181.
Tractor Calculi for Parabolic Geometries
- Andreas Cap,A. Rod Gover
. Parabolic geometries may be considered as curved analogues
of the homogeneous spaces G=P where G is a semi-simple Lie
group and P ae G a parabolic subgroup. Conformal geometries and
CR geometries are examples of such structures. We present a uniform
description of a calculus, called tractor calculus, based on natural bundles
with canonical linear connections for all parabolic geometries. It is
shown that this calculus is equivalent to the approach to these structures
based on Cartan connections and we characterize the normal Cartan
connection from this induced bundle/connection perspective. We construct
explicitly a fundamental first order differential operator which is
analogous to a covariant derivative and is defined...
182.
The Shapley Value on Convex Geometries
A game on a convex geometry is a real-valued function dened on the family L of the
closed sets of a closure operator which satises the nite Minkowski-Krein-Milman
property. If L is the boolean algebra 2
N
then we obtain a n-person cooperative
game. Faigle and Kern investigated games where L is the distributive lattice of the
order ideals of the poset of players. We obtain two classes of axioms that give rise
to a unique Shapley value for games on convex geometries.
Key words: Cooperative game, Convex geometry, Shapley value.
1 Games on convex geometries
The goal of this paper is to develop a theoretical framework in which to...
183.
Didáctica de las Ciencias y de la Matemática + Recursos Didácticos
- Abrate, Raquel Susana; Delgado, Graciela Isabel; Pochulu, Marcel David
El presente trabajo es un estudio de caso de naturaleza diagnóstico-descriptivo, cuyo objetivo ha sido caracterizar las actividades de Geometría que proponen los textos escolares más utilizados por los docentes de Matemática del tercer ciclo de la Escuela General Básica Argentina (alumnos de 12 a 15 años).
Para tal fin, entrevistamos a profesores de Matemática que desarrollan sus actividades en centros educativos públicos y privados de la ciudad de Villa María, Provincia de Córdoba.
Posteriormente caracterizamos las actividades de acuerdo a variables que devienen, por un lado, de las convergencias realizadas entre la experiencia que como docentes en el ejercicio...
184.
Representing Geometries Of Geographic Space
- Thomas Bittner,Andrew U. Frank
ion
ABSTRACT
This paper discusses the representation of phenomena of geographic space by means of
geometry. It is argued that different kinds of phenomena need to be represented by different
geometries. The notions of geometric and location abstraction are introduced. Geometric and
location abstraction is used to relate different geometries and their representations to each
other. In the analysis a conceptual model a model level and a representation level are
distinguished. The results of the analysis are applied to two classes of problems in GIS:
handling of uncertain data and effective organization of spatial data. It is shown that the
analysis on different levels provides a unified view on...
185.
Optical Geometries And Related Structures
- Scuola Internazionale,Superiore Studi Avanzati
In this work we interpret known facts from the twsitor theory in the language
of optical geometry.
Two natural optical geometries on the space P of all null directions over a 4dimensional
Lorentzian manifold M are defined and studied. One of this geometries
is never integrable and the other is integrable iff the metric of M is
conformally flat. The sections of P forming a zero set of integrability conditions
for the later optical geometry are interpreted as principal null directions on M.
Certain well defined conditions on P are shown to be equivalent to the vanishing
of the traceless part of the Ricci tensor of M. Sections...
186.
O conhecimento geometrico de alunos do CEFAM sobre figuras espaciais : um estudo das habilidades e dos niveis de conceito
- Odalea Aparecida Viana
Este trabalho avalia o conhecimento geométrico de alunos do curso Cefam (Centro Específico de Formação e Aperfeiçoamento do Magistério) sobre figuras tridimensionais mais comuns que deveriam ser, de acordo com várias propostas curriculares, objetos de estudo das séries iniciais do Ensino Fundamental. Foram sujeitos da pesquisa 377 alunos das quatro séries do Cefam de Mogi das Cruzes-SP, tendo sido aplicado um questionário tipo lápis e papel. Além de serem avaliados com relação ao desempenho, os alunos foram classificados de acordo com os graus de aquisição dentro dos níveis de conceituação propostos por Van Hiele. Foram também analisadas duas habilidades:...
187.
Dowling Geometries Are Line Closed: A Short Proof
- Thomas Zaslavsky
We use gain graphs to provide a short direct proof that Dowling geometries are
line closed.
188.
Several Aspects of Antimatroids and Convex Geometries
- Yoshio Okamoto
thesis, we discuss a kind of combinatorial convexity, in particular, antimatroids and
convex geometries.
189.
Weyl Structures for Parabolic Geometries
- Andreas Cap,Slov Ak
. Motivated by the rich geometry of conformal Riemannian manifolds
and by the recent development of geometries modeled on homogeneous
spaces G=P with G semisimple and P parabolic, Weyl structures and preferred
connections are introduced in this general framework. In particular, we extend
the notions of scales, closed and exact Weyl connections, and Rho--tensors, we
characterize the classes of such objects, and we use the results to give a new
description of the Cartan bundles and connections for all parabolic geometries.
1. Introduction
Cartan's generalized spaces are curved analogs of the homogeneous spaces G=P
defined by means of an absolute parallelism on a principal P --bundle. This very
general framework...
190.
