We investigate the covering problem in RT spaces induced by the RosenbloomTsfasman metric, extending the classical covering problem in Hamming spaces. Some connections between coverings in RT spaces and coverings in Hamming spaces are derived. Several lower and upper bounds are established for the smallest cardinality of a covering code in an RT space, generalizing results by Carnielli, Chen an...

In 1914 Lebesgue defined a ‘universal covering’ to be a convex subset of the plane that contains an isometric copy of any subset of diameter 1. His challenge of finding a universal covering with the least possible area has been addressed by various mathematicians: Pál, Sprague and Hansen have each created a smaller universal covering by removing regions from those known before. However, Hansen’...

Our main observation concerns closed geodesics on surfaces M with a smooth Finsler metric, i.e. a function F : TM → [0,∞) which is a norm on each tangent space TpM , p ∈ M , which is smooth outside of the zero section in TM , and which is strictly convex in the sense that Hess(F ) is positive definite on TpM \ {0}. One calls a Finsler metric F symmetric if F (p,−v) = F (p, v) for all v ∈ TpM . ...

We construct a maximal function associated with family of skewed cylinders. These cylinders, which are defined as tubular neighborhoods trajectories mollified flow, appear in the study fluid equations such Navier-Stokes and Euler equations. define subordinate to these show it is weak type $(1, 1)$ strong $(p, p)$ by covering lemma. As an application, we give alternative proof for higher derivat...

We present the near-Maximal Algorithm for Poisson-disk Sampling (nMAPS) to generate point distributions variable resolution Delaunay triangular and tetrahedral meshes in two three-dimensions, respectively. nMAPS consists of principal stages. In first stage, an initial distribution is produced using a cell-based rejection algorithm. second holes sample are detected efficient background grid fill...

Maximal ν e oscillations, Borexino and smoking guns... Abstract We examine the maximal ν e → ν s and ν e → ν µ,τ oscillation solutions to the solar neutrino problem. These solutions lead to roughly a 50% solar flux reduction for the large parameter range 3 × 10 −10 < ∼ δm 2 /eV 2 < ∼ 10 −3. It is known that the earth regeneration effect may cause a potentially large night-day asymmetry even for...

The orbital diameter of a primitive permutation group is the maximal its graphs. There has been lot interest in bounds for diameter. In this paper we provide explicit on diameters groups simple diagonal type. As consequence obtain classification with less than or equal to 4. part this, classify all finite covering number and conjugacy width at most 3. We also prove some general Lie