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## Meet the editor

Dr. Francisco Bulnes has a PhD in Mathematical Sciences from Instituto de Matematicas (IM/UNAM). He also has two post-doctorate degrees in Mathematics from Cuba and Russia. He is director of the International Advanced Research in Mathematics and Engineering Centre in Mexico (IINAMEI). He is also editor-in-chief and reviewer of several mathematics and physics journals as well as a member of various international science

committees. Since 2009, Dr. Bulnes has been head of the Research Department, TESCHA. He has published more than 100 papers in mathematics and physics journals, and authored several books. Dr. Bulnes is recognized in Eastern Europe, Asia, and Arab countries for his many theories, theorems, and math objects. He has received numerous recognitions and badges from universities and governmental and nongovernmental organizations. His biography has been included in numerous archives of great mathematicians. He is a distinguished member (JCFM) of the Czech Republic Mathematics Society.

Contents

**Section 1**

**Section 2**

in Space-Time

*Edgar Navarro*

Spacetimes

**Section 3**

*by Pınar Kirezli Uludağ*

in Nonequilibrium Process

*Augusto A. Melgarejo*

Fluid Motion Equations in Tensor Form *by Dmitry Nikushchenko and Valery Pavlovsky*

*by Claudia B. Ruscitti, Laura B. Langoni and*

Bilinear Applications and Tensors *by Rodrigo Garcia Eustaquio*

**Preface XI**

Fundamentals **1**

**Chapter 1 3**

Tensors in the Exploring of the Space-Time **19**

**Chapter 2 21**

**Chapter 3 35**

Tensors in Geometry and Continuum Media **47**

**Chapter 4 49**

**Chapter 5 73**

Kinematic-Energy Measurements of the Torsion Tensor

*by Francisco Bulnes, Isaías Martínez, Omar Zamudio and*

Brans-Dicke Solutions of Stationary, Axially Symmetric

Differential Geometry and Macroscopic Descriptions

## Contents



Preface

Generalization of the concepts of scalar, vector and matrix, which are independent of any elected coordinates systems, brought forth the concept of tensor. A tensor is a mathematical entity born of the invariance idea of the mentioned concepts in any election of coordinate systems and to any coordinate system transformation.

The concept has been of great importance in describing the invariance of physics laws with respect to any coordinate inertial reference framework where physics phenomena are measured. Likewise, gravitation theory is an example of the importance of describing physics laws through their invariants. Theories like general and special relativity brought forth diverse Einstein summation laws and other properties from Levi-Civita calculus, contributing to special tensors inside the Riemannian structure, which best describes the phenomena of the universe and their relations. Such is the case of Riemann tensors, Pseudo-tensors, and the different curvature tensor types arising from theories on torsion field, Cartan-Einstein theories, or supersymmetries in quantum mechanics. A more mathematical focus on tensors considers the multilinear forms and the tensor product of the vector spaces, which have more relevance to tensor applications of Hilbert spaces, for example, in QED

Applications in classical mechanics, electrodynamics, quantum mechanics and communication theory are well developed through tensors. In quantum communication theory and parallel geometries to Riemannian geometry, such as twistor geometry, spinors and twistors are considered new interpretations of the tensors in

**Dr. Francisco Bulnes**

Research Department in Mathematics and Engineering,

IINAMEI, Director

Professor,

TESCHA, Mexico

and quantum mechanics.

fields and waves.
