In this note, we give the details of how to calculate the parameters of the transformation from ... more In this note, we give the details of how to calculate the parameters of the transformation from STT or local coordinate system to the NTT coordinate system the Tunisian geodetic terrestrial system.
In this paper, we consider the $abc$ conjecture. Assuming the conjecture $c<rad^2(abc)$ is true,... more In this paper, we consider the $abc$ conjecture. Assuming the conjecture $c<rad^2(abc)$ is true, we give the proof of the $abc$ conjecture for $\epsilon \geq 1$. For the case $\epsilon \in ]0,1[$, we consider that the $abc$ conjecture is false, from the proof, we arrive in a contradiction.
In this note, we present another method of passing from geocentric coordinates (X, Y, Z) to geode... more In this note, we present another method of passing from geocentric coordinates (X, Y, Z) to geodetic coordinates (φ, λ, he) with respect to an ellipsoid of revolution with parameters (a, e) where a and e are the semi-major axis and the first eccentricity, respectively. Résumé. La méthode de passage des coordonnées géocentriques (X, Y, Z) par rapportà un système géodésique donné aux coordonnées géodésiques (φ, λ, he), traitée dans nos précédentes publications est la méthode itérative (A. Ben Hadj Salem,[1,2,3]). Dans cette note, on présente une méthode directe de passage (X, Y, Z) aux coordonnées (φ, λ, he).
In this paper, we consider the abc conjecture. Assuming that the conjecture c < rad^{1.63}(abc) i... more In this paper, we consider the abc conjecture. Assuming that the conjecture c < rad^{1.63}(abc) is true, we give the proof that the abc conjecture is true.
In this note, we give the proof of one propriety of the UTM plane representation.
Résumé Dans ce... more In this note, we give the proof of one propriety of the UTM plane representation. Résumé Dans cette note, on donne une démonstration d'une propriété de la représentation plane UTM.
Abstract: In this note, we give the list of all my scientific papers (except some papers) that I ... more Abstract: In this note, we give the list of all my scientific papers (except some papers) that I have submitted to the sites Vixra.org, Academia.edu and Researchgate.net since August 2015. Résumé: Dans cette note, je donne la liste de toutes mes publications scientifiques (sauf quelques exceptions) que j'ai soumises aux sites Vixra.org, Academia.edu et Researchgate.net depuis août 2015.
In this fascicle, we give some complementary elements concerning the theory of surfaces like the ... more In this fascicle, we give some complementary elements concerning the theory of surfaces like the lines of curvature, the asymptotic lines.
Dans cette note version2, on présente la transformation de passage d'un système géodésique à un a... more Dans cette note version2, on présente la transformation de passage d'un système géodésique à un autre système géodésique dite de Moldensky-Badekas à sept paramètres en montrant comment déterminer les 7 paramètres par la méthode des moindres carrés et les calculer numériquement suivant le nombre des paramètres 4, 5 ou 7.
Dans cette note, on présente la transformation de passage d'un système géodésique à un autre syst... more Dans cette note, on présente la transformation de passage d'un système géodésique à un autre système géodésique dite de Moldensky-Badekas à sept paramètres en montrant comment déterminer les 7 paramètres par la méthode des moindres carrés et les calculer numériquement suivant le nombre des paramètres 4, 5 ou 7.
In 1859, Georg Friedrich Bernhard Riemann had announced the following conjecture, called Riemann ... more In 1859, Georg Friedrich Bernhard Riemann had announced the following conjecture, called Riemann Hypothesis : The nontrivial roots (zeros) s=\sigma+it of the zeta function, defined by: \zeta(s) = \sum_{n=1}^{+\infty}\frac{1}{n^s}, for \Re(s)>1 have real part} \sigma= 1/2. In this note, I give the proof that \sigma=1/2 using an equivalent statement of the Riemann Hypothesis concerning the Dirichlet \eta function.
Dans cette note, on présente la transformation de passage d'un système géodésique à un autre syst... more Dans cette note, on présente la transformation de passage d'un système géodésique à un autre système géodésique dite de Bursa-Wolf à sept paramètres en montrant comment déterminer les 7 paramètres par la méthode des moindres carrés et les calculer numériquement suivant le nombre des paramètres 4,5 ou 7.
