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在研读教材的基础上设计数学实验单元教学
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作者 吴永皓 沈学锋 《基础教育研究》 2022年第9期52-55,共4页
在研读教材的基础上设计数学实验单元教学活动,需要教师以学生的实际认知水平为基础,对教材中的数学知识进行“有度”地再创造,促进学生深度学习。通过研读人教A版高二数学选修2-1“圆锥曲线与方程”和人教A版高三数学选修4-4中“圆锥... 在研读教材的基础上设计数学实验单元教学活动,需要教师以学生的实际认知水平为基础,对教材中的数学知识进行“有度”地再创造,促进学生深度学习。通过研读人教A版高二数学选修2-1“圆锥曲线与方程”和人教A版高三数学选修4-4中“圆锥曲线的参数方程”的内容,设计以“椭圆的定义”为主题的数学实验单元教学,让学生通过亲手制作模型或操作实验,利用计算机软件进行模拟实验,体验椭圆定义的发现和发展过程,理解椭圆的定义。 展开更多
关键词 研读教材 椭圆数学 实验单元
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Exact Jacobian Elliptic Function Solutions to sinh-Gordon Equation 被引量:3
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作者 FU Zun-Tao LIU Shi-Kuo LIU Shi-Da 《Communications in Theoretical Physics》 SCIE CAS CSCD 2006年第1期55-60,共6页
In this paper, two transformations are introduced to solve sinh-Gordon equation by using the knowledge of elliptic equation and Jacobian elliptic functions. It is shown that different transformations are required in o... In this paper, two transformations are introduced to solve sinh-Gordon equation by using the knowledge of elliptic equation and Jacobian elliptic functions. It is shown that different transformations are required in order to obtain more kinds of solutions to the sinh-Gordon equation. 展开更多
关键词 Jacobian elliptic function TRANSFORMATION sinh-Gordon equation
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Elliptic Function Waves of Spinor Bose-Einstein Condensates in an Optical Lattice 被引量:2
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作者 XIE Yuan-Dong 《Communications in Theoretical Physics》 SCIE CAS CSCD 2009年第3期445-449,共5页
An improved nonlinear Schrodinger equation different from usual one of spinor Bose-Einstein condensates (BECs) in an optical lattice are obtained by taking into account a nonlinear term in the equation of motion for... An improved nonlinear Schrodinger equation different from usual one of spinor Bose-Einstein condensates (BECs) in an optical lattice are obtained by taking into account a nonlinear term in the equation of motion for probability amplitude of spins carefully. The elliptic function wave solutions of the model are found under specific boundary condition, for example, the two ends of the atomic chain are fixed. In the case of limit the elliptic function wave solutions are reduced into spin-wave-like or solitons. 展开更多
关键词 spinor Bose Einstein condensates optical lattice elliptic tunction wave solution SOLITON
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Exact Periodic-Wave Solutions to Nizhnik-Novikov-Veselov Equation 被引量:1
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作者 ZHAOQiang LIUShi-Kuo FUZun-Tao 《Communications in Theoretical Physics》 SCIE CAS CSCD 2004年第5期719-722,共4页
Exact periodic-wave solutions to the generalized Nizhnik-Novikov-Veselov (NNV) equation are obtained by using the extended Jacobi elliptic-function method, and in the limit case, the solitary wave solution to NNV equa... Exact periodic-wave solutions to the generalized Nizhnik-Novikov-Veselov (NNV) equation are obtained by using the extended Jacobi elliptic-function method, and in the limit case, the solitary wave solution to NNV equation are also obtained. 展开更多
关键词 extended Jacobi elliptic-function method NNV equation periodic-wave solutions
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ELLIPTIC CURVE CRYPTOGRAPHY BASED AUTHENTICATED KEY AGREEMENT WITH PRE-SHARED PASSWORD 被引量:1
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作者 SuiAifen LucasC.K.Hui +1 位作者 YangYixian K.P.Chow 《Journal of Electronics(China)》 2005年第3期268-272,共5页
Based on elliptic curve Diffie-Hellman algorithm, an Elliptic Curve Authenticated Key Agreement (ECAKA) protocol with pre-shared password is proposed. Its security relies on the Elliptic Curve Discrete Logarithm Probl... Based on elliptic curve Diffie-Hellman algorithm, an Elliptic Curve Authenticated Key Agreement (ECAKA) protocol with pre-shared password is proposed. Its security relies on the Elliptic Curve Discrete Logarithm Problem (ECDLP). It provides identity authentication, key validation and perfect forward secrecy, and it can foil man-in-the-middle attacks. 展开更多
关键词 Elliptic Curve Cryptography (ECC) DIFFIE-HELLMAN Simple Authenticated Key Agreement (SAKA)
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Cryptanalysis and Improvement of Signcryption Schemes on Elliptic Curves 被引量:2
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作者 LIXiang-xue CHENKe-fei LIShi-qun 《Wuhan University Journal of Natural Sciences》 EI CAS 2005年第1期231-234,共4页
In this paper, we analyze two signcryption schemes on elliptic curves proposed by Zheng Yu-liang and Hideki Imai. We point out a serious problem with the schemes that the elliptic curve based signcryption schemes lose... In this paper, we analyze two signcryption schemes on elliptic curves proposed by Zheng Yu-liang and Hideki Imai. We point out a serious problem with the schemes that the elliptic curve based signcryption schemes lose confidentiality to gain non-repudiation. We also propose two improvement versions that not only overcome the security leak inherent in the schemes but also provide public verifiability or forward security. Our improvement versions require smaller computing cost than that required by signature-then-encryption methods. 展开更多
