CMV matrices in random matrix theory and integrable systems: a survey

We present a survey of recent results concerning a remarkable class of unitary matrices, the CMV matrices. We are particularly interested in the role they play in the theory of random matrices and integrable systems. Throughout the paper we also emphasize the analogies and connections to Jacobi matrices.Comment: Based on a talk given at the Short Program on Random Matrices, Random Processes and Integrable Systems, CRM, Universite de Montreal, 200

Nanospiral Formation by Droplet Drying: One Molecule at a Time

We have created nanospirals by self-assembly during droplet evaporation. The nanospirals, 60–70 nm in diameter, formed when solvent mixtures of methanol and m-cresol were used. In contrast, spin coating using only methanol as the solvent produced epitaxial films of stripe nanopatterns and using only m-cresol disordered structure. Due to the disparity in vapor pressure between the two solvents, droplets of m-cresol solution remaining on the substrate serve as templates for the self-assembly of carboxylic acid molecules, which in turn allows the visualization of solution droplet evaporation one molecule at a time

Atomic Layer Deposition of 2D Metal Dichalcogenides for Electronics, Catalysis, Energy Storage, and Beyond

2D transition metal dichalcogenides (TMDCs) are among the most exciting materials of today. Their layered crystal structures result in unique and useful electronic, optical, catalytic, and quantum properties. To realize the technological potential of TMDCs, methods depositing uniform films of controlled thickness at low temperatures in a highly controllable, scalable, and repeatable manner are needed. Atomic layer deposition (ALD) is a chemical gas-phase thin film deposition method capable of meeting these challenges. In this review, the applications evaluated for ALD TMDCs are systematically examined, including electronics and optoelectonics, electrocatalysis and photocatalysis, energy storage, lubrication, plasmonics, solar cells, and photonics. This review focuses on understanding the interplay between ALD precursors and deposition conditions, the resulting film characteristics such as thickness, crystallinity, and morphology, and ultimately device performance. Through rational choice of precursors and conditions, ALD is observed to exhibit potential to meet the varying requirements of widely different applications. Beyond the current state of ALD TMDCs, the future prospects, opportunities, and challenges in different applications are discussed. The authors hope that the review aids in bringing together experts in the fields of ALD, TMDCs, and various applications to eventually realize industrial applications of ALD TMDCs.Peer reviewe

Modelling human choices: MADeM and decision‑making

Research supported by FAPESP 2015/50122-0 and DFG-GRTK 1740/2. RP and AR are also part of the Research, Innovation and Dissemination Center for Neuromathematics FAPESP grant (2013/07699-0). RP is supported by a FAPESP scholarship (2013/25667-8). ACR is partially supported by a CNPq fellowship (grant 306251/2014-0)

On multilinear oscillatory integrals, nonsingular and singular

Basic questions concerning nonsingular multilinear operators with oscillatory factors are posed and partially answered. L-p norm inequalities are established for multilinear integral operators of Calderon-Zygmund type which incorporate oscillatory factors e(iP), where P is a real-valued polynomial

Carleson measures, trees, extrapolation, and T(b) theorems

The theory of Carleson measures, stopping time arguments, and atomic decompositions has been well-established in harmonic analysis. More recent is the theory of phase space analysis from the point of view of wave packets on tiles, tree selection algorithms, and tree size estimates. The purpose of this paper is to demonstrate that the two theories are in fact closely related, by taking existing results and reproving them in a unified setting. In particular we give a dyadic version of extrapolation for Carleson measures, as well as a two-sided local dyadic T(b) theorem which generalizes earlier T(b) theorems of David, Journé, Semmes, and Christ