In 1859, Georg Friedrich Bernhard Riemann had announced the following conjecture, called Riemann ... more In 1859, Georg Friedrich Bernhard Riemann had announced the following conjecture, called Riemann Hypothesis : The nontrivial roots (zeros) s = σ + it of the zeta function, defined by: ζ(s) = \sum^{+∞}_ n=1/n^s , for ℜ(s) > 1 have real part σ = 1/2. In this note, I give the proof that σ = 1/2 using an equivalent statement of the Riemann Hypothesis concerning the Dirichlet η function.
A l'occasion du démarrage du Projet " Système Tunisien des Informations Foncières Tunisien, (TLIS... more A l'occasion du démarrage du Projet " Système Tunisien des Informations Foncières Tunisien, (TLIS)", nous avons tenu à rappeler quelques éléments historiques de la Géodésie Tunisienne depuis sa mise en place et décrire en détail les systèmes géodésiques terrestres et spatiaux qui ont été utilisés depuis.
In this note, we give the details of how to calculate the parameters of the transformation from ... more In this note, we give the details of how to calculate the parameters of the transformation from STT or local coordinate system to the NTT coordinate system the Tunisian geodetic terrestrial system.
In this paper, we consider the $abc$ conjecture. Assuming the conjecture $c<rad^2(abc)$ is true,... more In this paper, we consider the $abc$ conjecture. Assuming the conjecture $c<rad^2(abc)$ is true, we give the proof of the $abc$ conjecture for $\epsilon \geq 1$. For the case $\epsilon \in ]0,1[$, we consider that the $abc$ conjecture is false, from the proof, we arrive in a contradiction.
In this note, we present another method of passing from geocentric coordinates (X, Y, Z) to geode... more In this note, we present another method of passing from geocentric coordinates (X, Y, Z) to geodetic coordinates (φ, λ, he) with respect to an ellipsoid of revolution with parameters (a, e) where a and e are the semi-major axis and the first eccentricity, respectively. Résumé. La méthode de passage des coordonnées géocentriques (X, Y, Z) par rapportà un système géodésique donné aux coordonnées géodésiques (φ, λ, he), traitée dans nos précédentes publications est la méthode itérative (A. Ben Hadj Salem,[1,2,3]). Dans cette note, on présente une méthode directe de passage (X, Y, Z) aux coordonnées (φ, λ, he).
In this paper, we consider the abc conjecture. Assuming that the conjecture c < rad^{1.63}(abc) i... more In this paper, we consider the abc conjecture. Assuming that the conjecture c < rad^{1.63}(abc) is true, we give the proof that the abc conjecture is true.
In this note, we give the proof of one propriety of the UTM plane representation.
Résumé Dans ce... more In this note, we give the proof of one propriety of the UTM plane representation. Résumé Dans cette note, on donne une démonstration d'une propriété de la représentation plane UTM.
Abstract: In this note, we give the list of all my scientific papers (except some papers) that I ... more Abstract: In this note, we give the list of all my scientific papers (except some papers) that I have submitted to the sites Vixra.org, Academia.edu and Researchgate.net since August 2015. Résumé: Dans cette note, je donne la liste de toutes mes publications scientifiques (sauf quelques exceptions) que j'ai soumises aux sites Vixra.org, Academia.edu et Researchgate.net depuis août 2015.
In this fascicle, we give some complementary elements concerning the theory of surfaces like the ... more In this fascicle, we give some complementary elements concerning the theory of surfaces like the lines of curvature, the asymptotic lines.
Dans cette note version2, on présente la transformation de passage d'un système géodésique à un a... more Dans cette note version2, on présente la transformation de passage d'un système géodésique à un autre système géodésique dite de Moldensky-Badekas à sept paramètres en montrant comment déterminer les 7 paramètres par la méthode des moindres carrés et les calculer numériquement suivant le nombre des paramètres 4, 5 ou 7.
Dans cette note, on présente la transformation de passage d'un système géodésique à un autre syst... more Dans cette note, on présente la transformation de passage d'un système géodésique à un autre système géodésique dite de Moldensky-Badekas à sept paramètres en montrant comment déterminer les 7 paramètres par la méthode des moindres carrés et les calculer numériquement suivant le nombre des paramètres 4, 5 ou 7.
