JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE)

Special elements, ideals in involutive m-semilattices and its categorical properties

LIANG Shaohui, ZHANG Xueting, XIA Xiaogang

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2024, 59(4): 1-8. doi:10.6040/j.issn.1671-9352.0.2022.590

Abstract ( 46 )

PDF (784KB) ( 48 )

Save

References | Related Articles | Metrics

The concept of involutive m-semilattices is given, and a series of important properties of involutive m-semilattices are obtained. The two order relationships ≪ and  are defined in involutive m-semilattices, and the interrelationships between the involutive m-semilattices *, special element and ≪、  are discussed. The subinvolutive m-semilattices are constructed by using special elements. The structures of ideals and filters in involutive m-semilattices are studied, the concrete forms of generating ideals and filters from elements are obtained. The definition of the category of involutive m-semilattices is introduced, and the specific form of the product of the category of involutive m-semilattices is discussed, and the limit structure of the category of involutive m-semilattices is obtained. It is proved that the category of involutive m-semilattices is complete.

Gorenstein FP-injective modules over Morita rings

CHEN Wenjing, GAO Wen

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2024, 59(4): 9-15. doi:10.6040/j.issn.1671-9352.0.2022.619

Abstract ( 37 )

PDF (938KB) ( 44 )

Save

References | Related Articles | Metrics

The method of constructing Gorenstein FP-injective modules on Morita rings with zero bimodule homomorphisms is given by the theory of recollements.

τ-tilting τ^-1-tilting modules and 1-Gorenstein algebras

ZHANG Xiaojin, CHEN Yuxuan, GU Biao

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2024, 59(4): 16-18. doi:10.6040/j.issn.1671-9352.0.2022.546

Abstract ( 30 )

PDF (689KB) ( 16 )

Save

References | Related Articles | Metrics

For an algebra A admitting a τ-tilting τ^-1-tilting module T, some homological properties of A are given, which generalize the homological properties of 1-Gorenstein algebras. Moreover, it is shown that A is not necessarily to be a 1-Gorenstein algebra.

Semi-Gorenstein-projective modules respect to a semidualizing module

YUAN Mengya, LIANG Li

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2024, 59(4): 19-22. doi:10.6040/j.issn.1671-9352.0.2022.621

Abstract ( 30 )

PDF (709KB) ( 44 )

Save

References | Related Articles | Metrics

Let SGC-Prj denote the class of all semi-Gorenstein-projective modules respect to a semidualizing module C, and let GC-Prj denote the class of all Gorenstein-projective modules respect to a semidualizing module C. Several equivalent conditions for C to be weak Gorenstein are given. In particular, an equivalent characterization such that M and M^* are SGC-projective modules is obtained.

Smooth skew morphisms of a kind of maximal class 3-groups which have abelian maximal subgroups

CAO Jianji, WANG Junxin, BAI Pengfei

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2024, 59(4): 23-30. doi:10.6040/j.issn.1671-9352.0.2023.252

Abstract ( 26 )

PDF (773KB) ( 32 )

Save

References | Related Articles | Metrics

A skew morphism φ of a finite group G is a permutation of G fixing the identity of G and satisfying the property φ(gh)=φ(g)φ^π(g)(h) for any g,h∈G, where π is a function from G to {1,2,…,d-1} for the order d of φ. If for any g∈G, π(g)=1, then φ is an automorphism of G. Hence a skew morphism is a generalization of an automorphism. When π(φ(g))=π(g)for any g∈G, the skew morphism φ is called a smooth skew morphism. In this paper, we classify all smooth skew morphisms of a kind of maximal class 3-groups which have abelian maximal subgroups.

Some subvarieties of semiring variety COS^·_n

FU Yuchen, SHAO Yong

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2024, 59(4): 31-37. doi:10.6040/j.issn.1671-9352.0.2022.368

Abstract ( 27 )

PDF (745KB) ( 22 )

Save

References | Related Articles | Metrics

Greens relations on a semiring satisfying additional identities xⁿ≈x,(2ⁿ-1)x≈x,(x+y)^n-1≈x^n-1+y^n-1 and(xy)^n-1≈x^n-1y^n-1 are studied. Equivalent characterizations of H∧H, H∧L, H∧R, H+∧D, H∨L, H+∨R, H∨D and H+∨H are obtained. The necessary and sufficient conditions for the above relations to be congruent are characterized, and then it is proved that the semiring classes determined by the above congruences are varieties.

