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THE MEAN VALUE THEOREM AND CONVERSE THEOREM OF ONE CLASS THE FOURTH-ORDER PARTIAL DIFFERENTIAL EQUATIONS
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作者 同小军 同登科 陈绵云 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 2001年第6期717-723,共7页
For the formal presentation about the definite problems of ultra-hyperbolic equations, the famous Asgeirsson mean value theorem has answered that Cauchy problems are ill-posed to ultra-hyperbolic partial differential ... For the formal presentation about the definite problems of ultra-hyperbolic equations, the famous Asgeirsson mean value theorem has answered that Cauchy problems are ill-posed to ultra-hyperbolic partial differential equations of the second-order. So it is important to develop Asgeirsson mean value theorem. The mean value of solution for the higher order equation hay been discussed primarily and has no exact result at present. The mean value theorem for the higher order equation can be deduced and satisfied generalized biaxial symmetry potential equation by using the result of Asgeirsson mean value theorem and the properties of derivation and integration. Moreover, the mean value formula can be obtained by using the regular solutions of potential equation and the special properties of Jacobi polynomials. Its converse theorem is also proved. The obtained results make it possible to discuss on continuation of the solutions and well posed problem. 展开更多
关键词 Asgeirsson mean value theorem generalized biaxial symmetry potential equation Jacobi polynomials
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A Note on the Mean Value Theorems
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作者 Kung Kuen Tse 《Advances in Pure Mathematics》 2021年第5期395-399,共5页
The mean value theorem for derivatives says that for a given function over a closed and bounded interval, there is a point <em>P</em> on the graph such that the tangent at <em>P</em> is paralle... The mean value theorem for derivatives says that for a given function over a closed and bounded interval, there is a point <em>P</em> on the graph such that the tangent at <em>P</em> is parallel to the secant through the two endpoints. The mean value theorem for definite integrals says that the area under the function is equal to the area of a rectangle whose base is the length of the interval and height of some point <em>Q</em> on the graph. These two theorems have been studied and utilized extensively and they form the backbone of many important theorems in different branches of mathematics. In this note, we pose the question: for what functions do the two points <em>P </em>and <em>Q</em> always coincide? We find that the only analytic functions satisfying this condition are linear or exponential functions. 展开更多
关键词 mean value theorem Real Analytic Functions Identity theorem Power Series
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Existence of Positive Solutions for Systems of Second-order Nonlinear Singular Differential Equations with Integral Boundary Conditions on Infinite Interval 被引量:18
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作者 LI Yao-hong 《Chinese Quarterly Journal of Mathematics》 CSCD 2014年第1期55-64,共10页
By using cone theory and the MSnch fixed theorem combined with a monotone iterative technique, we investigate the existence of positive solutions for systems of second- order nonlinear singular differential equations ... By using cone theory and the MSnch fixed theorem combined with a monotone iterative technique, we investigate the existence of positive solutions for systems of second- order nonlinear singular differential equations with integral boundary conditions on infinite interval and establish the existence theorem of positive solutions and iterative sequence for approximating the positive solutions. The results in this paper improve some known results. 展开更多
关键词 boundary value problems positive solutions integral boundary conditions theMSnch fixed point theorem
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Solution of Singular Integrals in Mathematical Model of Mode I Crack near Strength Mismatched Interface
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作者 Sunil Bhat Vijay G. Ukadgaonker 《American Journal of Computational Mathematics》 2012年第2期156-162,共7页
