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函数方程问题的求解策略 被引量:2
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作者 周晓文 《中学数学教学》 2003年第5期29-30,共2页
关键词 高中 函数方程问题 解题方法 数学教学
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解答函数方程问题的思维误区辨析
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作者 陈海云 《数理化解题研究(高中版)》 2013年第3期4-4,共1页
函数与方程思想是中学数学中重要数学思维方法之一,也是解答数学问题的常用策略所谓函数与方程思想就是在解答某些数学问题时,将函数问题看成方程问题或将方程问题看成函数问题来处理,即将函数与方程相互转化,体现了数学思维中的转... 函数与方程思想是中学数学中重要数学思维方法之一,也是解答数学问题的常用策略所谓函数与方程思想就是在解答某些数学问题时,将函数问题看成方程问题或将方程问题看成函数问题来处理,即将函数与方程相互转化,体现了数学思维中的转化与化归的数学思想.但在实际运用这一思维方法求解数学问题时。 展开更多
关键词 函数方程问题 数学思维方法 解答 误区 数学问题 方程思想 函数问题 中学数学
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函数方程问题的题组教学
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作者 陈小书 《数理化解题研究(高中版)》 2004年第7期12-13,共2页
高中课本部分习题,许多高考复习资料,以至高考试题中,与函数方程有关的问题都有渗透和考查.函数方程问题一般较为抽象,由于没有统一的分类和解法,加上解题过程涉及函数性质和多种数学思想方法,要求学生有较强的逻辑思维能力与灵... 高中课本部分习题,许多高考复习资料,以至高考试题中,与函数方程有关的问题都有渗透和考查.函数方程问题一般较为抽象,由于没有统一的分类和解法,加上解题过程涉及函数性质和多种数学思想方法,要求学生有较强的逻辑思维能力与灵活转化本领,因此。 展开更多
关键词 函数方程问题 题组教学 高中 数学教学 数学思想方法 数学思想方法 逻辑思维能力
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利用对称性解函数方程问题
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作者 姜华 《高中数理化》 2012年第22期22-22,共1页
我们熟知若函数为偶函数,则图象关于y轴对称;若对定义域内任意x都有f(x)=f(2a-x)或f(a+x)=f(b-x)。
关键词 函数方程问题 对称性 利用 函数 轴对称 定义域 图象 直线
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怎样解数学竞赛中的函数方程问题
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作者 姚荣峰 《中学数学研究(华南师范大学)(上半月)》 2003年第3期36-38,共3页
所谓函数方程就是含有未知数的等式.在数学竞赛中,经常会出现一些与函数方程有关的问题,这类问题一般是求解某一给定的方程.解决这类问题的方法灵活多样,技巧性很强,下面通过例题介绍解决这类问题的一些基本方法和技巧.1.换元法基本思路... 所谓函数方程就是含有未知数的等式.在数学竞赛中,经常会出现一些与函数方程有关的问题,这类问题一般是求解某一给定的方程.解决这类问题的方法灵活多样,技巧性很强,下面通过例题介绍解决这类问题的一些基本方法和技巧.1.换元法基本思路:先对函数方程中的变量进行适当的代换,得到一个关于未知函数的代数方程组,再解方程组,得出所求函数的解析表达式. 展开更多
关键词 解题方法 中学 数学竞赛 函数方程问题
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对一函数方程问题的思考
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作者 齐迪 《中学生数学(高中版)》 2011年第7期27-27,共1页
文[1]给出了由fn(x+1/x)=x^n+1/x^n(n是整数)确定的fn(x)的解析式
关键词 函数方程问题 解析式 中学 数学教学
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例说函数方程问题的分析与求解
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作者 冯祥德 《高中数学教与学》 2018年第7期7-8,共2页
函数是中学数学的主线,函数的思想方法始终贯穿于整个中学数学教学之中;而函数方程又是高中函数知识的一大重点难点.面对此类考题,许多同学理不清头绪,无从着手,望而生畏,乃至中途弃笔.为此,本文通过对函数方程意义的探寻以及几道例题... 函数是中学数学的主线,函数的思想方法始终贯穿于整个中学数学教学之中;而函数方程又是高中函数知识的一大重点难点.面对此类考题,许多同学理不清头绪,无从着手,望而生畏,乃至中途弃笔.为此,本文通过对函数方程意义的探寻以及几道例题的剖析,谈谈函数方程问题的解题方法,以飨读者,期达抛砖引玉.函数方程问题是抽象函数问题的一类,说它抽象,是因为它的解析表达式在条件里并没有具体给定. 展开更多
关键词 函数方程问题 中学数学教学 抽象函数问题 求解 解析表达式 思想方法 函数知识 解题方法
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函数方程高考试题分类解读
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作者 廖运章 《中学数学研究(华南师范大学)(上半月)》 2006年第5期24-26,共3页