关键词 SIGNCRYPTION elliptic curve CRYPTANALYSIS
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Weierstrass Elliptic Function Solutions to Nonlinear Evolution Equations
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作者 YU Jian-Ping SUN Yong-Li 《Communications in Theoretical Physics》 SCIE CAS CSCD 2008年第8期295-298,共4页
This paper is based on the relations between projection Riccati equations and Weierstrass elliptic equation, combined with the Groebner bases in the symbolic computation.Then the novel method for constructing the Weie... This paper is based on the relations between projection Riccati equations and Weierstrass elliptic equation, combined with the Groebner bases in the symbolic computation.Then the novel method for constructing the Weierstrass elliptic solutions to the nonlinear evolution equations is given by using the above relations. 展开更多
关键词 nonlinear evolution equations Weierstrass elliptic function solutions Groebner bases
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Extended Hyperbola Function Method and Its Application to Nonlinear Equations 被引量:1
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作者 HUANGDing-Jiang ZHANGHong-Qing 《Communications in Theoretical Physics》 SCIE CAS CSCD 2004年第6期801-804,共4页
An extended hyperbola function method is proposed to construct exact solitary wave solutions to nonlinear wave equation based upon a coupled Riccati equation. It is shown that more new solitary wave solutions can be f... An extended hyperbola function method is proposed to construct exact solitary wave solutions to nonlinear wave equation based upon a coupled Riccati equation. It is shown that more new solitary wave solutions can be found by this new method, which include kink-shaped soliton solutions, bell-shaped soliton solutions and new solitary wave.The new method can be applied to other nonlinear equations in mathematical physics. 展开更多
关键词 nonlinear wave equations exact solitary wave solution hyperbola function method
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Different-Periodic Travelling Wave Solutions for Nonlinear Equations
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作者 YELi-Jun LINJi 《Communications in Theoretical Physics》 SCIE CAS CSCD 2004年第4期481-486,共6页
Using Jacobi elliptic function linear superposition approach for the (1+1)-dimensional Caudrey–Dodd–Gibbon–Sawada–Kotera (CDGSK) equation and the (2+1)-dimensional Nizhnik–Novikov–Veselov (NNV) equation, many ne... Using Jacobi elliptic function linear superposition approach for the (1+1)-dimensional Caudrey–Dodd–Gibbon–Sawada–Kotera (CDGSK) equation and the (2+1)-dimensional Nizhnik–Novikov–Veselov (NNV) equation, many new periodic travelling wave solutions with different periods and velocities are obtained based on the known periodic solutions. This procedure is crucially dependent on a sequence of cyclic identities involving Jacobi elliptic functions sn(), cn(), and dn(). 展开更多
关键词 linear superposition nonlinear equation travelling wave solution
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Least Squares Fitting Based Fault Classification in Distribution Systems 被引量:1
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作者 Omar A. Saraereh Qais Alsafasfeh +2 位作者 Anas Al Tarabsheh Aouda Arfoa Issa Etier 《Journal of Energy and Power Engineering》 2014年第3期560-567,共8页
Power systems are the largest and most complex human made systems, consisting of thousands of electrical sources, loads, transmission and distribution lines, power transformers, circuit breakers, etc. where faults alw... Power systems are the largest and most complex human made systems, consisting of thousands of electrical sources, loads, transmission and distribution lines, power transformers, circuit breakers, etc. where faults always occurred. Faults can cause personnel and equipment safety problems, and can result in significant disruption to power supply and thus financial losses. In this paper we will present comprehensive mathematical suite to detect and classify fault dependent models of various types of power systems. This work will extract fault unique signatures by using polarization ellipse during the healthy condition and the polarization will be circular shape with radius equal the rated voltage of the system, but during the fault condition the polarization will be ellipse shape and the fault signature will be defined according the ellipse parameters major axis, minor axis, ellipticity and orientation angle, by using least squares criterion will define the ellipse parameters this system will identify and classify. This paper will be a milestone for extended paper based on the proposed mathematical modelling and applying it to identify, classify and localize with simulation model. 展开更多
关键词 Distribution systems major axis minor axis ELLIPTICITY FAULT ELLIPSE least squares criterion.