Characteristics of Mode I crack near the interface of elasticity matched but plasticity and strength mismatched materials differ from those of the crack in a homogenous body. Interface body of different strength influ... Characteristics of Mode I crack near the interface of elasticity matched but plasticity and strength mismatched materials differ from those of the crack in a homogenous body. Interface body of different strength influences the plastic or cohesive zone at the crack tip in parent body. The mathematical model for load line opening of the crack near the interface in linear elastic regime involves singular integrals. The paper presents explicit solution of these integrals with the help of Cauchy’s principal value theorem. Cases of thin and thick welds between the materials are investigated. Solutions of the integrals are well substantiated. Final results are provided in a consolidated form. 展开更多
关键词 Crack OPENING Displacement SINGULAR integralS Strength MISMATCH WELD INTERFACE Cauchy’s Principal value theorem
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Observer design for induction motor: an approach based on the mean value theorem 被引量:1
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作者 Mohamed Yacine HAMMOUDI Abdelkarim ALLAG +2 位作者 Mohamed BECHERIF Mohamed BENBOUZID Hamza ALLOUI 《Frontiers in Energy》 SCIE CSCD 2014年第4期426-433,共8页
In this paper, observer design for an induction motor has been investigated. The peculiarity of this paper is the synthesis of a mono-Luenberger observer for highly coupled system. To transform the nonlinear error dyn... In this paper, observer design for an induction motor has been investigated. The peculiarity of this paper is the synthesis of a mono-Luenberger observer for highly coupled system. To transform the nonlinear error dynamics for the induction motor into the linear parametric varying (LPV) system, the differential mean value theorem combined with the sector nonlinearity transformation has been used. Stability conditions based on the Lyapunov function lead to solvability of a set of linear matrix inequalities. The proposed observer guarantees the global exponential convergence to zero of the estimation error. Finally, the simulation results are given to show the performance of the observer design. 展开更多
关键词 observer design differential mean value theorem (DMVT) sector nonlinearity transformation linear matrix inequalities (LMI) induction motor
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Classical state feedback controller for nonlinear systems using mean value theorem: closed Ioop-FOC of PMSM motor application
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作者 Abrar ALLAG Abdelhamid BENAKCHA +2 位作者 Meriem ALLAG Ismail ZEIN Mohamed Yacine AYAD 《Frontiers in Energy》 SCIE CSCD 2015年第4期413-425,共13页
The problem of state feedback controllers for a class of Takagi-Sugeno (T-S) Lipschitz nonlinear systems is investigated. A simple systematic and useful synthesis method is proposed based on the use of the different... The problem of state feedback controllers for a class of Takagi-Sugeno (T-S) Lipschitz nonlinear systems is investigated. A simple systematic and useful synthesis method is proposed based on the use of the differential mean value theorem (DMVT) and convex theory. The proposed design approach is based on the mean value theorem (MVT) to express the nonlinear error dynamics as a convex combination of known matrices with time varying coefficients as linear parameter varying (LPV) systems. Using the Lyapunov theory, stability conditions are obtained and expressed in terms of linear matrix inequalities (LMIs). The controller gains are then obtained by solving linear matrix inequalities. The effectiveness of the proposed approach for closed loop-field oriented control (CL-FOC) of permanent magnet synchronous machine (PMSM) drives is demonstrated through an illustrative simulation for the proof of these approaches. Furthermore, an extension for controller design with parameter uncertainties and perturbation performance is discussed. 展开更多
关键词 Takagi-Sugeno (T-S) fuzzy systems sectornonlinearity nonlinear controller linear matrix inequality(LMI) approach differential mean value theorem (DMVT) field oriented control (FOC) linear parameter varying(LPV)
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实Clifford分析中双正则函数的一些性质
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作者 王海燕 乔玉英 +1 位作者 李小伶 扈玮玮 《河北师范大学学报(自然科学版)》 CAS 北大核心 2008年第3期281-286,共6页
研究了含有2个变量的正则函数,所谓的双正则函数.正则函数是单复分析中全纯函数在高维空间的推广,全纯函数的经典函数理论如Morera定理,开拓定理等都可推广到正则函数,同样也可推广到双正则函数.以双正则函数的柯西积分公式为基础,得到... 研究了含有2个变量的正则函数,所谓的双正则函数.正则函数是单复分析中全纯函数在高维空间的推广,全纯函数的经典函数理论如Morera定理,开拓定理等都可推广到正则函数,同样也可推广到双正则函数.以双正则函数的柯西积分公式为基础,得到了双正则函数的Morera定理,开拓定理,平均值定理. 展开更多
关键词 双正则函数 Morera定理 开拓定理 平均值定理
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实Clifford分析中双正则函数的最大模原理
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作者 彭维玲 王丽萍 《河北师范大学学报(自然科学版)》 CAS 北大核心 2009年第2期170-175,共6页
在给出了实Clifford分析中双正则函数的柯西积分公式的基础上,讨论了双正则函数的平均值定理和最大模原理以及它的一些推论.
