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In the paper we describe derivations of some classes of Leibniz algebras. It is shown that any derivation of a simple Leibniz algebra can be written as a combination of three derivations. Two of these ingredients are a Lie algebra…
Instantaneous derivation of the Thomas precession with only basic vector calculus.
We have designed, built and operated a physical pendulum which allows one to demonstrate experimentally the behaviour of the pendulum under any equation of motion for such a device for any initial conditions. All parameters in the equation…
L. Weinstein's brilliant short proof of de Branges's Theorem is made even shorter by using computer algebra.
"Mathematicians, like physicists, are pushed by a strong fascination. Research in mathematics is hard, it is intellectually painful even if it is rewarding, and you would not do it without some strong urge." [D. Ruelle]. We shall give some…
A method based on the symbolic methods of the classical invariant theory is developed for a representation of elements of kernel of Weitzenb\"ok derivations.
The looping pendulum is a simple physical system consisting of two masses connected by a string that passes over a rod. We derive equations of motion for the looping pendulum using Newtonian mechanics, and show that these equations can be…
In this paper, we introduce a generalization of derivations. Using these so-called secondary derivations, along with an analogue of Connes' Long Exact Sequence, we are able to provide computations in low dimension for the secondary…
We propose an Euclidean geometric representation for the classical detection theory. The proposed representation is so generic that can be employed to almost all communication problems. The hypotheses and observations are mapped into R^N in…
We consider simple modules over the McConnell--Pettit algebras. We show that both induction and contraction yield simple modules for the extremes of the global dimension.
It was shown that pedal coordinates provides natural framework in which to study force problems of classical mechanics in the plane. A trajectory of a test particle under the influence of central and Lorentz-like forces can be translated…
In this paper we propose a very specific educational challenge that teachers can use to motivate ambitious and enthusiastic mathematics students who have mastered basic trigonometry and trig functions. The objective is to lead students to a…
We propose a simple low-energy classical experiment in which the effects of noncommutativity can be clearly separated from commutative physics. The ensuing bound on the noncommutative scale is remarkable, especially in view of its…
In this paper we give the outline of a lecture given to undergraduate students aiming at understanding why physicists are so much interested in the Higgs boson. The lecture has been conceived for students not yet familiar with advanced…
Scientific calculations involving multiplication, division, exponents, inverse exponents of real numbers, geometric mean, reciprocal, Euler number, logarithm, and antilogarithm are generally carried out using battery operated electronic…
Several recent results concerning Hom-Leibniz algebra are reviewed, the notion of symmetric Hom-Leibniz superalgebra is introduced and some properties are obtained. Classification of 2-dimensional Hom-Leibniz algebras is provided. Centroids…
We develop differential calculus and gauge theory on a finite set G. An elegant formulation is obtained when G is supplied with a group structure and in particular for a cyclic group. Connes' two-point model (which is an essential…
In this article we discuss an important students' misconception about derivatives, that the expression of the derivative of the function contains the information as to whether the function is differentiable or not where the expression is…
We present a simple and elementary procedure to sketch the tropical conic given by a degree--two homogeneous tropical polynomial. These conics are trees of a very particular kind. Given such a tree, we explain how to compute a defining…
In this paper, we discuss some problems of elementary plane differential geometry and kinematics. Although the results are not new, the consistent use of complex-valued functions (plane curves) of a real variable (parameter) allows to…