In 1859, Georg Friedrich Bernhard Riemann had announced the following conjecture, called Riemann ... more In 1859, Georg Friedrich Bernhard Riemann had announced the following conjecture, called Riemann Hypothesis : The nontrivial roots (zeros) s=\sigma+it of the zeta function, defined by: \zeta(s) = \sum_{n=1}^{+\infty}\frac{1}{n^s}, for \Re(s)>1 have real part} \sigma= 1/2. In this note, I give the proof that \sigma=1/2 using an equivalent statement of the Riemann Hypothesis concerning the Dirichlet \eta function.
Dans cette note, on présente la transformation de passage d'un système géodésique à un autre syst... more Dans cette note, on présente la transformation de passage d'un système géodésique à un autre système géodésique dite de Bursa-Wolf à sept paramètres en montrant comment déterminer les 7 paramètres par la méthode des moindres carrés et les calculer numériquement suivant le nombre des paramètres 4,5 ou 7.
In 1859, Georg Friedrich Bernhard Riemann had announced the following conjecture, called Riemann ... more In 1859, Georg Friedrich Bernhard Riemann had announced the following conjecture, called Riemann Hypothesis : The nontrivial roots (zeros) s = σ + it of the zeta function, defined by: ζ(s) = \sum^{+∞}_ n=1/n^s , for ℜ(s) > 1 have real part σ = 1/2. In this note, I give the proof that σ = 1/2 using an equivalent statement of the Riemann Hypothesis concerning the Dirichlet η function.
A l'occasion du démarrage du Projet " Système Tunisien des Informations Foncières Tunisien, (TLIS... more A l'occasion du démarrage du Projet " Système Tunisien des Informations Foncières Tunisien, (TLIS)", nous avons tenu à rappeler quelques éléments historiques de la Géodésie Tunisienne depuis sa mise en place et décrire en détail les systèmes géodésiques terrestres et spatiaux qui ont été utilisés depuis.
In this fascicle, we give elements of the Theory of Errors for Technical Assistants working in th... more In this fascicle, we give elements of the Theory of Errors for Technical Assistants working in the field of surveying and topography.
This article is a numerical version of the first chapter of the long paper of Henri Poincaré " Th... more This article is a numerical version of the first chapter of the long paper of Henri Poincaré " The Three-Body Problem and the Equations of Dynamics " published by the celebrate journal Acta Mathematica (Vol.13, n • 1 − 2, 1889), created by the Swedish mathematician Gösta Mittag-Leffler in 1882, and he was the Editor-in-Chief. The new version kept the original text with some minimal changes and adding the bibliography which summarizes all the references cited in the article.
In this note, we give the expression of the tolerance of the closure of the horizontal angles of ... more In this note, we give the expression of the tolerance of the closure of the horizontal angles of a plane triangle and its numerical estimation for an equilateral triangle.
In this paper, we consider the abc conjecture. Firstly, we give an elementary proof the conjectur... more In this paper, we consider the abc conjecture. Firstly, we give an elementary proof the conjecture c < rad^ 2 (abc). Secondly, the proof of the abc conjecture is given for \epsilon≥ 1, then for \epsilon ∈]0, 1[. We choose the constant K(\epsilon) as K(\epsilon) = e^( 1/(\epsilon^2)). Some numerical examples are presented.
In this paper, from a, b, c positive integers relatively prime with c = a + b, we consider a boun... more In this paper, from a, b, c positive integers relatively prime with c = a + b, we consider a bounded of c depending of a, b, then we do a choice of K(\epsilon) and finally we obtain that the ABC conjecture is true. Four numerical examples confirm our proof.
In this paper, supposing that Beal conjecture is true, we give a complete proof of the ABC conjec... more In this paper, supposing that Beal conjecture is true, we give a complete proof of the ABC conjecture. We consider that Beal conjecture is false ⇒ we arrive that the ABC conjecture is false. Then taking the negation of the last statement, we obtain: ABC conjecture is true ⇒ Beal conjecture is true. But, if the Beal conjecture is true, then we deduce that the ABC conjecture is true.
Lors de la réduction des distances à la surface de l’ellipsoïde de référence, on utilise une val... more Lors de la réduction des distances à la surface de l’ellipsoïde de référence, on utilise une valeur moyenne R du rayon terrestre dans la formule passant de DP la distance suivant la pente à D0 la distance corde au niveau zéro. Dans cette note, on évalue l’erreur sur la distance en utilisant le rayon terrestre défini par la formule d’Euler en tenant compte de l’azimut de la direction de la distance.
