Review of AdS/CFT Integrability. Chapter VI.2: Yangian Algebra

Letters in Mathematical Physics - We review the study of Hopf algebras, classical and quantum R-matrices, infinite-dimensional Yangian symmetries and their representations in the context of...     

Organic Stereochemistry. Part 1. Symmetry Elements and Operations,Classification of Stereoisomers

This review initiates a general presentation of the principles of stereochemistry with special reference to medicinal compounds. The format is essentially identical with that of a previous Series of seven reviews on the Metabolism of Drugs and Other Xenobiotics published between October 2006 and October 2009 by B. T. and Stefanie Krämer in Chemistry & Biodiversity. Here, there will be eight reviews published in Helvetica Chimica Acta, to be grouped and published in book form together with some additional material. Part 1 introduces this new series by presenting and illustrating basic concepts on which the edifice of stereochemistry is built. At the most basic level of such foundations, we find symmetry as presented here in terms of its elements, operations, and point groups. This is followed by a classification of isomeric molecular structures, as well as a classification of steric relationships between molecular fragments.     

Path-integral solution of the one-dimensional Dirac quantum cellular automaton

Quantum cellular automata, which describe the discrete and exactly causal unitary evolution of a lattice of quantum systems, have been recently considered as a fundamental approach to quantum field theory and a linear automaton for the Dirac equation in one dimension has been derived. In the linear case a quantum cellular automaton is isomorphic to a quantum walk and its evolution is conveniently formulated in terms of transition matrices. The semigroup structure of the matrices leads to a new kind of discrete path-integral, different from the well known Feynman checkerboard one, that is solved analytically in terms of Jacobi polynomials of the arbitrary mass parameter.     

Acetone‐induced polymerisation of 3‐aminopropyltrimethoxysilane (APTMS) as revealed by NMR spectroscopy

We followed the reactivity of acetone with 3‐aminopropyltrimethoxysilane, a potential organosilane coupling agent, by ¹H, ¹³C and ²⁹Si NMR spectroscopy. Selective 1D and 2D‐edited NMR experiments significantly contributed to simplify the spectral complexity of reaction solution and elucidated molecular structures within progressive reaction phases. The course of the 3‐aminopropyltrimethoxysilane reaction with acetone was shown by a progressive decrease of both reactants, and a concomitant appearance of water and methanol, due to formation of imine and hydrolysis of alkoxysilane groups, respectively. The occurrence of multiple siloxane linkages in a progressively larger cross‐linked macromolecular structure was revealed by DOSY‐NMR experiments and new signals in ²⁹Si‐NMR spectra at different reaction times. The NMR approach described here may be applied to investigate the reactivity of other γ‐aminopropylalkoxysilanes and contribute to define procedures for the preparation of silica‐based materials. Copyright © 2014 John Wiley & Sons, Ltd.