Non-conservation of quasiparticles

An adequate canonical transformation of the hamiltonian permitted the full observance of the specific Pauli commutation relations and the elimination of the main quasiparticle non-conservative term. This will allow a correct treatment of the kinematic part of the interaction in many problems.     

Optical electron transitions in a two-dimensional disordered semiconductor

The frequency dependence of the light absorption coefficient associated with electron transitions between states of strong and weak localization is studied.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 11, pp. 22–24, November, 1982.One of us (V. L. Bonch-Bruevich) is grateful to Dr. M. Pepper for sending a preprint.     

On some problems of analysis of isotropic antiferromagnets

An equivalent Hamiltonian method for the analysis of isotropic antiferromagnets is proposed. The Hamiltonian does not contain the terms corresponding to the processes of non-conservation of spin waves and gives the possibility to perform the calculations with a limited and controlled error. The high as well as the low temperature analysis of the system was carried out with the help of the equivalent Hamiltonian. Some results are compared with those of the u?v transformation method.     

Champs affines

The purpose of this work is to introduce a notion of affine stacks, which is a homotopy version of the notion of affine schemes, and to give several applications in the context of algebraic topology and algebraic geometry. As a first application we show how affine stacks can be used in order to give a new point of view (and new proofs) on rational and p-adic homotopy theory. This gives a first solution to A. Grothendieck’s schematization problem described in [18]. We also use affine stacks in order to introduce a notion of schematic homotopy types. We show that schematic homotopy types give a second solution to the schematization problem, which also allows us to go beyond rational and p-adic homotopy theory for spaces with arbitrary fundamental groups. The notion of schematic homotopy types is also used in order to construct various homotopy types of algebraic varieties corresponding to various co-homology theories (Betti, de Rham, l-adic, ...), extending the well known constructions of the various fundamental groups. Finally, just as algebraic stacks are obtained by gluing affine schemes we define $$ \infty $$-geometric stacks as a certain gluing of affine stacks. Examples of $$ \infty $$-geometric stacks in the context of algebraic topology (moduli spaces of dga structures up to quasi-isomorphisms) and Hodge theory (non-abelian periods) are given.     

Synthesis, structure and dioxygen reactivity of a bis(micro-iodo)dicopper(I) complex supported by the [N-(3,5-di-tert-butyl-2-hydroxybenzyl)-N,N-di-(2-pyridylmethyl)]amine ligand

The air-sensitive bis(micro-iodo)dicopper(I) complex 1 supported by [N-(3,5-di-tert-butyl-2-hydroxybenzyl)-N,N-di-(2-pyridylmethyl)]amine (L) has been prepared by treating copper(I) iodide with L in anhydrous THF. Compound 1 crystallizes as a dimer in space group C2/c. Each copper(I) center has distorted tetrahedral N2I2 coordination geometry with Cu-N(pyridyl) distances 2.061(3) and 2.063(3) A, Cu-I distances 2.6162(5) and 2.7817(5) and a Cu...Cu distance of 2.9086(8) A. Complex 1 is rapidly oxidized by dioxygen in CH2Cl2 with a 1 : 1 stoichiometry giving the bis(micro-iodo)peroxodicopper(II) complex [Cu(L)(micro-I)]2O2 (2). The reaction of 1 with dioxygen has been characterized by UV-vis, mass spectrometry, EPR and Cu K-edge X-ray absorption spectroscopy at low temperature (193 K) and above. The mass spectrometry and low temperature EPR measurements suggested an equilibrium between the bis(micro-iodo)peroxodicopper(II) complex 2 and its dimer, namely, the tetranuclear (peroxodicopper(II))2 complex [Cu(L)(micro-I)]4O4 (2'). Complex 2 undergoes an effective oxo-transfer reaction converting PPh3 into O=PPh3 under anaerobic conditions. At sufficiently high concentration of PPh3, the oxygen atom transfer from 2 to PPh3 was followed by the formation of [Cu(PPh3)3I]. The dioxygen reactivity of 1 was compared with that known for other halo(amine)copper(I) dimers.     

Synthesis of new amphiphilic dendrons bearing aliphatic hydrocarbon surface sectors and a monocarboxylic or dicarboxylic acid focal point

[structure: see text]. A new series of amphiphilic G1-G3 dendrons containing purely aliphatic hydrocarbon dendritic surface sectors and one or two carboxylic acid group(s) at the focal point was synthesized in good yields. The key branching steps involve diallylation reactions of diethyl malonate or Meldrum's acid. These dendrons are highly soluble in hexane despite having highly polar carboxylic acid groups at the focal point.     

Iron porphyrin catalysed light driven C–H bond amination and alkene aziridination with organic azides

Visible light driven nitrene transfer and insertion reactions of organic azides are an attractive strategy for the design of C–N bond formation reactions under mild reaction conditions, the challenge being lack of selectivity as a free nitrene reactive intermediate is usually involved. Herein is described an iron(iii) porphyrin catalysed sp³ C–H amination and alkene aziridination with selectivity by using organic azides as the nitrogen source under blue LED light (469 nm) irradiation. The photochemical reactions display chemo- and regio-selectivity and are effective for the late-stage functionalization of natural and bioactive compounds with complexity. Mechanistic studies revealed that iron porphyrin plays a dual role as a photosensitizer and as a catalyst giving rise to a reactive iron–nitrene intermediate for subsequent C–N bond formation.

An iron(iii) porphyrin catalysed sp³ C–H amination and alkene aziridination with broad substrate scope under mild conditions is conducted, with selectivity through the use of organic azides as the nitrogen source under blue LED light irradiation.