In this short paper we briefly discuss the issue of the theory of general relativity as a suppose... more In this short paper we briefly discuss the issue of the theory of general relativity as a supposed generalization of the theory of special relativity to see if general relativity did really generalize special relativity as a relativity theory. The simple conclusion that we reach in this discussion is that the theory of general relativity is not actually a generalization of the theory of special relativity and hence general relativity is neither a general theory nor a relativity theory. In short, the so-called "general theory of relativity” should more appropriately be called the “special theory of general covariance” since it is special in content (as it is essentially a gravitation theory) and it lacks the physical substance of relativity (as it is actually about mathematical artwork of general covariance rather than about physical relativity).
In this paper we investigate "inertial forces" and "fictitious forces" and the relationship betwe... more In this paper we investigate "inertial forces" and "fictitious forces" and the relationship between them as understood from the literature of physics where the majority seem to consider them as two labels for the same thing while some seem to suggest they are not identical. Our view and preference is to distinguish between them where fictitious forces should be considered a subset of inertial forces. We also investigate the issue of the reality of fictitious forces and whether they have authentic existence in the physical world or they are a kind of "delusion". Our view is that what is called "fictitious forces" can be either. In this regard, we identify and propose several physical characterizations and distinctions between the two types (i.e. the "apparently fictitious forces" which are physically real and the "really fictitious forces" which are illusory because they are purely frame-dependent as viewed by a non-inertial observer). This is consistent with our preference that fictitious forces should be considered a subset of inertial forces, i.e. "inertial forces" which are real should not be classified as "fictitious" in the real sense while "inertial forces" which are not real should be classified as "fictitious" in the real sense.
In this paper we investigate the concept of "absolute frame of reference" in contemporary physics... more In this paper we investigate the concept of "absolute frame of reference" in contemporary physics as well as its properties, instances (or potential instances), types, conceptualizations, evidence, problems, controversies, and so on. This investigation is essentially epistemological in nature and hence we do not discuss or investigate any technical formulation related to this subject.
In this paper we investigate the legitimate and useful role of mathematics in science (and physic... more In this paper we investigate the legitimate and useful role of mathematics in science (and physics in particular). We also investigate the illegitimate and harmful role (or "lure") of mathematics in modern science (and theoretical physics in particular). Thanks to the obsession of contemporary scientists with complex mathematics and the wrong belief (as well as the wrong scientific values and standards) among these scientists that mathematics is the gold standard of excellent science, highly-mathematized and theoretized science (especially in modern physics) reaches these days a shocking level of irrationality and non-sensibility which often approaches the degree of delusion and hallucination. This obsession with complex mathematics and excessive theoretization inflicts serious damages to modern science and results in a huge waste of efforts and resources as well as the emergence of stray trends and bogus scientific theories inside and outside the main stream of science.
In this paper of "The Epistemology of Contemporary Physics" series we investigate Newton's third ... more In this paper of "The Epistemology of Contemporary Physics" series we investigate Newton's third law and discuss and analyze its epistemological significance from some aspects with special attention to its relation to the principle of conservation of linear and angular momentum. The main issue in this investigation is the potential violations of this law according to the claims made in the literature of mainstream physics. This issue may cast a shadow on the validity of classical mechanics, and its Newtonian formulation in particular, formally and epistemologically and could have important implications and consequences on contemporary physics in general. However, what is more important about this issue from our perspective is the lack of clarity, comprehensibility and coherence in the investigation and analysis of this issue and its implications marked by the absence of appropriate conceptual and epistemological frameworks to deal with this issue properly and systematically. As a result, what we find in the literature is a collection of contradicting views which are mostly based on personal choices and preferences and selective or biased theoretical analysis with the lack of proper experimental verification and substantiation.
In this paper of "The Epistemology of Contemporary Physics" series we investigate the epistemolog... more In this paper of "The Epistemology of Contemporary Physics" series we investigate the epistemological significance and sensibility (and hence interpretability and interpretation) of classical mechanics in its Newtonian and non-Newtonian formulations. As we will see, none of these formulations provide a clear and consistent framework for understanding the physics which they represent and hence they all represent valid formalism without proper epistemology or sensible interpretation.
