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1.
一般扩展原理   总被引:5,自引:2,他引:3  
本文中称Zadeh(1975)给出的扩展原理为极大扩展原理,我们给出了一个极小扩展原理,并研究了它的一些基本性质。之后,建立了一般扩展原理的公理化结构,并给出了几种具体结构形式,为近似推理和信息分析提供了有效的工具。  相似文献   

2.
We state a maximum principle for the gradient of the minima of integral functionals
just assuming that I is strictly convex. We do not require that f, g be smooth, nor that they satisfy growth conditions. As an application, we prove a Lipschitz regularity result for constrained minima.  相似文献   

3.
In the context of the linear theory of thermoelasticity without energy dissipation for homogeneous and isotropic materials, variational principles of Biot-and Hamilton-types and a reciprocal principle of Betti-Rayleigh-type are presented.  相似文献   

4.
New criteria for the existence of a maximum or antimaximum principle of a general second order operator with periodic conditions, as well as conditions for nonresonance, are provided and compared with the related literature.  相似文献   

5.
随着计算机技术的飞速发展,数据的收集和存储能力得到了极大的提高,在科学研究和社会生活的各个领域,海量表现形式复杂的数据涌现。针对同一对象从不同途径或不同层面获得的特征数据被称为多视角数据。多视角学习是利用事物的多种视角表征进行建模求解的一种新的机器学习方法,它一般需遵循两个原则:1)一致性原则;2)互补性原则。近年来,多视角学习已经引起了广泛的关注和研究。本文对多视角学习算法的研究以及相关理论研究的进展进行了综述,并指出了多视角学习面临的挑战及下一步可能的研究方向。  相似文献   

6.
We reconsider Ishihara (1991, 1992) within a weak formalised framework of constructive reverse mathematics, focusing on Brouwer’s continuity principle for a mapping from the Baire space into the natural numbers.  相似文献   

7.
8.
It is shown that the maximum principle in optimal control and the min-max principle in differential games are consequences of a certain global principle which is stated here.  相似文献   

9.
The purpose of this paper is to establish the necessary conditions for optimality of a controlled stochastic differential system without differentiability assumptions on the drift. We use an approximation argument in order to obtain a sequence of smooth control problems, and we apply Ekeland's variational principle to derive the associated adjoint processes. Passing at the Limit with respect to the stable convergence, we obtain a weak adjoint process and the inequality between Hamiltonians. This result is a generalisation of Kushner's maximum principle  相似文献   

10.
In this note, we present the necessary conditions of optimality for time-optimal controls for a class of distributed-boundary control problems in general Banach spaces using the semigroup theory. Theorem 3.1 is based on a recent general maximum principle due to Barbu (Ref. 1), which was proved for strictly convex reflexive Banach spaces. Theorem 3.2 generalizes this result (for time-optimal control problems) by lifting the assumption.This work was supported by the National Science and Engineering Council of Canada under Grant No. 7109.  相似文献   

11.
In this paper, we introduce the concept of approximate solutions for set-valued optimization problems. A sufficient condition for the existence of approximate solutions is obtained. A general Ekeland's variational principle for set-valued mappings in complete ordered metric spaces and complete metric spaces are derived. These results are generalizations of results for vector-valued functions in Refs. 1–4.  相似文献   

12.
运用Riemann-Schwarz对称原理和线弹性力学解的叠加原理建立了半无限平面及含孔无限平面在各种边界条件下基本解的一般求解方法,并分别导出边界上受不同荷载以及边界固定等各种边界条件下的复位势基本解。  相似文献   

13.
We show that for each n ≥ 1, if T2n does not prove the weak pigeonhole principle for Σbn functions, then the collection scheme B Σ1 is not finitely axiomatizable over T2n. The same result holds with Sn2 in place of T 2n (© 2010 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)  相似文献   

14.
The maximum principle is one of the basic characteristic properties of solutions of second order partial differential equations of parabolic (and elliptic) types. The preservation of this property for solutions of corresponding discretized problems is a very natural requirement in reliable and meaningful numerical modelling of various real-life phenomena (heat conduction, air pollution, etc.). In the present paper we analyse a full discretization of a quite general class of linear parabolic equations and present sufficient conditions for the validity of a discrete analogue of the maximum principle in the case when bilinear finite elements are used for discretization in space.  相似文献   

15.
Sticks and clubs     
We study combinatorial principles known as stick and club. Several variants of these principles and cardinal invariants connected to them are also considered. We introduce a new kind of side by-side product of partial orderings which we call pseudo-product. Using such products, we give several generic extensions where some of these principles hold together with ¬CH and Martin's axiom for countable p.o.-sets. An iterative version of the pseudo-product is used under an inaccessible cardinal to show the consistency of the club principle for every stationary subset of limits of ω1 together with ¬CH and Martin's axiom for countable p.o.-sets.  相似文献   

16.
微极连续统的耦合场理论的再研究(I)——微极热弹性理论   总被引:3,自引:3,他引:0  
在传统的微极连续统理论框架下微极热弹性理论问题已被某些学者提出并做过讨论。这篇文章对现有的微极热弹性理论进行了再研究,找出了该理论局限于线性情形的原因。建立了微极热弹性理论的更为普遍的虚功原理和新的内力虚功表达式以及Hamilton原理。从这个新的Hamilton原理不仅可以得到运动方程、熵均衡方程、应力和偶应力以及热量边界条件,而且还可同时推导出位移和微转动以及温度边界条件。  相似文献   

17.
A control problem is considered where the coefficients of the linear dynamics are functions of a noisily observed Markov chain. The approximation introduced is to consider these coefficients as functions of the filtered estimate of the state of the chain; this gives rise to a finite-dimensional conditional Kalman filter. A minimum principle and a new equation for an adjoint process are obtained.This research was partially supported by NSERC under Grant A-7964, by the US Air Force Office of Scientific Research under Contract AFOSR-86-0332, and by the US Army Research Office under Contract DAAL03-87-0102.The authors obtained these results during a visit to UCSD by the first author in January 1990. This author wishes to thank Professor D. D. Sworder and his department for their hospitality.  相似文献   

18.
1. Introduction Anciellt Chinese mathematicians have done many fund~al discoveries, even thoughmad of them are now usually called by western names, e.g., the Pascal triangle, the HornerIcheme, the Gaussian elimination, see [231. In the modern era3 Chinese mathematiciare have.jalso got many priorities. For instance, the fast Proof Of convergence of the finite element methodfor a linear elliptic boundary vajue problem was done in the pioneering work [61 by K. Feng in1965 (for the English tra…  相似文献   

19.
建立有关压电热弹性动力学的各种Gurtin型分区变分原理,由此变分原理可以得到压电热弹性动力学所有方程式、关系式和边界条件,并且可以直接得到各相邻区域交界面上的连续条件。Gurtin型分区变分原理是压电热弹性动力学的重要组成部分,并能反映压电热弹性动力学初值-边值问题的全部特征。  相似文献   

20.
The authors consider Sidon sets of first kind. By comparing them with the Steinhaus sequence, they prove a local Khintchine-Kahane inequality on compact sets. As consequences, they prove the following results for Sidon series taking values in a Banach space: the summability on a set of positive measure implies the almost everywhere convergence; the contraction principle of Billard-Kahane remains true for Sidon series. As applications, they extend a uniqueness theorem of Zygmund concerning lacunary Fourier series and an analytic continuation theorem of Hadamard concerning lacunary Taylor series. Some of their results still hold for Sidon sets of second kind.  相似文献   

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