Existence of solutions for a class of third-order multi-point boundary value problems with dim Ker L=3 at resonance on a half-line

DU Ruijuan

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2024, 59(4): 38-44. doi:10.6040/j.issn.1671-9352.0.2023.078

Abstract ( 26 )

PDF (757KB) ( 13 )

Save

References | Related Articles | Metrics

The author considers the solvability for a class of third-order multi-point boundary value problems at resonance with dim Ker L=3{ x(t)=f(t,x(t),x'(t),x″(t))+e(t), t∈［0,+∞),x(0)=∑^m_i=1α_ix(ξ_i), x(1)=∑ⁿ_j=1β_jx(η_j), lim_t→+∞x'(t)=∑^l_k=1γ_kx″(ζ_k)where f:［0,1］×R→R satisfies S-Carathéodory conditions, e∈L¹［0,∞), α_i, β_j, γ_k∈R, 0<ξ₁<ξ₂<…<ξ_m<+∞, 0<η₁<η₂<…<η_n<+∞, 0<ζ₁<ζ₂<…<ζ_l<+∞(m,n,l∈Z⁺), and satisfy the following conditions:(C₁)∑^m_i=1α_i=1, ∑^m_i=1α_iξ_i=0, ∑^m_i=1α_iξ²_i=0, ∑ⁿ_j=1β_j=1, ∑ⁿ_j=1β_jη_j=1, ∑ⁿ_j=1β_jη²_j=1, ∑^l_k=1γ_k=1; 山东大学学报 (理学版)第59卷- 第4期杜睿娟:一类半直线上三阶多点边值问题在dim Ker L=3共振情形下解的存在性 \=- (C₂)Δ=|Q₁e^-t Q₂e^-t Q₃e^-tQ₁te^-t Q₂te^-t Q₃te^-tQ₁t²e^-t Q₂t²e^-t Q₃t²e^-t|:=|a₁₁ a₁₂ a₁₃a₂₁ a₂₂ a₂₃a₃₁ a₃₂ a₃₃|≠0;whereQ₁y=∑^m_i=1α_i∫^ξ_i₀∫^s₀∫^τ₀y(v)dvdτds, Q₂y=∑ⁿ_j=1β_j∫^η_j₀∫^s₀∫^τ₀y(v)dvdτds, Q₃y=∑^l_k=1γ_k∫^+∞_{γ_k}y(s)ds.

Existence results for a coupled system of fractional differential equations with cyclic periodic boundary conditions

ZHANG Wei, FU Xinyu, NI Jinbo

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2024, 59(4): 45-52. doi:10.6040/j.issn.1671-9352.0.2023.005

Abstract ( 27 )

PDF (764KB) ( 21 )

Save

References | Related Articles | Metrics

A new class of coupled fractional systems with resonance boundary value problems is studied, considering the case of cyclic periodic boundary conditions. In this case, not only are the equations coupled, but the boundary conditions are also interdependent. By using Mawhins continuation theorem, the existence criteria for solutions are obtained and the main results are illustrated by an example.

Existence and uniqueness of positive solutions of integral boundary value problems for a class of fractional differential equations with Hadamard derivatives

HU Fangfang, HU Weimin, ZHANG Yong

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2024, 59(4): 53-61. doi:10.6040/j.issn.1671-9352.0.2022.565

Abstract ( 29 )

PDF (779KB) ( 23 )

Save

References | Related Articles | Metrics

A class of boundary value problems for Hadamard fractional differential equations with integral boundary value conditions is studied. The existence of positive solutions is obtained by Schauder fixed point theorem and the upper and lower solution method. The uniqueness result is obtained by Banach compression mapping principle, and an example is given to illustrate the effectiveness of the results.