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. 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 are general notes on tensor calculus originated from a collection of personal notes which I... more These are general notes on tensor calculus originated from a collection of personal notes which I prepared some time ago for my own use and reference when I was studying the subject. I decided to put them in the public domain hoping they may be beneficial to some students in their effort to learn this subject. Most of these notes were prepared in the form of bullet points like tutorials and presentations and hence some of them may be more concise than they should be. Moreover, some notes may not be sufficiently thorough or general. However this should be understandable considering the level and original purpose of these notes and the desire for conciseness. There may also be some minor repetition in some places for the purpose of gathering similar items together, or emphasizing key points, or having self-contained sections and units. These notes, in my view, can be used as a short reference for an introductory course on tensor algebra and calculus. I assume a basic knowledge of calculus and linear algebra with some commonly used mathematical terminology. I tried to be as clear as possible and to highlight the key issues of the subject at an introductory level in a concise form. I hope I have achieved some success in reaching these objectives at least for some of my target audience. The present text is supposed to be the first part of a series of documents about tensor calculus for gradually increasing levels or tiers. I hope I will be able to finalize and publicize the document for the next level in the near future.
We investigate the possibility that the spatial dependency of stress in generalized Newtonian flo... more We investigate the possibility that the spatial dependency of stress in generalized Newtonian flow systems is a function of the applied pressure field and the conduit geometry but not of the fluid rheology. This possibility is well established for the case of a one-dimensional flow through simply connected regions, specifically tubes of circular uniform cross sections and plane thin slits. If it can also be established for the more general case of generalized Newtonian flow through non-circular or multiply connected geometries, such as the two-dimensional flow through conduits of rectangular or elliptical cross sections or the flow through annular circular pipes, then analytical or semi-analytical or highly accurate numerical solutions; regarding stress, rate of strain, velocity profile and volumetric flow rate; for these geometries can be obtained from the stress function, which can be easily obtained from the Newtonian case, in combination with the constitutive rheological relation for the particular non-Newtonian fluid, as done previously for the case of the one-dimensional flow through simply connected regions.
This is the first of a series of papers that we intend to publish about the epistemology of funda... more This is the first of a series of papers that we intend to publish about the epistemology of fundamental physics in its current state. One of the main objectives of these papers is to improve our understanding of fundamental physics (and modern physics in particular) from an epistemological and interpretative perspective (i.e. versus formal perspective). Another main objective is to investigate and assess the merit of searching for a unified physical theory (the so-called "theory of everything") considering the fact that contemporary physics is a collection of theories created and developed by different individuals and groups of scientists in different eras of history reflecting different levels of scientific, philosophical and epistemological development and dealing with largely separate physical phenomena and hence such unification may mean "stitching together" an inhomogeneous collection of theoretical structures which may be clumsy (if not impossible) at least from an epistemological viewpoint.
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
Monthly Notices of the Royal Astronomical Society, Apr 5, 2016
In this paper we compute the collision strengths and their thermally averaged Maxwellian values f... more In this paper we compute the collision strengths and their thermally averaged Maxwellian values for electron transitions between the 15 lowest levels of doubly ionized cobalt, Co 2+ , which give rise to forbidden emission lines in the visible and infrared region of spectrum. The calculations also include transition probabilities and predicted relative line emissivities. The data are particularly useful for analysing the thermodynamic conditions of supernova ejecta.
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
We use a generic and general numerical method to obtain solutions for the flow of generalized New... more We use a generic and general numerical method to obtain solutions for the flow of generalized Newtonian fluids through circular pipes and plane slits. The method, which is simple and robust can produce highly accurate solutions which virtually match any analytical solutions. The method is based on employing the stress, as a function of the pipe radius or slit thickness dimension, combined with the rate of strain function as represented by the fluid rheological constitutive relation that correlates the rate of strain to stress. Nine types of generalized Newtonian fluids are tested in this investigation and the solutions obtained from the generic method are compared to the analytical solutions which are obtained from the Weissenberg-Rabinowitsch-Mooney-Schofield method. Very good agreement was obtained in all the investigated cases. All the required quantities of the flow which include local viscosity, rate of strain, flow velocity profile and volumetric flow rate, as well as shear stress, can be obtained from the generic method. This is an advantage as compared to some traditional methods which only produce some of these quantities. The method is also superior to the numerical meshing techniques which may be used for resolving the flow in these systems. The method is particularly useful when analytical solutions are not available or when the available analytical solutions do not yield all the flow parameters.
