منابع مشابه
Convex Sets and Convex Combinations
Convexity is one of the most important concepts in a study of analysis. Especially, it has been applied around the optimization problem widely. Our purpose is to define the concept of convexity of a set on Mizar, and to develop the generalities of convex analysis. The construction of this article is as follows: Convexity of the set is defined in the section 1. The section 2 gives the definition...
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In this section, we introduce one of the most important ideas in economic modelling, in the theory of optimization and, indeed in much of modern analysis and computatyional mathematics: that of a convex set. Almost every situation we will meet will depend on this geometric idea. As an independent idea, the notion of convexity appeared at the end of the 19 century, particularly in the works of M...
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Javier Alonso*, Pedro Mart́ın. Universidad de Extremadura, Badajoz, Spain. Characterizations of ellipsoids by sections. Let S be the boundary of a convex body in the d-dimensional Euclidean space E (d ≥ 3). It is well known that S is an ellipsoid if and only if the section of S given by any hyperplane is ellipsoidal. The question of whether it is actually necessary to consider “any” hyperplane t...
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ژورنال
عنوان ژورنال: Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics
سال: 1987
ISSN: 0263-6115
DOI: 10.1017/s144678870002958x