函数方程(含有未知函数的等式)是一个经典的数学课题,许多数学大家都曾研究过,但至今尚未形成完整而系统的一般方法与理论.然而,一些能用初等数学工具解决的简单函数方程问题已成为数学竞赛的重要内容,几乎每隔一两年就有函数方... 函数方程(含有未知函数的等式)是一个经典的数学课题,许多数学大家都曾研究过,但至今尚未形成完整而系统的一般方法与理论.然而,一些能用初等数学工具解决的简单函数方程问题已成为数学竞赛的重要内容,几乎每隔一两年就有函数方程的IMO或CMO试题出现.20世纪90年代后,函数方程开始渗透于我国高考数学试题,主要涉及解函数方程、函数方程确定的函数性质、函数值的界定等三类.本文分类解读近年高考数学试题中的函数方程问题. 展开更多
关键词 函数方程问题 高考数学试题 试题分类 解读 20世纪90年代后 数学课题 CMO试题 数学竞赛 数学工具 函数性质
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研究解函数方程思想和方法并提高应用能力
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作者 蒋玉国 《数理化解题研究(高中版)》 2013年第1期27-28,共2页
一、从观察、比较入手,通过思考,从中找出解决函数方程问题的一般方法例1已知f(x)是定义在R~+上的减函数,且满足f(x·y)=f(x)+f(y)f(1/3)=1.(1)求f(1)的值;(2)若f(x)+f(2-x)&lt;2,求x的取值范围.解(1)令x... 一、从观察、比较入手,通过思考,从中找出解决函数方程问题的一般方法例1已知f(x)是定义在R~+上的减函数,且满足f(x·y)=f(x)+f(y)f(1/3)=1.(1)求f(1)的值;(2)若f(x)+f(2-x)&lt;2,求x的取值范围.解(1)令x=1/3,y=1,得f(1/3·1)=f(1/3)+f(1).所以f(1)=0.(2)令x=y=1/3。 展开更多
关键词 函数 应用能力 方程思想 函数方程问题 取值范围
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图形助你学三角函数
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作者 宋楠 《新高考(高一数学)》 2015年第12期23-24,共2页
虽说三角函数名中有“数”,但解题时又与“形”有着千丝万缕的联系.我们在解决三角函数问题时,如果能做到“数”和“形”结合,定然能事半功倍.一、由值求角 求解简单的三角函数方程问题,可以借助函数图象求出方程在一个周期内的... 虽说三角函数名中有“数”,但解题时又与“形”有着千丝万缕的联系.我们在解决三角函数问题时,如果能做到“数”和“形”结合,定然能事半功倍.一、由值求角 求解简单的三角函数方程问题,可以借助函数图象求出方程在一个周期内的解,然后再根据函数的周期性得出全部解. 展开更多
关键词 三角函数问题 函数方程问题 图形 事半功倍 函数图象 “数” “形” 周期
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高考不等式的命题特点分析与展望
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作者 周友良 《上海中学数学》 2005年第1期37-39,共3页
关键词 不等式试题 考查 高考 命题特点 函数方程问题 题型特征 分析问题 性质 解决问题 覆盖
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On Feasibility of Variable Separation Method Based on Hamiltonian System for a Class of Plate Bending Equations 被引量:5
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作者 额布日力吐 阿拉坦仓 《Communications in Theoretical Physics》 SCIE CAS CSCD 2010年第3期569-574,共6页
The eigenfunction system of infinite-dimensional Hamiltonian operators appearing in the bending problem of rectangular plate with two opposites simply supported is studied. At first, the completeness of the extended e... The eigenfunction system of infinite-dimensional Hamiltonian operators appearing in the bending problem of rectangular plate with two opposites simply supported is studied. At first, the completeness of the extended eigenfunction system in the sense of Cauchy's principal value is proved. Then the incompleteness of the extended eigenfunction system in general sense is proved. So the completeness of the symplectic orthogonal system of the infinite-dimensional Hamiltonian operator of this kind of plate bending equation is proved. At last the general solution of the infinite dimensional Hamiltonian system is equivalent to the solution function system series expansion, so it gives to theoretical basis of the methods of separation of variables based on Hamiltonian system for this kind of equations. 展开更多