Bilinear θ-type Calderón-Zygmund operators on generalized weighted variable exponent Morrey spaces

RUI Li, LU Guanghui, LI Xuemei

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2024, 59(4): 62-72. doi:10.6040/j.issn.1671-9352.0.2022.624

Abstract ( 32 )

PDF (837KB) ( 56 )

Save

References | Related Articles | Metrics

Via the boundedness of the bilinear θ-type Calderón-Zygmund operators in the variable index Lebesgue space and the control relations in the function spaces, and assuming that the functions u meet certain conditions, the authors prove that the bilinear θ-type Calderón-Zygmund operators are bounded from product generalized weighted variable exponent Morrey spaces to generalized weighted variable exponent Morrey spaces. Furthermore, the authors also prove that the commutators generated by the bilinear θ-type Calderón-Zygmund operators and b1,b2∈BMO(Rⁿ)are bounded on generalized weighted variable exponent Morrey spaces.

ε-approximations of continuous generalized frames

ZHANG Wei

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2024, 59(4): 73-80. doi:10.6040/j.issn.1671-9352.0.2022.468

Abstract ( 24 )

PDF (773KB) ( 18 )

Save

References | Related Articles | Metrics

This paper addresses the continuous generalized frame theory in Hilbert spaces. We introduce the concepts of ε-approximation, ε-closeness of continuous generalized frames, and establish a link between ε-approximation and ε-closeness. We present that the ε-approximations of continuous generalized frames are continuous generalized frames under certain conditions. Interestingly, the ε-approximations of tight continuous generalized frames can not be tight continuous generalized frames. Given a dual frame and ε-closeness of a continuous generalized frame, one can find a dual continuous generalized frame of its ε-closeness that makes the two dual continuous generalized frames close to each other.

Some generalizations of Ostrowski type fractional integral inequalities

DANG Xiaonan, LIAN Tieyan, LI Ran

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2024, 59(4): 81-89. doi:10.6040/j.issn.1671-9352.0.2022.622

Abstract ( 22 )

PDF (804KB) ( 45 )

Save

References | Related Articles | Metrics

By using the definitions of k-β-convex functions and preinvex functions, the definition of strong k-β-preinvex functions is proposed. Based on constructing a k-Riemann-Liouville fractional integral identity, the properties of strong k-β-preinvex functions and some methods of integral inequalities, some Ostrowski type inequalities for strong k-β-preinvex functions via k-Riemann-Liouville fractional integral are established.

Dynamic behaviors analysis of delayed HIV model with cell-to-cell transmissions and protease inhibitors

MIAO Hui, ABDURAHMAN Xamxinur

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2024, 59(4): 90-97. doi:10.6040/j.issn.1671-9352.0.2023.150

Abstract ( 29 )

PDF (2486KB) ( 11 )

Save

References | Related Articles | Metrics

In this paper, considering the transmission mechanism of HIV and antiviral drug therapy, a delayed HIV model with cell-to-cell transmission f2(G,J)and a protease inhibitor therapy is investigated. The global stability of equilibria E₀ and E₁ is proven. Our analysis shows that neglecting cell-to-cell transmission f2(G,J)or virus-to-cell infection f1(G,L)can lead to an underestimation of the basic number of virus infections R₀, and the theoretical results were validated through numerical simulation.

Perpetual American lookback option pricing under mixed bi-fractional Brownian motion

ZHANG Yaru, XIA Li, ZHANG Dianqiu

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2024, 59(4): 98-107. doi:10.6040/j.issn.1671-9352.0.2022.629

Abstract ( 28 )

PDF (4121KB) ( 10 )

Save

References | Related Articles | Metrics

A pricing model for a perpetual American lookback option with dividends driven by mixed bi-fractional Brownian motion is constructed in this paper. First, the partial differential equations of mixed bi-fractional Brownian motion for perpetual American lookback call and put options are given by the Δ-hedging principle. Then, the established partial differential equations are solved by variable substitution method and characteristic equation method. Finally, numerical experiments are adopted to verify the linear proportional scaling properties of the solution, and the effects of mixed bi-fractional Brownian motion parameters H,K and volatility on the option prices are further discussed.

