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We analyse the geometric properties of the high derivatives of the distance function from a submanifold of the Euclidean space. In particular, we show some relations with the second fundamental form and its covariant derivatives of…
In this paper we give the Bohr-Sommerfeld-Heisenberg quantization of the mathematical pendulum.
We describe a variant of the popular game "Pictionary" based on terms used in elementary and high school physics. We believe that drawing of physical terms helps students develop a deeper understanding of physical concepts behind them, as…
The development of the trigonometric functions in introductory texts usually follows geometric constructions using right triangles or the unit circle. While these methods are satisfactory at the elementary level, advanced mathematics…
These lecture notes are based on [arXiv: math/0702714, 0907.4469, 0907.4470]. We introduce and study basic aspects of non-Euclidean geometries from a coordinate-free viewpoint.
We show how Geophysics may illustrate and thus improve classical Mechanics lectures concerning the study of Coriolis force effects. We are then interested in atmospheric as well as oceanic phenomena we are familiar with, and are for that…
This two-page note gives a non-computational derivation of the dual Steenrod algebra as the automorphisms of the formal additive group. Instead of relying on computational tools like spectral sequences and Steenrod operations, the argument…
We use Herbrand's theorem to give a new proof that Euclid's parallel axiom is not derivable from the other axioms of first-order Euclidean geometry. Previous proofs involve constructing models of non-Euclidean geometry. This proof uses a…
The Jacobi and Weierstrass elliptic functions used to be part of the standard mathematical arsenal of physics students. They appear as solutions of many important problems in classical mechanics: the motion of a planar pendulum (Jacobi),…
The leading idea of the paper is to treat the theorem of Wigner with methods inspired by geometry. The exercise mentionned in the title has two functions: On the one hand it can serve as a pedagogical text in order to make the reader…
Derivations of a noncommutative algebra can be used to construct differential calculi, the so-called derivation-based differential calculi. We apply this framework to a version of the Moyal algebra ${\cal{M}}$. We show that the differential…
Motivated by the general problem of extending the classical theory of holomorphic functions of a complex variable to the case of quater- nion functions, we give a notion of an H-derivative for functions of one quaternion variable. We show…
The main aim of this article is that students, at the basic level of education, gain a quantitative understanding of the size of molecules by performing a simple experiment easily designed within the classroom.
We give a classification of the graded simple modules of cyclotomic quiver Hecke algebras of type A using the diagram calculus of the diagrammatic Cherednik algebra. We also obtain a non-trivial lower bound for the dimension of the simple…
Second part of a didactic sequence of activities on some topics of Astronomy, related mainly with the real shape of the Earth, the gravitational interactions between our planet and other celestial bodies, and the resulting movement of the…
The theory of bi-orthogonal polynomials on the unit circle is developed for a general class of weights leading to systems of recurrence relations and derivatives of the polynomials and their associated functions, and to…
We describe a simple, but effective, method for deriving families of elliptic curves, with high rank, all of whose members have the same torsion subgroup structure.
Lagrangian submanifolds are becoming a very essential tool to generalize and geometrically understand results and procedures in the area of mathematical physics. Here we use general Lagrangian submanifolds to provide a geometric version of…
Non-Newtonian calculus that starts with elementary non-Diophantine arithmetic operations of a Burgin type is applicable to all fractals whose cardinality is continuum. The resulting definitions of derivatives and integrals are simpler from…
The Digamma and Polygamma functions are important tools in mathematical physics, not only for its many properties but also for the applications in statistical mechanics and stellar evolution. In many textbooks is found its develop almost by…