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In this paper, we propose a new type of matroids, namely covering matroids, and investigate the connections with the second type of covering-based rough sets and some existing special matroids. Firstly, as an extension of partitions,…

Artificial Intelligence · Computer Science 2012-12-03 Yanfang Liu , William Zhu

We study completions of Archimedean vector lattices relative to any nonempty set of positively-homogeneous functions on finite-dimensional real vector spaces. Examples of such completions include square mean closed and geometric closed…

Functional Analysis · Mathematics 2014-10-23 Gerard Buskes , Chris Schwanke

In this paper we study the asymptotic properties of point configurations that achieve optimal covering of sets lacking smoothness. Our results include the proofs of the existence of asymptotics of best covering and maximal polarization for…

Classical Analysis and ODEs · Mathematics 2022-01-20 A. Anderson , A. Reznikov , O. Vlasiuk , E. White

We show how 3-dimensional, N=2 supersymmetric theories, including super QCD with matter fields, can be put on the lattice with existing techniques, in a way which will recover supersymmetry in the small lattice spacing limit. Residual…

High Energy Physics - Lattice · Physics 2010-11-05 Joshua W. Elliott , Guy D. Moore

We introduce the property of convex normality of rational polytopes and give a dimensionally uniform lower bound for the edge lattice lengths, guaranteeing the property. As an application, we show that if every edge of a lattice d-polytope…

Combinatorics · Mathematics 2011-12-14 Joseph Gubeladze

It is well known that the lattice packing density and the lattice covering density of a triangle are $\frac{2}{3}$ and $\frac{3}{2}$ respectively. We also know that the lattices that attain these densities both are unique. Let…

Metric Geometry · Mathematics 2014-12-22 Kirati Sriamorn

Present paper is devoted to formulation of the system of the master equations of the problem and analytical considerations of the limiting cases, which have an exact solutions (transversal and longitudinal flat bunches, linear approxim-…

Accelerator Physics · Physics 2007-05-23 A. Ts. Amatuni , S. G. Arutunian , M. R. Mailian

Given a point set, mostly a grid in our case, we seek upper and lower bounds on the number of curves that are needed to cover the point set. We say a curve covers a point if the curve passes through the point. We consider such coverings by…

Combinatorics · Mathematics 2025-11-05 Arijit Bishnu , Mathew Francis , Pritam Majumder

This paper concerns the number of lattice points in a circle.

Number Theory · Mathematics 2014-09-18 Sylvain E. Cappell , Julius L. Shaneson

We describe a normal form for a smooth intersection of two quadrics in even-dimensional projective space over an arbitrary field of characteristic 2. We use this to obtain a description of the automorphism group of such a variety. As an…

Algebraic Geometry · Mathematics 2018-04-04 Igor Dolgachev , Alexander Duncan

In this note we give the answer to the question posed by V. N. Dubinin concerning covering properties of complex polynomials

Numerical Analysis · Mathematics 2014-10-27 Alexey Solyanik

We construct lattice actions for a variety of (2,2) supersymmetric gauge theories in two dimensions with matter fields interacting via a superpotential.

High Energy Physics - Lattice · Physics 2010-02-03 Michael G. Endres , David B. Kaplan

We study the Fourier transforms of indicator functions of some special high-dimensional finite type domains and obtain estimates of the associated lattice point discrepancy.

Number Theory · Mathematics 2015-12-17 Jingwei Guo

This paper is concerned with analysis on metric spaces in a variety of settings and with several kinds of structure.

Classical Analysis and ODEs · Mathematics 2007-05-23 Stephen Semmes

This article discusses various methods of representing and manipulating arbitrary coverage information in two dimensions, with a focus on space- and time-efficiency when processing such coverages, storing them on disk, and transmitting them…

Instrumentation and Methods for Astrophysics · Physics 2015-08-19 Martin Reinecke , Eric Hivon

We study lattice point visibility along polynomial lines of sight and prove the Visibility Density Conjecture of Chaubey and Pandey for a large class of polynomials.

Number Theory · Mathematics 2026-04-29 Abraham Lobsenz , Tristan Phillips

In this paper we are concerned with three lattice problems: the lattice packing problem, the lattice covering problem and the lattice packing-covering problem. One way to find optimal lattices for these problems is to enumerate all finitely…

Metric Geometry · Mathematics 2008-09-26 Achill Schuermann , Frank Vallentin

We present filling as a type of spatial subdivision problem similar to covering and packing. Filling addresses the optimal placement of overlapping objects lying entirely inside an arbitrary shape so as to cover the most interior volume. In…

Soft Condensed Matter · Physics 2015-06-04 Carolyn L. Phillips , Joshua A. Anderson , Greg Huber , Sharon C. Glotzer

We study genus one curves that arise as 2-, 3- and 4-coverings of elliptic curves. We describe efficient algorithms for testing local solubility and modify the classical formulae for the covering maps so that they work in all…

Number Theory · Mathematics 2011-03-28 Tom Fisher , Graham Sills

We list up to M\"obius equivalence all possible degrees and embedding dimensions of real surfaces that are covered by at least two pencils of circles, together with the number of such pencils. In addition, we classify incidences between the…

Algebraic Geometry · Mathematics 2024-09-16 Niels Lubbes