当前位置:文档之家 > The Euclidean Space

The Euclidean Space

FORMALIZED MATHEMATICS

Vol.2, No. 4, September–October 1991

Universit´e Catholique de Louvain

The Euclidean Space

Agata Darmochwa l

Warsaw University

Bia l ystok

Summary. The general definition of Euclidean Space.

MML Identifier:EUCLID .

The papers [14],[6],[9],[8],[12],[1],[5],[10],[3],[13],[4],[15],[16],[7],[11], and [2]provide the notation and terminology for this paper. In the sequel k , n denote natural numbers and r denotes a real number. Let us consider n . The functor R n yields a non-empty set of finite sequences of and is defined as follows:

(Def.1)R n =n .

In the sequel x will denote a finite sequence of elements of . The function ||from into is defined as follows:

(Def.2)for every r holds ||(r ) =|r |.

Let us consider x . The functor |x |yields a finite sequence of elements of and is defined as follows:

(Def.3)|x |=||·x .

Let us consider n . The
functor 0, ... , 0

Let us consider n . The functor 0, ... , 0

n yields a finite sequence of elements of and is defined by:

(Def.4) 0, ... , 0

n =n − → 0qua a real number .

Let us consider n . Then 0, ... , 0

n is an element of R n .

In the sequel x , x 1, x 2, y denote elements of R n . One can prove the following proposition

(1)x is an element of n .

601 c 1991Fondation Philippe le Hodey ISSN 0777–4028

下载Word文档免费下载:

The Euclidean Space下载

(共5页)

A Covariance Approximation on Euclidean Space for Visual Tracking

A Covariance Approximation on Euclidean Space for Visual Tracking Stefan Kluckner, Thomas Mauthner, and Horst Bischof Institute for Computer Graphics and Vision...

(L^p, L^q)-Boundedness of Hausdorff Operators with Power Weight on Euclidean Spaces

(L^p, L^q)-Boundedness of Hausdorff Operators with Power Weight on Euclidean Spaces_电子/电路_工程科技_专业资料。Analysis in Theory and Applications ...

An Addressing and Routing Scheme Based on Modified Euclidean Space for Hexagonal Networks

An Addressing and Routing Scheme Based on Modified Euclidean Space for Hexagonal Networks_电子/电路_工程科技_专业资料。NETWORK TECHNOLOGY AND APPLICATlON An ...

Minimal Surfaces in Euclidean Space Lecture Notes, UAB, Spring

Minimal Surfaces in Euclidean Space Lecture Notes, UAB, Spring Minimal Surfaces in Euclidean Space Lecture Notes, UAB, SpringMinimal Surfaces in Euclidean ...

Gauge Model With Extended Field Transformations in Euclidean Space

更多>>An SO(4) gauge invariant model with extended field transformations is examined in four dimensional Euclidean space. The gauge field is $(A^\mu)^...

ON SPACELIKE AUSTERE SUBMANIFOLDS IN PSEUDO-EUCLIDEAN SPACE

ON SPACELIKE AUSTERE SUBMANIFOLDS IN PSEUDO-EUCLIDEAN SPACE_专业资料。 ACTA ATHEMATIMCA SCIENTIA Vb1 e..SrB 31 I hi oentsnt,wegneaieBrn ...

Let F be a framework in the Euclidean d-space E

Key Words: In nitesimal exibility, exible polyhedra, octahedra MSC 1994: 53A17 1 Introduction Let F be a framework in the Euclidean d-space E with ...

MP2013_04-SR_Spacetime&LorentzTransformations

This is the time axis of the frame S’ 15 Frame S’ as viewed from S Euclidean space through circular angle φ Minkowski spacetime through hyperbolic...

Spacetimology(翻译)

Time and space science is the study of time, space, matter and their ...spaces: 1 Cartesian and Euclidean space, vector space 2 微分几何,黎曼几何 ...

Self-Dual Fields on the space of a Kerr-Taub-bolt Instanton

Kerr and Taub-NUT spacetimes through analytically continuing them to the Euclidean sector.1,2 The Euclidean Schwarzschild and Euclidean Kerr solutions do ...