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1.
The uniqueness theorem and the theorem of reciprocity in the linearized porous piezoelectricity are established under the
assumption of positive definiteness of elastic and electric fields. General theorems in the linear theory of porous piezoelectric
materials are proved for the quasi-static electric field approximation. The uniqueness theorem is also proved without using
the positive definiteness of the elastic field. An eigenvalue problem associated with free vibrations of a porous piezoelectric
body is studied using the abstract formulation. Some properties of operators are also proved. The problem of frequency shift
due to small disturbances, based on an abstract formulation, is studied using a variational and operator approach. A perturbation
analysis of a special case is also given. 相似文献
2.
Galerkin representations for the displacement vector, polarization vector and the potential field are obtained by elementary matrix inversions of the equations of equilibrium. Matrices of fundamental solutions of an infinite elastic dielectric continuum subjected to a concentrated body force, an electric force, and a charge density, are constructed. Theorems are proved on the discontinuity of double layer potentials and R, M, M operators of single layer potentials. By means of these theorems, the solution of the two basic boundary value problems has been reduced to the solution of a system of seven singular integral equations. 相似文献
3.
IntroductionIn 1 991 ,Tarafdar[1]firstestablishedthefollowingcollectivelyfixedpointtheoremontheproductspaceofnonemptycompactconvexsubsetsoftopologicalvectorspacesandgaveitsapplicationstotheexistenceofequilibriumpointsforabstracteconomies.Theorem 1 Let Xi i∈I… 相似文献
4.
Recently Zheng & Hwang established a series of independence theorems concerning with planar effective elastic properties.
It is manifested that the estimation of the effective elastic properties of microcracked solids through the generalized self-consistent
method (GSCM) contradicts with these independence theorems. In this paper it is shown that such contradiction is actually
caused by the approximate algorithm adopted, while the exact solution of GSCM is consistent with these rigorously established
independence theorems. Since only an approximate algorithm in GCSM is available in dealing with problems involving non-circular
inclusions or holes, an intrinsic GSCM is proposed, which can be performed based on an approximate algorithm and the corresponding
estimations are consistent with the independence theorems. 相似文献
5.
丁协平 《应用数学和力学(英文版)》1999,20(5):485-494
IntroductionRecentlytherehaveappearedanumberofnewfixedpointtheoremsandcoincidencetheoremsinvolvingso_caledKakutanifactorizabl... 相似文献
6.
IntroductionItiswell_knownthattheextensiontheoremofthelinearfunctionalisoneofthebasictheoremsinfunctionalanalysis.Ithasbeenextendedtomanyforms,and ,ofcourse,hasfoundmanyimportantapplicationinsuchfieldsasnonsmoothanalysis,optimizationandvariationalproble… 相似文献
7.
In this paper, the definitions of Nielsen’s and Euler’s operators of higher order are presented. These operators are concerned in analysis for systems with holonomic constraints and non-holonomic constraints of higher order. Some theorems that indicating relation between the two operators are established. Moreover, using the theorems, the new equations of mechanical systems with constraints of higher order are derived. Finally, an example is given. 相似文献
8.
In this paper, we study minimal and maximal fixed point theorems and iterative technique for nonlinear operators in product spaces. As a corollary of our result, some coupled fixed point theorems are obtained, which generalize the coupled fixed point theorems obtained by Guo Da-jun and Lankshmikanthamt and the results obtained by Lan in, and. 相似文献
9.
As well as proving stability, Lyapunov functions can also be used to prove instability, for which there are two well-known theorems: Lyapunov’s first and second instability theorems, in the integer-order (ordinary differential equation) case. However, these instability theorems for Caputo fractional-order systems remain blank, due to the long lack of general results on continuation of solution and Caputo fractional derivative of Lyapunov functions along trajectories. In this paper, based on recent advances in these two aspects, the Lyapunov’s first and second instability theorems for Caputo fractional-order systems are presented with proofs and then illustrated by examples.
相似文献10.
IntroductionIn 1 996,Khamsi[1]establishedthehyperconvexversionofthefamousFan_KKMprincipleinhyperconvexspace .Yuan[2 ,3]obtainsomecharacterizationofKKMprincipleinhyperconvexspaces,andasapplicationsoftheirresults,somefixedpointtheoremsandmatchingtheoremsforopena… 相似文献
11.
In this paper,the class of uniform limit mappings of set-valued,strick set-contractivemappings is discussed.Furthermore,the fixed point index theory for the uniform limitmappings is established.Using the fixed point index theory,some positive fixed pointtheorems are proved.Our theorems generalize some results in[1,4,5,7]. 相似文献
12.
International Applied Mechanics - The theorems on the birth of attractors from homoclinic loops are proved. Applications of the theorems are considered. 相似文献
13.
