Related papers: Notes on angles and solid angles, in relation with…
This is an expository treatise on the development of the classical geometries, starting from the origins of Euclidean geometry a few centuries BC up to around 1870. At this time classical differential geometry came to an end, and the…
The aim of this paper is i) to argue for the feasibility and fruitfulness of a balance between the phenomenological method seeking intuitive evidence and the axiomatic-deductive method and ii) that there should be a mutual understanding…
We introduce orbifolds from the classical point of view, using charts, and present orbifold versions of elementary objects from Algebraic Topology, such as the fundamental group, coverings and Euler characteristic; Differential…
These lecture notes provide a self-contained introduction to Euler integrals, which are frequently encountered in applications. In particle physics, they arise as Feynman integrals or string amplitudes. Our four selected topics demonstrate…
Partial generalizations of virtual polyhedra theory (sometimes under different names) appeared recently in the theory of torus manifolds. These generalizations look very different from the original virtual polyhedra theory. They are based…
In this paper, the global existence of smooth solution and the long-time asymptotic stability of the equilibrium to vacuum free boundary problem of the spherically symmetric Euler equations with damping and solid core have been obtained for…
We realize specific classical symmetric spaces, like the semi-K\"ahler symmetric spaces discovered by Berger, as cotangent bundles of symmetric flag manifolds. These realizations enable us to describe these cotangent bundles' geodesics and…
This book intends to give the main definitions and theorems in mathematics which could be useful for workers in theoretical physics. It gives an extensive and precise coverage of the subjects which are addressed, in a consistent and…
This is a translation from Latin of E348 'Methodus facilis motus corporum coelestium utcunque perturbatos ad rationem calculi astronomici revocandi', in which Euler develops a method to alleviate the astronomical computations in a typical…
We study a 1D model for the 3D incompressible Euler equations in axisymmetric geometries, which can be viewed as a local approximation to the Euler equations near the solid boundary of a cylindrical domain. We prove the local well-posedness…
We give a simple and self contained introduction to quaternions and their practical usage in dynamics. The rigid body dynamics are presented in full details. In the appendix, some more exotic relations are given that allow to write more…
Expository notes which combine a historical survey of the development of quantum physics with a review of selected mathematical topics in quantization theory (addressed to students that are not complete novices in quantum mechanics). After…
A mostly expository account of old questions about the relationship between polyhedra and topological manifolds. Topics are old topological results, new gauge theory results (with speculations about next directions), and history of the…
We compare several approaches to the history of mathematics recently proposed by Blasjo, Fraser--Schroter, Fried, and others. We argue that tools from both mathematics and history are essential for a meaningful history of the discipline. In…
A solution to the part and whole problem is presented in this paper by using a complex mathematical representation that permits to define the Holon concept as a Basic Unit System that remains itself in spite of complex operations such as…
The purpose of this paper is to present a new proposal to both dualistic and holistic paradigm, by introducing a complex basic unit system mathematical concept in which the quantitative and the qualitative aspects of reality commingle in a…
This is the translation of Leonhard Euler's paper "De Seriebus divergentibus" written in Latin into English. Leonhard Euler defines and discusses divergent series. He is especially interested in the example $1!-2!+3!-\text{etc.}$ and uses…
Dealing with Eugene Wigner's ideas on the measurement procedure in quantum physics and unearthing the controversy that pitted him against supporters of the interpretation of complementarity, I will show how Wigner and his followers…
Since the dawn of civilization, humanity has grappled with the big questions of existence and creation. Modern cosmology seeks to answer some of these questions using a combination of mathematics and measurement. The questions people hope…
Polyhedral surfaces are fundamental objects in architectural geometry and industrial design. Whereas closeness of a given mesh to a smooth reference surface and its suitability for numerical simulations were already studied extensively, the…