Concept

Rectangle

Related publications (17)

A Note on Lenses in Arrangements of Pairwise Intersecting Circles in the Plane

Let F be a family of n pairwise intersecting circles in the plane. We show that the number of lenses, that is convex digons, in the arrangement induced by F is at most 2n - 2. This bound is tight. Furthermore, if no two circles in F touch, then the geometr ...

Electronic Journal Of Combinatorics2024

ON THE INDEPENDENCE NUMBER OF INTERSECTION GRAPHS OF AXIS-PARALLEL SEGMENTS

Jana Tabea Cslovjecsek

We prove that for any triangle-free intersection graph of n axis-parallel line segments in the plane, the independence number alpha of this graph is at least alpha n/4+ohm(root n). We complement this with a construction of a graph in this class satisfying ...

Ottawa2023

Effects of aquifer geometry on seawater intrusion in annulus segment island aquifers

David Andrew Barry, Zhaoyang Luo

Seawater intrusion in island aquifers was considered analytically, specifically for annulus segment aquifers (ASAs), i.e., aquifers that (in plan) have the shape of an annulus segment. Based on the Ghijben–Herzberg and hillslope-storage Boussinesq equation ...

2021

Extremal Eigenvalues Of The Dirichlet Biharmonic Operator On Rectangles

We study the behaviour of extremal eigenvalues of the Dirichlet biharmonic operator over rectangles with a given fixed area. We begin by proving that the principal eigenvalue is minimal for a rectangle for which the ratio between the longest and the shorte ...

2020

Quantifying bacterial structure of aerobic granular sludge using image analysis

Karen Gemayel

This Master’s project entitled ’Quantifying Bacterial Structure of Aerobic Granular Sludge using Image Analysis’ aims to quantitatively describe various aspects of cell activity inside aerobic granular sludge using image analysis. It entails the theory of ...

2019

Bisector Energy and Few Distinct Distances

Frank de Zeeuw

We define the bisector energy E(P) of a set P in R-2 to be the number of quadruples (a, b, c, d) is an element of P-4 such that a, b determine the same perpendicular bisector as c, d. Equivalently, E(P) is the number of isosceles trapezoids determined by P ...

Springer2016

Hexagonal Patterning of the Insect Compound Eye: Facet Area Variation, Defects, and Disorder

Sangwoo Kim

The regular hexagonal array morphology of facets (ommatidia) in the Drosophila compound eye is accomplished by regulation of cell differentiation and planar cell polarity during development. Mutations in certain genes disrupt regulation, causing a breakdow ...

2016

Non-rectangular RC walls: A review of experimental investigations

Katrin Beyer, Raluca-Tereza Constantin

When compared to tests on reinforced concrete (RC) walls with a rectangular or barbelled cross-section, only very few tests on RC walls with open cross-section exist. Most of these walls were subjected to unidirectional or bidirectional loading along one o ...

2014

Model and design of dielectric elastomer minimum energy structures

Herbert Shea, Samuel Rosset, Jun Shintake

Fixing a prestretched dielectric elastomer actuator (DEA) on a flexible frame allows transformation of the intrinsic in-plane area expansion of DEAs into complex three-dimensional (3D) structures whose shape is determined by a configuration that minimizes ...

Institute of Physics2014

The number of distinct distances from a vertex of a convex polygon

János Pach, Rom Pinchasi, Gabriel Nivasch

Erd\H{o}s conjectured in 1946 that every n-point set P in convex position in the plane contains a point that determines at least floor(n/2) distinct distances to the other points of P. The best known lower bound due to Dumitrescu (2006) is 13n/36 - O(1). I ...

2013

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