共查询到20条相似文献,搜索用时 31 毫秒
1.
Peter Smith 《Acta Appl Math》1986,6(3):293-308
The usual notion of a saddle functional in the calculus of variations assumes a vex/concave structure over the product space
of two inner product spaces. Here the ideas extended to include some convexity in both spaces whilst still retaining an overall
saddle property. Dual extremum principles are established for these functionals. Examples include periodic solutions of Duffing's
equation, an iterative scheme and a pair of simultaneous partial differential equations which arise in magnetohydrodynamics. 相似文献
2.
《Optimization》2012,61(5):653-662
Duality results for a class of nondifferentiable mathematical programming problems are given. These results allow for the weakening of the usual convexity conditions required for duality to hold. A pair of symmetric and self dual nondifferentiable programs under weaker convexity conditions are also given. A subgradient symmetric duality is proposed and its limitations discussed. Finally, a pair of nondifferentiable mathematical programs containing arbitrary norms is presented. 相似文献
3.
对带端面负载的半无限带状各向异性弹性材料建立了Saint-Venant原理.应用能量方法确立了应力效应衰减率的下界,得出了用各向异性材料的弹性常量表示的估计显式.最后,为了说明所得结果,对带端面负载、纤维偏离主轴的石墨-环氧树脂的衰减率给出数值实例. 相似文献
4.
The stress fields around the first butterfly martensite in an Fe-Ni based alloy were calculated. The calculation results inducate
that there are tensile stress fields near the convexity and the two ends of a butterfly martensite. There is a compressive
stress field near the concavity. New butterfly martensite is likely induced not only near the convexity but also probably
near the concavity. The butterfly martensites induced in tensile stress fields are bigger than those in compressive stress
fields. The second butterfly martensite is likely induced near the convexity within 2πm region. All these results agree with
the experimental observation. 相似文献
5.
周期裂纹削弱的无限长板条的应力分析 总被引:2,自引:0,他引:2
作出了周期裂纹削弱的无限长板条的应力分析.假设这些裂纹均在水平位置,又板条承受 y方向的拉伸力p.此时边值问题归结为一个复杂混合边值问题.发现,对此问题言,特征展开变分原理方法 ( eigenfunction expansion variational method,简称为EEVM)是非常有效的.研究了裂纹端的应力强度因子和T-应力.从拉伸力作用下的弹性变形考虑,开裂板条可等价于一不开裂的正交异性板条.还分析了等价正交异性板条的弹性性质.最后给出了算例和数值结果. 相似文献
6.
7.
Two main existence conditions for solutions of variational relation problems are established without convexity. The first one is based on a finite solvability property and the second one on generalized KKM mappings. These conditions unify and strengthen several existing results in the literature on the topic. A model of satisficing process by rejection is considered which gives an economic interpretation of the introduced concepts. 相似文献
8.
Karoly Bezdek Zsolt Langi Marton Naszodi Peter Papez 《Discrete and Computational Geometry》2007,38(2):201-230
We study two notions. One is that of spindle convexity. A set of circumradius not greater than one is spindle convex if, for
any pair of its points, it contains every short circular arc of radius at least one, connecting them. The other objects of
study are bodies obtained as intersections of finitely many balls of the same radius, called ball-polyhedra. We find analogues
of several results on convex polyhedral sets for ball-polyhedra. 相似文献
9.
A feasible family of paths in a connected graph G is a family that contains at least one path between any pair of vertices in G. Any feasible path family defines a convexity on G. Well-known instances are: the geodesics, the induced paths, and all paths. We propose a more general approach for such ‘path properties’. We survey a number of results from this perspective, and present a number of new results. We focus on the behaviour of such convexities on the Cartesian product of graphs and on the classical convexity invariants, such as the Carathéodory, Helly and Radon numbers in relation with graph invariants, such as the clique number and other graph properties. 相似文献
10.
In this paper several finite cracks with constant length (Yoffe-type crack) propagating in an orthotropic strip were studied. The distributed dislocation technique is used to carry out stress analysis in an orthotropic strip containing moving cracks under anti-plane loading. The solution of a moving screw dislocation is obtained in an orthotropic strip by means of Fourier transform method. The stress components reveal the familiar Cauchy singularity at the location of dislocation. The solution is employed to derive integral equations for a strip weakened by moving cracks. Finally several examples are solved and the numerical results for the stress intensity factor are obtained. The influences of the geometric parameters, the thickness of the orthotropic strip, the crack size and speed have significant effects on the stress intensity factors of crack tips which are displayed graphically. 相似文献
11.
Rudolf Herschbach 《Mathematische Nachrichten》1996,181(1):215-229
The absence of atoms in Lyapunov's Convexity Theorem is a sufficient, but not a necessary condition for the convexity of the range of an n - dimensional vector measure. In this paper algebraic and topological convexity conditions generalizing Lyapunov's Theorem are developed which are sufficient and necessary as well. From these results the converse of Lyapunov's Theorem is derived in the form of a nonconvexity statement which gives insight into the geometric structure of the ranges of vector measures with atoms. Further, a characterization of the one-dimensional faces of a zonoid Zμ, is given with respect to the generating spherical Borel measure μ. As an application, it is shown that the absence of μ - atoms is a necessary and sufficient convexity condition for the range of the indefinite integral ∫ x dμ where x denotes the identical function on Sn-1. 相似文献
12.
