Spin Dynamics and Dirac Nodes in a Kagome Lattice

Herein, the spin dynamics for various magnetic configurations arranged on a Kagome lattice is investigated. Using a Holstein–Primakoff expansion of the isotropic Heisenberg Hamiltonian with multiple exchange parameters, the development and evolution of magnetic Dirac nodes with both anisotropy and magnetic field are examined. From the classical energies, the phase diagrams for the ferromagnetic (FM), antiferrimagnetic (AfM), and the 120°  phases are shown as functions of J₁, J₂, J₃, and anisotropy. Furthermore, the production of bosonic Dirac and Weyl nodes in the spin-wave spectra is shown. Through frustration of the magnetic geometry, a connection to the asymmetric properties of the Kagome lattice and the various antiferromagnetic configurations is discerned. Most interesting is the 120°  phase, which does not have Dirac nodes when considering only J₁ due to the formation of an analogous antiferromagnetic honeycomb lattice, but gains Dirac symmetry with next-nearest neighbor interactions. Additionally, the presence of flat modes that are characteristic of cluster excitations is shown. Further study of external frustrations from a magnetic field and anisotropy reveals a tunability of the exchange interactions and nodal points.     

Asymptotics for Szegö polynomial zeros

The Wiener-Levinson method and algorithm, formulated here in terms of Szegö polynomials _n ( _N,I ;z) orthogonal on the unit circle, is used to find unknown frequencies _j from anN-sample of a discrete time signal consisting of the superposition of sinusoidal waves with frequencies ₁,...,₁. In a recent paper the authors (and W.J. Thron) have shown that zerosz(j, n, N, I) of _n ( _N,I ;z) converge asN to the critical points ,j=1, 2,...,I, providednn ₀ (I)=2I+L, whereL is 0 or 1. The present paper gives results on the convergence of zerosz(j, n, N, I) to some of the for the case in whichnn ₀ (I), wheren is the degree of _n ( _N,I ;z).Research supported in part by the United States Educational Foundation in Norway (Fulbright Grant), the Norwegian Research Council (NAVF) and the US National Science Foundation under Grant No. DMS-9103141.     

INLA goes extreme: Bayesian tail regression for the estimation of high spatio-temporal quantiles

This work is motivated by the challenge organized for the 10th International Conference on Extreme-Value Analysis (EVA2017) to predict daily precipitation quantiles at the \(99.8\%\) level for each month at observed and unobserved locations. Our approach is based on a Bayesian generalized additive modeling framework that is designed to estimate complex trends in marginal extremes over space and time. First, we estimate a high non-stationary threshold using a gamma distribution for precipitation intensities that incorporates spatial and temporal random effects. Then, we use the Bernoulli and generalized Pareto (GP) distributions to model the rate and size of threshold exceedances, respectively, which we also assume to vary in space and time. The latent random effects are modeled additively using Gaussian process priors, which provide high flexibility and interpretability. We develop a penalized complexity (PC) prior specification for the tail index that shrinks the GP model towards the exponential distribution, thus preventing unrealistically heavy tails. Fast and accurate estimation of the posterior distributions is performed thanks to the integrated nested Laplace approximation (INLA). We illustrate this methodology by modeling the daily precipitation data provided by the EVA2017 challenge, which consist of observations from 40 stations in the Netherlands recorded during the period 1972–2016. Capitalizing on INLA’s fast computational capacity and powerful distributed computing resources, we conduct an extensive cross-validation study to select the model parameters that govern the smoothness of trends. Our results clearly outperform simple benchmarks and are comparable to the best-scoring approaches of the other teams.     

Convergence acceleration of limit periodic continued fractions under asymptotic side conditions

Summary We present a method of convergence acceleration for limitk-periodic continued fractionsK(a _n /1) orK(1/b _n ) satisfying certain asymptotic side conditions. The method represents an improvement of the fixed point modification considered by Thron and Waadeland [8], under these conditions. The regularC-fraction expansions of hypergeometric functions₂ F ₁(a, 1;c; z) and₂ F ₁(a, b; c; z)/₂ F ₁(a, b+1;c+1;z) are examples of continued fractions satisfying these conditions.     

Contributions to the Chemistry of the Binary Compounds of the Transition Elements

Phase and structural relationships of the sulfur, selenium, and tellurium compounds of the 4d and 5d transition elements of groups IV to VII of the periodic system are discussed. Homologous elements behave very similarly with respect to the chalcogens, and this is particularly the case for niobium and tantalum, and for molybdenum and tungsten. However, zirconium, niobium, and molybdenum have a greater tendency towards formation of chalcogen-poor phases than their homologues hafnium, tantalum, and tungsten. Subchalcogenides are known only for zirconium and niobium. The number of phases and the tendency towards formation of solid solutions are considerably smaller among the tellurides than among the sulfides and selenides. The crystal structures of the telluride phases also differ from those of the sulfide and selenide phases of analogous composition. In addition, a review of the phase and structural relationships of the arsenic and antimony compounds of the 4d and 5d transition elements of groups V to VII is given.     

Evidence of AlII Radical Addition to Benzene

Electrophilic Al^III species have long dominated the aluminum reactivity towards arenes. Recently, nucleophilic low-valent Al^I aluminyl anions have showcased oxidative additions towards arenes C−C and/or C−H bonds. Herein, we communicate compelling evidence of an Al^II radical addition reaction to the benzene ring. The electron reduction of a ligand stabilized precursor with KC₈ in benzene furnishes a double addition to the benzene ring instead of a C−H bond activation, producing the corresponding cyclohexa-1,3(orl,4)-dienes as Birch-type reduction product. X-ray crystallographic analysis, EPR spectroscopy, and DFT results suggest this reactivity proceeds through a stable Al^II radical intermediate, whose stability is a consequence of a rigid scaffold in combination with strong steric protection.