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Some Constacyclic Codes over Z4[u]/〈u^2〉, New Gray Maps, and New Quaternary Codes

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Algebra Colloquium 2018年第3期25卷 369-376页

作者： Yasemin Cengellenmis Abdullah Dertli Nuh Aydin department of mathematics Trakya University Edirne Turkey department of mathematics Ondokuz Mayls University Samsun Turkey department of mathematics and statistic Kenyon College Gambler OH USA

In this paper, we study λ-constacyclic codes over the ring R = Z4 ＋ uZ4, where u^2 = 0, for λ= 1 ＋ 3u and 3 ＋ u. We introduce two new Gray maps from R to Z4^4 and show that the Gray images of λ-constacyclic codes over R are quasi-cyclic over Z4. Moreover, we present many examples of λ-constacyclic codes over R whose Z4-images have better parameters than the currently best-known linear codes over Z4.

关键词： constacyclic codes codes over rings quaternary codes Gray maps

Minimizing the Risk of Absolute Ruin Under a Diffusion Approximation Model with Reinsurance and Investment

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Journal of Systems Science & Complexity 2015年第1期28卷 144-155页

作者： BI Xiuchun ZHANG Shuguang department of statistic and Finance University of Science and Technology of China

This paper studies the optimization problem with both investment and proportional reinsurance control under the assumption that the surplus process of an insurance entity is represented by a pure diffusion *** company can buy proportional reinsurance and invest its surplus into a Black-Scholes risky asset and a risk free asset without *** authors define absolute ruin as that the liminf of the surplus process is negative infinity and propose absolute ruin minimization as the optimization *** the HJB method the authors obtain explicit expressions for the minimal absolute ruin function and the associated optimal investment *** authors find that the minimal absolute ruin function here is convex,but not S-shaped investigated by Luo and Taksar(2011).And finally,from behavioral finance point of view,the authors come to the conclusion:It is the restrictions on investment that results in the kink of minimal absolute ruin function.

关键词： Absolute ruin probability dynamic investment control HJB equation proportional reinsnance.

Melting heat transfer effects on stagnation point flow of micropolar fluid saturated in porous medium with internal heat generation(absorption)

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Applied mathematics and Mechanics(English Edition) 2014年第8期35卷 979-992页

作者： M.A.A.MAHMOUD S.E.WAHEED department of mathematics Faculty of ScienceBenha University 13518BenhaEgypt department of mathematics and statistic Faculty of ScienceTaif University 21974TaifKingdom of Saudi Arabia

The effect of melting heat transfer on the two dimensional boundary layer flow of a micropolar fluid near a stagnation point embedded in a porous medium in the presence of internal heat generation/absorption is investigated. The governing non-linear partial differential equations describing the problem are reduced to a system of non-linear ordinary differential equations using similarity transformations solved numerically using the Chebyshev spectral method. Numerical results for velocity, angular velocity and temperature profiles are shown graphically and discussed for different values of the inverse Darcy number, the heat generation/absorption parameter, and the melting parameter. The effects of the pertinent parameters on the local skin-friction coefficient, the wall couple stress, and the local Nusselt number are tabulated and discussed. The results show that the inverse Darcy number has the effect of enhancing both velocity and temperature and suppressing angular velocity. It is also found that the local skin-friction coefficient decreases, while the local Nusselt number increases as the melting parameter increases.

关键词： melting effect stagnation point micropolar fluid porous medium heat generation (absorption)

Global behavior of dynamical agents in directed network

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控制理论与应用（英文版） 2009年第3期7卷 307-314页

作者： Hongwang YU Yufan ZHENG School of mathematics and statistic Nanjing Audit University Nanjing Jiangsu 211815 China department of mathematics East China Normal University Shanghai 200062 China

This paper investigates the global behavior of controlled dynamical agents in directed networks. The agents are Lyapunov stable, are distributed in a line, and communicate through a directed network. The communication topology of the network is characterized by a directed graph and the control protocol is designed in simple linear decentralized feedback law. We study the different conditions under which agents will achieve aggregation, and critical and divergent trajectories, respectively. Our investigation on the dynamical agent system under network is extended to the time-delay network case. Furthermore, we study the case with two pre-specified virtual leaders in the system. Numerical simulations are given and demonstrate that our theoretical results are effective.

关键词： Dynamical agents Directed graph Laplacian Hurwitz criteria

Neutrosophicκ-Structures in Ordered Semigroups

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Computer Modeling in Engineering & Sciences 2022年第5期131卷 979-999页

作者： G.Muhiuddin K.Porselvi B.Elavarasan D.Al-Kadi department of mathematics Faculty of ScienceUniversity of TabukTabuk71491Saudi Arabia department of mathematics Karunya Institute of Technology and SciencesCoimbatore641114India department of mathematics and statistic College of ScienceTaif UniversityTaif21944Saudi Arabia

In general,ordered algebraic structures,particularly ordered semigroups,play an important role in fuzzification in many applied areas,such as computer science,formal languages,coding theory,error correction,***,the concept of ambiguity is important in dealing with a variety of issues related to engineering modeling problems,network theory,decision-making problems in real-life situations,and so *** theories have been developed by various researchers to overcome the difficulties that arise from uncertainty,including fuzzy sets,intuitionistic fuzzy sets,probability,softsets,neutrosophic sets,***,we focus solelyonneutrosophic set *** ordered semigroups,we define and investigate the properties of neutrosophicκ-ideals and neutrosophicκ-interior *** also use neutrosophicκ-ideals and neutrosophicκ-interior ideals to characterize ordered semigroups.

