameters in the framework of Bayesian theory. Experimental results show that the proposed model can effectively deal with the data with complex noise and obtain better and more stable denoising performance.

Optimization of material allocation under public health events based on SEIR model

ZHUANG Yuan-yuan, ZHANG Ke-yong

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2023, 58(3): 109-120. doi:10.6040/j.issn.1671-9352.0.2021.256

Abstract ( 701 )

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The SEIR model is used to predict the demand for emergency relief materials after the outbreak of a public health event, and the optimization model is constructed with the goal of minimizing the loss of emergency material demand and the shortest total distance of material distribution. In order to ensure the accuracy of the allocation, the model parameters are adjusted according to real-time data every cycle. The scientificity and rationality of the model are verified through the case of emergency material distribution. The results show that this method can effectively solve the problem of emergency material allocation under dynamic demand under major public health incidents, and provides a new idea for solving emergency material allocation under public health emergencies.

Characteristics and sources analysis of microplastics in precipitation of Mount Tai

XU Xin-miao, ZHEN Jie-bo, JIANG Yu-qian, DU Ping, YUAN Xian-zheng, WU Di, YIN Xiang-kun, WANG Yan

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2023, 58(3): 121-126. doi:10.6040/j.issn.1671-9352.0.2022.636

Abstract ( 721 )

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In order to explore the distribution characteristics of microplastics in high altitude wet deposition, this study collected precipitation samples in the summer of 2021 in Mt. Tai. The morphology and composition characteristics of the microplastics were observed by stereo microscope, Fourier infrared spectroscopy and Raman spectroscopy. The transmission and source were analyzed by using backward flow trajectory analysis and concentration weight trajectory model. It was found that the abundance ranged from 0 to 858 L^-1, in which the number of fragments, fibers and films accounted for 53%, 31% and 16% respectively, and most particles were smaller than 250 μm. The polymer components were mainly polyethylene(PE), polystyrene(PS), polypropylene(PP), polyethylene terephthalate(PET)and polyamide(PA). The analysis of air mass trajectory showed that the distribution characteristics of microplastics in Mt. Tai were mainly affected by the airflow in Shandong and southwest, and the potential source areas were mainly in Shandong, Jiangsu and Henan province.

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