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A Decay Result to an Elliptic Equation with Dynamical Boundary Condition
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作者 呼青英 朱碧 张宏伟 《Chinese Quarterly Journal of Mathematics》 CSCD 2009年第3期365-369,共5页
The decay estimations of the solution to an elliptic equation with dynamical boundary condition is considered.We proved that,for suitable initial datum,the energy of the solution decays "in time" exponential... The decay estimations of the solution to an elliptic equation with dynamical boundary condition is considered.We proved that,for suitable initial datum,the energy of the solution decays "in time" exponentially if p=0,whereas the decay is polynomial order if p>0. 展开更多
关键词 elliptic equation dynamical boundary condition DECAY
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Schauder Estimates for Elliptic and Parabolic Equations 被引量:7
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作者 Xu-Jia WANG 《Chinese Annals of Mathematics,Series B》 SCIE CSCD 2006年第6期637-642,共6页
In this note the author gives an elementary and simple proof for the Schauder estimates for elliptic and parabolic equations. The proof also applies to nonlinear equations.
关键词 Schauder estimate Elliptic equation Parabolic equation
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OSCILLATION CRITERIA FOR NONLINEAR SECOND ORDER ELLIPTIC DIFFERENTIAL EQUATIONS 被引量:12
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作者 ZHANG BINGGEN ZHAO TAO B. S. LALLI (Department of Mathematics, Ocean University of Qingdao, Qingdao 266003, China.)(Department of Mathematics, Arizona State University, U.S.A.)(Departmemt of Mathematics, University of Saskatchewan, Canada.) 《Chinese Annals of Mathematics,Series B》 SCIE CSCD 1996年第1期89-102,共14页
The second order elliptic differential equations are considered in an exterior domain Ω Rn, n≥2, where p can chang sign. Some new sufficient conditions for the oscillation of solutions of (1.1) and (1.2) are establi... The second order elliptic differential equations are considered in an exterior domain Ω Rn, n≥2, where p can chang sign. Some new sufficient conditions for the oscillation of solutions of (1.1) and (1.2) are established. 展开更多
关键词 OSCILLATION Nonlinear elliptic equation Riccati inequality
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Sign-Changing Solutions for a Class of Nonlinear Elliptic Problems
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作者 Aixia QIAN 《Chinese Annals of Mathematics,Series B》 SCIE CSCD 2007年第5期609-616,共8页
In the present paper, the author studies the existence of sign-changing solutions for nonlinear elliptic equations, which have jumping nonlinearities, and may or may not be resonant with respect to Fucik spectrum, via... In the present paper, the author studies the existence of sign-changing solutions for nonlinear elliptic equations, which have jumping nonlinearities, and may or may not be resonant with respect to Fucik spectrum, via linking methods under Cerami condition. 展开更多
关键词 Sign-changing solutions Fucik spectrum Jumping nonlinearities
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Gradient estimates for parabolic systems from composite material
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作者 LI HaiGang LI YanYan 《Science China Mathematics》 SCIE CSCD 2017年第11期2011-2052,共42页
In this paper, we derive W^(1,∞) and piecewise C^(1,α) estimates for solutions, and their t-derivatives, of divergence form parabolic systems with coefficients piecewise H¨older continuous in space variables x ... In this paper, we derive W^(1,∞) and piecewise C^(1,α) estimates for solutions, and their t-derivatives, of divergence form parabolic systems with coefficients piecewise H¨older continuous in space variables x and smooth in t. This is an extension to parabolic systems of results of Li and Nirenberg [Comm Pure Appl Math, 2003, 56:892–925] on elliptic systems. These estimates depend on the shape and the size of the surfaces of discontinuity of the coefficients, but are independent of the distance between these surfaces. 展开更多
关键词 gradient estimates parabolic system composite material linear system of elasticity
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