A Greedy Algorithm for Convex Geometries
- Kenji Kashiwabara,Yoshio Okamoto
Convex geometries are closure spaces which satisfy anti-exchange property,
and they are known as dual of antimatroids. We consider functions
defined on the sets of the extreme points of a convex geometry. Faigle--
Kern (1996) presented a greedy algorithm to linear programming problems
for shellings of posets, and Kr uger (2000) introduced b-submodular
functions and proved that Faigle--Kern's algorithm works for shellings of
posets if and only if the given set function is b-submodular. We extend
their results to all classes of convex geometries, that is, we prove that the
same algorithm works for all convex geometries if and only if the given set
function on the extreme sets...
191.
A Greedy Algorithm for Convex Geometries
- Kenji Kashiwabara,Yoshio Okamoto
Convex geometries are closure spaces which satisfy anti-exchange property,
and they are known as dual of antimatroids. We consider functions
defined on the sets of the extreme points of a convex geometry. Faigle--
Kern (1996) presented a greedy algorithm to linear programming problems
for shellings of posets, and Kr uger (2000) introduced b-submodular
functions and proved that Faigle--Kern's algorithm works for shellings of
posets if and only if the given set function is b-submodular. We extend
their results to all classes of convex geometries, that is, we prove that the
same algorithm works for all convex geometries if and only if the given set
function on the extreme sets...
192.
The residually weakly primitive geometries of J2
- Dimitri Leemans; Université Libre; Bruxelles C. P. Géométrie
Abstract. We announce the end of the classification of all firm and residually connected geometries satisfying the conditions (IP)2 and (2T)1 and on which the Hall-Janko group J2 acts flag-transitively and residually weakly primitively. We state some facts regarding the results. The complete list of geometries is available as a supplement to this paper [9].
193.
Non-Standard Invariant Operators For Quaternionic Geometries
. This is a survey along the lines of the talk at the conference Lie
III, held in Clausthal in July 1999. The aim is to present amazing problems
related to the invariant operators which are not curved analogues of the so
called standard operators in the Bernstein{Gelfand{Gelfand resolutions. On
the way, we provide some background and recent achievements, as well as a
guide to some of the old and new bibliography.
The lecture is based on a long time project of the author joint with Andreas
Cap
and Vladimr Soucek, and further joint papers with Mike Eastwood, Rod Gover,
and Gerd Schmalz. The main reference is [22] and...
194.
Several Aspects of Antimatroids and Convex Geometries
Convexity is important in several fields, and we have some theories on it. In this thesis, we discuss a kind of combinatorial convexity, in particular, antimatroids and convex geometries. An antimatroid is a combinatorial abstraction of convexity. It has some different origins; by Dilworth in lattice theory, by Edelman and Jamison in the notions of convexity, by Korte-Lovász who were motivated by scheduling problems. A convex geometry is known as a dual object of an antimatroid. In this thesis, we have four main topics. The first topic is a characterization result. We characterize line-search antimatroids of rooted digraphs by their...
195.
The Banzhaf power index on convex geometries
In this paper, we introduce the Banzhaf power indices for simple games on convex geometries.
We define the concept of swing for these structures, obtaining convex swings. The number of
convex swings and the number of coalitions such that a player is an extreme point are the basic
tools to define the convex Banzhaf indices, one normalized and other probabilistic. We obtain a
family of axioms that give rise to the Banzhaf indices. In the last section, we present a method to
calculate the convex Banzhaf indices with the computer program Mathematica, and we apply this
to compute power indices in the Spanish and Catalan parliaments...
196.
Problemario de Análisis y Geometría Analítica
- Navarro, E.
197.
Geometria discreta e codigos
- João Eloir Strapasson
Este trabalho está dividido em duas partes. A primeira e dedicada ao problema de encontrar o menor vetor não nulo de um reticulado. Este é um problema de alta complexidade computacional e que tem grande interesse tanto para a Teoria dos Códigos, como para diversas outras áreas. Esse mínimo está associado a performance do reticulado em termos da codificação: quanto maior for a razão entre este mínimo e o determinante do reticulado, melhor e a distribuição dos pontos no espaço (alta densidade de empacotamento). Nesta tese demos ênfase ao caso especial dos reticulados obtidos por uma projeção ortogonal do reticulado...
198.
Introducción a la geometría superior
- Echegaray, José
1832-1916
199.
On Representing Geometries of Geographic Spaces
- Kuratowski K
this paper we argued that different classes of phenomena need to be represented by different geometries. We
discussed techniques of geometric and location abstraction and their application to the representation of spatial
phenomena of geographic space in GIS. These techniques provide means to relate different geometries and their
representation to each other. We discussed the application of these concepts to problems of handling uncertainty
of spatial data and effective organization of spatial data.
200.
Affine Representations of Abstract Convex Geometries
- Kenji Kashiwabara
A convex geometry is a combinatorial abstract
model introduced by Edelman and Jamison
which captures a combinatorial essence of "convexity
" shared by some structures including finite
point sets, partially ordered sets, trees,
rooted graphs. In this paper, we introduce a
generalized convex shelling, and we show that
any convex geometry can be represented as a
generalized convex shelling. This is "the representation
theorem for convex geometries" similar
to "the representation theorem for oriented
matroids" by Folkman and Lawrence. An important
feature is that our representation theorem
is affine-geometric while that for oriented
matroids is topological. Namely our representation
theorem indicates the intrinsic simplicity of
convex geometries.
