Results 321 to 330 of about 6,795,119 (352)

Convex Sets and Convex Functions

2014
Convex sets and functions have been studied since the nineteenth century; the twentieth century literature on convexity began with Bonnesen and Fenchel’s book [1], subsequently reprinted as [2].
Dan A. Simovici, Chabane Djeraba
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Convex Sets and Convex Functions

2002
This chapter explores sets that can be represented as intersections of (a possibly infinite number of) halfspaces of Rn . As will be shown, these are exactly the closed convex subsets. Furthermore, convex functions are studied, which are closely connected to convex sets and provide a natural generalization of linear functions.
Ulrich Faigle, Walter Kern, Georg Still
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Convex-set description of quantum phase transitions in the transverse Ising model using reduced-density-matrix theory.

Journal of Chemical Physics, 2009
Quantum phase transitions in N-particle systems can be identified and characterized by the movement of the two-particle reduced density matrix (2-RDM) along the boundary of its N-representable convex set as a function of the Hamiltonian parameter ...
Christine A. Schwerdtfeger, D. Mazziotti
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Convex Sets and Convex Functions [PDF]

, 1979
Because of their useful properties, the notions of convex sets and convex functions find many uses in the various areas of Applied Mathematics. We begin with the basic definition of a convex set in n-dimensional Euclidean Space (En), where points are ordered n-tuples of real numbers such as x’ = (x1, x2,…, xn) and y’ = (y1, y2,…,yn).
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THE COMPLEX EQUILIBRIUM MEASURE OF A SYMMETRIzC CONVEX SET IN Rn

, 2009
We give a formula for the measure on a convex symmetric set K in Rn which is the Monge-Ampere operator applied to the extremal plurisubharmonic function L K for the convex set.
Eric Bedford, B. A. Taylor
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Arcwise convex sets

Proceedings of the American Mathematical Society, 1951
1. The concept of arcwise convex set is a natural generalization of the notion of L set. The latter was studied by Horn and Valentine [2]1. It is especially interesting to observe how the theorem about the complement of an arcwise convex continuum sheds light on the corresponding theorem for L sets.
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Improving the Efficiency of Stochastic Dominance Techniques Using Convex Set

, 1985
The advantages of convex set stochastic dominance (CSD) are discussed in terms of extending other stochastic dominance criteria in a way which will decrease Type II errors (large efficient sets) without increasing the Type I errors (inaccurate rankings).
M. Cochran, L. Robison, W. Lodwick
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Convex set theoretic image recovery by extrapolated iterations of parallel subgradient projections

IEEE Transactions on Image Processing, 1997
Solving a convex set theoretic image recovery problem amounts to finding a point in the intersection of closed and convex sets in a Hilbert space. The projection onto convex sets (POCS) algorithm, in which an initial estimate is sequentially projected ...
P. Combettes
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Convex Sets and Convex Functions

2016
The first chapter introduces the fundamental concepts and conclusions of functional analysis so that readers can have a foundation for going on reading this book successfully and can also understand notations used in the book. The arrangement of this chapter is as follows: The first section deals with normed linear spaces and inner product spaces which
Zhengzhi Han, Xiushan Cai, Jun Huang
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The Minimization of a Smooth Convex Functional on a Convex Set

, 1967
A method is given for the minimization of a convex functional. on a convex set in Banach space. The paper proves the convergence of the method and presents its applications to problems of optimal linear programming and of convex programming.
V. F. Dem'yanov, A. Rubinov
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