关键词： Ordered semigroup ideals neutrosophicκ-structures neutrosophicκ-ideals neutrosophicκ-interior ideals

Finite-time cluster synchronization in nonlinearly-coupled delayed networks of nonidentical delayed dynamic systems 36

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Finite-time cluster synchronization in nonlinearly-coupled d...

A Geometric Based Connection between Fractional Calculus and Fractal Functions

第36届中国控制会议

作者： Junhong Shen Yi Zhao Jianwen Feng Haiyu Zhang College of Mathematic and statistic Shenzhen University department of mathematics The University of Hong Kong

ISBN: (纸本)9781538629185

In this paper,we investigate the finite-time cluster synchronization problem for networks with nonlinearly coupled delayed networks of nonidentical delayed dynamic *** derive sufficient conditions for finite-time cluster synchronization through a proper controller based on finite-time stability *** numerical examples are then given to illustrate the theoretical results.

关键词： Complex networks finite-time cluster synchronization nonlinearly-coupled networks nonidentical delayed dynamics

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Acta Mathematica Sinica,English Series 2024年第2期40卷 537-567页

作者： Yong Shun LIANG Wei Yi SU School of mathematics and statistic Nanjing University of Science and TechnologyNanjing 210094P.R.China department of mathematics Nanjing UniversityNanjing 210023P.R.China

Establishing the accurate relationship between fractional calculus and fractals is an important research content of fractional calculus *** the present paper,we investigate the relationship between fractional calculus and fractal functions,based only on fractal dimension *** dimension of the Riemann-Liouville fractional integral of continuous functions seems no more than fractal dimension of functions *** fractal dimension of the Riemann-Liouville fractional differential of continuous functions seems no less than fractal dimension of functions themselves when they *** further discussion,fractal dimension of the Riemann-Liouville fractional integral is at least linearly decreasing and fractal dimension of the Riemann-Liouville fractional differential is at most linearly increasing for the Holder continuous *** about other fractional calculus,such as the Weyl-Marchaud fractional derivative and the Weyl fractional integral has also been given *** work is helpful to reveal the mechanism of fractional calculus on continuous *** the same time,it provides some theoretical basis for the rationality of the definition of fractional *** is also helpful to reveal and explain the internal relationship between fractional calculus and fractals from the perspective of geometry.

关键词： Fractional calculus fractal functions fractal dimension fractional calculus equation relationship

Hopf bifurcation of nonlinear incidence rates SIR epidemiological models with stage structure

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Communications in Nonlinear Science and Numerical Simulation 2001年第4期6卷 205-209页

作者： Zhonghua LU, Xianning LIU and Lansun CHEN Institute of mathematics, Academy of mathematics and System Sciences, Chinese Academy of Sciences, Beijing 100080, China e-mail: lschen@*** Xi'an statistic College, Xi'an 710061, China e-mail: lzh Institute of mathematics Academy of Mathematics and System Sciences Chinese Academy of Sciences Beijing 100080 China Xi'an statistic College Xi'an 710061 China department of mathematics Southwest China Normal University Chongging 400715 China

A nonlinear incidence rates SIR epidemiological model with stage structure is considered. Different to bilinear incidence rates models, there exist two positive equilibria and whether or not the disease will eventuall... 详细信息

关键词： Hopf bifurcation SIR epidemiological model. disease-free equilibrium endemic equilibrium

The double auxiliary equations method and its application to space-time fractional nonlinear equations

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Journal of Ocean Engineering and Science 2019年第1期4卷 7-13页

作者： L.A.Alhakim A.A.Moussa Unit of mathematics and statistic College of Business&EconomicsQassim UniversityBuraidahSaudi Arabia Thoeoretical Reseach Group Department of MathematicsFaculty of ScienceDamascus UniversityDamascusSyria

This paper reflects the execution of a reliable technique which we proposed as a new method called the double auxiliary equations method for constructing new traveling wave solutions of nonlinear fractional differential *** proposed scheme has been successfully applied on two very important evolution equations,the space-time fractional differential equation governing wave propagation in low-pass electrical transmission lines equation and the time fractional Burger’s *** obtained results show that the proposed method is more powerful,promising and convenient for solving nonlinear fractional differential equations(NFPDEs).To our knowledge,the solutions obtained by the proposed method have not been reported in former literature.

关键词： Double auxiliary equations method Fractional partial differential equation Exact solution Traveling wave solution Nonlinear low-pass electrical Transmission lines Fractional Burger’s equation.