We study the explicit factorization of 2nr-th cyclotomic polynomials over finite field Fq where q, r are odd with (r, q) = 1. We show that all irreducible factors of 2nr-th cyclotomic polynomials can be obtained easily from irreducible factors of cyclotomic polynomials of small orders. In particular, we obtain the explicit factorization of 2n5-th cyclotomic polynomials over finite fields and co...

We derive a posteriori error estimates for two classes of explicit finite difference schemes for ordinary differential equations. To facilitate the analysis, we derive a systematic reformulation of the finite difference schemes as finite element methods. The a posteriori error estimates quantify various sources of discretization errors, including effects arising from explicit discretization. Th...

Let V be a finite dimensional real vector space, let g be the real span of a finite set of commuting endomorphisms of V , and G = exp g. We study the orbit structure in elements of a finite partition of V into explicit G-invariant connected sets. In particular, we prove that either there is an open conull G-invariant subset of V in which every G-orbit is regular, or there is a G-invariant, conu...

Towers of function fields over a fixed finite field have attracted much attention, specially for the connections with Coding Theory and Cryptography (see [TV], [NX], [Z], [GS2] and [GS3]). Ihara was the first to realize that the so-called Hasse-Weil upper bound was weak if the genus of the function field is large with respect to the cardinality of the finite field (see [Iha]). The first explici...

We calculate the self-energy of the ∆(1232) resonance in a finite volume, using chiral effective field theory with explicit spin-3/2 fields. The calculations are performed up-to-and-including fourth order in the small scale expansion and yield an explicit parameterization of the energy spectrum of the interacting pion-nucleon pair in a finite box in terms of both the quark mass and the box size...

In sheet metal forming processes with complex strain paths, a part is subjected to large plastic deformation. This severe plastic deformation leads to high plastic strain localization zones and subsequent accumulation of those strains. Then internal and superficial micro-defects and in other words ductile damage is created. This damage causes quality problems such as fracture. Therefore, design...

In this article, we conjugate time marching schemes with Finite Differences splittings into low and high modes in order to build fully explicit methods with enhanced temporal stability for the numerical solutions of PDEs. The main idea is to apply explicit schemes with less restrictive stability conditions to the linear term of the high modes equation, in order that the allowed time step for th...

We propose a design methodology for explicit Model Predictive Control (MPC) that guarantees hard constraint satisfaction in the presence of finite precision arithmetic errors. The implementation of complex digital control techniques, like MPC, is becoming increasingly adopted in embedded systems, where reduced precision computation techniques are embraced to achieve fast execution and low power...

For a finite field GF(q) of odd prime power order q, and n > 1, we construct explicitly a sequence of monic irreducible reciprocal polynomials o f degree n2 m (m = 1, 2, 3 . . . . ) over GF(q). It is the analog for fields of odd order of constructions of Wiedemann and of Meyn over GF(2). We also deduce iterated presenn2** tations of GF(q ).

We approximate the solution of initial boundary value problems for nonlinear parabolic equations. In space we discretize by finite element methods. The discretization in time is based on linear multistep schemes. One part of the equation is discretized implicitly and the other explicitly. The resulting schemes are stable, consistent and very efficient, since their implementation requires at eac...