Clusters in the (Be, B, C)@Si(n)((0,1,2+)) (n = 6-10) series, isoelectronic to Si(n)(2-), present multiple symmetric structures, including rings, cages and open structures, which the doping atom stabilizes using contrasting bonding mechanisms. The most striking feature of these clusters is the absence of electron transfer (for Be) or even the inversion (for B and C) in comparison to classic end...

A triangulation of a surface is irreducible if there is no edge whose contraction produces another triangulation of the surface. We prove that every irreducible triangulation of a surface with Euler genus g ≥ 1 has at most 13g − 4 vertices. The best previous bound was 171g − 72.

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Consider the class of n-dimensional Riemannian spin manifolds with bounded sectional curvatures and diameter, and almost non-negative scalar curvature. Let r = 1 if n = 2, 3 and r = 2 + 1 if n ≥ 4. We show that if the square of the Dirac operator on such a manifold has r small eigenvalues, then the manifold is diffeomorphic to a nilmanifold and has trivial spin structure. Equivalently, if M is ...

We prove that for every proper minor-closed class I of graphs there exists a constant c such that for every integer n the class I includes at most n!c graphs with vertex-set {1, 2, . . . , n}. This answers a question of Welsh.

A k-lift of an n-vertex base-graph G is a graph H on n× k vertices, where each vertex of G is replaced by k vertices and each edge (u, v) in G is replaced by a matching representing a bijection πuv so that the edges of H are of the form ( (u, i), (v, πuv(i)) ) . H is a (uniformly) random lift of G if for every edge (u, v) the bijection πuv is chosen uniformly and independently at random. The ma...

F ive years ago there were little more than 200 known microRNAs (miRNAs) — small regulatory nucleic acids that bind to complementary sites on mRNAs and prevent their translation into protein. Today, that number has swelled to more than 700 and counting. The explosion in knowledge about these small, noncoding RNAs, which appear to be evolutionarily ancient but were discovered less than two decad...

Thunderstorm is a severe phenomenon which can produce downburst winds capable for causing significant damage or even the collapse of low-rise structures. Experimental tests and numerical simulations are widely used by Wind Engineering (WE) community gaining increased understanding complex like downbursts. In this paper, accuracy Unsteady Reynolds-averaged Navier-Stokes (URANS) Scale-Adaptive Si...