关键词 plate bending equation infinite-dimensioanl Hamiltonian operator eigenfunction system COMPLETENESS general solution
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Hamiltonian Formalism of mKdV Equation with Non-vanishing Boundary Values 被引量:1
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作者 HE Jing-Song CHEN Shi-Rong 《Communications in Theoretical Physics》 SCIE CAS CSCD 2005年第2X期321-325,共5页
Hamiltonian formalism of the mKdV equation with non-vanishing boundary valueis re-examined by a revised form of the standard procedure. It is known that the previous papers did not give the final results and involved ... Hamiltonian formalism of the mKdV equation with non-vanishing boundary valueis re-examined by a revised form of the standard procedure. It is known that the previous papers did not give the final results and involved some questionable points [T.C. Au Yeung and P.C.W. Fung, J. Phys. A 21 (1988) 3575]. In this note, simple results are obtained in terms of an affine parameter and a Galileo transformation is introduced to ensure the results compatible with those derived from the inverse scattering transform. 展开更多
关键词 Hamiltonian formalism mKdV equation
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Spectral Method for Three-Dimensional Nonlinear Klein-Gordon Equation by Using Generalized Laguerre and Spherical Harmonic Functions 被引量:3
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作者 Xiao-Yong Zhang Ben-Yu Guo Yu-Jian Jiao 《Numerical Mathematics(Theory,Methods and Applications)》 SCIE 2009年第1期43-64,共22页
In this paper,a generalized Laguerre-spherical harmonic spectral method is proposed for the Cauchy problem of three-dimensional nonlinear Klein-Gordon equation. The goal is to make the numerical solutions to preserve ... In this paper,a generalized Laguerre-spherical harmonic spectral method is proposed for the Cauchy problem of three-dimensional nonlinear Klein-Gordon equation. The goal is to make the numerical solutions to preserve the same conservation as that for the exact solution.The stability and convergence of the proposed scheme are proved.Numerical results demonstrate the efficiency of this approach.We also establish some basic results on the generalized Laguerre-spherical harmonic orthogonal approximation,which play an important role in spectral methods for various problems defined on the whole space and unbounded domains with spherical geometry. 展开更多
关键词 Generalized Laguerre-spherical harmonic spectral method Cauchy problem of nonlinear Klein-Gordon equation.
