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A NOTE ON THE GENERAL STABILIZATION OF DISCRETE FEEDBACK CONTROL FOR NON-AUTONOMOUS HYBRID NEUTRAL STOCHASTIC SYSTEMS WITH A DELAY

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Acta Mathematica Scientia 2024年第3期44卷 1145-1164页

作者：冯立超张春艳曹进德武志辉 college of Science North China University of Science and TechnologyTangshan063210China School of mathematics Southeast UniversityNanjing210096China Department of mathematics Harbin University of Science and TechnologyHarbin150080China

Discrete feedback control was designed to stabilize an unstable hybrid neutral stochastic differential delay system(HNSDDS) under a highly nonlinear constraint in the H_∞ and exponential ***,the existing work just adapted to autonomous cases,and the obtained results were mainly on exponential *** comparison with autonomous cases,non-autonomous systems are of great interest and represent an important ***,discrete feedback control has here been adjusted with a time factor to stabilize an unstable non-autonomous HNSDDS,in which new Lyapunov-Krasovskii functionals and some novel technologies are *** should be noted,in particular,that the stabilization can be achieved not only in the routine H_∞ and exponential forms,but also the polynomial form and even a general form.

关键词： hybrid neutral stochastic differential delay system discrete feedback control general stabilization polynomial stabilization

Local MFS Matrix Decomposition Algorithms for Elliptic BVPs in Annuli

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Numerical mathematics(Theory,Methods and Applications) 2024年第1期17卷 93-120页

作者： C.S.Chen Andreas Karageorghis Min Lei School of mathematics and Natural Sciences University of Southern MississippiHattiesburgMS 39406USA Department of mathematics and Statistics University of CyprusP.O.Box 20537Nicosia 1678Cyprus college of mathematics Taiyuan University of TechnologyTaiyuan 030024P.R.China

We apply the local method of fundamental solutions(LMFS)to boundary value problems(BVPs)for the Laplace and homogeneous biharmonic equations in *** appropriately choosing the collocation points,the LMFS discretization yields sparse block circulant system *** a result,matrix decomposition algorithms(MDAs)and fast Fourier transforms(FFTs)can be used for the solution of the systems resulting in considerable savings in both computational time and storage *** accuracy of the method and its ability to solve large scale problems are demonstrated by applying it to several numerical experiments.

关键词： Local method of fundamental solutions Poisson equation biharmonic equation matrix decomposition algorithms fast Fourier transforms

Benchmarking Algorithms for Gene Set Scoring of Single-cell ATAC-seq Data

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Genomics, Proteomics & Bioinformatics 2024年第2期22卷 27-42页

作者： Xi Wang Qiwei Lian Haoyu Dong Shuo Xu Yaru Su Xiaohui Wu Pasteurien college Suzhou Medical College of Soochow UniversitySoochow UniversitySuzhou 215000China Department of Automation Xiamen UniversityXiamen 361005China college of mathematics and Computer Science Fuzhou UniversityFuzhou 350116China

Gene set scoring(GSS)has been routinely conducted for gene expression analysis of bulk or single-cell RNA sequencing(RNA-seq)data,which helps to decipher single-cell heterogeneity and cell type-specific variability by incorporating prior knowledge from functional gene ***-cell assay for transposase accessible chromatin using sequencing(scATAC-seq)is a powerful technique for interrogating single-cell chromatin-based gene regulation,and genes or gene sets with dynamic regulatory potentials can be regarded as cell type-specific markers as if in single-cell RNA-seq(scRNA-seq).However,there are few GSS tools specifically designed for scATAC-seq,and the applicability and performance of RNA-seq GSS tools on scATAC-seq data remain to be ***,we systematically benchmarked ten GSS tools,including four bulk RNA-seq tools,five scRNA-seq tools,and one scATAC-seq ***,using matched scATAC-seq and scRNA-seq datasets,we found that the performance of GSS tools on scATAC-seq data was comparable to that on scRNA-seq,suggesting their applicability to ***,the performance of different GSS tools was extensively evaluated using up to ten scATAC-seq ***,we evaluated the impact of gene activity conversion,dropout imputation,and gene set collections on the results of *** show that dropout imputation can significantly promote the performance of almost all GSS tools,while the impact of gene activity conversion methods or gene set collections on GSS performance is more dependent on GSS tools or ***,we provided practical guidelines for choosing appropriate preprocessing methods and GSS tools in different application scenarios.

