scholarly journals Riemannian Structures on Z 2 n -Manifolds

Mathematics ◽  
2020 ◽  
Vol 8 (9) ◽  
pp. 1469
Author(s):  
Andrew James Bruce ◽  
Janusz Grabowski
Keyword(s):  
Riemannian Geometry ◽  
Fundamental Theorem ◽  
Scalar Product ◽  
Riemannian Metric ◽  
Theoretical Framework ◽  
Similarities And Differences

Very loosely, Z2n-manifolds are ‘manifolds’ with Z2n-graded coordinates and their sign rule is determined by the scalar product of their Z2n-degrees. A little more carefully, such objects can be understood within a sheaf-theoretical framework, just as supermanifolds can, but with subtle differences. In this paper, we examine the notion of a Riemannian Z2n-manifold, i.e., a Z2n-manifold equipped with a Riemannian metric that may carry non-zero Z2n-degree. We show that the basic notions and tenets of Riemannian geometry directly generalize to the setting of Z2n-geometry. For example, the Fundamental Theorem holds in this higher graded setting. We point out the similarities and differences with Riemannian supergeometry.

Organizing and Reorganizing Markets

2018 ◽  
Author(s):  
Nils Brunsson ◽  
Mats Jutterström
Keyword(s):  
Organization Theory ◽  
Institutional Economics ◽  
Theoretical Framework ◽  
Intermediate Result ◽  
Field Of Study ◽  
Mainstream Economics ◽  
Formal Organizations ◽  
Partial Organization ◽  
Similarities And Differences ◽  
Market Organization

Organizing and Reorganizing Markets is an edited volume that brings organization theory to the study of markets. The differences between markets and organizations are often exaggerated. Both are organized. Organizing exists in addition to other processes and phenomena that form markets: the mutual adaption among sellers and buyers as described in mainstream economics and the institutions described in institutional economics and economic sociology. Market organization can be analysed with the same type of theories used for analysing organization within formal organizations. Through the use of many empirical examples, the book demonstrates how this can be done. We argue that the way a certain market is organized can be understood as the (intermediate) result of previous organizing processes. We discuss such questions as ‘What drives market organizing and reorganizing processes? What makes various organizations intervene as market organizers? And how are the specific contents of market organization determined?’ The answers to these questions help us to analyse similarities and differences among organizing processes in formal organizations and those in markets. The arguments are illustrated by in-depth studies of many types of markets. The book is intended to open up markets as a field of study for scholars of organization. Although the chapters have different authors, they use and elaborate upon the same general theoretical framework. The book contributes to the issue of organization outside and among organizations where a fundamental concept is that of partial organization.

Holonomies of Yang–Mills connections for bundles on a surface with disconnected structure group

1994 ◽  
Vol 116 (2) ◽  
pp. 375-384 ◽  
Author(s):  
Johannes Huebschmann
Keyword(s):  
Moduli Space ◽  
Scalar Product ◽  
Additive Group ◽  
Closed Surface ◽  
Riemannian Metric ◽  
Compact Lie Group ◽  
Universal Central Extension ◽  
Yang Mills ◽  
Disconnected Structure ◽  
Image Position

AbstractLet Σ be a closed surface of genus ≥ 1, G a compact Lie group, not necessarily connected with Lie algebra g, ξ,: P → Σ a principal G-bundle, and suppose Σ equipped with a Riemannian metric and g with an invariant scalar product so that the Yang—Mills equations on ξ are defined. Further, letbe the universal central extension of the fundamental group π of Σ and ΓR the group obtained from Γ when its centre Z is extended to the additive group R of the reals. We show that there are bijective correspondences between various spaces of classes of Yang—Mills connections on ξ and spaces of representations of Γ and ΓR (as appropriate) in G. In particular, we show that the holonomy establishes a homeomorphism between the moduli space N(ξ) of central Yang–Mills connections on ξ and the space Repξ(Γ, G) of representations of Γ in G determined by ξ. Our results rely on a detailed study of the holonomy of a central Yang–Mills connection and extend corresponding ones of Atiyah and Bott for the case where G is connected.