The study of flow of non-Newtonian fluids in porous media is very important and serves a wide var... more The study of flow of non-Newtonian fluids in porous media is very important and serves a wide variety of practical applications in processes such as enhanced oil recovery from underground reservoirs, filtration of polymer solutions and soil remediation through the removal of liquid pollutants. These fluids occur in diverse natural and synthetic forms and can be regarded as the rule rather than the exception. They show very complex strain and time dependent behavior and may have initial yield-stress. Their common feature is that they do not obey the simple Newtonian relation of proportionality between stress and rate of deformation. Non-Newtonian fluids are generally classified into three main categories: time-independent whose strain rate solely depends on the instantaneous stress, time-dependent whose strain rate is a function of both magnitude and duration of the applied stress and viscoelastic which shows partial elastic recovery on removal of the deforming stress and usually demonstrates both time and strain dependency. In this article the key aspects of these fluids are reviewed with particular emphasis on single-phase flow through porous media. The four main approaches for describing the flow in porous media are examined and assessed. These are: continuum models, bundle of tubes models, numerical methods and pore-scale network modeling. * In preparing this Appendix, we consulted most of our references. The main ones are [
Monthly Notices of the Royal Astronomical Society, Nov 21, 2014
We provide a data set of emission and recombination coefficients of hydrogen using a κdistributio... more We provide a data set of emission and recombination coefficients of hydrogen using a κdistribution of electron energies rather than the more traditional Maxwell-Boltzmann (MB) distribution. The data are mainly relevant to thin and relatively cold plasma found in planetary nebulae and H II regions. The data set extends the previous data sets provided by Storey and Hummer which were computed using an MB distribution. The data set, which is placed in the public domain, is structured as a function of electron number density, temperature and κ. Interactive FORTRAN 77 and C++ data servers are also provided as an accessory to probe the data and obtain Lagrange-interpolated values for any choice of all three variables between the explicitly computed values.
In this short paper we briefly discuss the issue of the theory of general relativity as a suppose... more In this short paper we briefly discuss the issue of the theory of general relativity as a supposed generalization of the theory of special relativity to see if general relativity did really generalize special relativity as a relativity theory. The simple conclusion that we reach in this discussion is that the theory of general relativity is not actually a generalization of the theory of special relativity and hence general relativity is neither a general theory nor a relativity theory. In short, the so-called "general theory of relativity” should more appropriately be called the “special theory of general covariance” since it is special in content (as it is essentially a gravitation theory) and it lacks the physical substance of relativity (as it is actually about mathematical artwork of general covariance rather than about physical relativity).
In this paper we investigate "inertial forces" and "fictitious forces" and the relationship betwe... more In this paper we investigate "inertial forces" and "fictitious forces" and the relationship between them as understood from the literature of physics where the majority seem to consider them as two labels for the same thing while some seem to suggest they are not identical. Our view and preference is to distinguish between them where fictitious forces should be considered a subset of inertial forces. We also investigate the issue of the reality of fictitious forces and whether they have authentic existence in the physical world or they are a kind of "delusion". Our view is that what is called "fictitious forces" can be either. In this regard, we identify and propose several physical characterizations and distinctions between the two types (i.e. the "apparently fictitious forces" which are physically real and the "really fictitious forces" which are illusory because they are purely frame-dependent as viewed by a non-inertial observer). This is consistent with our preference that fictitious forces should be considered a subset of inertial forces, i.e. "inertial forces" which are real should not be classified as "fictitious" in the real sense while "inertial forces" which are not real should be classified as "fictitious" in the real sense.
In this paper we investigate the concept of "absolute frame of reference" in contemporary physics... more In this paper we investigate the concept of "absolute frame of reference" in contemporary physics as well as its properties, instances (or potential instances), types, conceptualizations, evidence, problems, controversies, and so on. This investigation is essentially epistemological in nature and hence we do not discuss or investigate any technical formulation related to this subject.
