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On classification of 2-dimensional evolution algebras and its applications

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Journal of Physics: Conference Series 2020年第1期1489卷

作者： H Ahmed U Bekbaev I Rakhimov Department of Math. Faculty of Science UPM Selangor Malaysia & Depart. of Math. Faculty of Science Taiz University Taiz Yemen Department of Mathematical and Natural Sciences TTPU Tashkent Uzbekistan & Department of Science in Engineering Faculty of Engineering IIUM Malaysia Department of Mathematics Faculty of Computer and Mathematical Sciences UiTM Malaysia & V.I.Romanovskiy Institute of Mathematics Uzbekistan Academy of Science

In the paper we give a complete classification of 2-dimensional evolution algebras over algebraically closed fields, we compare the list of representatives of the isomorphism classes with that of obtained earlier by t...

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An empirical study on the knowledge management practice in software testing 21

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An empirical study on the knowledge management practice in s...

21st Ibero-American Conference on Software Engineering, CIbSE 2018

作者： Maciel, Claudia P.C. De Souza, Erica Ferreira Vijaykumar, Nandamudi L. De Almeida Falbo, Ricardo Meinerz, Giovani Volnei Felizardo, Katia Romero Department of Computer Federal Technological University of Paraná/UTFPR Cornelio Procópio/PR Brazil Lab. of Comp and Applied Math. National Institute for Space Research INPE Sao José dos Campos/SP Brazil Department of Computer Science Federal University of Espirito Santo UFES Vitória/ES Brazil

ISBN: (纸本)9789584837547

Context: Software testing is a knowledge intensive process, and therefore can benefit from the use of experience gained from past projects. In this context, principles of Knowledge Management (KM) can be applied to promote knowledge capture and sharing as well as the emergence of new knowledge. In spite of this, there are only few studies that present practitioners' perspective about KM initiatives in software testing. Objective: The main goal of this study is to identify the perception of professionals in software testing on the use of KM initiatives in software engineering companies, such as KM adoption, potential benefits or hindrances. Method: A survey was conducted in software development companies. In addition, the survey results were compared with another survey conducted previously in the same context, however, with different objectives and target audience. 39 software companies participated in this research. Results: Testing planning activity and the test case reuse are the aspects that have received more attention by companies. A strategic planning and reuse of existing test cases have a potential to significantly reduce software development costs and time. Conclusion: Applying KM in software companies can bring several benefits in terms of quality of results, reduction costs, time and effort. However, it is still a challenge to be faced and tackled. © 2018 Conferencia Iberoamericana de Software Engineering - CIbSE. All Rights Reserved.

关键词： Software testing

Crouzeix’s Conjecture and Related Problems

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arXiv 2020年

作者： Bickel, Kelly Gorkin, Pamela Greenbaum, Anne Ransford, Thomas Schwenninger, Felix Wegert, Elias Department of Mathematics Bucknell University LewisburgPA17837 United States Department of Mathematics Bucknell University LewisburgPA17837 United States Department of Applied Mathematics University of Washington Département de mathématiques et de statistique Université Laval QuébecQCG1V 0A6 Canada Department of Mathematics Universität Hamburg Department of Applied Mathematics University of Twente Netherlands Department of Mathematics and Computer Science Technische Universität Bergakademie Freiberg Division of Mathematical Sciences National Science Foundation United States NSERC and the Canada Research Chairs program

In this paper, we establish several results related to Crouzeixs conjecture. We show that the conjecture holds for contractions with eigenvalues that are sufficiently well-separated. This separation is measured by the so-called separation constant, which is defined in terms of the pseudohyperbolic metric. Moreover, we study general properties of related extremal functions and associated vectors. Throughout, compressions of the shift serve as illustrating examples which also allow for refined *** Codes 47A25, 47A12, 15A60, 47A20, 30J10 Copyright © 2020, The Authors. All rights reserved.

关键词： Eigenvalues and eigenfunctions

Inverse scattering on the quantum graph - Edge model for graphen

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arXiv 2019年

作者： Ando, Kazunori Isozaki, Hiroshi Korotyaev, Evgeny Morioka, Hisashi Department of Electrical and Electronic Engineering and Computer Science Ehime University Matsuyama790-8577 Japan Graduate School of Pure and Applied Sciences Emeritus University of Tsukuba Tsukuba305-8571 Japan Department of Math. Analysis Saint-Petersburg State University Universitetskaya nab. 7/9 St. Petersburg199034 Russia

We consider the inverse scattering on the quantum graph associated with the hexagonal lattice. Assuming that the potentials on the edges are compactly supported, we show that the S-matrix for all energies in any open set in the continous spectrum determines the *** Codes 81U40, 47A40 Copyright © 2019, The Authors. All rights reserved.

