IMath Webinar Series: Dr. Somphong Jitman and Gervy Marie Angeles
You’re all invited to attend the 3rd seminar of our webinar series on Monday, April 17, 2023 at 1:30 PM. Our speakers are Dr. Somphong Jitman (from Silpakorn University, Thailand, hosted by the Coding and Number Theory Research Group) and Ms. Gervy Marie Angeles (from the Modelling and Applications Research Group).
Dr. Somphong Jitman (Department of Mathematics, Silpakorn University, Thailand, hosted by the Coding and Number Theory Group)
Title: Special Divisors of \(x^n-1\) over finite fields and applications in Coding Theory
Abstract: Self-reciprocal and self-conjugate-reciprocal polynomials over finite fields have been of interest due to their rich algebraic structures and wide applications. In this talk, we focus on self-reciprocal irreducible monic (SRIM) and self-conjugate-reciprocal irreducible monic (SCRIM) divisors of \(x^n-1\) over finite fields. Characterizations and constructions of such divisors are given together with their enumeration formulas. As applications, various properties of complementary dual and self-dual cyclic and negacyclic codes over finite fields are discussed in terms of SRIM and SCRIM factors of \(x^n-1\).
Gervy Marie Angeles (Modelling and Applications Group)
Title: Rigid filaments with pressure and tension of center-of-mass curve
Abstract: We consider a generalized gradient flow for rigid filaments whose interaction is generated by electrostatic energy. It can be considered as a model for the motion of rods in a friction-dominated regime with a local Coulomb force leading to a pressure-like repulsion. With the assumption of a quasi-stationary force balance, we minimise a potential energy containing contributions from filament-to-surface adhesions, pressure between filaments, tension of the center-of-mass curve, and prescribed external forces.
The opposing effects of pressure and tension create a pitchfork bifurcation away from the trivial and stationary equilibrium when a stiffness parameter reaches a critical value. This bifurcation produces a nontrivial state with a non-vanishing velocity which allows translocation of the filament strip. Filament configurations in trivial side-by-side with the nontrivial equilibrium are illustrated.