Peter Greim 《manuscripta mathematica》1977,22(4):311-323
Day's characterization of those spaces 1p(Xi) which are uniformly convex, in terms of the moduli of convexity of the Xi, is generalized for arbitrary integral modules on measure spaces (K,m) and simplified when m is finite. For this latter purpose a lemma on the moduli of convexity and of smoothness is proved which incidentally gives a further necessary condition for the existence of integral modules in given direct integrals. Further the notions of strict convexity and smoothness of an integral module are related to those of its components. 相似文献
13.
We show that it is possible to project out in an exact manner the lowest eigenstate of Schrödinger equations. Taking into account the nodeless property of the lowest eigenstate one can replace the full Schrödinger equation by a moment problem whose measure is the eigenstate itself. The infinite set of positivity inequalities linked to this moment problem provides a framework which allows to compute sequences of upper and lower bounds to the unknown eigenvalue and eigenfunction.The effective computation is based on deep convexity properties embedded in the set of hierarchical inequalities associated to this moment problem. The convexity allows to get the bounds through linear programming. We illustrate the method with simple one dimensional problems.Laboratoire de la Direction des Sciences de la Matière du Commissariat à l'Energie Atomique. 相似文献
14.
Conditions for the convexity of compound geometric tails and compound geometric convolution tails are established. The results are then applied to analyze the convexity of the ruin probability and the Laplace transform of the time to ruin in the classical compound Poisson risk model with and without diffusion. An application to an optimization problem is given. 相似文献
15.
《Optimization》2012,61(5):745-754
A generalized Fan's section theorem has proposed by replacing convexity assumptions with merely topological properties. A generalized reformulation of Browder's fixed point theorem has derived. The Minimax Inequalities for vector-valued mapping in an ordered Banach space have established without the convexity and with convexity, respectively. 相似文献
16.
Pseudoconvexity of a function on one set with respect to some other set is defined and duality theorems are proved for nonlinear programming problems by assuming a certain kind of convexity property for a particular linear combination of functions involved in the problem rather than assuming the convexity property for the individual functions as is usually done. This approach generalizes some of the well-known duality theorems and gives some additional strict converse duality theorems which are not comparable with the earlier duality results of this type. Further it is shown that the duality theory for nonlinear fractional programming problems follows as a particular case of the results established here. 相似文献
17.
Otis Chodosh 《Journal of Functional Analysis》2012,262(10):4570-4581
We examine the entropic measure, recently constructed by von Renesse and Sturm, a measure over the metric space of probability measures on the unit interval equipped with the 2-Wasserstein distance. We show that equipped with this measure, Wasserstein space over the interval does not admit generalized Ricci lower bounds in the entropic displacement convexity sense of Lott–Villani–Sturm. We discuss why this is contrary to what one might expect from heuristic considerations. 相似文献
18.
19.
We develop a variational method for the solution of biharmonic problems for a rectangular domain where, at one pair of its
opposite sides, the unknown function and its normal derivative take zero values, and, at the other pair, certain inhomogeneous
conditions are valid. The cases of semiinfinite and finite domain are considered. The method is based on the minimization
of a quadratic functional determining the deviation of the solution from the given inhomogeneous conditions in the norm of
L
2. To solve this variational problem, we apply the expansion of the solution in the systems of complex biharmonic functions
(the so-called Papkovich homogeneous solutions), which satisfy identically the given homogeneous conditions at the pair of
opposite sides of the rectangle. This representation of the solution is somewhat different from that proposed earlier [V.
F. Chekurin, “A variational method for the solution of direct and inverse problems of the theory of elasticity for a semiinfinite
strip,” Izv. Ross. Akad. Nauk, Mekh. Tverdogo Tela, No. 2, 58–70 (1999)]. We consider several variants of inhomogeneous boundary conditions arising in the problems of the two-dimensional
theory of elasticity. Finally, we give an example of applying the proposed method for the determination of stress distributions
in a rectangular area one of whose sides is rigidly fastened and the opposite one is subjected to the action of normal forces.
Translated from Matematychni Metody ta Fizyko-Mekhanichni Polya, Vol. 51, No. 1, pp. 88–98, January–March, 2008. 相似文献
20.
The method of images is utilized to derive the solution of a screw dislocation under time-harmonic conditions for an elastic strip from the solution of infinite planes. The displacement and stress components are obtained for a strip under concentrated antiplane, time-harmonic traction. The dislocation solution is employed to formulate integral equation for a strip weakened by cracks and cavities. The effects of load frequency and crack orientation on the stress intensity factors are studied. 相似文献