On a discrete

Stability of additive functional equation on discrete quantum semigroups

We construct  a noncommutative analog of additive functional equations on discrete quantum semigroups and show that this noncommutative functional equation has Hyers-Ulam stability on amenable discrete quantum semigroups. The discrete quantum semigroups that we consider in this paper are in the sense of van Daele, and the amenability is in the sense of Bèdos-Murphy-Tuset. Our main result genera...

Generalized Jacobian and Discrete Logarithm Problem on Elliptic Curves

Let E be an elliptic curve over the finite field F_{q}, P a point in E(F_{q}) of order n, and Q a point in the group generated by P. The discrete logarithm problem on E is to find the number k such that Q = kP. In this paper we reduce the discrete logarithm problem on E[n] to the discrete logarithm on the group F*_{q} , the multiplicative group of nonzero elements of Fq, in the case where n | q...

A general construction of Reed-Solomon codes based on generalized discrete Fourier transform

In this paper, we employ the concept of the Generalized Discrete Fourier Transform, which in turn relies on the Hasse derivative of polynomials, to give a general construction of Reed-Solomon codes over Galois fields of characteristic not necessarily co-prime with the length of the code. The constructed linear codes  enjoy nice algebraic properties just as the classic one.

On the Discrete Cumulative Residual Entropy

Calculation of the Induced Charge Distribution on the Surface of a Metallic Nanoparticle Due to an Oscillating Dipole Using Discrete Dipole Approximation method

In this paper, the interaction between an oscillating dipole moment and a Silver nanoparticle has been studied. Our calculations are based on Mie scattering theory and discrete dipole approximation(DDA) method.At first, the resonance frequency due to excitingthe localized surface plasmons has been obtained using Mie scattering theory and then by exciting a dipole moment in theclose proximity of...

On discrete a-unimodal and a-monotone distributions

Unimodality is one of the building structures of distributions that like skewness, kurtosis and symmetry is visible in the shape of a function. Comparing two different distributions, can be a very difficult task. But if both the distributions are of the same types, for example both are unimodal, for comparison we may just compare the modes, dispersions and skewness. So, the concept of unimodali...