We consider the perturbation of Schwarzschild solution by perimeter action. The asymptotic behaviour at infinity and horizon are calculated analysed in first approximation. is characterised ratio Plank length to radius. It demonstrated that modified theory appear space-time regions radius scale unreachable test particles. These located places where standard gravity has singularities.

We derive area limit laws for the various symmetry classes of staircase polygons on the square lattice, in a uniform ensemble where, for fixed perimeter, each polygon occurs with the same probability. This complements a previous study by Leroux and Rassart, where explicit expressions for the area and perimeter generating functions of these classes have been derived. MSC numbers: 82B41, 05A16, 3...

In this paper we consider an isotropic variant of the BMO-type norm recently introduced in [6]. We prove that, when considering characteristic functions of sets, this norm is related to the perimeter. A byproduct of our analysis is a new characterization of the perimeter of sets in terms of this norm, independent of the theory of distributions.

What is the minimum perimeter of a convex lattice n-gon? This question was answered by Jarník in 1926. We solve the same question, and prove a limit shape result, in the case when perimeter is measured by a (not necessarily symmetric) norm.

BACKGROUND The correlation between the increase in visceral fat and insulin resistance makes the sagittal abdominal diameter and the waist perimeter as potential tools for the prediction of insulin resistance. OBJECTIVE To assess the reproducibility of different measurements of the sagittal abdominal diameter and the waist perimeter and analyze the discriminating power of the measurements whe...

We present an eecient method for the partitioning of rectangular domains into equi-area sub-domains of minimum total perimeter. For a variety of applications in parallel computation, this corresponds to a load-balanced distribution of tasks that minimize interprocessor communication. Our method is based on utilizing, to the maximum extent possible, a set of optimal shapes for sub-domains. We pr...

INTRODUCTION The purpose of this study was to evaluate the alveolar bone dimensions and arch perimeter discrepancy in unilateral palatally impacted canines. METHODS This retrospective split-mouth study reviewed 207 cone-beam computed tomography (CBCT) scans of patients with unilateral or bilateral impacted canines referred for orthodontic treatment. Out of 207 CBCT scans, only 39 scans in whi...