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Copyright of Advances in New & Renewable Energy is the property of Editorial Office of Advances in New & Renewable Energy and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

This paper focuses on the numerical solution method of the van der Pol equation with fractional differential operators. In this paper, a discretization scheme based on the Adams discretization is proposed for Caputo fractional derivative. Then, a complete iterative scheme is constructed based on the Newmark-β method. Finally, the numerical solution of the nonlinear discretization equation is obtained by Newton-Raphson iteration. In the numerical examples, the numerical responses of van der Pol systems with fractional order 0 < α < 1 and 1 < α < 2 are discussed respectively. Moreover, the comparison between the proposed method and the fourth-order Runge-Kutta method is also discussed. The results proved that the proposed numerical scheme is also suitable for integer-order differential systems. [ABSTRACT FROM AUTHOR]

Copyright of Journal of Zhejiang University (Science Edition) is the property of Journal of Zhejiang University (Science Edition) Editorial Office and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Copyright of Journal of Beijing University of Technology is the property of Journal of Beijing University of Technology, Editorial Department and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Copyright of Fly Ash Comprehensive Utilization is the property of Hebei Fly Ash Comprehensive Utilization Magazine Co., Ltd. and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Copyright of Journal of Harbin University of Science & Technology is the property of Journal of Harbin University of Science & Technology and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Copyright of Journal of Central China Normal University is the property of Huazhong Normal University and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

This paper considered the Schrödinger equation with different types of nonlocal integral term coefficients. By using the algebraic analysis method and the spectrum theory of differential equations, the existence of solutions was transformed into the existence of roots for some algebraic equations, the shape of the corresponding curve for the solution of the one-dimensional case. Compared with the results on the existence of solutions in the references, improved results were derived with the help of simpler methods. In order to promote the combination of theory and practice, as the auxiliaries, some curves of solutions were set in the progress of proving main results. [ABSTRACT FROM AUTHOR]

Copyright of Control Theory & Applications / Kongzhi Lilun Yu Yinyong is the property of Editorial Department of Control Theory & Applications and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Copyright of Transactions of the Chinese Society of Agricultural Engineering is the property of Chinese Society of Agricultural Engineering and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Copyright of Control Theory & Applications / Kongzhi Lilun Yu Yinyong is the property of Editorial Department of Control Theory & Applications and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Copyright of Journal of Central China Normal University is the property of Huazhong Normal University and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Copyright of Control Theory & Applications / Kongzhi Lilun Yu Yinyong is the property of Editorial Department of Control Theory & Applications and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

In order to study the effects of the predator's fear effect, hunting cooperation between predators. and environmental factors on the number of prey and predator.this paper established a I.eslie-Gower predator-prey model with fear effect and hunting cooperation. The boundedness of the solutions is proved by the comparison theorem of differential equations. and the conditions for the existence of periodic solutions are given by coincidence degree theorem, and the global attractivity of the periodic solution is analyzed by constructing a I.yapunov function. Numerical simulations are performed through matlab to verify the theoretical results. [ABSTRACT FROM AUTHOR]

Copyright of Journal of Engineering Geology / Gongcheng Dizhi Xuebao is the property of Journal of Engineering Geology and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Copyright of Electric Machines & Control / Dianji Yu Kongzhi Xuebao is the property of Electric Machines & Control and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Copyright of Journal of Central China Normal University is the property of Huazhong Normal University and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Copyright of Journal of Harbin Institute of Technology. Social Sciences Edition / Haerbin Gongye Daxue Xuebao. Shehui Kexue Ban is the property of Harbin Institute of Technology and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

We are concerned with the dynamic properties for the class of differential equation x + εp(t)x =q(t)x β. Dynamic properties include existence, nonexistence, stability and instability. Here β> 0٠β ≠ l,٠ε>0 is a small parameter and p,g are continuous T-periodic functions. Our results are proved using the averaging method and the third approximation method. Compared with the existing literature，the periodic solutions obtained in this paper are obtained. [ABSTRACT FROM AUTHOR]

Copyright of Journal of Central China Normal University is the property of Huazhong Normal University and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Copyright of Journal of Harbin Institute of Technology. Social Sciences Edition / Haerbin Gongye Daxue Xuebao. Shehui Kexue Ban is the property of Harbin Institute of Technology and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Copyright of Journal of Harbin University of Science & Technology is the property of Journal of Harbin University of Science & Technology and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

The topological structure of geostationary earth orbit (GEO) communication satellite constellation network is usually very complex and it is often difficult to define system state accurately. In this paper, we first analyze the topological relationships of a GEO constellation system containing three working satellites and one warm backup satellite, and then define and aggregate the system operating states by means of stochastic process. Based on Kolmogorov theorem, differential equations of aggregated state residence probabilities are built. In addition, with Laplace transform and its inverse transform, reliability indexes of the constellation network are deduced. Furthermore, probability sensitivity of the system's visiting various state sets containing safe state subset, deteriorating state subset, alert state subset and failed state subset is studied with failure rate change of the backup satellite, which can provide quantitative support for improving the constellation network reliability and adopting a backup strategy. In the case study part, we study a specific GEO constellation system of a commercial company and compare the effect of different varied failure rates of the backup satellite, which supports the theoretical conclusion in the previous part. [ABSTRACT FROM AUTHOR]

Basing on good performance of sliding-mode controlling, the paper investigated finite-time synchronization of fractal-order chaotic system by Terminal sliding-mode control strategy, and realized synchronization of drive-response chaotic Sprott-C system (with the fractal order α : 0 < a < 1 ) with unknown parameters and disturbance by designing property slidingmode surface and fractal-order controller. Moreover, one estimated the unknown parameters and upper bound of the unknown systematic parameters and disturbance successfully by some appropriate adaptive update laws combining with fractal-order differential equations theory and finite-time stability theory. Finally, by choosing proper parameters, numerical simulations provide illustration to show the effectiveness and feasibility of the theoretical results. [ABSTRACT FROM AUTHOR]

Copyright of Piezoelectrics & Acoustooptics is the property of Piezoelectric & Acoustooptic and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Copyright of Acta Materiae Compositae Sinica is the property of Acta Materiea Compositae Sinica Editorial Department and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Copyright of Journal of Central China Normal University is the property of Huazhong Normal University and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Copyright of Journal of Harbin University of Science & Technology is the property of Journal of Harbin University of Science & Technology and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

In order to solve the problem of the Green's theory in the linear time-varying system, this paper studies the Green's function for solving differential equations and proposes a formular corresponding to the Green's equation for partial differential equations. Two algorithms based on the Green's function for solving the differential equation are summarized, including the eigen-value based algorithm and the fundamental algorithm. Their equivalence for both algorithms are also discussed. Furthermore, two methods to determine the initial displacement for a free string vibration equation are presented, i. e. the Green's function based string displacement method and the eigen-value of the differential equation besed Green's function method. These results are very important in theory and applications for the development of the theory on the linear time-varying system and non-stationary signal processing. [ABSTRACT FROM AUTHOR]

Many researches on the fields of different applied mathematics and physics can be attributed to the boundary value problem with p-Laplacian. So the research on this issue has important theoretical significance and application value. In this paper, we consider the existence of triple positive solutions for third-order differential equation boundary value problems with p-Laplacian ... where φp(s) = |s|p-2 s, p > 1. By using Avery-peterson's fixed point theorem, under f satisfies certain growth conditions, we study the existence of at least three positive solutions for the above boundary value problem. [ABSTRACT FROM AUTHOR]

Copyright of Applied Mathematics & Mechanics (1000-0887) is the property of Applied Mathematics & Mechanics and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)