相关论文: Nonuniform Thickness and Weighted Distance

We develop a theory for the eigenvalue density of arbitrary non-Hermitian Euclidean matrices. Closed equations for the resolvent and the eigenvector correlator are derived. The theory is applied to the random Green's matrix relevant to wave…

We study infinite Euclidean distance discriminants of algebraic varieties, defined as the loci of data points whose fibers under the second projection from the Euclidean distance correspondence are positive-dimensional. In particular, these…

We investigate the topology and geometry of compact submanifolds in space forms of nonnegative curvature that satisfy a lower bound on the sectional curvature, depending only on the length of the mean curvature vector of the immersion. We…

Many known Radon-type transforms of symmetric (radial or zonal) functions are represented by one-dimensional Riemann-Liouville fractional integrals or their modifications. The present article contains new examples of such transforms in the…

The classical isoperimetric inequality can be extended to a general normed plane. In the Euclidean plane, the defect in the isoperimetric inequality can be calculated in terms of the signed areas of some singular sets. In this paper we…

We study the non-embddability property for a class of real hypersurfaces, called real hypersurfaces of involution type, into the sphere in the low codimensional case, by making use of property of a naturally related Gauss curvature. We also…

We discuss the problem of optimizing the distance function from a given point, subject to polynomial constraints. A key algebraic invariant that governs its complexity is the Euclidean distance degree, which pertains to first-order…

In this paper we present a mathematical framework on linking of embeddings of compact topological spaces into Euclidean spaces and separability of linked embeddings under a specific class of dimension reduction maps. As applications of the…

Some geometry on non-singular cubic curves, mainly over finite fields, is surveyed. Such a curve has 9,3,1 or 0 points of inflexion, and cubic curves are classified accordingly. The group structure and the possible numbers of rational…

We consider two well-known classes of unitarization of Born amplitudes of hadron elastic scattering. The standard class, which saturates at the black disk limit includes the standard eikonal representation, while the other class, which goes…

We survey the distributional properties of progressively dilating sets under projection by covering maps, focusing on manifolds of constant sectional curvature. In the Euclidean case, we review previously known results and formulate some…

Non-Euclidean triangle centers can be described using homogeneous coordinates that are proportional to the generalized sines of the directed distances of a given center from the edges of the reference triangle. Identical homogeneous…

We study ordered configuration spaces of $n$ hard discs inside a unit disc, and how the topology changes with the radius $r$ of the hard discs. We describe the full homotopy type of this space for all radii when $n = 4$ and exhibit…

We show a coincidence of index of rigidity of differential equations with irregular singularities on a compact Riemann surface and Euler characteristic of the associated spectral curves which are recently called irregular spectral curves.…

This article introduces and studies the tight approximation property, a property of algebraic varieties defined over the function field of a complex or real curve that refines the weak approximation property (and the known cohomological…

We give a generalization of Thurston's Bounded Image Theorem for skinning maps, which applies to pared 3-manifolds with incompressible boundary that are not necessarily acylindrical. Along the way we study properties of divergent sequences…

In this paper, uniform pointwise regularity estimates for the solutions of conductivity equations are obtained in a unit conductivity medium reinforced by a epsilon-periodic lattice of highly conducting thin rods. The estimates are derived…

An important application of distance geometry to biochemistry studies the embeddings of the vertices of a weighted graph in the three-dimensional Euclidean space such that the edge weights are equal to the Euclidean distances between…

For real projective spaces, (a) the Euclidean immersion dimension, (b) the existence of axial maps, and (c) the topological complexity are known to be three facets of the same problem. But when it comes to embedding dimension, the classical…

Derivation-based differential calculi are of great importance in noncommutative geometry, noncommutative gauge theory and integrable systems. In this paper, we propose the connection and curvature from a class of deformed derivation-based…