We envisage theoretical structures (especially in pure mathematics and theoretical physics) as ne... more We envisage theoretical structures (especially in pure mathematics and theoretical physics) as networks made of elementary propositions (representing nodes) interconnected through deductive relationships (representing throats). This vision can be exploited as a basis for employing traditional network modeling techniques in the automated search for new theorems as well as for automated proving of proposed theorems and conjectures. This deductive, deterministic and intuitive approach can replace some of the conventional approaches (which are generally more sophisticated and elaborate and hence they are more expensive) in certain areas of automated and assisted theorem proving in addition to its benefit in the automated search for novel theorems. However, we admit that it has a number of limitations and shortcomings although this similarly applies to other methods in this field; moreover some of these limitations and shortcomings can be overcome by the reformulation of certain theoretical structures where we rely for the viability of this reformulation on our perception of theoretical structures as elaborate high-level linguistic systems.
<p>This list provides an extensive data set for the emission and total recombination coeffi... more <p>This list provides an extensive data set for the emission and total recombination coefficients of hydrogen and total recombination coefficients to the 2s two-photon transitions with a kappa electron energy distribution rather than the more traditional Maxwell-Boltzmann distribution. The data are mainly relevant to thin and relatively cold plasma found in planetary nebulae and H II regions. The data set is complementary to previous data sets provided by Hummer and Storey and Storey and Hummer under a Maxwell-Boltzmann distribution assumption based on thermodynamic equilibrium. The data set is structured as a function of electron number density, temperature and kappa. An interactive fortran 77 and C++ data servers are also provided as an accessory to probe the data and obtain Lagrange-interpolated values in all three variables between the explicitly given values.</p
Color X-ray images can be obtained by X-ray diffraction computed tomography (XRD-CT) where the ma... more Color X-ray images can be obtained by X-ray diffraction computed tomography (XRD-CT) where the mapping of the diffraction signal from the interiors of solid objects enables material-specific imaging. In their Communication on page 10 148 ff., S. D. M. Jacques et al. describe the first time-resolved XRD-CT experiment, which reveals the mechanism by which a catalyst evolves from its precursor during the preparation of millimeter-sized industrial hydrogenation catalyst body
1 Cardiac Arrhythmias: Mechanistic Knowledge and Innovation from Computer Models. Natalia A. Tray... more 1 Cardiac Arrhythmias: Mechanistic Knowledge and Innovation from Computer Models. Natalia A. Trayanova and Patrick M. Boyle.- 2 Discrete Mechanical Modeling of Mechanoelectrical Feedback in Cardiac Tissue: Novel Mechanisms of Spiral Wave Initiation. Louis D. Weise and Alexander V. Panfilov.- 3 Multiscale Modelling of Cardiac Perfusion. Jack Lee, Andrew Cookson, Radomir Chabiniok, Simone Rivolo, Eoin Hyde, Matthew Sinclair, Christian Michler, Taha Sochi and Nicolas Smith.- 4 Using image-based CFD to investigate the intracardiac turbulence. C. Chnafa, S. Mendez, R. Moreno and F. Nicoud.- 5 Multiscale Modeling of Sickle Cell Anemia. Huan Lei and George Em Karniadakis.- 6 A three-dimensional continuum model of active contraction in single cardiomyocytes. Alessio Gizzi, Ricardo Ruiz-Baier, Simone Rossi, Aymen Laadhari, Christian Cherubini, and Simonetta Filippi.- 7 On the Assumption of Laminar ow in Physiological Flows: Cerebral Aneurysms as an Illustrative Example. Oyvind Evju and Kent-Andre Mardal.- 8 Effects of poroelasticity on fluid-structure interaction in arteries: a computational sensitivity study. M. Bukac, I. Yotov, R. Zakerzadeh, P. Zunino.- 9 Personalized Anatomical Meshing of Human Body with Applications. Yuri Vassilevski, Alexander Danilov, Yuri Ivanov, Sergey Simakov and Timur Gamilov.