关键词： Single-cell ATAC-seq Gene set scoring Pathway analysis Single-cell RNA-seq Benchmark

A Study on the Transmission Dynamics of the Omicron Variant of COVID-19 Using Nonlinear Mathematical Models

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Computer Modeling in Engineering & Sciences 2024年第6期139卷 2265-2287页

作者： S.Dickson S.Padmasekaran Pushpendra Kumar Kottakkaran Sooppy Nisar Hamidreza Marasi Department of mathematics Periyar UniversitySalemTamilnadu636011India Faculty of Engineering and Natural Sciences Istanbul Okan UniversityIstanbulTurkey Department of mathematics College of Science and Humanities in AlkharjPrince Sattam Bin Abdulaziz UniversityAlkharj11942Saudi Arabia Department of Applied mathematics Faculty of MathematicsStatistics and Computer ScienceUniversity of TabrizTabrizIran

This research examines the transmission dynamics of the Omicron variant of COVID-19 using SEIQIcRVW and SQIRV models,considering the delay in converting susceptible individuals into infected *** significant delays eventually resulted in the pandemic’s *** ensure the safety of the host population,this concept integrates quarantine and the COVID-19 *** investigate the stability of the proposed *** fundamental reproduction number influences stability *** to our findings,asymptomatic cases considerably impact the prevalence of Omicron infection in the *** real data of the Omicron variant from Chennai,Tamil Nadu,India,is used to validate the outputs.

关键词： Omicron local stability reproduction number steady states global stability

Stability Analysis of Inverse Lax-Wendroff Procedure for a High order Compact Finite Difference Schemes

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Communications on Applied mathematics and Computation 2024年第1期6卷 142-189页

作者： Tingting Li Jianfang Lu Pengde Wang School of mathematics and Statistics Henan UniversityKaifeng475004HenanChina School of mathematics South China University of TechnologyGuangzhou510641GuangdongChina college of mathematics and Information Science Henan University of Economics and LawZhengzhou450046HenanChina

This paper considers the finite difference(FD)approximations of diffusion operators and the boundary treatments for different boundary *** proposed schemes have the compact form and could achieve arbitrary even order of *** main idea is to make use of the lower order compact schemes recursively,so as to obtain the high order compact schemes ***,the schemes can be implemented efficiently by solving a series of tridiagonal systems recursively or the fast Fourier transform(FFT).With mathematical induction,the eigenvalues of the proposed differencing operators are shown to be bounded away from zero,which indicates the positive definiteness of the *** obtain numerical boundary conditions for the high order schemes,the simplified inverse Lax-Wendroff(SILW)procedure is adopted and the stability analysis is performed by the Godunov-Ryabenkii method and the eigenvalue spectrum visualization *** numerical experiments are provided to demonstrate the effectiveness and robustness of our algorithms.

关键词： Compact scheme Diffusion operators Inverse Lax-Wendroff(ILW) Fourier analysis Eigenvalue analysis

DYNAMICS FOR A CHEMOTAXIS MODEL WITH GENERAL LOGISTIC DAMPING AND SIGNAL DEPENDENT MOTILITY

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Acta Mathematica Scientia 2024年第3期44卷 1046-1063页

作者：涂馨予穆春来邱蜀燕张静 School of mathematics and Statistics Southwest UniversityChongqing400715China Department of Applied mathematics The Hong Kong Polytechnic UniversityHung HomHong KongChina college of mathematics and Statistics Chongqing UniversityChongqing401331China School of Sciences Southwest Petroleum UniversityChengdu610500China

In this paper,we consider the fully parabolic Chemotaxis system with the general logistic source{ut=Δ(γ(v)u)+λu-μu^(k),x∈Ω,t>0,vt=△v+wz,x∈Ω,t>0,wt=-wz,x∈Ω,t>0,zt=△z-z+u,x∈Ω,t>0 whereΩ⊂ℝn(n≥1)is a smooth and bounded domain,λ≥0,μ≥0,κ>1,and the motility function satisfies thatγ(v)∈C3([0,∞)),γ(v)>0,γ′(v)≤0 for all v≥*** the Neumann boundary condition,we obtain the global boundedness of solutions if one of the following conditions holds:(i)λ=μ=0,1≤nλ3;(ii)λ>0,μ>0,combined withκ>1,1≤n≤3 or k>n+2.4,,n>***,we prove that the solution (u, v, w, z) exponentially converges to the constant steady state ((λ/μ)1/k-1,∫Ωv0dx+∫Ωw0dx/|Ω|,0,(λ/μ)1/k-1).