关键词 实CLIFforD分析 双正则函数 柯西积分公式 平均值定理 最大模原理
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Clifford分析中超正则函数的几个基本定理
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作者 李小伶 乔玉英 +1 位作者 扈玮玮 王海燕 《河北师范大学学报(自然科学版)》 CAS 北大核心 2008年第2期153-158,共6页
超正则函数是复分析中解析函数的一种推广形式.近年来,超正则函数已得到了较系统的研究.给出了有关超正则函数的几个基本定理,如开拓定理,平均值定理以及区域内的超正则函数与定义在边界上连续函数的关系等,使得对超正则函数的研究更加... 超正则函数是复分析中解析函数的一种推广形式.近年来,超正则函数已得到了较系统的研究.给出了有关超正则函数的几个基本定理,如开拓定理,平均值定理以及区域内的超正则函数与定义在边界上连续函数的关系等,使得对超正则函数的研究更加完善. 展开更多
关键词 超正则函数 开拓定理 平均值定理
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Theory of truth degrees of formulas in Lukasiewicz n-valued propositional logic and a limit theorem 被引量:30
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作者 LI Bijing WANG Guojun 《Science in China(Series F)》 2005年第6期727-736,共10页
The concept of truth degrees of formulas in Lukasiewicz n-valued propositional logic Ln is proposed. A limit theorem is obtained, which says that the truth function τ-n induced by truth degrees converges to the integ... The concept of truth degrees of formulas in Lukasiewicz n-valued propositional logic Ln is proposed. A limit theorem is obtained, which says that the truth function τ-n induced by truth degrees converges to the integrated truth function τ when n converges to infinite. Hence this limit theorem builds a bridge between the discrete valued Lukasiewicz logic and the continuous valued Lukasiewicz logic. Moreover, the results obtained in the present paper is a natural generalization of the corresponding results obtained in two-valued propositional logic. 展开更多
关键词 Lukasiewicz n-valued propositional logic truth degree limit theorem integrated truth degree
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FAST APPROXIMATE INVERSION OF MAGNETOTELLURIC(FAIMT) DATA FOR A HORIZONTALLY LAYERED EARTH WITH NEAR-SURFACE INHOMOGENEITIES
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作者 孙传文 《Chinese Journal of Oceanology and Limnology》 SCIE CAS CSCD 1997年第1期7-18,共12页
This paper discusses use of approximations and the Integral Mean Value Theorem to show that 6 coefficients approximately describe the distortions of near surface inhomogeneities on the MT field of a horizontally layer... This paper discusses use of approximations and the Integral Mean Value Theorem to show that 6 coefficients approximately describe the distortions of near surface inhomogeneities on the MT field of a horizontally layered earth model. When these 6 coefficients are considered together with those of the magnetic field of a horizontally layered earth model,the analytic and approximate wave impedance equations can be derived for the MT response of a horizontally layered earth model with near-surface 2-D and 3-D inhomogeneities. These approximate wave impedance equations are used with inverted MT data for 2-D and 3-D forward modelling. Although these 6 coefficients cannot be determined before inversion,initial estimates can be used. The 6 coefficients and the asistivity and thickness of each layer of a horizontally layered earth can be obtained by using published inversion methods. The 6 coefficients give important informaion (depths and resistivities) on the near-surface inhomogenelties.The authors inverted 2-D and 3-D theoretical models for Fast Approximate Inversion of Magnetotelluric (FAIMT) data for a horizontally layered earth with near-surface inhomogeneities compares favorably with traditional invrsion methods, especially for inverting regional or basin structures. This method simplifies computation and gives a reasonable 1 -D geological model with fewer nonuniquenas problems. 展开更多
关键词 MAGNETOTELLURIC 3-D INVERSIONS inhomogeneity integral mean value theorem LAYERED EARTH approximation
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Common Properties of Riemann Zeta Function, Bessel Functions and Gauss Function Concerning Their Zeros 被引量:1
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作者 Alfred Wünsche 《Advances in Pure Mathematics》 2019年第3期281-316,共36页