关键词： Inverse problems

Simultaneous dimensionality and complexity model selection for spectral graph clustering

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arXiv 2019年

作者： Yang, Congyuan Priebe, Carey E. Park, Youngser Marchette, David J. Department of Electrical and Computer Engineering Johns Hopkins University Department of Applied Math and Statistics Johns Hopkins University Center for Imaging Science Johns Hopkins University Applied Mathematics and Data Analytics Group Naval Surface Warfare Center Dahlgren Division

Our problem of interest is to cluster vertices of a graph by identifying underlying community structure. Among various vertex clustering approaches, spectral clustering is one of the most popular methods because it is easy to implement while often outperforming more traditional clustering algorithms. However, there are two inherent model selection problems in spectral clustering, namely estimating both the embedding dimension and number of clusters. This paper attempts to address the issue by establishing a novel model selection framework specifically for vertex clustering on graphs under a stochastic block model. The first contribution is a probabilistic model which approximates the distribution of the extended spectral embedding of a graph. The model is constructed based on a theoretical result of asymptotic normality of the informative part of the embedding, and on a simulation result providing a conjecture for the limiting behavior of the redundant part of the embedding. The second contribution is a simultaneous model selection framework. In contrast with the traditional approaches, our model selection procedure estimates embedding dimension and number of clusters simultaneously. Based on our conjectured distributional model, a theorem on the consistency of the estimates of model parameters is stated and proven. The theorem provides statistical support for the validity of our method. Heuristic algorithms via the simultaneous model selection framework for vertex clustering are proposed, with good performance shown in the experiment on synthetic data and on the real application of connectome analysis. Copyright © 2019, The Authors. All rights reserved.

关键词： Embeddings

HIV and COVID-19 co-infection: A math.matical model and optimal control

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Informatics in Medicine Unlocked 2022年 31卷 100978页

作者： Ringa, N. Diagne, M.L. Rwezaura, H. Omame, A. Tchoumi, S.Y. Tchuenche, J.M. Data and Analytic Services British Columbia Centre for Disease Control 655 W 12th Ave Vancouver BC V5Z 4R4 Canada School of Population and Public Health University of British Columbia 2329 West Mall Vancouver BC V6T 1Z4 Canada Département de Mathématiques UFR des Sciences et Technologies Université de Thiès Thiès BP 967 Senegal Mathematics Department University of Dar es Salaam P.O. Box 35062 Dar es Salaam Tanzania Department of Mathematics Federal University of Technology Owerri Nigeria Abdus Salam School of Mathematical Sciences Government College University Lahore Pakistan Department of Mathematics and Computer Sciences ENSAI University of Ngaoundéré P.O. Box 455 Ngaoundéré Cameroon School of Computer Science and Applied Mathematics University of the Witwatersrand Private Bag 3 Wits 2050 Johannesburg South Africa School of Computational and Communication Sciences and Engineering Nelson Mandela African Institution of Science and Technology P.O. Box 447 Arusha Tanzania

A new math.matical model for COVID-19 and HIV/AIDS is considered to assess the impact of COVID-19 on HIV dynamics and vice-versa. Investigating the epidemiologic synergy between COVID-19 and HIV is important. The dynamics of the full model is driven by that of its sub-models;therefore, basic analysis of the two sub-models;HIV-only and COVID-19 only is carried out. The basic reproduction number is computed and used to prove local and global asymptotic stability of the sub-models’ disease-free and endemic equilibria. Using the fmincon function in the Optimization Toolbox of MATLAB, the model is fitted to real COVID-19 data set from South Africa. The impact of intervention measures, namely, COVID-19 and HIV prevention interventions and COVID-19 treatment are incorporated into the model using time-dependent controls. It is observed that HIV prevention measures can significantly reduce the burden of co-infections with COVID-19, while effective treatment of COVID-19 could reduce co-infections with opportunistic infections such as HIV/AIDS. In particular, the COVID-19 only prevention strategy averted about 10,500 new co-infection cases, with similar number also averted by the HIV-only prevention control. © 2022 The Author(s)

