Symposia Mathematica - 1st Edition - ISBN: 9781483229959, 9781483258836

Symposia Mathematica

1st Edition

Authors: Yong Zhou
eBook ISBN: 9781483258836
Imprint: Academic Press
Published Date: 1st January 1969
Page Count: 454
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Symposia Mathematica, Volume I focuses on research in the field of mathematics and its applications.

This book discusses the definition of S-semigroup, extensions of R modules, structure of H, laws of conservation and equations of motion, and measures of strain. The basic equations for continua with internal rotations, general concepts of the discrete particle mechanics of matter, and implications of the first law of thermodynamics are also elaborated. This text likewise covers the homomorphism theorem, magneto-elastic interactions, transition from discrete particle mechanics to continuum mechanics, and passage to the continuum.

This publication is suitable for mathematicians, specialists, and students interested in mathematical structures.

Table of Contents

Chapter 1. An Extension of OEOUP Theory

1. The Definition of S-semigroup

2. T-subgroups

3. T-normal Subgroups

4. The Homomorphism Theorem

5. The Isomorphism Theorems

6. T-subnormal Subgroups

7. A Generalization of Conjugacy in Groups


Chapter 2. Extensions of R-modules

1. Introduction

2. Extensions of R modules

3. A Special Case

Chapter 3. Some New Simple Groups of Finite Order

1. Introduction

2. The Structure of H

3. Some Consequences of the Fusion in G of All Involutions in E

4. The Character Table of H

5. The Case (1) of Lemma 3.3


Chapter 4. Operatori Idempotenti nel Reticolo dei Sottogruppi di un Gruppo


Chapter 5. Partizioni ed S-partizioni dei Gruppi Finiti

1. Partizioni dei Gruppi Finiti

2. S-partizioni dei Gruppi Finiti


Chapter 6. Das F-hyperzentrum

Chapter 7. Sui Semigruppi che Contengono Unità

I. La Struttura di S

II. Il Problema di Ampliamento

III. Ill Problema dell'isomorfismo


Chapter 8. Varietà Abeliane su Corpi p-Adici; Parte Prima


Chapter 9. Indice Alfabetico Delle Definizioni e dei Simboli

Chapter 10. Le Problème des Mots dans les Groupes de Coxeter

1. Groupes de Coxeter

2. Deux Solutions du Problème des Mots

3. Application à la Détermination des Groupes de Coxeter Finis


Chapter 11. Factors of Groups

1. F[G]

2. Q[G]


Chapter 12. Problemi di Complementazione in Teoria dei Gruppi


Teoria dei Continui Polari

Chapter 13. On the Measures of Strain in the Theory of the Elastic Generalized Cosserat Continuum

1. Introduction

2. Laws of Conservation and Equations of Motion

3. Constitutive Relations. Measures of Strain

4. Strain of Orientation and the Distribution of Dislocations

5. Conclusion


Chapter 14. Continuum Mechanics of Media with Internal Structure

1. Introduction

2. Basic Equations for Continua with Internal Rotations

3. Application to Fluids

4. Application to Solids

5. Magneto-elastic Interactions


Chapter 15. Das Dreidimensionale Cosserat-Kontinuum und die Cosserat-Schale im Kalkül der Differentialformen

