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THE KILLING FORMS AND DECOMPOSITION THEOREMS OF LIE SUPERTRIPLE SYSTEMS

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Acta Mathematica Scientia 2009年第2期29卷 360-370页

作者：张知学贾培佩 Institute of Mathematics and Computers Hebei University Fundamental Department Hebei College of Finance

In this article, the Killing form of a Lie supertriple system （LSTS） and that of its imbedding Lie superalgebra （LSA） are investigated, and a unique decomposition theorem for a quasiclassical LSTS with trivial cen... 详细信息

关键词： Killing form Lie supertriple system quasiclassical

On the Nilpotence of Malcev Algebras

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Northeastern Mathematical Journal 2005年第1期21卷 81-86页

作者：张知学冯建强 Institute of Mathematics and Computers Hebei University Baoding 071002

We investigate the nilpotence of a Malcev algebra M and of its standard enveloping Lie algebra L(M) = M(?)D(M, M). The main result shows that an ideal A of M is nilpotent in M if and only if the corresponding ideal I(... 详细信息

关键词： Malcev algebra enveloping Lie algebra nilpotence

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Lie三系的Killing型(英文)

Journal of Mathematical Research and Exposition 2009年第4期29卷 745-752页

作者：张知学高瑞 Institute of Mathematics and Computers Hebei University Department of mathematics Cangzhou Teacher's College

For Lie triple systems in the characteristic zero setting,we obtain by means of the Killing forms two criterions for semisimplicity and for solvability respectively,and then investi-gate the relationship among the Kil... 详细信息

关键词：李三角系统特性可解性复化

A Hybrid Classification and Identification of Pneumonia Using African Buffalo Optimization and CNN from Chest X-Ray Images

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Computer Modeling in Engineering & Sciences 2024年第3期138卷 2497-2517页

作者： Nasser Alalwan Ahmed I.Taloba Amr Abozeid Ahmed Ibrahim Alzahrani Ali H.Al-Bayatti Computer Science Department Community CollegeKing Saud UniversityRiyadh11437Saudi Arabia Information System Department Faculty of Computers and InformationAssiut UniversityAssiutEgypt mathematics Department Faculty of ScienceAl-Azhar UniversityCairoEgypt Cyber Technology institute(CTI) De Montfort UniversityLeicesterUK

An illness known as pneumonia causes inflammation in the lungs.Since there is so much information available fromvarious X-ray images,diagnosing pneumonia has typically proven challenging.To improve image quality and speed up the diagnosis of pneumonia,numerous approaches have been devised.To date,several methods have been employed to identify pneumonia.The Convolutional Neural Network(CNN)has achieved outstanding success in identifying and diagnosing diseases in the fields of medicine and radiology.However,these methods are complex,inefficient,and imprecise to analyze a big number of datasets.In this paper,a new hybrid method for the automatic classification and identification of Pneumonia from chest X-ray images is proposed.The proposed method(ABOCNN)utilized theAfrican BuffaloOptimization(ABO)algorithmto enhanceCNNperformance and accuracy.The Weinmed filter is employed for pre-processing to eliminate unwanted noises from chest X-ray images,followed by feature extraction using the Grey Level Co-Occurrence Matrix(GLCM)approach.Relevant features are then selected from the dataset using the ABO algorithm,and ultimately,high-performance deep learning using the CNN approach is introduced for the classification and identification of Pneumonia.Experimental results on various datasets showed that,when contrasted to other approaches,the ABO-CNN outperforms them all for the classification tasks.The proposed method exhibits superior values like 96.95%,88%,86%,and 86%for accuracy,precision,recall,and F1-score,respectively.

