Publications related to Five points determine a conic

Free Boundary Regularity for Almost Every Solution to the Signorini Problem

We investigate the regularity of the free boundary for the Signorini problem in Rn+1. It is known that regular points are (n−1)-dimensional and C∞. However, even for C∞ obstacles φ, the set of non-regular (or degenerate) points could be very large—e.g. wit ...

2021

Visual feature integration: how long can it last?

Michael Herzog, Leila Drissi Daoudi - Kleinbauer, Lukas Vogelsang

Spatiotemporal features are integrated along motion trajectories. For example, when a central line is followed by pairs of flanking lines, two motion streams diverging from the center are perceived. The central line is rendered invisible by the subsequent ...

SAGE Publishing2021

What determines the temporal extent of unconscious feature integration?

Michael Herzog, Leila Drissi Daoudi - Kleinbauer, Lukas Vogelsang

Visual features are spatiotemporally integrated along motion trajectories. For instance, when a central line is followed by pairs of flanking lines, two motion streams diverging from the center are perceived. The central line is rendered unconscious by the ...

2021

Leveraging wafer-level manufacturing process limitations to increase large scale fused silica microlens array uniformity

Toralf Scharf, Wilfried Noell, Raoul Kirner, Jeremy Béguelin

The wafer-level production of Fused Silica microlens arrays is limited by systematic process non-uniformities. The common molten resist-reflow process with subsequent dry-etching allows for manufacturing of microlens arrays on 200 mm wafers. A thorough pro ...

SPIE-INT SOC OPTICAL ENGINEERING2019

Specification of aspherical surfaces used as refractive elements in micro-optical systems

Toralf Scharf, Wilfried Noell, Jeremy Béguelin

The optical performance of refractive plano-convex microlenses is mainly related to the quality of their (a)spherical surface. An efficient tolerancing of this surface is a key step towards the manufacturing of high quality microlenses. However, we demonst ...

SPIE-INT SOC OPTICAL ENGINEERING2019

On Sets Defining Few Ordinary Circles

Frank de Zeeuw

An ordinary circle of a set P of n points in the plane is defined as a circle that contains exactly three points of P. We show that if P is not contained in a line or a circle, then P spans at least ordinary circles. Moreover, we determine the exact minimu ...

Springer2018

On the existence of ordinary triangles

Sebastian Urban Stich, Radoslav Fulek, Márton Naszódi

Let P be a finite point set in the plane. A \emph{c-ordinary triangle} in P is a subset of P consisting of three non-collinear points such that each of the three lines determined by the three points contains at most c points of P. Motivated by a question o ...

Elsevier2017

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

Large subsets of discrete hypersurfaces in Z d contain arbitrarily many collinear points

Florian Karl Richter

In 1977 L.T. Ramsey showed that any sequence in Z 2 with bounded gaps contains arbitrarily many collinear points. Thereafter, in 1980, C. Pomerance provided a density version of this result, relaxing the condition on the sequence from having bounded gaps t ...

2016

Few distinct distances implies no heavy lines or circles

Frank de Zeeuw

We study the structure of planar point sets that determine a small number of distinct distances. Specifically, we show that if a set of n points determines o(n) distinct distances, then no line contains Omega(n (7/8)) points of and no circle contains Omega ...

Springer Heidelberg2016

Five points determine a conic

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Free Boundary Regularity for Almost Every Solution to the Signorini Problem

Visual feature integration: how long can it last?

What determines the temporal extent of unconscious feature integration?

Leveraging wafer-level manufacturing process limitations to increase large scale fused silica microlens array uniformity

Specification of aspherical surfaces used as refractive elements in micro-optical systems

On Sets Defining Few Ordinary Circles

On the existence of ordinary triangles

On some algebraic and extremal problems in discrete geometry

Large subsets of discrete hypersurfaces in Z d contain arbitrarily many collinear points

Few distinct distances implies no heavy lines or circles

Visual feature integration: how long can it last?

Free Boundary Regularity for Almost Every Solution to the Signorini Problem

On Sets Defining Few Ordinary Circles

On the existence of ordinary triangles

On some algebraic and extremal problems in discrete geometry

Large subsets of discrete hypersurfaces in Z d contain arbitrarily many collinear points

What determines the temporal extent of unconscious feature integration?

Few distinct distances implies no heavy lines or circles

Leveraging wafer-level manufacturing process limitations to increase large scale fused silica microlens array uniformity

Specification of aspherical surfaces used as refractive elements in micro-optical systems