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Icosahedron

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The Intricate Structural Chemistry of MII2nLn-Type Assemblies

Rosario Scopelliti, Kay Severin, Farzaneh Fadaei Tirani, Philip Pattison, Euro Solari, Giacomo Cecot, Mathieu Jérémie Marmier

The reaction of cis-blocked, square-planar MII complexes with tetratopic N-donor ligands is known to give metallasupramolecular assemblies of the formula M2nLn. These assemblies typically adopt barrel-like structures, with the ligands paneling the sides of ...

Amer Chemical Soc2017

Curve Graphs On Surfaces Of Infinite Type

Hugo Parlier, Ariadna Fossas Tenas

We define and study analogs of curve graphs for infinite type surfaces. Our definitions use the geometry of a fixed surface and vertices of our graphs are infinite multicurves which are bounded in both a geometric and a topological sense. We show that the ...

Suomalainen Tiedeakatemia2015

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

Icosahedral quasicrystal-enhanced nucleation of the fcc phase in liquid gold alloys

Michel Rappaz, Güven Kurtuldu, Alberto Sicco

Although the grain refinement of yellow gold alloys with Jr has been used in industry and known for nearly half a century, the basic mechanism is still unknown. The present contribution shows that the mechanism is the same as that evidenced recently in Al- ...

Elsevier2014

New Zn(II) complexes with N2S2 Schiff base ligands. Experimental and theoretical studies of the role of Zn(II) in disulfide thiolate-exchange

Kurt Schenk, Maryam Bagheri

Described are the synthesis and characterization of two, potentially tetradentate, N2S2 Schiff-base ligands, containing a disulfide bond, N,N'-bis(3-phenylprop-2-en-l-ylidene)-2,2'-disulfanediyldianiline (L-1) and N,N'-bis(3,3-diphenylprop-2-en-1-ylidene)- ...

Elsevier2014

On grids in topological graphs

János Pach

A topological graph G is a graph drawn in the plane with vertices represented by points and edges represented by continuous arcs connecting the vertices. If every edge is drawn as a straight-line segment, then G is called a geometric graph. A k-grid in a t ...

Elsevier Science Bv2014

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

Influence of Cr on the nucleation of primary Al and formation of twinned dendrites in Al-Zn-Cr alloys: Can icosahedral solid clusters play a role?

Michel Rappaz, Güven Kurtuldu

The equiaxed solidification of Al-20 wt.% Zn alloys revealed an unexpectedly large number of fine grains which are in a twin, or near-twin, relationship with their nearest neighbors when minute amounts of Cr (1000 ppm) are added to the melt. Several occurr ...

Elsevier2013

Tangles and Degenerate Tangles

Andres Jacinto Ruiz Vargas

We study some variants of Conway’s thrackle conjecture. A tangle is a graph drawn in the plane such that its edges are represented by continuous arcs, and any two edges share precisely one point, which is either a common endpoint or an interior point at wh ...

Springer Berlin Heidelberg2013

Small distances in convex polygons

Filip Moric

Let d(1) < d(2) < ... denote the set of all distances between two vertices of a convex n-gon. We show that the number of pairs of vertices at distance d(2) from one another is at most n + O(1). (C) 2013 Elsevier B.V. All rights reserved. ...

Elsevier Science Bv2013