This paper is an exploration of relationships between the Jones polynomial and quantum computing. We discuss the structure of the Jones polynomial in relation to representations of the Temperley Lieb algebra, and give an example of a unitary representation of the braid group. We discuss the evaluation of the polynomial as a generalized quantum amplitude and show how the braiding part of the eva...

‎This paper obtains the exact solutions of the wave equation as a second-order partial differential equation (PDE)‎. ‎We are going to calculate polynomial and non-polynomial exact solutions by using Lie point symmetry‎. ‎We demonstrate the generation of such polynomial through the medium of the group theoretical properties of the equation‎. ‎A generalized procedure for polynomial solution is pr...

Cloud computing platforms have created the possibility for computationally limited users to delegate demanding tasks strong but untrusted servers. Verifiable algorithms help build trust in such interactions by enabling server provide a proof of correctness his results which user can check very efficiently. In this article, we present doubly-efficient interactive algorithm verifiable polynomial ...

Based on the evaluation at t = −1 of the generating polynomial for the hyperoctahedral group by the number of descents, an observation recently made by Hirzebruch, a new q-secant number is derived by working with the Chow-Gessel q-polynomial involving the flag major index. Using the doubloon combinatorial model we show that this new q-secant number is a polynomial with positive integral coeffic...