Invariants of 3-manifolds and projective representations of mapping class groups via quantum groups at roots of unity

An example of a finite dimensional factorizable ribbon Hopf -algebra is given by a quotientH=u _q (g) of the quantized universal enveloping algebraU _q (g) at a root of unityq of odd degree. The mapping class groupM _g,1 of a surface of genusg with one hole projectively acts by automorphisms in theH-moduleH ^*g , ifH ^* is endowed with the coadjointH-module structure. There exists a projective representation of the mapping class groupM _g,n of a surface of genusg withn holes labeled by finite dimensionalH-modulesX ₁, ...,X _n in the vector space Hom _H (X ₁ ... X _n ,H ^*g ). An invariant of closed oriented 3-manifolds is constructed. Modifications of these constructions for a class of ribbon Hopf algebras satisfying weaker conditions than factorizability (including most ofu _q (g) at roots of unityq of even degree) are described.This work was supported in part by the EPSRC research grant GR/G 42976.     

A heterotrimetallic Cu–Co–Zn complex with the 2,2′‐iminodiethanol ligand

The crystal structure of the title compound, triacetato‐1κO;3κ⁴O,O′‐(2,2′‐imino­diethanol)‐1κ³O,N,O′‐bis­(μ‐2,2′‐iminodi­ethanol­ato)‐1κ²O:2κ⁶O,N,O′:3κ²O′‐cobalt(III)copper(II)zinc(II), [CoCuZn(C₄H₉NO₂)₂(C₂H₃O₂)₃(C₄H₁₁NO₂)], shows a mol­ecule with a triangular three‐metal core. The metal sites were refined with full occupancies, but the possibility that the Zn and Cu positions are actually mixed Cu/Zn sites cannot be excluded. The inter­metallic Cu⋯Co and Co⋯Zn distances are 2.924 (3) and 2.906 (3) Å, respectively. The neutral mol­ecules are held together by N—H⋯O hydrogen bonds involving amine groups from the 2,2′‐iminodiethanol ligands and acetate groups to build two‐dimensional layers.     

Synthesis and Antioxidant Activity Evaluation of Novel 5,7-dimethyl-3H-Thiazolo[4,5-B]Pyridines

Abstract

5,7-Dimethyl-3H-thiazolo[4,5-b]pyridine-2-one was obtained under the reaction of 4-iminothiazolidin-2-one with acetylacetone. Further structural modifications include the introduction of diversity at the N³ and C⁶ positions. The antioxidant activity of the synthesized compounds was evaluated in vitro by the method of scavenging effect on 2,2-diphenyl-1-picrylhydrazyl (DPPH) radicals.

[Supplemental materials are available for this article. Go to the publisher's online edition of Phosphorus, Sulfur, and Silicon and the Related Elements to view the following free supplemental files: Additional figures]     

Crystal Structure and Non-Hydrostatic Stress-Induced Phase Transition of Urotropine Under High Pressure

High-pressure behavior of hexamethylenetetramine (urotropine) was studied in situ using angle-dispersive single-crystal synchrotron X-ray diffraction (XRD) and Fourier-transform infrared absorption (FTIR) spectroscopy. Experiments were conducted in various pressure-transmitting media to study the effect of deviatoric stress on phase transformations. Up to 4 GPa significant damping of molecular librations and atomic thermal motion was observed. A first-order phase transition to a tetragonal structure was observed with an onset at approximately 12.5 GPa and characterized by sluggish kinetics and considerable hysteresis upon decompression. However, it occurs only in non-hydrostatic conditions, induced by deviatoric or uniaxial stress in the sample. This behavior finds analogies in similar cubic crystals built of highly symmetric cage-like molecules and may be considered a common feature of such systems. DFT computations were performed to model urotropine equation of state and pressure dependence of vibrational modes. The first successful Hirshfeld atom refinements carried out for high-pressure diffraction data are reported. The refinements yielded more realistic C−H bond lengths than the independent atom model even though the high-pressure diffraction data are incomplete.     

Synthesis and Characterization of Oxazaborinin Phosphonate for Blue OLED Emitter Applications

A blue-light emitting material based on a boron complex containing heteroaromatic phosphonate ligand is synthesized and characterized. The Phospho-Fries rearrangement is used in the synthesis route of the ligand as a convenient method of introducing phosphonate groups into phenols. Structural, thermal and photophysical properties of the resulting oxazaborinin phosphonate compound have been characterized. DFT geometry optimizations were studied as well as the spatial position and symmetry of the HOMO and LUMO. Good thermal stability up to 250 °C enables vacuum deposition methods next to solution processing. Combining the work function with the optical band gap from UV-Vis measurements shows that band alignment is possible with standard contact materials. Photoluminescence reveals an emission peak at 428 nm, which is suitable for a blue light-emitter.     

Spin fluctuations in hydrogen-stabilized Laves phase UTi2H5

Uranium Laves phase UTi₂ does not exist in a pure form, but can be stabilised by the presence of hydrogen, which can be absorbed in concentration exceeding 5?H atoms/f.u. Low temperature specific heat, magnetic susceptibility, and resistivity indicate that UTi₂H₅ is a spin fluctuator close to the verge of magnetic ordering. Its susceptibility follows at high temperatures the Curie–Weiss law with U effective moment µ_eff[ ?= 3.1?µ_B/U and paramagnetic Curie temperature Θ_p = ?200 K. The temperature dependence of specific heat exhibits a pronounced and weakly field dependent upturn in C_p/T versus T below 10 K reflecting the effect of spin fluctuations. It can be described by an additional T^½ term. The Sommerfeld coefficient γ = 256?mJ/mol K² classifies the compound as a mid-weight heavy fermion. Spin fluctuations are affecting also electrical and thermal transport and thermoelectric power, which all resemble UAl₂. A lattice anomaly at ≈ 240?K, attributed to the melting of hydrogen sublattice, reflects in most of bulk properties.