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Stabilization and Blow-up in an Infinite Memory Wave Equation with Logarithmic Nonlinearity and Acoustic Boundary Conditions

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Journal of Systems Science & Complexity 2024年第4期37卷 1368-1391页

作者： PENG Qingqing ZHANG Zhifei School of Mathematics and Statistics Huazhong University of Science and Technology Hubei Key Laboratory of Engineering modeling and Scientific computing Huazhong University of Science and Technology

In this paper, the authors consider the stabilization and blow up of the wave equation with infinite memory, logarithmic nonlinearity and acoustic boundary conditions. The authors discuss the existence of global solutions for the initial energy less than the depth of the potential well and investigate the energy decay estimates by introducing a Lyapunov function. Moreover, the authors establish the finite time blow up results of solutions and give the blow up time with upper bounded initial energy.

关键词： Acoustic boundary condition finite time blow-up general decay infinite memory logarithmic nonlinearity

Spontaneous Infection and Periodic Evolving of Domain in a Diffusive SIS Epidemic Model

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Acta Mathematicae Applicatae Sinica 2024年第1期40卷 164-191页

作者： Qiang Wen Guo-qiang Ren Bin Liu School of Mathematics and Statistics Huazhong University of Science and TechnologyWuhan430074China Hubei Key Laboratory of Engineering modeling and Scientific computing Huazhong University of Science and TechnologyWuhan430074China

In this paper, we consider a susceptible-infective-susceptible(SIS) reaction-diffusion epidemic model with spontaneous infection and logistic source in a periodically evolving domain. Using the iterative technique,the uniform boundedness of solution is established. In addition, the spatial-temporal risk index R0(ρ) depending on the domain evolution rate ρ(t) as well as its analytical properties are discussed. The monotonicity of R0(ρ)with respect to the diffusion coefficients of the infected dI, the spontaneous infection rate η(ρ(t)y) and interval length L is investigated under appropriate conditions. Further, the existence and asymptotic behavior of periodic endemic equilibria are explored by upper and lower solution method. Finally, some numerical simulations are presented to illustrate our analytical results. Our results provide valuable information for disease control and prevention.

关键词： diffusive SIS model spontaneous infection periodically evolving domain periodic endemic equilibrium

ONE-PARAMETER FINITE DIFFERENCE METHODS AND THEIR ACCELERATED SCHEMES FOR SPACE-FRACTIONAL SINE-GORDON EQUATIONS WITH DISTRIBUTED DELAY

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Journal of Computational Mathematics 2024年第3期42卷 705-734页

作者： Tao Sun Chengjian Zhang Haiwei Sun School of Mathematics and Statistics Huazhong University of Science and TechnologyWuhan 430074China Hubei Key Laboratory of Engineering modeling and Scientific computing Huazhong University of Science and TechnologyWuhan 430074China Department of Mathematics University of MacaoMacaoChina

This paper deals with numerical methods for solving one-dimensional(1D)and twodimensional(2D)initial-boundary value problems(IBVPs)of space-fractional sine-Gordon equations(SGEs)with distributed delay.For 1D problems,we construct a kind of oneparameter finite difference(OPFD)method.It is shown that,under a suitable condition,the proposed method is convergent with second order accuracy both in time and space.In implementation,the preconditioned conjugate gradient(PCG)method with the Strang circulant preconditioner is carried out to improve the computational efficiency of the OPFD method.For 2D problems,we develop another kind of OPFD method.For such a method,two classes of accelerated schemes are suggested,one is alternative direction implicit(ADI)scheme and the other is ADI-PCG scheme.In particular,we prove that ADI scheme can arrive at second-order accuracy in time and space.With some numerical experiments,the computational effectiveness and accuracy of the methods are further verified.Moreover,for the suggested methods,a numerical comparison in computational efficiency is presented.