A Generalization of Finsler Geometry

1962 ◽  
Vol 14 ◽  
pp. 87-112 ◽  
Author(s):  
J. R. Vanstone
Keyword(s):  
Differential Geometry ◽  
General Theory ◽  
Distance Function ◽  
Riemannian Geometry ◽  
Finsler Geometry ◽  
Riemannian Metric ◽  
Elliptic Partial Differential Equations ◽  
Theory Of Relativity ◽  
General Theory Of Relativity ◽  
Metric Function

Modern differential geometry may be said to date from Riemann's famous lecture of 1854 (9), in which a distance function of the form F(xi, dxi) = (γij(x)dxidxj½ was proposed. The applications of the consequent geometry were many and varied. Examples are Synge's geometrization of mechanics (15), Riesz’ approach to linear elliptic partial differential equations (10), and the well-known general theory of relativity of Einstein.Meanwhile the results of Caratheodory (4) in the calculus of variations led Finsler in 1918 to introduce a generalization of the Riemannian metric function (6). The geometry which arose was more fully developed by Berwald (2) and Synge (14) about 1925 and later by Cartan (5), Busemann, and Rund. It was then possible to extend the applications of Riemannian geometry.

scholarly journals Los orígenes, difusión y conexiones interreligiosas en torno a las cuentas de oración: un caso de estudio de la evangelización de Japón

2021 ◽  
pp. 209-247
Author(s):  
Rie Arimura
Keyword(s):  
Organizational Structure ◽  
Theoretical Framework ◽  
Point Of View ◽  
Ordinary People ◽  
Pure Land ◽  
Religious Traditions ◽  
Asian Religions ◽  
Pure Land Buddhism ◽  
Similarities And Differences ◽  
Jodo Shinshu

Praying with a string of beads is not exclusive to Catholicism. Various Asian religions have had a similar tradition since before the advent of Christ. This paper addresses the parallels between different religious traditions, as well as the origin, formation and spread of the Holy Rosary and its variants called “crowns.” It also analyzes the intersections between Buddhist and Catholic prayer traditions during the period of the evangelization of Japan (1549-1639). To this end, it draws on a theoretical framework aimed at interpreting the acceptance of Christianity from the point of view of ordinary people, by comparing the similarities and differences between the beliefs, practices, and organizational structure of popular Buddhism (in particular, Jōdo-shū and Jōdo-Shinshū, branches of Pure Land Buddhism) and those of Catholicism.

scholarly journals Family Business in Vietnam and in Poland: Review of Characteristics and Trends of Development

2019 ◽  
Vol 54 (6) ◽  
Author(s):  
Nguyen Hoang Tien ◽  
Ho Thien Thong Minh ◽  
Nguyen Minh Ngoc ◽  
Vo Kim Nhan
Keyword(s):  
Comparative Analysis ◽  
Family Business ◽  
High Performance ◽  
Theoretical Framework ◽  
Business Activity ◽  
The Family ◽  
Management Literature ◽  
Similarities And Differences

Enterprise and entrepreneurship are well-known phenomena that have their history development of over 300 years. However, in relation to the family business they are still not well explored in the literature of management. Based on the overview of management literature, this article is an attempt to construct a theoretical framework for the purpose of comparative analysis of family business and entrepreneurship issues in Poland and in Vietnam. As a result, their similarities and differences are revealed in order to propose adequate solutions and recommendations for business and authority to support and promote this specific business activity towards their prosperity and high performance.

scholarly journals Directions in Discourse Analysis: Theory & Method. Jalilifar A. R. (Eds.). Ahvaz, Iran: University of Ahvaz Press, 2014. 370 pp. ISBN 978-600-141-158-8

2017 ◽  
Vol 3 (4) ◽  
pp. 76-77
Author(s):  
Aiyoub Jodairi Pineh
Keyword(s):  
Discourse Analysis ◽  
Applied Linguistics ◽  
Theoretical Framework ◽  
Theory Method ◽  
Fast Growing ◽  
Analysis Theory ◽  
Wide Range ◽  
Similarities And Differences

