Congruence lattices ofp-algebras

T. Kartriák proved the following theorem:Every finite distributive lattice is the congruence lattice of a finite p-algebra. We provide a short proof, and a generalization, of this result.Presented by J. Berman.The research of the first author was supported by the NSERC of Canada.The research of the second author was supported by the Hungarian National Foundation for Scientific Research, under Grant No. 1903.     

Weak convergence of random <Emphasis Type="Bold">p</Emphasis>-mappings and the exploration process of inhomogeneous continuum random trees

We study the asymptotics of the p-mapping model of random mappings on [n] as n gets large, under a large class of asymptotic regimes for the underlying distribution p. We encode these random mappings in random walks which are shown to converge to a functional of the exploration process of inhomogeneous random trees, this exploration process being derived (Aldous-Miermont-Pitman 2004) from a bridge with exchangeable increments. Our setting generalizes previous results by allowing a finite number of “attracting points” to emerge.Research supported by NSF Grant DMS-0203062.Research supported by NSF Grant DMS-0071468.     

Matrix‐valued Szegő polynomials and quantum random walks

We consider quantum random walks (QRW) on the integers, a subject that has been considered in the last few years in the framework of quantum computation. We show how the theory of CMV matrices gives a natural tool to study these processes and to give results that are analogous to those that Karlin and McGregor developed to study (classical) birth‐and‐death processes using orthogonal polynomials on the real line. In perfect analogy with the classical case, the study of QRWs on the set of nonnegative integers can be handled using scalar‐valued (Laurent) polynomials and a scalar‐valued measure on the circle. In the case of classical or quantum random walks on the integers, one needs to allow for matrix‐valued versions of these notions. We show how our tools yield results in the well‐known case of the Hadamard walk, but we go beyond this translation‐invariant model to analyze examples that are hard to analyze using other methods. More precisely, we consider QRWs on the set of nonnegative integers. The analysis of these cases leads to phenomena that are absent in the case of QRWs on the integers even if one restricts oneself to a constant coin. This is illustrated here by studying recurrence properties of the walk, but the same method can be used for other purposes. The presentation here aims at being self‐contained, but we refrain from trying to give an introduction to quantum random walks, a subject well surveyed in the literature we quote. For two excellent reviews, see [1, 9]. See also the recent notes [20]. © 2009 Wiley Periodicals, Inc.     

Angular distributions in quasi-fission reactions: Evidence for incomplete relaxation of the tilting mode

The integral β^?-spectra of²³⁵U and²³⁹Pu fission products have been measured with a plastic scintillator telescope at an external neutron guide tube at the high flux reactor of the ILL in Grenoble. The highly enriched targets (150 – 800 γg/cm²) were placed in a fission chamber at a distance of approximately 110 m from the reactor core. From the measured beta-spectra absolute counting rates per MeV and fission have been calculated, which are compared with the results of earlier experiments of other authors and with recent theoretical calculations.     

Snapshot location for POD in control of a linear heat equation

In the present work, we study the approximation of a distributed optimal control problem for a linear heat equation with model order reduction based on Proper Orthogonal Decomposition (POD-MOR). We show that snapshot location for control problems is crucial in model reduction. For the determination of the time instances (snapshot locations) we utilize an a-posteriori error control concept which is based on a reformulation of the optimality system of the underlying optimal control problem as a second order in time and fourth order in space elliptic system. Finally, we present a numerical test to illustrate our approach. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

The free \mathfrak{m} -lattice on the poset H

Let H={a ₀, a ₁, a ₂, b ₀, b ₁, b ₂} be the poset defined by a ₀<a ₂<a ₁, b ₀<b ₂<b ₁, a ₀<b ₁, and b ₀<a ₁. For an infinite regular cardinal , we describe the free -lattice on H. This continues the work of I. Rival and R. Wille who accomplished the same for =. In subsequent papers, we show how to apply this result to describe the free -lattice on a poset for a large class of posets, called slender posets.     

The CRT is the scaling limit of unordered binary trees

We prove that a uniform, rooted unordered binary tree (also known as rooted, binary Pólya tree) with n leaves has the Brownian continuum random tree as its scaling limit for the Gromov‐Hausdorff topology. The limit is thus, up to a constant factor, the same as that of uniform plane trees or labeled trees. Our analysis rests on a combinatorial and probabilistic study of appropriate trimming procedures of trees. © 2011 Wiley Periodicals, Inc. Random Struct. Alg., 38, 467–501, 2011     

On the congruence lattice of a Scott-domain

We prove that the congruence lattice of a Scott-domain can be characterized as a complete lattice.Presented by V. Trnkova.The research of the first author was supported by the NSERC of Canada.The research of the second author was supported by the Hungarian National Foundation for Scientific Research, under Grant No. 1903.