关键词： African buffalo optimization convolutional neural network pneumonia X-ray

Attention-Based and Time Series Models for Short-Term Forecasting of COVID-19 Spread

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computers, Materials & Continua 2022年第1期70卷 695-714页

作者： Jurgita Markeviciute Jolita Bernataviciene Ruta Levuliene Viktor Medvedev Povilas Treigys Julius Venskus institute of Applied mathematics Vilnius UniversityVilnius03225Lithuania institute of Data Science and Digital Technologies Vilnius UniversityVilnius08412Lithuania

The growing number of COVID-19 cases puts pressure on healthcare services and public institutions worldwide.The pandemic has brought much uncertainty to the global economy and the situation in general.Forecasting methods and modeling techniques are important tools for governments to manage critical situations caused by pandemics,which have negative impact on public health.The main purpose of this study is to obtain short-term forecasts of disease epidemiology that could be useful for policymakers and public institutions to make necessary short-term decisions.To evaluate the effectiveness of the proposed attention-based method combining certain data mining algorithms and the classical ARIMA model for short-term forecasts,data on the spread of the COVID-19 virus in Lithuania is used,the forecasts of epidemic dynamics were examined,and the results were presented in the study.Nevertheless,the approach presented might be applied to any country and other pandemic situations.The COVID-19 outbreak started at different times in different countries,hence some countries have a longer history of the disease with more historical data than others.The paper proposes a novel approach to data registration and machine learning-based analysis using data from attention-based countries for forecast validation to predict trends of the spread of COVID-19 and assess risks.

关键词： COVID-19 spread modeling attention-based forecasting machine learning data registration data analysis ARIMA

Stochastic Epidemic Model of Covid-19 via the Reservoir-People Transmission Network

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computers, Materials & Continua 2022年第7期72卷 1495-1514页

作者： Kazem Nouri Milad Fahimi Leila Torkzadeh Dumitru Baleanu Department of mathematics Faculty of MathematicsStatistics and Computer SciencesSemnan UniversityP.O.Box 35195-363SemnanIran Department of mathematics Faculty of Arts and SciencesCankaya UniversityAnkaraTurkey institute of Space Sciences Magurele-BucharestRomania

The novel Coronavirus COVID-19 emerged in Wuhan,China in December 2019.COVID-19 has rapidly spread among human populations and other mammals.The outbreak of COVID-19 has become a global challenge.Mathematical models of epidemiological systems enable studying and predicting the potential spread of disease.Modeling and predicting the evolution of COVID-19 epidemics in near real-time is a scientific challenge,this requires a deep understanding of the dynamics of pandemics and the possibility that the diffusion process can be completely random.In this paper,we develop and analyze a model to simulate the Coronavirus transmission dynamics based on Reservoir-People transmission network.When faced with a potential outbreak,decision-makers need to be able to trust mathematical models for their decision-making processes.One of the most considerable characteristics of COVID-19 is its different behaviors in various countries and regions,or even in different individuals,which can be a sign of uncertain and accidental behavior in the disease outbreak.This trait reflects the existence of the capacity of transmitting perturbations across its domains.We construct a stochastic environment because of parameters random essence and introduce a stochastic version of theReservoir-Peoplemodel.Then we prove the uniqueness and existence of the solution on the stochastic model.Moreover,the equilibria of the system are considered.Also,we establish the extinction of the disease under some suitable conditions.Finally,some numerical simulation and comparison are carried out to validate the theoretical results and the possibility of comparability of the stochastic model with the deterministic model.

关键词： Coronavirus infectious diseases stochastic modeling brownian motion reservoir-people model transmission simulation stochastic differential equation

LEAST-SQUARES MIXED FINITE ELEMENT METHOD FOR A CLASS OF STOKES EQUATION

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Applied mathematics and Mechanics(English Edition) 2000年第5期21卷 557-566页

作者：顾海明羊丹平隋树林刘新民 Department of computers Qingdao Institute of Chemical Technology Qingdao P R China Department of mathematics Shandong University Jinan P R China

A least-squares mixed finite element method was formulated for a class of Stokes equations in two dimensional domains. The steady state and the time-dependent Stokes' equations were considered. For the stationary equation, optimal H-t and L-2-error estimates are derived under the standard regularity assumption on the finite element partition ( the LBB-condition is not required). Far the evolutionary equation, optimal L-2 estimates are derived under the conventional Raviart-Thomas spaces.