关键词： chemotaxis signal-dependent motility logistic source boundedness asymptotic behavior

Viscoelastic potential flow instability theory of Rivlin-Ericksen electrified fluids of cylindrical interface

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Journal of Ocean Engineering and Science 2024年第4期9卷 311-316页

作者： D.M.Mostafa Department of mathematics College of ScienceQassim UniversityPO Box 6644Buraidah 51452Saudi Arabia Department of mathematics Faculty of EducationAin Shams UniversityRoxyCairoEgypt

A linear electrohydrodynamic Kelvin-Helmholtz instability of the interface between two viscoelastic Rivlin-Ericksen fluids enclosed by two concentric horizontal cylinders has been studied via the viscoelastic potential flow *** dispersion equation of complex coefficients for asymmetric disturbance has been obtained by using normal mode *** stability criteria are analyzed theoretically and illustrated *** imaginary part of growth rate is plotted versus the wave *** influences of dynamic viscoelastic,uniform velocities,Reynolds number,electric field,dynamic viscosity,density fluids ratio,dielectric constant ratio and inner fluid fraction on the stability of the system are *** study finds its significance in Ocean pipelines to transfer oil or gas such as Eastern Siberia-Pacific Ocean oil pipeline.

关键词： Rivlin-Ericksen fluid Cylindrical flow Viscoelastic potential flow Electrohydrodynamics stability

THE GLOBAL EXISTENCE AND UNIQUENESS OF SMOOTH SOLUTIONS TO A FLUID-PARTICLE INTERACTION MODEL IN THE FLOWING REGIME

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Acta Mathematica Scientia 2024年第5期44卷 1877-1885页

作者： Lin ZHENG Shu WANG college of mathematics and Statistics North China University of Water Resources and Electric PowerZhengzhou450046China School of mathematics Statistics and MechanicsBeijing University of TechnologyBeijing100124China

This paper is concerned with the Cauchy problem for a 3D fluid-particle interaction model in the so-called flowing regime inℝ*** the smallness assumption on both the external potential and the initial perturbation of the stationary solution in some Sobolev spaces,the existence and uniqueness of global smooth solutions in H3 of the system are established by using the careful energy method.

关键词： fluid-particle flowing regime global existence

Detection and defending the XSS attack using novel hybrid stacking ensemble learning-based DNN approach

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Digital Communications and Networks 2024年第3期10卷 716-727页

作者： Muralitharan Krishnan Yongdo Lim Seethalakshmi Perumal Gayathri Palanisamy IMS Sungkyunkwan UniversitySuwon16419South Korea Department of mathematics Sungkyunkwan UniversitySuwon16419South Korea Department of Information Technology Madras Institute of TechnologyChennaiIndia Department of mathematics PSG College of Arts and ScienceTamilnaduIndia

Existing web-based security applications have failed in many situations due to the great intelligence of *** web applications,Cross-Site Scripting(XSS)is one of the dangerous assaults experienced while modifying an organization's or user's *** avoid these security challenges,this article proposes a novel,all-encompassing combination of machine learning(NB,SVM,k-NN)and deep learning(RNN,CNN,LSTM)frameworks for detecting and defending against XSS attacks with high accuracy and *** on the representation,a novel idea for merging stacking ensemble with web applications,termed“hybrid stacking”,is *** order to implement the aforementioned methods,four distinct datasets,each of which contains both safe and unsafe content,are *** hybrid detection method can adaptively identify the attacks from the URL,and the defense mechanism inherits the advantages of URL encoding with dictionary-based mapping to improve prediction accuracy,accelerate the training process,and effectively remove the unsafe JScript/JavaScript keywords from the *** simulation results show that the proposed hybrid model is more efficient than the existing detection *** produces more than 99.5%accurate XSS attack classification results(accuracy,precision,recall,f1_score,and Receiver Operating Characteristic(ROC))and is highly resistant to XSS *** order to ensure the security of the server's information,the proposed hybrid approach is demonstrated in a real-time environment.

关键词： Machine learning Deep neural networks Classification Stacking ensemble XSS attack URL encoding JScript/JavaScript Web security