The behavior of the zeros in finite Taylor series approximations of the Riemann Xi function (to the zeta function), of modified Bessel functions and of the Gaussian (bell) function is investigated and illustrated in t... The behavior of the zeros in finite Taylor series approximations of the Riemann Xi function (to the zeta function), of modified Bessel functions and of the Gaussian (bell) function is investigated and illustrated in the complex domain by pictures. It can be seen how the zeros in finite approximations approach to the genuine zeros in the transition to higher-order approximation and in case of the Gaussian (bell) function that they go with great uniformity to infinity in the complex plane. A limiting transition from the modified Bessel functions to a Gaussian function is discussed and represented in pictures. In an Appendix a new building stone to a full proof of the Riemann hypothesis using the Second mean-value theorem is presented. 展开更多
关键词 RIEMANN Zeta and Xi Function Modified BESSEL Functions Second mean-value theorem or Gauss-Bonnet theorem RIEMANN Hypothesis
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GENERAL SOLUTION OF A 2-D WEAK SINGULAR INTEGRAL EQUATION WITH CONSTRAINT AND ITS APPLICATIONS
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作者 云天铨 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 1997年第8期749-755,共7页
In this paper, the solution, more general than [1], of a weak singular integral equation integral(0)(pi)integral(-infinity)(infinity) p(s,psi)d sk(psi)d psi=F(r,theta), (r,theta)epsilon (Q) over bar=Q+partial derivati... In this paper, the solution, more general than [1], of a weak singular integral equation integral(0)(pi)integral(-infinity)(infinity) p(s,psi)d sk(psi)d psi=F(r,theta), (r,theta)epsilon (Q) over bar=Q+partial derivative Q subject to constraint p(s,psi)=0, for (s,psi)=(r,theta)is not an element of Q={r,theta)/F(r,theta)>c*} is found p=2/pi[root w g'(0)+integral(0)(w) root w-u g '(u)du] where k and F are given continuous functions; (s,psi) is a local polar coordinating with origin at M(r,theta); (r,theta) is the global polar coordinating with origin at O(0,0) F(r,theta)=c* (const.) is the boundary contour partial derivative Q of the considered range Q; g(w)=F(r,theta)/[pi k(psi(0))]; g'=dg/dw; w=N-r(2)sin(2)(theta+psi(0)); psi(0) and N are mean values. The solution shown in type (2.19) of [1] is a special case of the above solution and only suits F(r,theta)=w. The solution of a rigid cone contact with elastic half space, more simple and clear than Love's (1939), is given as an example of application. 展开更多
关键词 radon transform Abel integral equation theorem mean value Hertz's solution
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A Different Version of Flett's Mean Value Theorem and an Associated Functional Equation
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作者 Thomas RIEDEL Maciej SABLIK 《Acta Mathematica Sinica,English Series》 SCIE CSCD 2004年第6期1073-1078,共6页
In this paper we present a mean value theorem derived from Flett's mean value theorem. It turns out that cubic polynomials have the midpoint of the interval as their mean value point.To answer what class of functi... In this paper we present a mean value theorem derived from Flett's mean value theorem. It turns out that cubic polynomials have the midpoint of the interval as their mean value point.To answer what class of functions have this property,we consider a functional equation associated with this mean value theorem.This equation is then solved in a general setting on abelian groups. 展开更多
关键词 Flett's mean value theorem Functional equations Polynomial functions
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Generation of a Problem about Mean Value Theorem
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作者 Hua Ming SU You Du HUANG Jie PAN 《Journal of Mathematical Research and Exposition》 CSCD 2010年第1期186-190,共5页
This paper presents a generalized form and its application to a problem, which was proposed by F.P. Callham.
关键词 mean value theorem difference quotient DIFFERENCE polynomial.
