Extreme Points in the Complex of Multy-ary Relations

Cataranciuc Sergiu; Braguţa Galina

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CATARANCIUC, Sergiu, BRAGUŢA, Galina. Extreme Points in the Complex of Multy-ary Relations. In: Conference on Applied and Industrial Mathematics: CAIM 2018, 20-22 septembrie 2018, Iași, România. Chișinău, Republica Moldova: Casa Editorial-Poligrafică „Bons Offices”, 2018, Ediţia a 26-a, pp. 86-87. ISBN 978-9975-76-247-2.

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Conference on Applied and Industrial Mathematics
Ediţia a 26-a, 2018

Conferința "Conference on Applied and Industrial Mathematics"
Iași, România, Romania, 20-22 septembrie 2018

Extreme Points in the Complex of Multy-ary Relations

Pag. 86-87

Cataranciuc Sergiu, Braguţa Galina

Moldova State University

Disponibil în IBN: 1 iunie 2022

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Let Rn+1 = R1;R2; :::;Rn+1 be a complex of multy-are relations, de ned in the work [1]. We denote by dmk the distance function de ned on the set Rk [2]. Let dmk -conv(A) be the convex hull of a subset A from the metric space (Rk; dmk ). De nition 1. The cortege r = (xi1 ; xi2 ; :::xik ) 2 Rk is called m-extreme point of the set A Rk, 1 k < m n + 1 if: a) r 2 A; b) r =2 dmk - conv(A C r). Knowing m-extreme points of a set often simpli es the procedure of convex hull construction and the study of its properties. Let denote by extm(A) the set of all m-extreme points of the set A.

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<dc:creator>Cataranciuc, S.G.</dc:creator>
<dc:creator>Braguţa, G.</dc:creator>
<dc:date>2018</dc:date>
<dc:description xml:lang='en'><p>Let Rn+1 =&nbsp; R1;R2; :::;Rn+1  be a complex of multy-are relations, de ned in the work [1]. We denote by dmk the distance function de ned on the set Rk [2]. Let dmk -conv(A) be the convex hull of a subset A from the metric space (Rk; dmk ). De nition 1. The cortege r = (xi1 ; xi2 ; :::xik ) 2 Rk is called m-extreme point of the set A  Rk, 1  k &lt; m  n + 1 if: a) r 2 A; b) r =2 dmk - conv(A C r). Knowing m-extreme points of a set often simpli es the procedure of convex hull construction and the study of its properties. Let denote by extm(A) the set of all m-extreme points of the set A.</p></dc:description>
<dc:source>Conference on Applied and Industrial Mathematics (Ediţia a 26-a) 86-87</dc:source>
<dc:title>Extreme Points in the Complex of Multy-ary Relations</dc:title>
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