This monograph presents the last version (4.) of the proofs of 4 important conjectures in the fie... more This monograph presents the last version (4.) of the proofs of 4 important conjectures in the field of the number theory, namely: - Beal's conjecture.\newline - The Riemann Hypothesis. - The $c<R^{1.63}$ conjecture is true. - The $abc$ conjecture is true. We give the details of the different proofs.
It is a tribute to the memory of my professor of geodesy Jacques Le Menestrel. We give a numerica... more It is a tribute to the memory of my professor of geodesy Jacques Le Menestrel. We give a numerical version of the two first chapters of his booklet "Dynamical Geodesy". It is part of his complete geodesy course, taught in the 70s of the last century, at the Ecole Nationale des Sciences Géographiques (ENSG), France.
This report contains a collection of exams and subjects of mathematics and physics for competitiv... more This report contains a collection of exams and subjects of mathematics and physics for competitive entrance to the Grandes Ecoles as well as some exams of the Faculty of Sciences of Tunis. I had passed some of these exams throughout my student life since September 1973.
This monograph (version 3, December 2022) presents the proofs of 4 important conjectures in the f... more This monograph (version 3, December 2022) presents the proofs of 4 important conjectures in the field of number theory: - The Beal's conjecture (update of the proof).
This monograph presents the proofs of 4 important conjectures in the field of number theory:
-... more This monograph presents the proofs of 4 important conjectures in the field of number theory:
From the lectures for an advanced course on celestial mechanics which Prof. Richard Moeckel gave... more From the lectures for an advanced course on celestial mechanics which Prof. Richard Moeckel gave in Trieste in 1994 on the topic - \textbf{\textit{Central configurations of the n-body problem}} - that was one of his favorites, I have decided to develop a part of it as an introduction course for the undergraduate students where I have added more details (gray boxes) of the proofs to be understood by undergraduate students.
It is based on the handwritten notes from the 1994 Trieste course. Part I of the notes concerns 3 chapters :
- chapter 1: introduction,
- chapter 2: the two-body problem,
- chapter 3: special solutions to the $n$ body problem. \\
From the lectures for an advanced course on celestial mechanics which Prof. Richard Moeckel gave... more From the lectures for an advanced course on celestial mechanics which Prof. Richard Moeckel gave in Trieste in 1994 on the topic - Central configurations of the n-body problem - that was one of his favorites, I have decided to develop a part of it as an introduction course for the undergraduate students where I have added more details (gray boxes) of the proofs to be understood by undergraduate students.
It is based on the handwritten notes from the 1994 Trieste course. Part I of the notes concerns 3 chapters : - chapter 1: introduction, - chapter 2: the two-body problem, - chapter 3: special solutions to the n body problem.
This monograph presents the proofs of 4 important conjectures in the field of number theory:
- ... more This monograph presents the proofs of 4 important conjectures in the field of number theory: - The Beal's conjecture. - The Riemann Hypothesis. - The $c<R^{1.63}$ Conjecture. - The $abc$ conjecture is true.
The purpose of this paper is to give complete proof of Beal's conjecture. Our idea is to construc... more The purpose of this paper is to give complete proof of Beal's conjecture. Our idea is to construct a polynomial $P(x)$ of order three having as roots $A^m, B^n$ and $-C^l$. The paper is organized as follows. In chapter 1, we begin with the trivial case where $A^m=B^n$. Then we consider the polynomial $P(x)=(x-A^m)(x-B^n)(x+C^l)=x^3-px+q$. We express the three roots of $P(x)=x^3-px+q=0$ in function of two parameters $p,\theta$ that depend of $A^m,B^n,C^l$. Chapter 2 is a preamble of the proof of the main theorem. We find the expression of $A^{2m}$ equal to $\ds \frac{4p}{3}cos^2\frac{\theta}{3}$. As $A^{2m}$ is an integer, it follows that $\ds cos^2\frac{\theta}{3}$ must be written as $\ds \frac{a}{b}$ where $a,b$ are two positive coprime integers. We discuss the conditions of divisibility of $p,a,b$ so that the expression of $A^{2m}$ is an integer. Depending on each individual case, we obtain that $A,B,C$ have or do have not a common factor. The chapter 3 treats the hypothesis $3|a$ and $b|4p$. We study the second hypothesis $3|p$ and $b|4p$ in chapter 4. Finally, we present three numerical examples and the conclusion in chapter 5.
