Q. Does the Lorentz transformation reduce to the Galilean transformation when the ratio v /c is small? A. No. At least two routes are available to substantiate the negative response. I will first give a direct, algebraic route and then a more sophisticated indirect route. Consider the usual pair of inertial reference frames, the primed frame moving with speed v along the x axis of the unprimed ...

Space-like and time-like invariant space-time intervals are used to analyse measurements of spatial and temporal distances. The former are found to be Lorentz invariant –there is no 'relativistic length contraction', whereas the latter exhibit the experimentally confirmed 'time dilatation' effect, without, however, 'relativity of simultaneity'. It is shown how the spurious predictions of length...

let $g$ be a finite simple graph whose vertices and edges are weighted by two functions. in this paper we shall define and calculate entropy of a dynamical system on weights of the graph $g$, by using the weights of vertices and edges of $g$. we examine the conditions under which entropy of the dynamical system is zero, possitive or $+infty$. at the end it is shown that, for $rin [0,+infty]$, t...

Lorentz invariant supersymmetric deformations of superspaces based on Moyal star product parametrized by Majorana spinor λ a and Ramond grassmannian vector ψ m = − 1 2 (¯ θγ m λ) in the spinor realization [35] are proposed. The map of supergravity background into composite supercoordinates: (B −1 mn , Ψ a m , C ab) ↔ (iψ m ψ n , ψ m λ a , λ a λ b) valid up to the second order corrections in def...

I propose a model of mutually interacting particles on an M -dimensional unit sphere. I derive the dynamics of the particles by extending the dynamics of the Kuramoto–Sakaguchi model. The dynamics include a natural-frequency matrix, which determines the motion of a particle with no external force, and an external force vector. The position (state variable) of a particle at a given time is obtai...

In order to study the variation of electronic properties, a set of bithiophene derivatives has been ‎developed. Here, the effect of substitution on the aromaticity properties of some cyclic ‎bithiophene derivative compounds was investigated using theoretical calculations. Calculations ‎were performed at B3LYP/6-31+G (d,p) level; and calculated properties included energy, dipole ‎moment, total c...