Model averaging study with a cured group right-censored data

WANG Shuying, ZHANG Yanan, CHENG Yunfei, ZHOU Lifang

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2024, 59(4): 108-116. doi:10.6040/j.issn.1671-9352.0.2022.465

Abstract ( 28 )

PDF (895KB) ( 13 )

Save

References | Related Articles | Metrics

In the existing survival analysis studies, most of them directly assume the model form of response variables and specified covariates, and then estimate the covariate effect. However, when the assumption of the model is wrong, the corresponding conclusion may be wrong. Under the right-censored data with a cured group, in order to avoid the inaccuracy caused by the construction of the model with specified covariates, an accelerated failure time model(AFT model)based on the model averaging method is proposed. In the framework of maximum likelihood estimation, model selection and model averaging based on information criteria are used for statistical inference. The numerical simulation results show that under the right-censored data with a cured group, the estimation and prediction accuracy of the AFT model based on the model averaging method is higher than that of model selection method. Finally, the feasibility and practicability of the proposed method are verified by analysis of trial data on melanoma clinical.

Parameters calibration method of JWL equation of state based on time varying response surface methodology

LIANG Xiao, WANG Shuo, WANG Ruili, CHEN Jiangtao

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2024, 59(4): 117-126. doi:10.6040/j.issn.1671-9352.0.2023.061

Abstract ( 31 )

PDF (10399KB) ( 10 )

Save

References | Related Articles | Metrics

Calibration of phenomenological parameters of Jones-Wilkins-Lee(JWL)equation of state based on experimental data and modeling and simulation result plays a vital role in comprehension of detonation-driven expansion process and evaluating the work performance of detonation product. Time varying response surface methodology(RSM)can establish a simpler functional relation between prominent parameters and system response quantity(SRQ). It provides a rapid and high-accurate computational method of describing the dynamical behavior and calibrating parameters. Firstly, Latin hypercube sampling(LHS)technique is used to sample the uncertainty in the uncertain parameters of JWL equation of state in the detonation production, and then effective data is selected and divided into two groups. High-resolution simulation is implemented based on group I, and the radial position and radial velocity is obtained through full intellectual software—CFD2D. Time varying RSM between uncertain JWL parameters and SRQ is constructed through output of the high fidelity simulation. Group II is used to evaluate the accuracy of the time varying RSM. Then Residual error between the simulation results of surrogate model and experiment data is constructed. Furthermore, the minimum residual error is searched among all the residual error and the corresponding parameters are obtained as the optimum parameters. The result shows that output of SRQ coincides with and experimental data perfectly, when these optimum parameters are substituted into the high fidelity computational methods. That means, the parameters are calibrated and model validated. The result will provide guidance for weapon design and munitions assessment.

Research on XCH₄ remote sensing inversion algorithm based on DEM and broadband structure joint optimization

WANG Chen, XU Degang, DA Hongju, TANG Zhihe, LUAN Hui, FAN Haihao

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2024, 59(4): 127-134. doi:10.6040/j.issn.1671-9352.0.2023.376

Abstract ( 24 )

PDF (3241KB) ( 14 )

Save

References | Related Articles | Metrics

A well-known approach for remote sensing inversion of the mean dry air mole fraction of methane(XCH₄)is weighted function modified differential optical absorption spectroscopy(WFM-DOAS). The ability to distinguish between the spectral structures of "broadband absorption" and "narrowband absorption" is one of its primary technologies. In the meantime, the inversion of XCH₄ is greatly influenced by the digital elevation model(DEM). Currently available methane inversion products mostly fit broadband structures with polynomials; however, the selection parameters for polynomial order are not well defined, and the broadband structure fitting is not precise enough. In local areas, the high-precision inversion requirements cannot be met by the accuracy of the employed DEM. This paper selects the Qinghai Tibet Plateau region, where the Waliguan Atmospheric Background Reference Observatory is located, as the research area. A higher precision digital elevation model(GLO-30)is used, and a fully connected neural network is used instead of a low order polynomial for “broadband structure” fitting. Furthermore, a “skip” structure is added to the traditional fully connected neural network, and a dropout strategy is used to optimize the network. By Comparing the experimental results with the XCH₄ inverted using the global multi resolution terrain elevation data 2010(GMTED2010)and low order polynomial fitting methods. The results show that the improved fully connected neural network can better fit the broadband spectral structure, and combining it with a higher precision DEM can improve the inversion accuracy of XCH₄, with the highest correlation coefficient increased to 0.92. The joint optimization method used can be used for remote sensing inversion of XCH₄ in oil and gas production areas, thereby better serving the investigation of methane abnormal emissions in oil and gas production areas.

Table of Content