We envisage theoretical structures (especially in pure mathematics and theoretical physics) as ne... more We envisage theoretical structures (especially in pure mathematics and theoretical physics) as networks made of elementary propositions (representing nodes) interconnected through deductive relationships (representing throats). This vision can be exploited as a basis for employing traditional network modeling techniques in the automated search for new theorems as well as for automated proving of proposed theorems and conjectures. This deductive, deterministic and intuitive approach can replace some of the conventional approaches (which are generally more sophisticated and elaborate and hence they are more expensive) in certain areas of automated and assisted theorem proving in addition to its benefit in the automated search for novel theorems. However, we admit that it has a number of limitations and shortcomings although this similarly applies to other methods in this field; moreover some of these limitations and shortcomings can be overcome by the reformulation of certain theoretical structures where we rely for the viability of this reformulation on our perception of theoretical structures as elaborate high-level linguistic systems.
<p>This list provides an extensive data set for the emission and total recombination coeffi... more <p>This list provides an extensive data set for the emission and total recombination coefficients of hydrogen and total recombination coefficients to the 2s two-photon transitions with a kappa electron energy distribution rather than the more traditional Maxwell-Boltzmann distribution. The data are mainly relevant to thin and relatively cold plasma found in planetary nebulae and H II regions. The data set is complementary to previous data sets provided by Hummer and Storey and Storey and Hummer under a Maxwell-Boltzmann distribution assumption based on thermodynamic equilibrium. The data set is structured as a function of electron number density, temperature and kappa. An interactive fortran 77 and C++ data servers are also provided as an accessory to probe the data and obtain Lagrange-interpolated values in all three variables between the explicitly given values.</p
Color X-ray images can be obtained by X-ray diffraction computed tomography (XRD-CT) where the ma... more Color X-ray images can be obtained by X-ray diffraction computed tomography (XRD-CT) where the mapping of the diffraction signal from the interiors of solid objects enables material-specific imaging. In their Communication on page 10 148 ff., S. D. M. Jacques et al. describe the first time-resolved XRD-CT experiment, which reveals the mechanism by which a catalyst evolves from its precursor during the preparation of millimeter-sized industrial hydrogenation catalyst body
1 Cardiac Arrhythmias: Mechanistic Knowledge and Innovation from Computer Models. Natalia A. Tray... more 1 Cardiac Arrhythmias: Mechanistic Knowledge and Innovation from Computer Models. Natalia A. Trayanova and Patrick M. Boyle.- 2 Discrete Mechanical Modeling of Mechanoelectrical Feedback in Cardiac Tissue: Novel Mechanisms of Spiral Wave Initiation. Louis D. Weise and Alexander V. Panfilov.- 3 Multiscale Modelling of Cardiac Perfusion. Jack Lee, Andrew Cookson, Radomir Chabiniok, Simone Rivolo, Eoin Hyde, Matthew Sinclair, Christian Michler, Taha Sochi and Nicolas Smith.- 4 Using image-based CFD to investigate the intracardiac turbulence. C. Chnafa, S. Mendez, R. Moreno and F. Nicoud.- 5 Multiscale Modeling of Sickle Cell Anemia. Huan Lei and George Em Karniadakis.- 6 A three-dimensional continuum model of active contraction in single cardiomyocytes. Alessio Gizzi, Ricardo Ruiz-Baier, Simone Rossi, Aymen Laadhari, Christian Cherubini, and Simonetta Filippi.- 7 On the Assumption of Laminar ow in Physiological Flows: Cerebral Aneurysms as an Illustrative Example. Oyvind Evju and Kent-Andre Mardal.- 8 Effects of poroelasticity on fluid-structure interaction in arteries: a computational sensitivity study. M. Bukac, I. Yotov, R. Zakerzadeh, P. Zunino.- 9 Personalized Anatomical Meshing of Human Body with Applications. Yuri Vassilevski, Alexander Danilov, Yuri Ivanov, Sergey Simakov and Timur Gamilov.