This monograph presents a course of mathematical cartography for engineers including essentially ... more This monograph presents a course of mathematical cartography for engineers including essentially the following elements:
- the definitions of characteristic terms, - the types of plane cartographic representations or "projections", - some known examples, - and a set of problems and exercises for the reader.
In this booklet, we provide the mathematical foundations necessary to follow the training courses... more In this booklet, we provide the mathematical foundations necessary to follow the training courses in geodesy and topography. It is a reminder of the main formulas and knowledge in mathematics for assistants and technical agents.
In this monograph, we present the essential elements of the
mathematical mapping including:
- the... more In this monograph, we present the essential elements of the mathematical mapping including: - the definitions of characteristic terms, - the types of cartographic plane representations, - some known examples, - and a set of problems and exercises for the reader.
In this book, we present the essential elements of the
mathematical mapping including:
- the defi... more In this book, we present the essential elements of the mathematical mapping including: - the definitions of characteristic terms, - the types of cartographic plane representations, - some known examples, - and a set of problems and exercises for the reader.
In this monograph, we present the essential elements of
the mathematical mapping including:
- the... more In this monograph, we present the essential elements of the mathematical mapping including: - the defi nitions of characteristic terms, - the types of cartographic plane representations, - some known examples, - and a set of problems and exercises for the reader.
This monograph presents the proofs of 3 important conjectures in the field of Number theory:
... more This monograph presents the proofs of 3 important conjectures in the field of Number theory: - The Beal's conjecture. - The Riemann Hypothesis. - The $abc$ conjecture.
We give in detail all the proofs. They are under review.
In this book, I present my collection of 23 papers written, with different approaches to try to r... more In this book, I present my collection of 23 papers written, with different approaches to try to resolve the $abc$ conjecture and others conjectures related to it like $c<rad^2(abc)$.
This monograph can give an idea about the advancement of the comprehension of the conjectures related to the problem cited above.
It is a digital version of a manuscript of a course about the theory of errors given by the Engin... more It is a digital version of a manuscript of a course about the theory of errors given by the Engineer-in-Chief Philippe Hottier at the '80s, at the French National School of Geographic Sciences. The course gives the foundation of the method of the least squares for the case of linear models.
Ce sont des papiers sélectionnés parmi les documents et notes techniques que j'ai rédigés au cou... more Ce sont des papiers sélectionnés parmi les documents et notes techniques que j'ai rédigés au cours de mes années de travail à l'OTC dont certains sont relatifs aux cours suivis lors de mes années d'études d'ingénieurs à l'Ecole Nationale des Sciences Géographiques de France. Ces papiers touchent différents thèmes à savoir: - la théorie des erreurs, - la géométrie différentielle de l'ellipsoïde de révolution, - la géodésie et en particulier les systèmes et les réseaux géodésiques, - les représentations planes, - la géophysique, - la géostatistique.
It is the part I of lectures on geodesy given to the technical personnel of the ETAP (Tunisian So... more It is the part I of lectures on geodesy given to the technical personnel of the ETAP (Tunisian Society of Oil Activities).
Dans cette note, on présente la transformation de passage d'un système géodésique à un autre syst... more Dans cette note, on présente la transformation de passage d'un système géodésique à un autre système géodésique dite de Bursa-Wolf à sept paramètres en montrant comment déterminer les 7 paramètres par la méthode des moindres carrés et les calculer numériquement.
This is the part III and the last of the correction of the collection of exams of geodesy and mat... more This is the part III and the last of the correction of the collection of exams of geodesy and mathematical cartography. These exams are from the German school, namely from the Institute of Geodesy of the University of Stuttgart where the eminent professor Erik W. Grafarend (1939-2020) taught geodesy courses and in particular mathematical cartography. This is an opportunity for French-speaking students to share the German methodology.
This is the part II of the correction of the collection of exams of geodesy and mathematical cart... more This is the part II of the correction of the collection of exams of geodesy and mathematical cartography. These exams are from the German school, namely from the Institute of Geodesy of the University of Stuttgart where the eminent professor Erik W. Grafarend (1939-2020) taught geodesy courses and in particular mathematical cartography. This is an opportunity for French-speaking students to share the German methodology.