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Four-Step Iteration Scheme to Approximate Fixed Point for Weak Contractions
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作者 Wasfi Shatanawi Anwar Bataihah Abdalla Tallafha 《Computers, Materials & Continua》 SCIE EI 2020年第9期1491-1504,共14页
Fixed point theory is one of the most important subjects in the setting of metric spaces since fixed point theorems can be used to determine the existence and the uniqueness of solutions of such mathematical problems.... Fixed point theory is one of the most important subjects in the setting of metric spaces since fixed point theorems can be used to determine the existence and the uniqueness of solutions of such mathematical problems.It is known that many problems in applied sciences and engineering can be formulated as functional equations.Such equations can be transferred to fixed point theorems in an easy manner.Moreover,we use the fixed point theory to prove the existence and uniqueness of solutions of such integral and differential equations.Let X be a non-empty set.A fixed point for a self-mapping T on X is a point𝑒𝑒∈𝑋𝑋that satisfying T e=e.One of the most challenging problems in mathematics is to construct some iterations to faster the calculation or approximation of the fixed point of such problems.Some mathematicians constructed and generated some new iteration schemes to calculate or approximate the fixed point of such problems such as Mann et al.[Mann(1953);Ishikawa(1974);Sintunavarat and Pitea(2016);Berinde(2004b);Agarwal,O’Regan and Sahu(2007)].The main purpose of the present paper is to introduce and construct a new iteration scheme to calculate or approximate the fixed point within a fewer number of steps as much as we can.We prove that our iteration scheme is faster than the iteration schemes given by Sintunavarat et al.[Sintunavarat and Pitea(2016);Agarwal,O’Regan and Sahu(2007);Mann(1953);Ishikawa(1974)].We give some numerical examples by using MATLAB to compare the efficiency and effectiveness of our iterations scheme with the efficiency of Mann et al.[Mann(1953);Ishikawa(1974);Sintunavarat and Pitea(2016);Abbas and Nazir(2014);Agarwal,O’Regan and Sahu(2007)]schemes.Moreover,we introduce a problem raised from Newton’s law of cooling as an application of our new iteration scheme.Also,we support our application with a numerical example and figures to illustrate the validity of our iterative scheme. 展开更多
关键词 Weak contraction fixed point iteration scheme mean value theorem
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Nonlinear unknown input observer using mean value theorem and genetic algorithm
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作者 Ramzi Ben Messaoud 《International Journal of Modeling, Simulation, and Scientific Computing》 EI 2019年第2期42-63,共22页
In this note,we consider a new unknown input observer design for nonlinear systems.The main idea consists in determining the estimation error and mean value theorem parameters(β)to introduce them into proposed observ... In this note,we consider a new unknown input observer design for nonlinear systems.The main idea consists in determining the estimation error and mean value theorem parameters(β)to introduce them into proposed observer structure.This process is designed on the basis of mean value theorem and genetic algorithm.The stability study relies on the use of a classical quadratic Lyapunov function.The observer’s gains are determined systematically.For the validation of theoretical development proposed in this paper,we consider two practical realizations that deals with the secure communication problem. 展开更多
关键词 Genetic algorithm unknown input observer nonlinear system mean value theorem state estimation
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The Mean-value of Meromorphic Functions with Respect to a Generalized Boolean Transformation
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作者 Nattiwut MAUGMAI Teerapat SRICHAN 《Acta Mathematica Sinica,English Series》 SCIE CSCD 2019年第5期662-670,共9页
A formula for the mean-value distribution of certain meromorphic functions on a vertical line s = σ +iR under a generalized Boolean transformation, called rational Boolean transformation from R into itself, is derive... A formula for the mean-value distribution of certain meromorphic functions on a vertical line s = σ +iR under a generalized Boolean transformation, called rational Boolean transformation from R into itself, is derived using Birkhoff 's ergodic theorem. This formula is represented as a computable integral. Using the Cauchy's integral theorem, values of this integral corresponding to various possible cases are explicitly computed. 展开更多
关键词 Birkhoff's ergodic theorem BOOLEAN TRANSforMATION mean-value MEROMORPHIC functions
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A Bombieri-type mean-value theorem concerning exponential sums over primes
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作者 展涛 刘建亚 《Chinese Science Bulletin》 SCIE EI CAS 1996年第5期363-366,共4页
In several classical problems in number theory,like the Goldbach problem or the twinprime problem,one has to treat the exponential
关键词 EXPONENTIAL sum over PRIMES mean-value theorem L-function.
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一个新的积分第二中值定理
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作者 龙波涌 吴然超 《大学数学》 2024年第5期61-64,共4页
在加强了假设条件的基础上,得到了一个新的积分第二中值定理.与原定理相比较,新的定理具有明显的几何意义,更富有数学美感.另外,说明了不同形式的积分第二中值定理的相互等价性.
关键词 积分第二中值定理 介值定理 单调函数
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