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Concave Minimization for Sparse Solutions of Absolute Value Equations 被引量:5
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作者 刘晓红 樊婕 李文娟 《Transactions of Tianjin University》 EI CAS 2016年第1期89-94,共6页
Based on concave function, the problem of finding the sparse solution of absolute value equations is relaxed to a concave programming, and its corresponding algorithm is proposed, whose main part is solving a series o... Based on concave function, the problem of finding the sparse solution of absolute value equations is relaxed to a concave programming, and its corresponding algorithm is proposed, whose main part is solving a series of linear programming. It is proved that a sparse solution can be found under the assumption that the connected matrixes have range space property(RSP). Numerical experiments are also conducted to verify the efficiency of the proposed algorithm. 展开更多
关键词 absolute value equations concave minimization SPARSITY linear programming range space property
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The Qualitative Analysis of a Solution of a Series Maintenance System with Two Components 被引量:1
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作者 GUOWei-hua YANGMing-zeng 《Chinese Quarterly Journal of Mathematics》 CSCD 2003年第3期320-327,共8页
In this paper, firstly we study the series ma intenance system with two components, obtain its exsistence and uniqueness of a dynamic state nonnegative solution by strongly continuous semigroups of operator s theory. ... In this paper, firstly we study the series ma intenance system with two components, obtain its exsistence and uniqueness of a dynamic state nonnegative solution by strongly continuous semigroups of operator s theory. Then we prove that 0 is the eigenvalue of the system’s host operators, a nd finally we study the eigenvector of the eigenvalue 0. 展开更多
关键词 series connection maintenance system semig roups of operators nonnegative solution
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Optimum Determination of Partial Transmission Ratios of Three-Step Helical Gearboxes for Getting Minimum Cross Section Dimension
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作者 Vu Ngoc Pi Nguyen Khac Tuan 《Journal of Environmental Science and Engineering(A)》 2016年第11期570-573,共4页
This paper presents a new study on optimum calculation of partial ratios of three-step helical gearboxes. The chosen objective function is the cross section dimension of the gearbox. In solving the optimization proble... This paper presents a new study on optimum calculation of partial ratios of three-step helical gearboxes. The chosen objective function is the cross section dimension of the gearbox. In solving the optimization problem, the design equation for pitting resistance of a gear set was investigated and equations on moment equilibrium condition of a mechanic system including three gear units and their regular resistance condition are analyses. From the results of the study, effective formula for determination of the partial ratios of three-step helical gearboxes is introduced. As the formulas are explicit, the partial ratios can be calculated accurately and simply. 展开更多
关键词 Gearbox design optimum design helical gearbox transmission ratio.
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Isomorphisms Between Quasi-Banach Algebras 被引量:1
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作者 Choonkil PARK 《Chinese Annals of Mathematics,Series B》 SCIE CSCD 2007年第3期353-362,共10页
In this paper, the author proves the Hyers-Ulam-Rassias stability of homomorphisms in quasi-Banach algebras. This is used to investigate isomorphisms between quasi-Banach algebras.
关键词 Cauchy functional equation Jensen functional equation Quasi-Banachalgebra Hyers-Ulam-Rassias stability HOMOMORPHISM p-Banach algebra
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Relationship Between the Restricted AKNS Flows and the Restricted KdV Flows 被引量:1
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作者 Ruguang ZHOU 《Chinese Annals of Mathematics,Series B》 SCIE CSCD 2012年第2期191-206,共16页
It is well-known that every member of the KdV hierarchy of equations can be obtained from the AKNS hierarchy of equations by imposing a simple reduction. The author finds that the reduction conditions of the potential... It is well-known that every member of the KdV hierarchy of equations can be obtained from the AKNS hierarchy of equations by imposing a simple reduction. The author finds that the reduction conditions of the potentials in the spectral problem can be replaced by adding additional eigenfunction equations to the spectral problem, and then shows that the restricted KdV flows, such as the Neumann system, the Gamier system and the generalized multicomponent Henon-Hieles system, are a kind of special reductions of the restricted AKNS flows. 展开更多
关键词 The restricted AKNS flow The restricted KdV flow Nonlinearization ofspectral problem Reduction condition Integrable Hamiltonian system
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Solution to Nonlinear Parabolic Equations Related to P-Laplacian 被引量:5
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作者 Huashui ZHAN 《Chinese Annals of Mathematics,Series B》 SCIE CSCD 2012年第5期767-782,共16页
Consider the following Cauchy problem:where 1 〈 p 〈 2, 1 〈 m 〈 p_~11, and # is a a-finite measure in N. By the Moser's iteration method, the existence of the weak solution is obtained, provided that (M+1)N 〈... Consider the following Cauchy problem:where 1 〈 p 〈 2, 1 〈 m 〈 p_~11, and # is a a-finite measure in N. By the Moser's iteration method, the existence of the weak solution is obtained, provided that (M+1)N 〈 P. In mN+l contrast, if 〉 p, there is no solution to the Cauchy problem with an initial value δ(X), where 5(x) is the classical Dirac function. 展开更多
关键词 Nonlinear parabolic equation Cauchy problem EXISTENCE a-Finite measure
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