关键词： Fractional sine-Gordon equation with distributed delay One-parameter finite difference methods Convergence analysis ADI scheme PCG method

SHARP POINTWISE-IN-TIME ERROR ESTIMATE OF L1 SCHEME FOR NONLINEAR SUBDIFFUSION EQUATIONS

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Journal of Computational Mathematics 2024年第3期42卷 662-678页

作者： Dongfang Li Hongyu Qin Jiwei Zhang School of Mathematics and Statistics Huazhong University of Science and TechnologyWuhan 430074China Hubei Key Laboratory of Engineering modeling and Scientific computing Huazhong University of Science and TechnologyWuhan 430074China School of Mathematics and Statistics Wuhan UniversityWuhan 430072China

An essential feature of the subdiffusion equations with theα-order time fractional derivative is the weak singularity at the initial time.The weak regularity of the solution is usually characterized by a regularity parameterσ∈(0,1)∪(1,2).Under this general regularity assumption,we present a rigorous analysis for the truncation errors and develop a new tool to obtain the stability results,i.e.,a refined discrete fractional-type Grönwall inequality(DFGI).After that,we obtain the pointwise-in-time error estimate of the widely used L1 scheme for nonlinear subdiffusion equations.The present results fill the gap on some interesting convergence results of L1 scheme onσ∈(0,α)∪(α,1)∪(1,2].Numerical experiments are provided to demonstrate the effectiveness of our theoretical analysis.

关键词： Sharp pointwise-in-time error estimate Ll scheme Nonlinear subdiffusion equations Non-smooth solutions

RB-DEM modeling and Simulation of Non-Persisting Rough Open Joints Based on the IFS-Enhanced Method

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Computer modeling in Engineering & Sciences 2024年第4期139卷 337-359页

作者： Hangtian Song Xudong Chen Chun Zhu Qian Yin Wei Wang Qingxiang Meng Key Laboratory of Ministry of Education for geomechanics and Embankment Engineering Hohai UniversityNanjing210098China Research Institute of Geotechnical Engineering Hohai UniversityNanjing210098China School of Earth Sciences and Engineering Hohai UniversityNanjing210098China State Key Laboratory for geomechanics and Deep Underground Engineering China University of Mining and TechnologyXuzhou221116China

When the geological environment of rock masses is disturbed,numerous non-persisting open joints can appear within it.It is crucial to investigate the effect of open joints on the mechanical properties of rock mass.However,it has been challenging to generate realistic open joints in traditional experimental tests and numerical simulations.This paper presents a novel solution to solve the problem.By utilizing the stochastic distribution of joints and an enhanced-fractal interpolation system(IFS)method,rough curves with any orientation can be generated.The Douglas-Peucker algorithm is then applied to simplify these curves by removing unnecessary points while preserving their fundamental shape.Subsequently,open joints are created by connecting points that move to both sides of rough curves based on the aperture distribution.Mesh modeling is performed to construct the final mesh model.Finally,the RB-DEM method is applied to transform the mesh model into a discrete element model containing geometric information about these open joints.Furthermore,this study explores the impacts of rough open joint orientation,aperture,and number on rock fracture mechanics.This method provides a realistic and effective approach for modeling and simulating these non-persisting open joints.

关键词： Non-persisting rough open joints stochastic distribution of joints enhanced-IFS method RB-DEM

Enhancing Ulcerative Colitis Diagnosis:A Multi-Level Classification Approach with Deep Learning

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Computer modeling in Engineering & Sciences 2024年第7期140卷 1129-1142页

作者： Hasan J.Alyamani Department of Information Systems Faculty of Computing and Information Technology in RabighKing Abdulaziz UniversityJeddah21589Saudi Arabia

The evaluation of disease severity through endoscopy is pivotal in managing patients with ulcerative colitis,a condition with significant clinical implications.However,endoscopic assessment is susceptible to inherent variations,both within and between observers,compromising the reliability of individual evaluations.This study addresses this challenge by harnessing deep learning to develop a robust model capable of discerning discrete levels of endoscopic disease severity.To initiate this endeavor,a multi-faceted approach is embarked upon.The dataset is meticulously preprocessed,enhancing the quality and discriminative features of the images through contrast limited adaptive histogram equalization(CLAHE).A diverse array of data augmentation techniques,encompassing various geometric transformations,is leveraged to fortify the dataset’s diversity and facilitate effective feature extraction.A fundamental aspect of the approach involves the strategic incorporation of transfer learning principles,harnessing a modified ResNet-50 architecture.This augmentation,informed by domain expertise,contributed significantly to enhancing the model’s classification performance.The outcome of this research endeavor yielded a highly promising model,demonstrating an accuracy rate of 86.85%,coupled with a recall rate of 82.11%and a precision rate of 89.23%.

