Wigner–Weyl–Moyal Formalism on Algebraic Structures

We first introduce theWigner–Weyl–Moyal formalism for a theorywhose phase space is an arbitrary Lie algebra. We alsogeneralize to quantum Lie algebras and to supersymmetrictheories. It turns out that the noncommutativity leads to a deformation ofthe classical phase space: instead of being a vectorspace, it becomes a manifold, the topology of which isgiven by the commutator relations. It is shown in fact that the classical phase space, for asemisimple Lie algebra, becomes a homogeneous symplecticmanifold. The symplectic product is also deformed. Wefinally make some comments on how to generalise to C*-algebras and other operator algebras,too.     

Sterically Demanding AgI and CuI N-Heterocyclic Carbene Complexes: Synthesis,Structures, Steric Parameters,and Catalytic Activity

The synthesis and full characterization of new air-stable Ag^I and Cu^I complexes bearing structurally bulky expanded-ring N-heterocyclic carbene (erNHC) ligands is presented. The condensation of protonated NHC salts with Ag₂O afforded a collection of Ag^I complexes, and their first use as ligand transfer reagents led to novel isostructural Cu^I or Au^I complexes. In situ deprotonation of the NHC salts in the presence of a copper(I) source, provides a library of new Cu^I complexes. The solid-state structures feature large N-C_NHC-N angles (118–128°) and almost identical angles between the aryl groups on the nitrogen atoms and the plane of the N-C-N unit of the carbene (i.e. torsion angles close to 0°). Among the steric parameters, the percent buried volume (%V_bur) values span easily in the 50–57 % range, and that one of (9-Dipp)CuBr complex (%V_bur=57.5) overcomes to other known erNHC–metal complexes reported to date. Preliminary catalytic experiments in the copper-catalyzed coupling between N-tosylhydrazone and phenylacetylene, afforded 76–93 % product at the 0.5–2.5 mol % catalyst loading, proving the stability of Cu^I erNHC complexes at elevated temperatures (100 °C).     

Multicompartment micelles from silicone-based triphilic block copolymers

An amphiphilic linear ternary block copolymer was synthesised in three consecutive steps via reversible addition–fragmentation chain transfer polymerisation. Oligo(ethylene glycol) monomethyl ether acrylate was engaged as a hydrophilic building block, while benzyl acrylate and 3-tris(trimethylsiloxy)silyl propyl acrylate served as hydrophobic building blocks. The resulting “triphilic” copolymer consists thus of a hydrophilic (A) and two mutually incompatible “soft” hydrophobic blocks, namely, a lipophilic (B) and a silicone-based (C) block, with all blocks having glass transition temperatures well below 0 °C. The triphilic copolymer self-assembles into spherical multicompartment micellar aggregates in aqueous solution, where the two hydrophobic blocks undergo local phase separation into various ultrastructures as evidenced by cryogenic transmission electron microscopy. Thus, a silicone-based polymer block can replace the hitherto typically employed fluorocarbon-based hydrophobic blocks in triphilic block copolymers for inducing multicompartmentalisation.     

Artin-Schreier extensions in NIP and simple fields

We show that NIP fields have no Artin-Schreier extension, and that simple fields have only a finite number of them.     

Stereoselective synthesis of individual isomers of Leu-enkephalin analogues containing substituted beta-turn bicyclic dipeptide mimetics

Novel constrained beta-turn dipeptide mimetics, 8-phenyl thiaindolizidinone amino acids 3, have been synthesized stereoselectively and incorporated into Leu-enkephalin peptides as a replacement of dipeptide Gly3-Phe4 to afford four individual isomers of Leu-enkephalin analogues 6.     

New Ga/N‐based Active Lewis Pairs,Trifunctional Ga–Ga Compounds,Reactions with Cyanamide and Dual Insertion of Isocyanate

Hydrogallation of Me₃Si–C≡C–NR'₂ with R₂Ga–H (R = tBu, CH₂tBu, iBu) yielded Ga/N‐based active Lewis pairs, R₂Ga–C(SiMe₃)=C(H)–NR'₂ ( 7 ). The Ga and N atoms adopt cis‐positions at the C=C bonds and show weak Ga–N interactions. tBu₂GaH and Me₃Si–C≡C–N(C₂H₄)₂NMe afforded under exposure of daylight the trifunctional digallium(II) compound [MeN(C₂H₄)₂N](H)C=C(SiMe₃)Ga(tBu)–Ga(tBu)C(SiMe₃)=C(H)[N(C₂H₄)₂NMe] ( 8 ), which results from elimination of isobutene and H₂ and Ga–Ga bond formation. 8 was selectively obtained from the ynamine and [tBu(H)Ga–Ga(H)tBu]₂[HGatBu₂]₂. 7a (R = tBu; NR'₂ = 2,6‐Me₂NC₅H₈) and H₈C₄N–C≡N afforded the adduct tBu₂Ga‐C(SiMe₃)=C(H)(2,6‐Me₂NC₅H₈) · N≡C–NC₄H₈ ( 11 ) with the nitrile bound to gallium. The analogous ALP with harder Al atoms yielded an adduct of the nitrile dimer or oligomers of the nitrile at room temperature. The reaction of 7a with Ph–N=C=O led to the insertion of two NCO groups into the Ga–C_vinyl bond to yield a GaOCNCN heterocycle with Ga bound to O and N atoms ( 12 ).     

A study of flux monitoring for instrumental neutron activation analysis

The accuracy of instrumental neutron activation analysis is dependent upon measurement of the neutron flux to which samples are submitted. Flux monitoring techniques described and evaluated include: target cooling water activity, BFa counters, plastic scintillators, and a simple reference sample system. Evaluation is made on the basis of results obtained for oxygen analysis using primary standard materials. The superiority of the reference sample system for flux measurement during irregular neutron flux production is shown.     

Monomers for Adhesive Polymers, 6

Summary: 1,3‐Bis(methacrylamido)propane‐2‐yl dihydrogen phosphate ( 1 ) was synthesised by phosphorylation of 1,3‐bis(methacrylamido)‐2‐hydroxypropane ( 2 ) with phosphorus oxychloride in tetrahydrofuran (THF) in the presence of triethylamine (TEA). The structure of the new monomer 1 was characterised by IR, ¹H NMR, ¹³C NMR and ³¹P NMR spectroscopies, elemental analysis and mass spectrometry. The monomer dissolves well in water, ethanol or aqueous THF and shows an improved hydrolytic stability compared to the corresponding methacrylate‐based dihydrogen phosphates. 1 was homopolymerised in ethanol with 2,2′‐azoisobutyronitrile (AIBN) as the initiator at 55–75 °C under the formation of an insoluble, cross‐linked product. Aqueous solutions of 1 are strongly acidic and enable to etch enamel and dentin. Nevertheless, 1 did not show any cytotoxic effect. Furthermore, the adhesive properties of 1 were measured.

1,3‐Bis(methacrylamido)propane‐2‐yl dihydrogen phosphate.