关键词： Basic reproduction number Co-infection COVID-19 HIV Optimal control

Topologically mixing properties of multiplicative integer system

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arXiv 2019年

作者： Ban, Jung-Chao Chang, Chih-Hung Hu, Wen-Guei Lai, Guan-Yu Wu, Yu-Liang Department of Mathematical Sciences National Chengchi University Taipei11605 Taiwan Math. Division National Center for Theoretical Science National Taiwan University Taipei10617 Taiwan Department of Applied Mathematics National University of Kaohsiung Kaohsiung81148 Taiwan College of Mathematics Sichuan University Chengdu610064 China Department of Applied Mathematics National Chiao Tung University Hsinchu30010 Taiwan

Motivated from the study of multiple ergodic average, the investigation of multiplicative shift spaces has drawn much of interest among researchers. This paper focuses on the relation of topologically mixing properties between multiplicative shift spaces and traditional shift spaces. Suppose that X(Ωl) is the multiplicative subshift derived from the shift space Ω with given l > 1. We show that X(Ωl) is (topologically) transitive/mixing if and only if Ω is extensible/mixing. After introducing l-directional mixing property, we derive the equivalence between l-directional mixing property of X(Ωl) and weakly mixing property of Ω.MSC Codes 37B10 Copyright © 2019, The Authors. All rights reserved.

关键词： Mixing

Bresse-Timoshenko type systems with thermodiffusion effects: Well-possedness, stability and numerical results

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arXiv 2020年

作者： Elhindi, Mohammad Zennir, Khaled Ouchenane, Djamel Choucha, Abdelbaki Arwadi, Toufic E.L. Department of Mathematics and Computer Science Faculty of Science Beirut Arab University Beirut Lebanon Department of Mathematics College of Sciences and Arts Qassim University Ar-Rass Saudi Arabia Laboratoire de Mathématiques Appliquées et de Modélisation Université 8 Mai 1945 Guelma. B.P. 401 Guelma24000 Algeria Laboratory of pure and applied mathematic Laghouat University Algeria Department of Mathematics Faculty of Exact Sciences University of El Oued B.P. 789 El Oued39000 Algeria

Bresse-Timoshenko beam model with thermal, mass diffusion and theormoelastic effects is studied. We state and prove the well-posedness of problem. The global existence and uniqueness of the solution is proved by using the classical Faedo-Galerkin approximations along with two a priori estimates. We prove an exponential stability estimate for problem under an unusual assumption, and by using a multiplier technique in two different cases, with frictional damping in the angular rotation and with frictional damping in the vertical displacement. In numerical parts, we first obtained a numerical scheme for problem by P1-finite element method for space discretization and implicit Euler scheme for time discretization. Then, we showed that the discrete energy decays, later a priori error estimates are established. Finally, some numerical simulations are presented. Copyright © 2020, The Authors. All rights reserved.

关键词： Damping

THE LIMIT THEOREM WITH RESPECT TO THE MATRICES ON NON-BACKTRACKING PATHS OF A GRAPH

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arXiv 2020年

作者： Hasegawa, Takehiro Komatsu, Takashi Konno, Norio Saigo, Hayato Saito, Seiken Sato, Iwao Sugiyama, Shingo Department of Education Shiga University Shiga Otsu520-0862 Japan Math. Research Institute Calc for Industry Minami Hiroshima732-0816 Japan Department of Applied Mathematics Faculty of Engineering Yokohama National University Hodogaya Yokohama240-8501 Japan Nagahama Institute of Bio-Science and Technology 1266 Tamura Nagahama526-0829 Japan Division of Liberal Arts Center for Promotion of Higher Education Kogakuin University 2665-1 Nakano Hachioji Tokyo192-0015 Japan Oyama National College of Technology Tochigi Oyama323-0806 Japan Department of Mathematics College of Science and Technology Nihon University Suruga-Dai Kanda Chiyoda Tokyo101-8308 Japan

We give a limit theorem with respect to the matrices related to non-backtracking paths of a regular graph. The limit obtained closely resembles the kth moments of the arcsine law. Furthermore, we obtain the asymptotics of the averages of the pmth Fourier coefficients of the cusp forms related to the Ramanujan graphs defined by A. Lubotzky, R. Phillips and P. *** Codes 05C38 (Primary), 05C50, 11F30 (Secondary) Copyright © 2020, The Authors. All rights reserved.

关键词： Graph theory