In this paper we investigate the legitimate and useful role of mathematics in science (and physic... more In this paper we investigate the legitimate and useful role of mathematics in science (and physics in particular). We also investigate the illegitimate and harmful role (or "lure") of mathematics in modern science (and theoretical physics in particular). Thanks to the obsession of contemporary scientists with complex mathematics and the wrong belief (as well as the wrong scientific values and standards) among these scientists that mathematics is the gold standard of excellent science, highly-mathematized and theoretized science (especially in modern physics) reaches these days a shocking level of irrationality and non-sensibility which often approaches the degree of delusion and hallucination. This obsession with complex mathematics and excessive theoretization inflicts serious damages to modern science and results in a huge waste of efforts and resources as well as the emergence of stray trends and bogus scientific theories inside and outside the main stream of science.
In this paper of "The Epistemology of Contemporary Physics" series we investigate Newton's third ... more In this paper of "The Epistemology of Contemporary Physics" series we investigate Newton's third law and discuss and analyze its epistemological significance from some aspects with special attention to its relation to the principle of conservation of linear and angular momentum. The main issue in this investigation is the potential violations of this law according to the claims made in the literature of mainstream physics. This issue may cast a shadow on the validity of classical mechanics, and its Newtonian formulation in particular, formally and epistemologically and could have important implications and consequences on contemporary physics in general. However, what is more important about this issue from our perspective is the lack of clarity, comprehensibility and coherence in the investigation and analysis of this issue and its implications marked by the absence of appropriate conceptual and epistemological frameworks to deal with this issue properly and systematically. As a result, what we find in the literature is a collection of contradicting views which are mostly based on personal choices and preferences and selective or biased theoretical analysis with the lack of proper experimental verification and substantiation.
In this paper of "The Epistemology of Contemporary Physics" series we investigate the epistemolog... more In this paper of "The Epistemology of Contemporary Physics" series we investigate the epistemological significance and sensibility (and hence interpretability and interpretation) of classical mechanics in its Newtonian and non-Newtonian formulations. As we will see, none of these formulations provide a clear and consistent framework for understanding the physics which they represent and hence they all represent valid formalism without proper epistemology or sensible interpretation.
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. 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 are general notes on tensor calculus originated from a collection of personal notes which I... more These are general notes on tensor calculus originated from a collection of personal notes which I prepared some time ago for my own use and reference when I was studying the subject. I decided to put them in the public domain hoping they may be beneficial to some students in their effort to learn this subject. Most of these notes were prepared in the form of bullet points like tutorials and presentations and hence some of them may be more concise than they should be. Moreover, some notes may not be sufficiently thorough or general. However this should be understandable considering the level and original purpose of these notes and the desire for conciseness. There may also be some minor repetition in some places for the purpose of gathering similar items together, or emphasizing key points, or having self-contained sections and units. These notes, in my view, can be used as a short reference for an introductory course on tensor algebra and calculus. I assume a basic knowledge of calculus and linear algebra with some commonly used mathematical terminology. I tried to be as clear as possible and to highlight the key issues of the subject at an introductory level in a concise form. I hope I have achieved some success in reaching these objectives at least for some of my target audience. The present text is supposed to be the first part of a series of documents about tensor calculus for gradually increasing levels or tiers. I hope I will be able to finalize and publicize the document for the next level in the near future.
We investigate the possibility that the spatial dependency of stress in generalized Newtonian flo... more We investigate the possibility that the spatial dependency of stress in generalized Newtonian flow systems is a function of the applied pressure field and the conduit geometry but not of the fluid rheology. This possibility is well established for the case of a one-dimensional flow through simply connected regions, specifically tubes of circular uniform cross sections and plane thin slits. If it can also be established for the more general case of generalized Newtonian flow through non-circular or multiply connected geometries, such as the two-dimensional flow through conduits of rectangular or elliptical cross sections or the flow through annular circular pipes, then analytical or semi-analytical or highly accurate numerical solutions; regarding stress, rate of strain, velocity profile and volumetric flow rate; for these geometries can be obtained from the stress function, which can be easily obtained from the Newtonian case, in combination with the constitutive rheological relation for the particular non-Newtonian fluid, as done previously for the case of the one-dimensional flow through simply connected regions.