关键词： least-squares mixed finite element method error estimates

Solution of Algebraic Lyapunov Equation on Positive-Definite Hermitian Matrices by Using Extended Hamiltonian Algorithm

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computers, Materials & Continua 2018年第2期54卷 181-195页

作者： Muhammad Shoaib Arif Mairaj Bibi Adnan Jhangir Department of mathematics Air UniversityPAF ComplexE-9IslamabadPakistan Department of mathematics Comsats Institute of Information TechnologyPark RoadChak-ShahzadIslamabadPakistan Department of mathematics Comsats Institute of Information TechnologyWah CanttPakistan

This communique is opted to study the approximate solution of the Algebraic Lyapunov equation on the manifold of positive-definite Hermitian matrices.We choose the geodesic distance between􀀀AHX􀀀XA and P as the cost function,and put forward the Extended Hamiltonian algorithm(EHA)and Natural gradient algorithm(NGA)for the solution.Finally,several numerical experiments give you an idea about the effectiveness of the proposed algorithms.We also show the comparison between these two algorithms EHA and NGA.Obtained results are provided and analyzed graphically.We also conclude that the extended Hamiltonian algorithm has better convergence speed than the natural gradient algorithm,whereas the trajectory of the solution matrix is optimal in case of Natural gradient algorithm(NGA)as compared to Extended Hamiltonian Algorithm(EHA).The aim of this paper is to show that the Extended Hamiltonian algorithm(EHA)has superior convergence properties as compared to Natural gradient algorithm(NGA).Upto the best of author’s knowledge,no approximate solution of the Algebraic Lyapunov equation on the manifold of positive-definite Hermitian matrices is found so far in the literature.

关键词： Information geometry algebraic lyapunov equation positive-definite hermitianmatrix manifold natural gradient algorithm extended hamiltonian algorithm

An Improved Jellyfish Algorithm for Multilevel Thresholding of Magnetic Resonance Brain Image Segmentations

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computers, Materials & Continua 2021年第9期68卷 2961-2977页

作者： Mohamed Abdel-Basset Reda Mohamed Mohamed Abouhawwash Ripon K.Chakrabortty Michael J.Ryan Yunyoung Nam Faculty of computers and Informatics Zagazig UniversityZagazig44519Egypt Department of mathematics Faculty of ScienceMansoura UniversityMansoura35516Egypt Department of Computational mathematics Scienceand Engineering(CMSE)Michigan State UniversityEast LansingMI48824USA Capability Systems Centre School of Engineering and ITUNSW CanberraAustralia Department of Computer Science and Engineering Soonchunhyang UniversityAsan31538Korea

Image segmentation is vital when analyzing medical images,especially magnetic resonance(MR)images of the brain.Recently,several image segmentation techniques based on multilevel thresholding have been proposed for medical image segmentation;however,the algorithms become trapped in local minima and have low convergence speeds,particularly as the number of threshold levels increases.Consequently,in this paper,we develop a new multilevel thresholding image segmentation technique based on the jellyfish search algorithm(JSA)(an optimizer).We modify the JSA to prevent descents into local minima,and we accelerate convergence toward optimal solutions.The improvement is achieved by applying two novel strategies:Rankingbased updating and an adaptive method.Ranking-based updating is used to replace undesirable solutions with other solutions generated by a novel updating scheme that improves the qualities of the removed solutions.We develop a new adaptive strategy to exploit the ability of the JSA to find a best-so-far solution;we allow a small amount of exploration to avoid descents into local minima.The two strategies are integrated with the JSA to produce an improved JSA(IJSA)that optimally thresholds brain MR images.To compare the performances of the IJSA and JSA,seven brain MR images were segmented at threshold levels of 3,4,5,6,7,8,10,15,20,25,and 30.IJSA was compared with several other recent image segmentation algorithms,including the improved and standard marine predator algorithms,the modified salp and standard salp swarm algorithms,the equilibrium optimizer,and the standard JSA in terms of fitness,the Structured Similarity Index Metric(SSIM),the peak signal-to-noise ratio(PSNR),the standard deviation(SD),and the Features Similarity Index Metric(FSIM).The experimental outcomes and the Wilcoxon rank-sum test demonstrate the superiority of the proposed algorithm in terms of the FSIM,the PSNR,the objective values,and the SD;in terms of the SSIM,IJSA was competitive with the others.

关键词： Magnetic resonance imaging brain image segmentation artificial jellyfish search algorithm ranking method local minima Otsu method