Plenty of books have written in Discourse Analysis, and the book, Directions in Discourse Analysis: Theory & Method, is another welcomed addition to this vital field of Applied Linguistics. Many books in this field are limited to a specific framework of discourse analysis (Coulthard, 1992; Christie, 2002; Gee, 1999; Walsh, 2006) to name but a few. Introducing a specific theoretical framework and orientation has almost been a tradition in preparing such textbooks, while it seems that there is a need for publications which take into account the fast-growing field of discourse analysis, where discerning similarities and differences are becoming subtle. I think similar to Hyland & Paltridge (2011), Directions in Discourse Analysis: Theory & Method by Professor Jalilifar is another attempt to meet such a need. As the title of the book indicates, the emphasis is on a wide range of recent approaches, wherein the author presents them under a separate but a related chapter. He successfully brings together similar and contradictory themes under a single topic.

scholarly journals Idempotent Analog of the Legendre Transformation and lts Application in Digital Processing of Signals

2020 ◽  
pp. 96-101
Author(s):  
M.V. Kurkina ◽  
S.P. Semenov ◽  
V.V. Slavsky ◽  
O.V. Samarina ◽  
O.A. Petuhova ◽  
...  
Keyword(s):  
Convex Functions ◽  
Riemannian Geometry ◽  
Duality Theory ◽  
Digital Processing ◽  
Riemannian Metric ◽  
Theoretical Physics ◽  
Vector Spaces ◽  
Legendre Transformation ◽  
Conformally Flat ◽  
Tropical Mathematics

In recent years, a new area of mathematics — idempotent or “tropical” mathematics — has been intensively developed within the framework of the Sofus Lee international center, which is reflected in the works of V.P. Maslov, G.L. Litvinov, and A.N. Sobolevsky. The Legendre transformation plays an important role in theoretical physics, classical and statistical mechanics, and thermodynamics. In mathematics and its applications, the Legendre transformation is based on the concept of duality of vector spaces and duality theory for convex functions and subsets of a vector space. The purpose of this paper is to go beyond linear vector spaces using similar notions of duality in conformally flat Riemannian geometry and in idempotent algebra.An abstract idempotent analog of the Legendre transformation is constructed in a way similar to the polar transformation of the conformally flat Riemannian metric introduced in the works of E.D. Rodionov and V.V. Slavsky. Its capabilities for digital processing of signals and images are being investigated

Rotation fields and the fundamental theorem of Riemannian geometry in

2006 ◽  
Vol 343 (6) ◽  
pp. 415-421 ◽  
Author(s):  
Philippe G. Ciarlet ◽  
Liliana Gratie ◽  
Oana Iosifescu ◽  
Cristinel Mardare ◽  
Claude Vallée
Keyword(s):  
Riemannian Geometry ◽  
Fundamental Theorem

Saliences, propositions, and amalgams: Emergent learning in nonhumans

2009 ◽  
Vol 32 (2) ◽  
pp. 213-214
Author(s):  
Heidi Lyn ◽  
Duane M. Rumbaugh
Keyword(s):  
Operant Conditioning ◽  
Theoretical Framework ◽  
Human Learning ◽  
Emergent Learning ◽  
Similarities And Differences

AbstractWe comment on the similarities and differences of Mitchell et al.'s framework for understanding classical and operant conditioning and the theoretical framework put forth by Rumbaugh et al. (2007). We propose that all nonhuman and human learning may be based on amalgams created by co-occurring stimuli that share their response-eliciting properties and that these amalgams may be propositional in nature.

scholarly journals Riemannian Geometry on Quantum Spaces

1997 ◽  
Vol 12 (05) ◽  
pp. 923-943 ◽  
Author(s):  
Pei-Ming Ho
Keyword(s):  
Projective Space ◽  
Riemannian Geometry ◽  
Riemannian Metric ◽  
Complex Manifolds ◽  
Quantum Sphere ◽  
Quantum Projective Space ◽  
Metric Distance ◽  
Algebraic Formulation

An algebraic formulation of Riemannian geometry on quantum spaces is presented, where Riemannian metric, distance, Laplacian, connection, and curvature have their counterparts. This description is also extended to complex manifolds. Examples include the quantum sphere, the complex quantum projective space and the two-sheeted space.

Sign in / Sign up

Export Citation Format

Share Document