This is the first of a series of papers that we intend to publish about the epistemology of funda... more This is the first of a series of papers that we intend to publish about the epistemology of fundamental physics in its current state. One of the main objectives of these papers is to improve our understanding of fundamental physics (and modern physics in particular) from an epistemological and interpretative perspective (i.e. versus formal perspective). Another main objective is to investigate and assess the merit of searching for a unified physical theory (the so-called "theory of everything") considering the fact that contemporary physics is a collection of theories created and developed by different individuals and groups of scientists in different eras of history reflecting different levels of scientific, philosophical and epistemological development and dealing with largely separate physical phenomena and hence such unification may mean "stitching together" an inhomogeneous collection of theoretical structures which may be clumsy (if not impossible) at least from an epistemological viewpoint.
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
Monthly Notices of the Royal Astronomical Society, Apr 5, 2016
In this paper we compute the collision strengths and their thermally averaged Maxwellian values f... more In this paper we compute the collision strengths and their thermally averaged Maxwellian values for electron transitions between the 15 lowest levels of doubly ionized cobalt, Co 2+ , which give rise to forbidden emission lines in the visible and infrared region of spectrum. The calculations also include transition probabilities and predicted relative line emissivities. The data are particularly useful for analysing the thermodynamic conditions of supernova ejecta.
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
We use a generic and general numerical method to obtain solutions for the flow of generalized New... more We use a generic and general numerical method to obtain solutions for the flow of generalized Newtonian fluids through circular pipes and plane slits. The method, which is simple and robust can produce highly accurate solutions which virtually match any analytical solutions. The method is based on employing the stress, as a function of the pipe radius or slit thickness dimension, combined with the rate of strain function as represented by the fluid rheological constitutive relation that correlates the rate of strain to stress. Nine types of generalized Newtonian fluids are tested in this investigation and the solutions obtained from the generic method are compared to the analytical solutions which are obtained from the Weissenberg-Rabinowitsch-Mooney-Schofield method. Very good agreement was obtained in all the investigated cases. All the required quantities of the flow which include local viscosity, rate of strain, flow velocity profile and volumetric flow rate, as well as shear stress, can be obtained from the generic method. This is an advantage as compared to some traditional methods which only produce some of these quantities. The method is also superior to the numerical meshing techniques which may be used for resolving the flow in these systems. The method is particularly useful when analytical solutions are not available or when the available analytical solutions do not yield all the flow parameters.
The study of flow of non-Newtonian fluids in porous media is very important and serves a wide var... more The study of flow of non-Newtonian fluids in porous media is very important and serves a wide variety of practical applications in processes such as enhanced oil recovery from underground reservoirs, filtration of polymer solutions and soil remediation through the removal of liquid pollutants. These fluids occur in diverse natural and synthetic forms and can be regarded as the rule rather than the exception. They show very complex strain and time dependent behavior and may have initial yield-stress. Their common feature is that they do not obey the simple Newtonian relation of proportionality between stress and rate of deformation. Non-Newtonian fluids are generally classified into three main categories: time-independent whose strain rate solely depends on the instantaneous stress, time-dependent whose strain rate is a function of both magnitude and duration of the applied stress and viscoelastic which shows partial elastic recovery on removal of the deforming stress and usually demonstrates both time and strain dependency. In this article the key aspects of these fluids are reviewed with particular emphasis on single-phase flow through porous media. The four main approaches for describing the flow in porous media are examined and assessed. These are: continuum models, bundle of tubes models, numerical methods and pore-scale network modeling. * In preparing this Appendix, we consulted most of our references. The main ones are [
Monthly Notices of the Royal Astronomical Society, Nov 21, 2014
We provide a data set of emission and recombination coefficients of hydrogen using a κdistributio... more We provide a data set of emission and recombination coefficients of hydrogen using a κdistribution of electron energies rather than the more traditional Maxwell-Boltzmann (MB) distribution. The data are mainly relevant to thin and relatively cold plasma found in planetary nebulae and H II regions. The data set extends the previous data sets provided by Storey and Hummer which were computed using an MB distribution. The data set, which is placed in the public domain, is structured as a function of electron number density, temperature and κ. Interactive FORTRAN 77 and C++ data servers are also provided as an accessory to probe the data and obtain Lagrange-interpolated values for any choice of all three variables between the explicitly computed values.
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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