This is the part I of the correction of the collection of exams of geodesy and mathematical carto... more This is the part I of the correction of the collection of exams of geodesy and mathematical cartography. These exams are from the German school, namely from the Institute of Geodesy of the University of Stuttgart where the eminent professor Erik W. Grafarend (1939-2020) taught geodesy courses and in particular mathematical cartography. This is an opportunity for French-speaking students to share the German methodology. Résumé : Ce papier contient la première partie de la correction la collection choisie d'examens de géodésie et de cartographie mathématique. Ces examens sont de l'école allemande à savoir de l'Institut de Géodésie de l'Université de Stuttgart où l'éminant professeur Erik W. Grafarend (1939-2020) enseignait les cours de géodésie et notamment la cartographie mathématique. C'est l'occasion pour les étudiants francophones de partager la méthodologie allemande.
It is a first course of elements of geostatistics given to the third-year students of the Geomati... more It is a first course of elements of geostatistics given to the third-year students of the Geomatics license of the Faculty of Sciences of Tunis.
Le présent document est une collection de travaux pratiques, d’exercices et de problèmes de géodé... more Le présent document est une collection de travaux pratiques, d’exercices et de problèmes de géodésie pour les étudiants en géodésie cycle des ingénieurs.
This paper is the digital version of a chapter taken from his final thesis entitled "Compensation... more This paper is the digital version of a chapter taken from his final thesis entitled "Compensation of Geodetic Networks". This is chapter V "Methods of Resolution " of the thesis. It concerns the methods for solving the equations of linear systems encountered during compensation calculations for geodetic networks using the least squares method.
This paper is the digital version of a chapter taken from the final thesis of the first author en... more This paper is the digital version of a chapter taken from the final thesis of the first author entitled "Compensation of Geodetic Networks". This is chapter V “Resolution Methods” of the thesis. It concerns the methods for solving the equations of linear systems encountered during compensation calculations for geodetic networks using the least squares method.
Some implications and consequences of the expansion of the universe are examined. In Chapter 1 it... more Some implications and consequences of the expansion of the universe are examined. In Chapter 1 it is shown that this expansion creates grave difficulties for the Hoyle-Narlikar theory of gravitation.
This paper concerns the study of systematic errors in the combination of Doppler data and classic... more This paper concerns the study of systematic errors in the combination of Doppler data and classical terrestrial observations in the adjustment of geodetic networks. This study is taken from the thesis presented in October 1986 for obtaining the Civil Geographic Engineer diploma from the National School of Geographic Sciences (ENSG / IGN France).
This work represent my thesis presented in October 1981 to obtain the diploma of Engineer from th... more This work represent my thesis presented in October 1981 to obtain the diploma of Engineer from the ENSG (French National School of Geographic Sciences, IGN France). The first part of the thesis is concerned with the determination of the equation of the observation of Laplace point in the option of 3D geodesy. The second part is about a study of a 3D model of deformation of geodetic networks that was presented by H.M. Dufour in two dimensions.
In this paper, we give in the part I some elements of geodesy and the geodetic systems used in Ma... more In this paper, we give in the part I some elements of geodesy and the geodetic systems used in Mauritania. The part II contains an introduction to GPS.
This is the summary of the lecture given by Prof. Michel Kasser director of the National School o... more This is the summary of the lecture given by Prof. Michel Kasser director of the National School of Geographical Sciences / IGN France on "New French Geodetic References and GPS Services" at ISET in Nabeul.
With these slides, we want to give high school students an introduction to astronomy and celestia... more With these slides, we want to give high school students an introduction to astronomy and celestial mechanics.
Uploads
Papers by Abdelmajid Ben Hadj Salem
Résumé. La méthode de passage des coordonnées géocentriques (X, Y, Z) par rapportà un système géodésique donné aux coordonnées géodésiques (φ, λ, he), traitée dans nos précédentes publications est la méthode itérative (A. Ben Hadj Salem,[1,2,3]). Dans cette note, on présente une méthode directe de passage (X, Y, Z) aux coordonnées (φ, λ, he).
Résumé Dans cette note, on donne une démonstration d'une propriété de la représentation plane UTM.
Résumé: Dans cette note, je donne la liste de toutes mes publications scientifiques (sauf quelques exceptions) que j'ai soumises aux sites Vixra.org, Academia.edu et Researchgate.net depuis août 2015.