关键词： Ulcerative colitis deep learning CLAHE transfer learning geometric transformations

Dimension by Dimension Finite Volume HWENO Method for Hyperbolic Conservation Laws

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Communications on Applied Mathematics and Computation 2024年第1期6卷 605-624页

作者： Feng Zheng Jianxian Qiu College of Mathematics and Statistics Fujian Normal UniversityFuzhou350117FujianChina School of Mathematical Sciences and Fujian Provincial Key Laboratory of Mathematical modeling&High-Performance Scientific computing Xiamen UniversityXiamen361005FujianChina

In this paper,we propose a finite volume Hermite weighted essentially non-oscillatory(HWENO)method based on the dimension by dimension framework to solve hyperbolic conservation laws.It can maintain the high accuracy in the smooth region and obtain the high resolution solution when the discontinuity appears,and it is compact which will be good for giving the numerical boundary conditions.Furthermore,it avoids complicated least square procedure when we implement the genuine two dimensional(2D)finite volume HWENO reconstruction,and it can be regarded as a generalization of the one dimensional(1D)HWENO method.Extensive numerical tests are performed to verify the high resolution and high accuracy of the scheme.

关键词： Finite volume Dimension by dimension HWENO Hyperbolic conservation laws

Two kinds of average approximation accuracy

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CAAI Transactions on Intelligence technology 2024年第2期9卷 481-490页

作者： Qingzhao Kong Wanting Wang Dongxiao Zhang Wenbin Zhang Department of Science Jimei UniversityXiamenChina Digital Fujian Big Data modeling and Intelligent computing Institute Jimei UniversityXiamenChina Department of Computer Science Michigan Technological UniversityHoughtonMichiganUSA

Rough set theory places great importance on approximation accuracy,which is used to gauge how well a rough set model describes a target concept.However,traditional approximation accuracy has limitations since it varies with changes in the target concept and cannot evaluate the overall descriptive ability of a rough set model.To overcome this,two types of average approximation accuracy that objectively assess a rough set model’s ability to approximate all information granules is proposed.The first is the relative average approximation accuracy,which is based on all sets in the universe and has several basic properties.The second is the absolute average approximation accuracy,which is based on undefinable sets and has yielded significant conclusions.We also explore the relationship between these two types of average approximation accuracy.Finally,the average approximation accuracy has practical applications in addressing missing attribute values in incomplete information tables.

关键词： rough sets rough set theory

A Deep Learning Approach for Landmines Detection Based on Airborne Magnetometry Imaging and Edge computing

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Computer modeling in Engineering & Sciences 2024年第5期139卷 2117-2137页

作者： Ahmed Barnawi Krishan Kumar Neeraj Kumar Bander Alzahrani Amal Almansour Faculty of computing and Information technology King Abdulaziz UniversityJeddahSaudi Arabia Department of Computer Science and Engineering Thapar Institute of Engineering and TechnologyDeemed to be UniversityPatialaIndia

Landmines continue to pose an ongoing threat in various regions around the world,with countless buried landmines affecting numerous human lives.The detonation of these landmines results in thousands of casualties reported worldwide annually.Therefore,there is a pressing need to employ diverse landmine detection techniques for their removal.One effective approach for landmine detection is UAV(Unmanned Aerial Vehicle)based AirborneMagnetometry,which identifies magnetic anomalies in the local terrestrial magnetic field.It can generate a contour plot or heat map that visually represents the magnetic field strength.Despite the effectiveness of this approach,landmine removal remains a challenging and resource-intensive task,fraughtwith risks.Edge computing,on the other hand,can play a crucial role in critical drone monitoring applications like landmine detection.By processing data locally on a nearby edge server,edge computing can reduce communication latency and bandwidth requirements,allowing real-time analysis of magnetic field data.It enables faster decision-making and more efficient landmine detection,potentially saving lives and minimizing the risks involved in the process.Furthermore,edge computing can provide enhanced security and privacy by keeping sensitive data close to the source,reducing the chances of data exposure during transmission.This paper introduces the MAGnetometry Imaging based Classification System(MAGICS),a fully automated UAV-based system designed for landmine and buried object detection and localization.We have developed an efficient deep learning-based strategy for automatic image classification using magnetometry dataset traces.By simulating the proposal in various network scenarios,we have successfully detected landmine signatures present in themagnetometry images.The trained models exhibit significant performance improvements,achieving a maximum mean average precision value of 97.8%.

关键词： CNN deep learning landmine detection magnetometer mean average precision UAV