Methods for the synthesis of haloimidazoles (review)

Published information on methods for the synthesis of haloimidazoles is summarized and classified.     

The reduction of Ag(I) by α‐silylamines R2NCH2SiX3

The introduction of the organosilicon substituent into the α‐position of an amino group results in cardinal change of the amine reactivity irrespective of the coordination state of silicon. Amines R₂NCH₂SiX₃ [R = Me, Et, PhCH₂, CH₂SiX₃; SiX₃ = SiMe₃, Si(OEt)₃, Si(OCH₂CH₂)₃N] easily react with AgNO₃, to give the corresponding ammonium salts (R₂NH⁺ CH₂SiX₃)·NO₃^?. At the same time, Ag(I) is reduced to Ag(0). The interaction of N‐methyl‐N,N‐bis(silatranylmethyl)amine with AgNO₃ has been investigated by EPR spectroscopy. It was proven that the reaction involved a single electron transfer stage with the formation of cation radical of this amine. A mechanism of the reaction is proposed. Copyright © 2006 John Wiley & Sons, Ltd.     

A beam summation algorithm for wave radiation and guidance in stratified media

A Gaussian beams summation (GBS) algorithm for tracking source excited wave fields in plane stratified media is presented. In the present application the medium is described by layers with constant gradient of the wave speed, and the GB propagators are calculated recursively in a closed form. The algorithm is calibrated for numerical efficacy and accuracy by defining simple physical criteria for choosing the expansion parameters (the beam collimation and the spectral discretization and truncation) that allow for sparse representation of the source-excited angular spectrum of beams. It is validated for a source-excited example in layered media, where it provides a smooth and physically meaningful solution under multipath and caustic conditions and remains accurate for long propagation ranges where phase error tends to accumulate.     

Coexistence of self-organized criticality and intermittent turbulence in the solar corona

An extended data set of extreme ultraviolet images of the solar corona provided by the SOHO spacecraft is analyzed using statistical methods common to studies of self-organized criticality (SOC) and intermittent turbulence (IT). The data exhibit simultaneous hallmarks of both regimes: namely, power-law avalanche statistics as well as multiscaling of structure functions for spatial activity. This implies that both SOC and IT may be manifestations of a single complex dynamical process entangling avalanches of magnetic energy dissipation with turbulent particle flows.     

Quantum Bayesian computation

Quantum Bayesian computation is an emerging field that levers the computational gains available from quantum computers. They promise to provide an exponential speed-up in Bayesian computation. Our article adds to the literature in three ways. First, we describe how quantum von Neumann measurement provides quantum versions of popular machine learning algorithms such as Markov chain Monte Carlo and deep learning that are fundamental to Bayesian learning. Second, we describe quantum data encoding methods needed to implement quantum machine learning including the counterparts to traditional feature extraction and kernel embeddings methods. Third, we show how quantum algorithms naturally calculate Bayesian quantities of interest such as posterior distributions and marginal likelihoods. Our goal then is to show how quantum algorithms solve statistical machine learning problems. On the theoretical side, we provide quantum versions of high dimensional regression, Gaussian processes and stochastic gradient descent. On the empirical side, we apply a quantum FFT algorithm to Chicago house price data. Finally, we conclude with directions for future research.     

A modified pseudospectral method for solving trajectory optimization problems with singular arc

This paper presents a direct method based on Legendre–Radau pseudospectral method for efficient and accurate solution of a class of singular optimal control problems. In this scheme, based on a priori knowledge of control, the problem is transformed to a multidomain formulation, in which the switching points appear as unknown parameters. Then, by utilizing Legendre‐Radau pseudospectral method, a nonlinear programming problem is derived which can be solved by the well‐developed parameter optimization algorithms. The main advantages of the present method are its superior accuracy and ability to capture the switching times. Accuracy and performance of the proposed method are examined by means of some numerical experiments. Copyright © 2016 John Wiley & Sons, Ltd.