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141.
Scalarization of vector optimization problems 总被引:5,自引:0,他引:5
D. T. Luc 《Journal of Optimization Theory and Applications》1987,55(1):85-102
In this paper, we investigate the scalar representation of vector optimization problems in close connection with monotonic functions. We show that it is possible to construct linear, convex, and quasiconvex representations for linear, convex, and quasiconvex vector problems, respectively. Moreover, for finding all the optimal solutions of a vector problem, it suffices to solve certain scalar representations only. The question of the continuous dependence of the solution set upon the initial vector problems and monotonic functions is also discussed.The author is grateful to the two referees for many valuable comments and suggestions which led to major imporvements of the paper. 相似文献
142.
The boundary value problem of elastostatics in terms of six components of the stress consists of nine equations and three
boundary conditions. In this paper, we distinguished between the possible cases and impossible cases, i.e., the problem is
or is not equivalent to a boundary value problem of six equations and six boundary conditions. 相似文献
143.
考虑具有导子的李三系.由李三系和一个导子称为LietsDer对.定义系数在表示中的LietsDer对的上同调理论.研究LietsDer对的中心扩张.接下来,将形变理论推广到由李三系和导子构成LietsDer对上,它由带有系数的LietsDer对的上同调所支配. 相似文献
144.
145.
Román Castañeda 《Optics Communications》2011,284(18):4114-4123
Random stationary electromagnetic fields can be modeled in terms of point sources disposed onto two distinct layers, named the radiant and the virtual layers. It allows describing the propagation of the power and the states of spatial coherence and polarization of the field by means of separate phase-space ray-maps. Spatial coherence of the field, correlation of the polarization angles and achievement of the Fresnel-Arago laws within the structured spatial coherence supports are the necessary conditions that determine the electromagnetic point sources in the virtual layer. The contributions of these sources produce two types of modulations on the electromagnetic field at the observation plane, one of them of scalar type is the interferometric power modulation, and the other one of vector type is de modulation of the polarization state provided by the radiant point sources, according to the Stokes' parameters. Some examples are presented. 相似文献
146.
We explicitly compute the Green’s function of the spinor Klein–Gordon equation on the Riemannian and Lorentzian manifolds of the form M0×?×MN, with each factor being a space of constant sectional curvature. Our approach is based on an extension of the method of spherical means to the case of spinor fields and on the use of Riesz distributions. 相似文献
147.
148.
A problem of decision making under uncertainty in which the choice must be made between two sets of alternatives instead of two single ones is considered. A number of choice rules are proposed and their main properties are investigated, focusing particularly on the generalizations of stochastic dominance and statistical preference. The particular cases where imprecision is present in the utilities or in the beliefs associated to two alternatives are considered. 相似文献
149.
150.
Motivated by a general dilation theory for operator-valued measures, framings and bounded linear maps on operator algebras, we consider the dilation theory of the above objects with special structures. We show that every operator-valued system of imprimitivity has a dilation to a probability spectral system of imprimitivity acting on a Banach space. This completely generalizes a well-known result which states that every frame representation of a countable group on a Hilbert space is unitarily equivalent to a subrepresentation of the left regular representation of the group. We also prove that isometric group representation induced framings on a Banach space can be dilated to unconditional bases with the same structure for a larger Banach space. This extends several known results on the dilations of frames induced by unitary group representations on Hilbert spaces. 相似文献