These are general notes on tensor calculus which can be used as a reference for an introductory c... more These are general notes on tensor calculus which can be used as a reference for an introductory course on tensor algebra and calculus. A basic knowledge of calculus and linear algebra with some commonly used mathematical terminology is presumed.
Solutions of Exercises of The Mechanics of Lorentz Transformations, 2018
This book contains the detailed solutions of all the exercises of my book: The Mechanics of Loren... more This book contains the detailed solutions of all the exercises of my book: The Mechanics of Lorentz Transformations. The solutions are generally very detailed and hence they are supposed to provide some sort of revision for the subject topic.
Solutions of Exercises of Principles of Tensor Calculus, 2018
This book contains the solutions of all the exercises of my book: Principles of Tensor Calculus. ... more This book contains the solutions of all the exercises of my book: Principles of Tensor Calculus. These solutions are sufficiently simplified and detailed for the benefit of readers of all levels particularly those at introductory levels.
This book is based on my previous book: Tensor Calculus Made Simple, where the development of ten... more This book is based on my previous book: Tensor Calculus Made Simple, where the development of tensor calculus concepts and techniques are continued at a higher level. Unlike the previous book which is largely based on a Cartesian approach, the formulation in the present book is based on a general coordinate system. The book is furnished with an index as well as detailed sets of exercises to provide useful revision and practice. To facilitate linking related concepts and sections, cross referencing is used extensively throughout the book. The book also contains a number of graphic illustrations to help the readers to visualize the ideas and understand the subtle concepts. The book can be used as a text for an introductory or an intermediate level course on tensor calculus.
Solutions of Exercises of Introduction to Differential Geometry of Space Curves and Surfaces, 2019
This book contains the solutions of the exercises of my book: Introduction to Differential Geomet... more This book contains the solutions of the exercises of my book: Introduction to Differential Geometry of Space Curves and Surfaces. These solutions are sufficiently simplified and detailed for the benefit of readers of all levels particularly those at introductory level.
Introduction to Differential Geometry of Space Curves and Surfaces, 2017
This book is about differential geometry of space curves and surfaces. The formulation and presen... more This book is about differential geometry of space curves and surfaces. The formulation and presentation are largely based on a tensor calculus approach. It can be used as part of a course on tensor calculus as well as a textbook or a reference for an intermediate-level course on differential geometry of curves and surfaces. The book is furnished with an index, extensive sets of exercises and many cross references, which are hyperlinked for the ebook users, to facilitate linking related concepts and sections. The book also contains a considerable number of 2D and 3D graphic illustrations to help the readers and users to visualize the ideas and understand the abstract concepts. We also provided an introductory chapter where the main concepts and techniques needed to understand the offered materials of differential geometry are outlined to make the book fairly self-contained and reduce the need for external references.
Solutions of Exercises of General Relativity Simplified & Assessed
This book contains detailed solutions of all the 606 exercises of my book: General Relativity Sim... more This book contains detailed solutions of all the 606 exercises of my book: General Relativity Simplified & Assessed. These exercises represent an integral part of the original book as they fill many gaps and provide essential extensions and elaborations.
Solutions of Exercises of Tensor Calculus Made Simple
This book contains the detailed solutions of all the exercises of my book: Tensor Calculus Made S... more This book contains the detailed solutions of all the exercises of my book: Tensor Calculus Made Simple. The solutions are generally very detailed and hence they are supposed to provide some sort of revision for the subject topic.
Notes and Problems in Number Theory (Volume II), 2024
This is the second volume of my book "Notes and Problems in Number Theory". We focus in this volu... more This is the second volume of my book "Notes and Problems in Number Theory". We focus in this volume on the type of problems that develop the basic and most essential skills which are required for dealing with number theory problems. We introduced some new topics in the first chapter (i.e. Introduction), while the remaining chapters are largely dedicated to solved problems from the main topics of elementary number theory (which are introduced in V1 or in the Introduction chapter of the present volume). We also introduced the subject of cryptography and computing in number theory in the last two chapters. So in brief, the materials in this volume are largely a mix of applications to the materials of V1 and some theoretical background of new topics as well as applications to the new topics.
