𝔖 Bobbio Scriptorium
✦   LIBER   ✦

On the Description of the Content-Equality by a Relation

✍ Scribed by Renate Jaritz

Publisher
John Wiley and Sons
Year
1990
Tongue
English
Weight
382 KB
Volume
147
Category
Article
ISSN
0025-584X

No coin nor oath required. For personal study only.

✦ Synopsis

Abstract

In the geometry of polyhedra we understand by an elementary content‐functional a real valued, non‐negative, finite additive measure on the set of polyhedra which is invariant under isometries. There are close relations between the content‐measurement and the relation of equidecomposability. Two polyhedra are called equidecomposable if they are decomposed into pairwise congruent pieces. For an example we consider the set of all polygons in the euclidean plane. It is well known that planar polygons have the same area if and only if they are equidecomposable. In the three‐dimensional euclidean space one also can describe the content‐equality of polyhedra by a relation. Two polyhedra have the same volume if they are equidecomposable with respect to equiaffine mappings (see [3]). In [4] the concept of an invariant content of polyhedra in a topological Klein space is introduced. Each regular closed quasicompact set ot the space is called polyhedron. Under this supposition two polyhedra have equal contents if they are equivalent by decomposition. The relation “equivalent by decomposition” is closely related to the relation “equidecomposable”.

📜 SIMILAR VOLUMES

Equality and Coequality Relations on the
Equality and Coequality Relations on the Cartesian Product of Sets
✍ Daniel A. Romano 📂 Article 📅 1988 🏛 John Wiley and Sons 🌐 English ⚖ 433 KB

EQUALITY AND COEQUALITY RELATIONS ON THE CARTESIAN PRODUCT O F SETS by DANEL A . ROMANO in Bihac (Yugoslavia) ## 0. Introduction The foundations on constructive mathematics, in BISHOP'S sense [l], rest on and comprise the three primitive notions of numbers, classes and computations. We believe tha

On the equality of the grundy and ochrom
On the equality of the grundy and ochromatic numbers of a graph
✍ P. Erdös; W. R. Hare; S. T. Hedetniemi; R. Laskar 📂 Article 📅 1987 🏛 John Wiley and Sons 🌐 English ⚖ 162 KB 👁 1 views

It is proved in this note that the Grundy number, r(G), and the ochromatic number, xo(G), are the same for any graph G. An n-coloring of a graph G = ( V , E ) is a f u n c t i o n f f r o m V onto N = { I , 2 , . . . , n } such that, whenever vertices id and u are adjacent, then f ( u ) f f(u). An

Cataloging professionals in the digital
Cataloging professionals in the digital environment: A content analysis of job descriptions
✍ Jung-ran Park; Caimei Lu; Linda Marion 📂 Article 📅 2009 🏛 John Wiley and Sons 🌐 English ⚖ 343 KB 👁 1 views

## Abstract This study assesses the current state of responsibilities and skill sets required of cataloging professionals. It identifies emerging roles and competencies focusing on the digital environment and relates these to the established knowledge of traditional cataloging standards and practic

On the Case of Equality in the Brunn–Min
On the Case of Equality in the Brunn–Minkowski Inequality for Capacity
✍ Luis A. Caffarelli; David Jerison; Elliott H. Lieb 📂 Article 📅 1996 🏛 Elsevier Science 🌐 English ⚖ 382 KB

Suppose that 0 0 and 0 1 are convex, open subsets of R N . Denote their convex combination by The Brunn Minkowski inequality says that (vol 0 t ) 1ÂN (1&t) vol 0 1ÂN 0 +t vol 0 1ÂN 1 for 0 t 1. Moreover, if there is equality for some t other than an endpoint, then the domains 0 1 and 0 0 are transl