\zeta(s) = \sum_{n=1}^{+\infty}\frac{1}{n^s}, for \Re(s)>1
have real part} \sigma= 1/2. In this note, I give the proof that \sigma=1/2 using an equivalent statement of the Riemann Hypothesis concerning the Dirichlet \eta function.
Résumé. La méthode de passage des coordonnées géocentriques (X, Y, Z) par rapportà un système géodésique donné aux coordonnées géodésiques (φ, λ, he), traitée dans nos précédentes publications est la méthode itérative (A. Ben Hadj Salem,[1,2,3]). Dans cette note, on présente une méthode directe de passage (X, Y, Z) aux coordonnées (φ, λ, he).
Résumé Dans cette note, on donne une démonstration d'une propriété de la représentation plane UTM.
Résumé: Dans cette note, je donne la liste de toutes mes publications scientifiques (sauf quelques exceptions) que j'ai soumises aux sites Vixra.org, Academia.edu et Researchgate.net depuis août 2015.
\zeta(s) = \sum_{n=1}^{+\infty}\frac{1}{n^s}, for \Re(s)>1
have real part} \sigma= 1/2. In this note, I give the proof that \sigma=1/2 using an equivalent statement of the Riemann Hypothesis concerning the Dirichlet \eta function.
- Beal's conjecture.\newline
- The Riemann Hypothesis.
- The $c<R^{1.63}$ conjecture is true.
- The $abc$ conjecture is true.
We give the details of the different proofs.
- The Beal's conjecture (update of the proof).
- The Riemann Hypothesis.
- The $c<R^{1.63}$ conjecture.
- The $abc$ conjecture is true.
We give in detail all the proofs.
- The Beal's conjecture.
- The Riemann Hypothesis.
- The $c<R^{1.63}$ conjecture.
- The $abc$ conjecture is true.
We give in detail all the proofs.
It is based on the handwritten notes from the 1994 Trieste course. Part I of the notes concerns 3 chapters :
- chapter 1: introduction,
- chapter 2: the two-body problem,
- chapter 3: special solutions to the $n$ body problem.
\\
It is based on the handwritten notes from the 1994 Trieste course. Part I of the notes concerns 3 chapters :
- chapter 1: introduction,
- chapter 2: the two-body problem,
- chapter 3: special solutions to the n body problem.
- The Beal's conjecture.
- The Riemann Hypothesis.
- The $c<R^{1.63}$ Conjecture.
- The $abc$ conjecture is true.
We give in detail all the proofs.
- the definitions of characteristic terms,
- the types of plane cartographic representations or "projections",
- some known examples,
- and a set of problems and exercises for the reader.
mathematical mapping including:
- the definitions of characteristic terms,
- the types of cartographic plane representations,
- some known examples,
- and a set of problems and exercises for the reader.
mathematical mapping including:
- the definitions of characteristic terms,
- the types of cartographic plane representations,
- some known examples,
- and a set of problems and exercises for the reader.
the mathematical mapping including:
- the defi nitions of characteristic terms,
- the types of cartographic plane representations,
- some known examples,
- and a set of problems and exercises for the reader.
- The Beal's conjecture.
- The Riemann Hypothesis.
- The $abc$ conjecture.
We give in detail all the proofs. They are under review.
This monograph can give an idea about the advancement of the comprehension of the conjectures related to the problem cited above.
Ces papiers touchent différents thèmes à savoir:
- la théorie des erreurs,
- la géométrie différentielle de l'ellipsoïde de révolution,
- la géodésie et en particulier les systèmes et les réseaux géodésiques,
- les représentations planes,
- la géophysique,
- la géostatistique.
Résumé : Ce papier contient la première partie de la correction la collection choisie d'examens de géodésie et de cartographie mathématique. Ces examens sont de l'école allemande à savoir de l'Institut de Géodésie de l'Université de Stuttgart où l'éminant professeur Erik W. Grafarend (1939-2020) enseignait les cours de géodésie et notamment la cartographie mathématique. C'est l'occasion pour les étudiants francophones de partager la méthodologie allemande.
This is chapter V “Resolution Methods” of the thesis. It concerns the methods for solving the equations of linear systems encountered during compensation calculations for geodetic networks using the least squares method.