Publications related to Möbius plane

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

A three-dimensional macroelement for modelling the in-plane and out-of-plane response of masonry walls

Katrin Beyer, Francesco Vanin, Andrea Penna

The seismic performance of unreinforced masonry buildings is commonly assessed using equivalent frame modelling. Its computational efficiency allows for a large number of analyses to be conducted, which are often required to account for epistemic and aleat ...

2020

Planar Point Sets Determine Many Pairwise Crossing Segments

János Pach, Gábor Tardos

We show that any set of n points in general position in the plane determines n(1-o(1)) pairwise crossing segments. The best previously known lower bound, Omega(root n), was proved more than 25 years ago by Aronov, Erdos, Goddard, Kreitman, Krugerman, Pach, ...

ASSOC COMPUTING MACHINERY2019

A Review and Mathematical Treatment of Infinity on the Smith Chart, 3D Smith Chart and Hyperbolic Smith Chart

Mihai Adrian Ionescu, Andrei Müller

This work describes the geometry behind the Smith chart, recent 3D Smith chart tool and previously reported conceptual Hyperbolic Smith chart. We present the geometrical properties of the transformations used in creating them by means of inversive geometry ...

MDPI2018

On some algebraic and extremal problems in discrete geometry

Seyed Hossein Nassajianmojarrad

In the present thesis, we delve into different extremal and algebraic problems arising from combinatorial geometry. Specifically, we consider the following problems. For any integer

n\ge 3

, we define

e(n)

to be the minimum positive integer such that an ...

EPFL2017

Beam-beam amplitude detuning with forced oscillations

Xavier Buffat, Tatiana Pieloni, Javier Barranco Garcia, Patrik Gonçalves Jorge

Recently, relations were established between the coefficients of free and forced amplitude detuning polynomial expansions. The forced oscillations were considered only in a single plane. In this paper we extend and generalize previous results by developing ...

Amer Physical Soc2017

Methods and Approaches for Blind Test Predictions of Out-Of-Plane Behavior of Masonry Walls: A Numerical Comparative Study

Katrin Beyer, Andrea Penna

Earthquakes cause severe damage to masonry structures due to inertial forces acting in the normal direction to the plane of the walls. The out-of-plane behavior of masonry walls is complex and depends on several parameters, such as material and geometric p ...

Taylor & Francis Inc2017

Extension complexity of stable set polytopes of bipartite graphs

Yuri Faenza, Manuel Francesco Aprile

The extension complexity xc(P) of a polytope P is the minimum number of facets of a polytope that affinely projects to P. Let G be a bipartite graph with n vertices, m edges, and no isolated vertices. Let STAB(G) be the convex hull of the stable sets of G. ...

Springer2017

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On some algebraic and extremal problems in discrete geometry

Seyed Hossein Nassajianmojarrad

In the present thesis, we delve into different extremal and algebraic problems arising from combinatorial geometry. Specifically, we consider the following problems. For any integer

n\ge 3

, we define

e(n)

to be the minimum positive integer such that an ...

EPFL2017

Möbius plane

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

A three-dimensional macroelement for modelling the in-plane and out-of-plane response of masonry walls

Planar Point Sets Determine Many Pairwise Crossing Segments

Distinct distances between points and lines

A Review and Mathematical Treatment of Infinity on the Smith Chart, 3D Smith Chart and Hyperbolic Smith Chart

On some algebraic and extremal problems in discrete geometry

Beam-beam amplitude detuning with forced oscillations

Methods and Approaches for Blind Test Predictions of Out-Of-Plane Behavior of Masonry Walls: A Numerical Comparative Study

Extension complexity of stable set polytopes of bipartite graphs

Upper limb rehabilitation system

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

On some algebraic and extremal problems in discrete geometry

A Review and Mathematical Treatment of Infinity on the Smith Chart, 3D Smith Chart and Hyperbolic Smith Chart

Planar Point Sets Determine Many Pairwise Crossing Segments

Extension complexity of stable set polytopes of bipartite graphs

A three-dimensional macroelement for modelling the in-plane and out-of-plane response of masonry walls

Distinct distances between points and lines

Methods and Approaches for Blind Test Predictions of Out-Of-Plane Behavior of Masonry Walls: A Numerical Comparative Study

Upper limb rehabilitation system