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Disparities in County-Level Vulnerability to Cardiovascular Mortality Associated With Extreme Heat Exposure. [PDF]
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SIAM Review, 1968
Abstract : It is shown that if A is an integral matrix having linearly independent rows, then the extreme points of the set of nonnegative solutions to Ax = b are integral for all integral b if and only if the determinant of every basis matrix is plus or minus 1.
Veinott, Arthur F. jun., Dantzig, G. B.
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Abstract : It is shown that if A is an integral matrix having linearly independent rows, then the extreme points of the set of nonnegative solutions to Ax = b are integral for all integral b if and only if the determinant of every basis matrix is plus or minus 1.
Veinott, Arthur F. jun., Dantzig, G. B.
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Extreme Point Mathematical Programming
Management Science, 1972The paper considers a class of optimization problems. The problems are linear programming problems: maximize cx subject to Ax = b with the additional constraint that x must also be an extreme point of a second convex polyhedron Dx = d, x ≧ 0. A cutting-plane algorithm for solving such problems is presented. Two numerical examples are also included.
M. J. L. Kirby, H. R. Love, Kanti Swarup
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Extreme Points and Strongly Extreme Points of Musielak–Orlicz Sequences Spaces
Acta Mathematica Sinica, English Series, 2004zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Liu, Xinbo, Wang, Tingfu, Yu, Feifei
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Disappearance of extreme points
Proceedings of the American Mathematical Society, 1983It is shown that every separable Banach space which contains an isomorphic copy of c 0 {c_0} is isomorphic to a strictly convex space E E such that no point of E E is an extreme point of the unit ball of E ∗ ∗
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Topology and its Applications, 2019
Compacta in this paper are compact Hausdorff spaces; continua are connected compacta. If $X$ is a space and $\{a,b\}\subset X$, then $[a,b]_X$ equals the intersection of the subcontinua of $X$ that contain the set $\{a,b\}$. One may think of $[a,b]_X$ as the ``subcontinuum interval'', or just the ``interval'', determined by $a$ and $b$.
Anderson, Daron, Bankston, Paul
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Compacta in this paper are compact Hausdorff spaces; continua are connected compacta. If $X$ is a space and $\{a,b\}\subset X$, then $[a,b]_X$ equals the intersection of the subcontinua of $X$ that contain the set $\{a,b\}$. One may think of $[a,b]_X$ as the ``subcontinuum interval'', or just the ``interval'', determined by $a$ and $b$.
Anderson, Daron, Bankston, Paul
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1997
The fact that the weighted equilibrium potential simultaneously solves a certain Dirichlet problem on connected components of C\S w coupled with the fact that the Fekete points are distributed according to the equilibrium distribution leads to a numerical method for determining Dirichlet solutions.
Edward B. Saff, Vilmos Totik
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The fact that the weighted equilibrium potential simultaneously solves a certain Dirichlet problem on connected components of C\S w coupled with the fact that the Fekete points are distributed according to the equilibrium distribution leads to a numerical method for determining Dirichlet solutions.
Edward B. Saff, Vilmos Totik
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Functional Analysis and Its Applications, 1985
An extreme point of the unit ball in a Banach space X is said to be preserved if its image under the canonical mapping from X into its second dual \(X^{**}\) is an extreme point of the unit ball in \(X^{**}\). The author proves that X is reflexive if and only if every extreme point of its unit ball is preserved in each equivalent norm.
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An extreme point of the unit ball in a Banach space X is said to be preserved if its image under the canonical mapping from X into its second dual \(X^{**}\) is an extreme point of the unit ball in \(X^{**}\). The author proves that X is reflexive if and only if every extreme point of its unit ball is preserved in each equivalent norm.
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