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Hitting Simplices with Points in $R^3$

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An improvement on the number of simplices in F-q(d)

Van Thang Pham

Let epsilon be a set of points in F-q(d). Bennett et al. (2016) proved that if \epsilon\ >> [GRAHICS] then epsilon determines a positive proportion of all k-simplices. In this paper, we give an improvement of this result in the case when epsilon is the Car ...

Elsevier Science Bv2017

PCB and circuit design for piezoelectric-NEMS characterization

Nanoelectromechanical resonators (NEMS) are being developed from more than two decades from now. The fabrication techniques as well as metrology ones are constantly improving, allowing a possible democratization of their uses in the consumer and industrial ...

2017

Breakdown of Optical Phonons' Splitting in Two-Dimensional Materials

Nicola Marzari, Marco Gibertini, Thibault Daniel Pierre Sohier

We investigate the long-wavelength dispersion of longitudinal and transverse optical phonon modes in pillar two-diinensional materials, mriltilayers, and their heterostructures. Using analytical models and density-functional perturbation theory in a two-di ...

Amer Chemical Soc2017

A size-sensitive inequality for cross-intersecting families

Andrei Kupavskii

Two families A and B, of k-subsets of an n-set are called cross intersecting if A boolean AND B not equal phi for all A,B epsilon b. Strengthening the classical ErclOs-Ko-Rado theorem, Pyber proved that vertical bar A vertical bar vertical bar B vertical b ...

Academic Press Ltd- Elsevier Science Ltd2017

An Improved Upper Bound for the ErdAs-Szekeres Conjecture

Let ES(n) denote the minimum natural number such that every set of ES(n) points in general position in the plane contains n points in convex position. In 1935, ErdAs and Szekeres proved that ES. In 1961, they obtained the lower bound , which they conjectur ...

Springer2016

Measurement and characterization of room impulse responses

Thomas Batschelet

Room acoustics refers to the audio capture of an enclosed room. It can be seen as its color and fully describes the characteristics of the room, including the shape, size or the population. The goal of the project is to set up a database of Room impulse re ...

2016

Search for the decay B-0 -> phi gamma

Olivier Schneider, Yiming Li, Mingkui Wang, Chao Wang, Tagir Aushev, Ho Ling Li, Sun Hee Kim, Tara Nanut, Jun Yong Kim, Ji Hyun Kim, Donghyun Kim, Dipanwita Dutta

We have searched for the decay B-0 -> phi gamma sing the full Belle data set of 772 x 10(6) B (B) over bar pairs collected at the gamma(4S) resonance with the Belle detector at the KEKB e(+)e(-) collider. No signal is observed, and we set an upper limit on ...

Amer Physical Soc2016

Remarks on Schur's conjecture

János Pach, Filip Moric

Let P be a set of n > d points in for d >= 2. It was conjectured by Zvi Schur that the maximum number of (d-1)-dimensional regular simplices of edge length diam(P), whose every vertex belongs to P, is n. We prove this statement under the condition that any ...

Elsevier Science Bv2015

Double-Normal Pairs In Space

János Pach

A double-normal pair of a finite set S of points that spans R-d is a pair of points {p, q} from S such that S lies in the closed strip bounded by the hyperplanes through p and q perpendicular to pq. A double-normal pair {p, q} is strict if S \ {p,q} lies i ...

London Mathematical Society, Cambridge2015

Diameter Graphs in R-4

Andrei Kupavskii

A diameter graph in is a graph whose set of vertices is a finite subset of and whose set of edges is formed by pairs of vertices that are at diameter apart. This paper is devoted to the study of different extremal properties of diameter graphs in and on a ...

Springer2014