Notes and Problems in Number Theory (Volume I), 2023
This book is the first volume of a collection of notes and solved problems about number theory. L... more This book is the first volume of a collection of notes and solved problems about number theory. Like my previous books, maximum clarity was one of the main objectives and criteria in determining the style of writing, presenting and structuring the book as well as selecting its contents.
This is the latest of my books. It is about the mathematical theory of probability. Paper copies ... more This is the latest of my books. It is about the mathematical theory of probability. Paper copies can be obtained form Amazon.
This book is based on my previous book: Tensor Calculus Made Simple, where the development of ten... more This book is based on my previous book: Tensor Calculus Made Simple, where the development of tensor calculus concepts and techniques are continued at a higher level. Unlike the previous book which is largely based on a Cartesian approach, the formulation in the present book is based on a general coordinate system. The book is furnished with an index as well as detailed sets of exercises to provide useful revision and practice. To facilitate linking related concepts and sections, cross referencing is used extensively throughout the book. The book also contains a number of graphic illustrations to help the readers to visualize the ideas and understand the subtle concepts. The book can be used as a text for an introductory or an intermediate level course on tensor calculus.
This is the latest of my books. It is about complex analysis. Paper copies can be obtained form A... more This is the latest of my books. It is about complex analysis. Paper copies can be obtained form Amazon.
This is the latest of my books with the solutions of its exercises combined in a single document.... more This is the latest of my books with the solutions of its exercises combined in a single document. It is about the general theory of relativity (which is generally known as general relativity).
This is my latest book with the solutions of its exercises combined in a single document. It is a... more This is my latest book with the solutions of its exercises combined in a single document. It is about the mechanics of Lorentz transformations (which is generally known as special relativity).
The present text is a collection of notes about differential geometry prepared to some extent as ... more The present text is a collection of notes about differential geometry prepared to some extent as part of tutorials about topics and applications related to tensor calculus. They can be regarded as continuation to the previous notes on tensor calculus as they are based on the materials and conventions given in those documents. They can be used as a reference for a first course on the subject or as part of a course on tensor calculus.
These notes are the second part of the tensor calculus documents which started with the previous ... more These notes are the second part of the tensor calculus documents which started with the previous set of introductory notes (see T. Sochi, Introduction to Tensor Calculus, arXiv:1603.01660, 2016). In the present text, we continue the discussion of selected topics of the subject at a higher level expanding, when necessary, some topics and developing further concepts and techniques. Unlike the previous notes which are largely based on a Cartesian approach, the present notes are essentially based on assuming an underlying general curvilinear coordinate system.
These notes are the second part of the tensor calculus documents which started with the previous ... more These notes are the second part of the tensor calculus documents which started with the previous set of introductory notes (see T. Sochi, Introduction to Tensor Calculus, arXiv:1603.01660, 2016). In the present text, we continue the discussion of selected topics of the subject at a higher level expanding, when necessary, some topics and developing further concepts and techniques. Unlike the previous notes which are largely based on a Cartesian approach, the present notes are essentially based on assuming an underlying general curvilinear coordinate system.
In this article, we argue that the theory of special relativity, as formulated by Einstein, is a ... more In this article, we argue that the theory of special relativity, as formulated by Einstein, is a philosophical rather than a scientific theory. What is scientific and experimentally supported is the formalism of the relativistic mechanics embedded in the Lorentz transformations and their direct mathematical, experimental and observational consequences. This is in parallel with the quantum mechanics where the scientific content and experimental support of this branch of physics is embedded in the formalism of quantum mechanics and not in its philosophical interpretations such as the Copenhagen school or the parallel worlds explanations. Einstein theory of special relativity gets unduly credit from the success of the relativistic mechanics of Lorentz transformations. Hence, all the postulates and consequences of Einstein interpretation which have no direct experimental or observational support should be reexamined and the relativistic mechanics of Lorentz transformations should be treated in education, academia and research in a similar fashion to that of quantum mechanics.
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