Bistable space-time discrete systems commonly possess a large variety of stable stationary solutions with periodic profile. In this context, it is natural to ask about the fate of trajectories composed of interfaces between steady configurations with periodic pattern and in particular, to study their propagation as traveling fronts. Here, we investigate such fronts in piecewise affine bistable ...

The classical (m, k)-Landen transform Fm,k is a self-map of the field of rational functions C(z) obtained by forming a weighted average of a rational function over twists by m’th roots of unity. Identifying the set of rational maps of degree d with an affine open subset of P, we prove that Fm,0 induces a dominant rational self-map Rd,m,0 of P 2d+1 of algebraic degree m, and for 1 ≤ k < m, the t...

Let S be a finite generating set of a torsion-free, nilpotent group G. We show that every automorphism of the Cayley graph Cay(G;S) is affine. (That is, every automorphism of the graph is obtained by composing a group automorphism with multiplication by an element of the group.) More generally, we show that if Cay(G1;S1) and Cay(G2;S2) are connected Cayley graphs of finite valency on two nilpot...

The central objects of study in this thesis are affine difference algebraic groups. Similar to the case of affine algebraic groups, these groups can all be realized as subgroups of some general linear group defined by algebraic difference equations. However, the defining equations here are not simply polynomials in the matrix entries but difference polynomials, i.e., the defining equations invo...

We propose a discriminative fuzzy clustering maximum a posterior linear regression (DFCMAPLR) model adaptation approach to compensate the acoustic mismatch due to speaker variability. The DFCMAPLR approach adopts the MAP criterion and a discriminative objective function to estimate shared affine transform and fuzzy weight sets, respectively. Then, through a linear combination of the calculated ...

Abstract In this paper, we classify the three-dimensional partially hyperbolic diffeomorphisms whose stable, unstable, and central distributions $E^s$ , $E^u$ $E^c$ are smooth, such that $E^s\oplus E^u$ is a contact distribution, non-wandering set equals whole manifold. We prove up to finite quotient or power, they smoothly conjugated either time-map of an algebraic contact-Anosov flow, affine ...

Proof. We will calculate the integral closure of A inside K. We begin with a more general discussion. Suppose C is an irreducible, affine curve, that is, C is some irreducible affine variety of dimension 1. Let A be the ring of regular functions on C, so that A is a noetherian domain of Krull dimension 1. Localization preserves the noetherian condition, as well as the domain condition. Thus, th...

Given a divisor D on a tropical curve Γ, we show that reduced divisors define an integral affine map from the tropical curve to the complete linear system |D|. This is done by providing an explicit description of the behavior of reduced divisors under infinitesimal modifications of the base point. We consider the cases where the reduced-divisor map defines an embedding of the curve into the lin...

Above Planck energies, the spacetime might become non–Riemannian, as it is known fron string theory and inflation. Then geometries arise in which nonmetricity and torsion appear as field strengths, side by side with curvature. By gauging the affine group, a metric affine gauge theory emerges as dynamical framework. Here, by using the harmonic map ansatz, a new class of multipole like solutions ...