Related papers: Skyrmions, Rational Maps & Scaling Identities

One defines two ways of constructing rational maps derived from other rational maps, in a characteristic-free context. The first introduces the Newton complementary dual of a rational map. One main result is that this dual preserves…

Functions with singularities are notoriously difficult to approximate with conventional approximation schemes. In computational applications, they are often resolved with low-order piecewise polynomials, multilevel schemes, or other types…

Consider a rational map from a projective space to a product of projective spaces, induced by a collection of linear projections. Motivated by the the theory of limit linear series and Abel-Jacobi maps, we study the basic properties of the…

The spherically symmetric hedgehog ansatz used in the description of the skyrmion is believed to be inadequate for the rotational states such as the nucleon (I=J=1/2) and the Delta (I=J=3/2) due to centrifugal forces. We study here a simple…

We prove a new classification result for (CR) rational maps from the unit sphere in some ${\mathbb C}^n$ to the unit sphere in ${\mathbb C}^N$. To so so, we work at the level of Hermitian forms, and we introduce ancestors and descendants.

A key issue for skyrmion dynamics and devices are pinning effects present in real systems. While posing a challenge for the realization of conventional skyrmionics devices, exploiting pinning effects can enable non-conventional computing…

In this paper, we formally investigate two mathematical aspects of Hermite splines which translate to features that are relevant to their practical applications. We first demonstrate that Hermite splines are maximally localized in the sense…

A rational approximation by a ratio of polynomial functions is a flexible alternative to polynomial approximation. In particular, rational functions exhibit accurate estimations to nonsmooth and non- Lipschitz functions, where polynomial…

We study the rational approximation properties of special manifolds defined by a set of polynomials with rational coefficients. Mostly we will assume the case of all polynomials to depend on only one variable. In this case the manifold can…

For each type of number, structures that differ by arbitrary scaling factors and are isomorphic to one another are described. The scaling of number values in one structure, relative to the values in another structure, must be compensated…

This work is motivated by a paper of Davenport and Schmidt, which treats the question of when Dirichlet's theorems on the rational approximation of one or of two irrationals can be improved and if so, by how much. We consider a…

The traditional view in numerical conformal mapping is that once the boundary correspondence function has been found, the map and its inverse can be evaluated by contour integrals. We propose that it is much simpler, and 10-1000 times…

We study how well a real number can be approximated by sums of two or more rational numbers with denominators up to a certain size.

We give a complete characterization of degree two rational maps with potential good reduction over local fields. We show this happens exactly when the map corresponds to an integral point in the moduli space. We detail an algorithm by which…

We prove that we can always construct strongly minimal linearizations of an arbitrary rational matrix from its Laurent expansion around the point at infinity, which happens to be the case for polynomial matrices expressed in the monomial…

In the Skyrme model, atomic nuclei are identified with solitonic configurations. If the pion mass is set to zero, these configurations are spherical shells of energy with a fullerene-like appearance and are well approximated by a simple…

We already saw in [A1] that the space of dynamically marked rational maps can be identified to a subspace of the space of covers between trees of spheres on which there is a notion of convergence that makes it sequentially compact. In the…

Pseudospectra and structured pseudospectra are important tools for the analysis of matrices. Their computation, however, can be very demanding for all but small matrices. A new approach to compute approximations of pseudospectra and…

Let X and Y be curves over a finite field. In this article we explore methods to determine whether there is a rational map from Y to X by considering L-functions of certain covers of X and Y and propose a specific family of covers to…

In this paper we aim to determine the baryon numbers at which the minimal energy Skyrmion has icosahedral symmetry. By comparing polyhedra which arise as minimal energy Skyrmions with the dual of polyhedra that minimize the energy of…