丁协平 《应用数学和力学(英文版)》2003,24(9)
IntroductionThispaperisacontinuumoftheprecedingpaperofauthor[1] .Fortheconceptsandnotationsofgeneralizedconvex (orG_convex)space ,CG_convexspace,theclassB(Y ,X)ofbetteradmissiblemappings ,GB_mappings,GB_majorizedmappingsandtherelatednotions,thereadermayconsultRef.[1].Themainaimofthispaperistogivesomeapplicationsoftheexistencetheoremsofmaximalelementsobtainedbyauthor[1] .ByapplyingourresultsinRef.[1],wegivesomecomponentversionofcoincidencetheoremandFan_Browdertypefixedpointtheorems .Somee… 相似文献
14.
丁协平 《应用数学和力学(英文版)》2001,22(2):160-172
IntroductionLetXandYbenonemptysetsand2 XbethefamilyofallsubsetsofX .LetT :X→Ybeasingle_valuedmapping ,A :X→ 2 Xbeaset_valuedmapping ,ψ :X×Y×X→R∪ ±∞ andf:X×Y→R∪ ±∞ betwofunctions.Thegeneralquasi_equilibriumproblemGQEP (T ,A ,ψ)istofind ^x∈Xsuchthat^x∈A( ^x) ,ψ( ^x ,T^x ,y)≤ 0… 相似文献
15.
J.-B. Bru W. de Siqueira Pedra C. Hertling 《Archive for Rational Mechanics and Analysis》2016,220(2):445-504
We extend (Bru et al. in J Math Phys 56:051901-1-51, 2015) in order to study the linear response of free fermions on the lattice within a (independently and identically distributed) random potential to a macroscopic electric field that is time- and space-dependent. We obtain the notion of a macroscopic AC-conductivity measure which only results from the second principle of thermodynamics. The latter corresponds here to the positivity of the heat production for cyclic processes on equilibrium states. Its Fourier transform is a continuous bounded function which is naturally called (macroscopic) conductivity. We additionally derive Green–Kubo relations involving time-correlations of bosonic fields coming from current fluctuations in the system. This is reminiscent of non-commutative central limit theorems. 相似文献
16.
By applying the technique of continuous partition of unity and Tychonoff’s fixed point theorem, some new collectively fixed point theorems for a family of set-valued mappings defined on the product space of noncompact G-convex spaces are proved. As applications, some nonempty intersetion theorems of Ky Fan type for a family of subsets of the product space of G-convex spaces are proved; An existence theorem of solutions for a system of nonlinear inequalities is given in G-convex spaces and some equilibrium existence theorems of abstract economies are also obtained in G-convex spaces. Our theorems improve, unify and generalized many important known results in recent literature. 相似文献
17.
Some new fixed point theorems in probabilistic metric spaces 总被引:21,自引:0,他引:21
朱传喜 《应用数学和力学(英文版)》1995,16(2):179-185
SOMENEWFIXEDPOINTTHEOREMSINPROBABILISTICMETRICSPACESzhuChuan-xi(朱传喜)(MathematiesDivision,Nanchang.University,Nanchang)(Receiv... 相似文献
18.
事件空间中非完整有势系统的参数方程 总被引:3,自引:0,他引:3
本文首先在事件空间中建立非完整有势系统的广义方程,然后给出此空间中表示Nielsen算子和Euler算子之间关系的两个定理,最后由这些定理得到广义Nielsen方程。 相似文献
19.
In this paper, we establish some new nonempty intersection theorems for generalized L-KKM mappings and prove some new fixed point theorems for set-valued mappings under suitable conditions in topological spaces. As applications, an existence theorem for an equilibrium problem with lower and upper bounds and two existence theorems for a quasi-equilibrium problem with lower and upper bounds are obtained in topological spaces. Our results generalize some known results in the literature. 相似文献
20.
Christos G. Panagiotopoulos G. D. Manolis 《Archive of Applied Mechanics (Ingenieur Archiv)》2010,80(12):1429-1447
Reciprocal theorems in elastodynamics are introduced as extensions of respective theorems from elastostatics. Inasmuch as
the latter is a subset of the former, the aim here is to present an elastodynamic reciprocal theorem that also includes elastostatics
as a special case when the time variable becomes irrelevant. This is accomplished by introducing a velocity-based reciprocal
theorem, whose basic properties are subsequently explored. The next step is to use this theorem and formulate a numerical
approach based on boundary integral equation statements and compare them with existing formulations based on conventional
reciprocity relations. The applications presented here involve the standard mechanical oscillator and the unidimensional axial
element as two simple, yet important problems of structural dynamics. Along with the numerical results, a thorough stability
analysis of the corresponding time-stepping algorithms is formulated. In both cases, the superior performance of the methodologies
built on velocity-based reciprocal theorems is clearly demonstrated. 相似文献