Maximal closed subroot systems of real affine root systems

We completely classify and give explicit descriptions of the maximal closed subroot systems of real affine root systems. As an application we describe a procedure to get the classification of all regular subalgebras of affine Kac Moody algebras in terms of their root systems

Equipopularity Classes of 132-Avoiding Permutations

The popularity of a pattern p in a set of permutations is the sum of the number of copies of p in each permutation of the set. We study pattern popularity in the set of 132-avoiding permutations. Two patterns are equipopular if, for all n, they have the same popularity in the set of length-n 132-avoiding permutations. There is a well-known bijection between 132-avoiding permutations and binary plane trees. The spines of a binary plane tree are defined as the connected components when all edges connecting left children to their parents are deleted, and the spine structure is the sorted sequence of lengths of the spines. Rudolph shows that patterns of the same length are equipopular if their associated binary plane trees have the same spine structure. We prove the converse of this result using the method of generating functions, which gives a complete classification of 132-avoiding permutations into equipopularity classes.Massachusetts Institute of Technology. Department of Mathematic

Cold-formed steel channel sections under end-two-flange loading condition:design for edge-stiffened holes, unstiffened holes and plain webs

In cold-formed steel (CFS) channel sections, web holes are becoming increasingly popular. Such holes, however, result in the sections becoming more susceptible to web crippling, especially under concentrated loads applied near the web holes. Traditional web holes are normally punched or bored and are unstiffened. Recently, a new generation of CFS channel sections with edge-stiffened web holes has been developed by the CFS industry and is being widely used. However, no research is available in the literature which investigated the web crippling strength of CFS channel sections with edge-stiffened circular web holes under the end-two-flange (ETF) loading conditions. A combination of experimental tests and non-linear FEA were used to investigate the effect of such stiffened holes on web crippling behaviour under ETF loading conditions. The results of 30 web crippling tests are presented. Non-linear FE models are described, and the results are compared against the laboratory test results; a good agreement was obtained in terms of both the strength and failure modes. The results indicate that the stiffened holes can significantly improve the web crippling strength of CFS channel sections. A parametric study involving 1116 FEA was then performed, covering the effect of different hole sizes, edge-stiffener lengths and fillet radii, length of the bearing plates and position of holes in the web. Finally, design recommendations in the form of web crippling strength reduction factors are proposed, that are conservative to both the experimental and FE results

Extremes of multitype branching random walks: Heaviest tail wins

We consider a branching random walk on a multitype (with Q types of particles), supercritical Galton-Watson tree which satisfies the Kesten-Stigum condition. We assume that the displacements associated with the particles of type Q have regularly varying tails of index α, while the other types of particles have lighter tails than the particles of type Q. In this paper we derive the weak limit of the sequence of point processes associated with the positions of the particles in the nth generation. We verify that the limiting point process is a randomly scaled scale-decorated Poisson point process using the tools developed by Bhattacharya, Hazra, and Roy (2018). As a consequence, we obtain the asymptotic distribution of the position of the rightmost particle in the nth generation

Extremes of multitype branching random walks: Heaviest tail wins

We consider a branching random walk on a multi(Q)-type, supercritical Galton-Watson tree which satisfies Kesten-Stigum condition. We assume that the displacements associated with the particles of type Q have regularly varying tails of index α, while the other types of particles have lighter tails than that of particles of type Q. In this article, we derive the weak limit of the sequence of point processes associated with the positions of the particles in the nth generation. We verify that the limiting point process is a randomly scaled scale-decorated Poisson point process (SScDPPP) using the tools developed in \cite{bhattacharya:hazra:roy:2016}. As a consequence, we shall obtain the asymptotic distribution of the position of the rightmost particle in the nth generation