1. Die Parallel-Übertragung eines Motors

2. Das Absolute Differential eines Motors in allgemeinen Koordinaten

3. Die Ableitungsgleichungen von FRENET-CARTAN im Dualraum D3

4. Das Absolute Differential der Linearen Konnexion im D3

5. Die Schale als zweidimensionales Cosserat-Kontinuum

6. Die Grundgleichungen der Schalenkinematik und -statik


Chapter 16. Questioni di Compatibilità per i Continui di Cosserat

1. Qualche Osservazione sugli Spostamenti Rotatori

2. Sulla Rotazione Locale nei Continui di Cosserat

3. Forma Lagrangiana del Lavoro Delle Forze Interne

4. Equazioni Costitutive

5. Incompatibilità in Generale dei Continui di Cosserat con Rotazioni Libere


Chapter 17. Sistemi Polari in Relatività

N. 1. Introduzione

N. 2. Prelimiuari Geometrici e Cinematici Riguardauti il Cronotopo Relativistico Σ4

N. 3. Equazione di Continuità. Sforzi e Coppie di Contatto

N. 4. Sulla Conduzione Termica

N. 5. Equazioni Gravitazionali

N. 6. Sul Coutributo delle Coppie di Contatto e della Conduzione Termica alle Equazioni di Conservazione

N. 7. Prima Equazione di Cauchy dei Sistemi Continui ed Equazione del Bilancio Energetico. Raffronto con la Teoria Classica

N. 8. Alternativa non Simmetrica Uαβ al Precedente Tensore Energetico Totale Uαβ in Relatività Ristretta

N. 9. Preliminari Cinematici di Tipo Lagrangiano

N. 10. Derivata Lagrangiana Trasversa e Teosori di Cauchy-Green

N. 11. Secondo Principio della Termodinamica. Elasticità Relativistica cou Coppie di Contatto


Chapter 18. The Mechanics of Generalized Continua: Physical Foundations Based Upon the Rigourous Discrete Particle Mechanics

1. Introduction

2. General Concepts of the Discrete Particle Mechanics of Matter

3. Transition from Discrete Particle Mechanics to Continuum Mechanics. Case of Perfect Crystals

4. Transition from Discrete Particle Mechanics to Continuum Mechanics. Case of Imperfect Crystals

5. Transition from Discrete Particle Mechanics to Continuum Mechanics. Case of Non-crystalline Bodies


Chapter 19. La Volta Sottile, Semplice Esempio di Sistema Continuo Polare Bidimensionale

1. Prime Definizioni

2. Alcune Relazioni Geometriche

3. Equazioni di Equilibrio

4. Lavoro Virtuale delle Forze Intime

5. Caratteristiche di Tensione Essenziali

6. Equazioni Indefinite della Meccanica delle Volte e Condizioni al Contorno

7. Caratteristiche di Deformazione

8. L'ipotesi di Kirchhoff: Caratteristiche di Tensione ed Equazione Indefinita

9. Condizioni al Contorno

10. Relazione Simbolica della Meccanica delle Volte

Riferimenti Bibliografici

Chapter 20. The Formulation of Theories in Generalized Continuum Mechanics and Their Physical Significance

1. Introduction

2. Passage to the Continuum

3. Implications of the First Law of Thermodynamics

4. Implications of the Second Law of Thermodynamics

5. Some Conclusions

6. Development of the Theory for a Different Model


Chapter 21. Sur les Corps du Type de Cosserat à Élasticité Linéaire

1. Aperçu Historique

2. Équations Fondamentales

3. Formulations à L'aide de Fonctions Potentiel

4. Théorèmes de Réciprocité

5. Solutions Fondamentales

6. Le Problème Plan

7. D'autres Problèmes

8. Conclusions


Chapter 22. La Condizione di Congruenza per Una Membrana Tesa su Una Generica Superficie



Indici e Indirizzi

Indice del Volume

Indice delle Comunicazioni

Indirizzi degli Autori

Finito di Stampare con i Tipi della Tipografia Oderisi Editrice in Gubbio 26 Aprile 1969


No. of pages:
© Academic Press 1969
Academic Press
eBook ISBN:

About the Author

Yong Zhou

Professor Yong Zhou is a recognized expert in the field of non-linear difference equations and their applications in China. He was Editor-in-Chief of Journal of Dynamical Systems and Differential Equations over 2007-2011, and is present Guest Editor at Optimization (T&F), Nonlinear Dynamics and Journal of Vibration and Control (Sage), and at Elsevier former Guest Editor of Computers & Mathematics with Applications over 2010-2012 and Applied Mathematics and Computation over 2014-2015.

Affiliations and Expertise

Faculty of Mathematics and Computer Sciences, Zhejiang Normal University, P.R. China.

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