Factorizations for self-dual gauge fields

For a particular class of patching matrices onP ₃(?), including those for the complex instanton bundles with structure group Sp(k,?) orO(2k,?), we show that the associated Riemann-Hilbert problemG(x, λ)=G?(x, λ)·G ₊ ^?1 (x, λ) can be generically solved in the factored formG _?=φ ₁ φ ₂.....φ _n . IfГ=Г _n is the potential generated in the usual way fromG _?, and we setψ _i =φ ₁.....,φ _i withψ _n =G _?, then eachψ _i also generates a selfdual gauge potentialΓ _i . The potentials are connected via the “dressing transformations” $$\Gamma _\iota = \phi _i^{ - 1} \cdot \Gamma _{\iota - 1} \cdot \phi _i + \phi _i ^{ - 1} D\phi _i$$ of Zakharov-Shabat. The factorization is not unique; it depends on the (arbitrary) ordering of the poles of the patching matrix.     

Synthese und Eigenschaften der Di‐tert‐butylphosphide [M(PtBu2)2]2 (M = Zn,Hg) und [Cu(PtBu2)]4

Syntheses and Properties of Di‐tert‐butylphosphides [M(PtBu₂)₂]₂ (M = Zn, Hg) and [Cu(PtBu₂)]₄ The phosphides [M(PtBu₂)₂]₂ (M = Zn, Hg) and [Cu(PtBu₂)]₄ are accessible from reaction of LiPtBu₂ with ZnI₂, HgCl₂ and CuCl, respectively. [M(PtBu₂)₂]₂ (M = Zn, Hg) are dimers in the solid state. X‐ray structural analyses of these phosphides reveal that [M(PtBu₂)₂]₂ (M = Zn, Hg) contain four‐membered M₂P₂‐rings whereas [Cu(PtBu₂)]₄ features a planar eight‐membered Cu₄P₄‐ring. Degradation reaction of LiPtBu₂(BH₃) in the presence of HgCl₂ results in the dimeric phosphanylborane BH₃ adduct [tBu₂PBH₂(BH₃)]₂. X‐ray quality crystals of [tBu₂PBH₂(BH₃)]₂ (monoclinic, P2₁/n) are obtained from a pentane solution at 6 °C. According to the result of the X‐ray structural analysis, the O₂‐oxidation product of [Hg(PtBu₂)₂]₂, [Hg{OP(O)(tBu)OPtBu₂}(μ‐OPtBu)]₂, features in the solid state structure two five‐membered HgP₂O₂‐rings and a six‐membered Hg₂P₂O₂‐ring. Herein the spiro‐connected Hg atoms are member of one five‐membered and of the six‐membered ring.     

Qualitative determination of low-molecular-weight organic acids in mixed hazardous wastes using thermospray liquid chromatography/mass spectrometry

A technique has been developed for the qualitative determination of low-molecular-weight organic acids in radioactive, mixed hazardous wastes using thermospray liquid chromatography/mass spectrometry. A tank waste was analyzed, and the results indicated the presence of citric, glycolic, acetic, and nitrosoiminodiacetic acid (NIDA). Further investigation revealed NIDA was formed under acidic conditions with the reaction of iminodiacetic acid and the high nitrate/nitrite concentration present in the waste.     

Consolidation of Bimetallic Nanosized Particles and Formation of Nanocomposites Depending on Conditions of Shock Wave Compaction

Russian Physics Journal - The authors consider and evaluate the physical parameters and regularities of the process of consolidation of Fe–Cu, Cu–Nb, Ag–Ni, Fe–Pb...     

Conformational studies on heteroleptic trifluoromethyl‐substituted phenylboranes

Organoboranes carrying electron‐withdrawing substituents are commonly used as Lewis acidic catalysts or cocatalysts in a variety of organic processes. These Lewis acids also became popular through their application in `frustrated Lewis pairs', i.e. combinations of Lewis acids and bases that are unable to fully neutralize each other due to steric or electronic effects. We have determined the crystal and molecular structures of four heteroleptic arylboranes carrying 2‐(trifluoromethyl)phenyl, 2,6‐bis(trifluoromethyl)phenyl, 3,5‐bis(trifluoromethyl)phenyl or mesityl substituents. [3,5‐Bis(trifluoromethyl)phenyl]bis[2‐(trifluoromethyl)phenyl]borane, C₂₂H₁₁BF₁₂, (I), crystallizes with two molecules in the asymmetric unit which show very similar geometric parameters. In one of the two molecules, both trifluoromethyl groups of the 3,5‐bis(trifluoromethyl)phenyl substituent are disordered over two positions. In [3,5‐bis(trifluoromethyl)phenyl]bis[2,6‐bis(trifluoromethyl)phenyl]borane, C₂₄H₉BF₁₈, (II), only one of the two meta‐trifluoromethyl groups is disordered. In [2,6‐bis(trifluoromethyl)phenyl]bis[3,5‐bis(trifluoromethyl)phenyl]borane, C₂₄H₉BF₁₈, (III), both meta‐trifluoromethyl groups of only one 3,5‐bis(trifluoromethyl)phenyl ring are disordered. [3,5‐Bis(trifluoromethyl)phenyl]dimesitylborane, C₂₆H₂₅BF₆, (IV), carries only one meta‐trifluoromethyl‐substituted phenyl ring, with one of the two trifluoromethyl groups disordered over two positions. In addition to compounds (I)–(IV), the structure of bis[2,6‐bis(trifluoromethyl)phenyl]fluoroborane, C₁₆H₆BF₁₃, (V), is presented. None of the ortho‐trifluoromethyl groups is disordered in any of the five compounds. In all the structures, the boron centre is in a trigonal planar coordination. Nevertheless, the bond angles around this atom vary according to the bulkiness and mutual repulsion of the substituents of the phenyl rings. Also, the ortho‐trifluoromethyl‐substituted phenyl rings usually show longer B—C bonds and tend to be tilted out of the BC₃ plane by a higher degree than the phenyl rings carrying ortho H atoms. A comparison with related structures corroborates the conclusions regarding the geometric parameters of the boron centre drawn from the five structures in this paper. On the other hand, CF₃ groups in meta positions do not seem to have a marked effect on the geometry involving the boron centre. Furthermore, it has been observed for the structures reported here and those reported previously that for CF₃ groups in ortho positions of the aromatic ring, disorder of the F atoms is less probable than for CF₃ groups in meta or para positions of the ring.     

Four (2,2′‐bipyridyl)(ferrocenyl)boronium derivatives

Crystal structures are reported for four (2,2′‐bipyridyl)(ferrocenyl)boronium derivatives, namely (2,2′‐bipyridyl)(ethenyl)(ferrocenyl)boronium hexafluoridophosphate, [Fe(C₅H₅)(C₁₇H₁₅BN₂)]PF₆, (Ib), (2,2′‐bipyridyl)(tert‐butylamino)(ferrocenyl)boronium bromide, [Fe(C₅H₅)(C₁₉H₂₂BN₃)]Br, (IIa), (2,2′‐bipyridyl)(ferrocenyl)(4‐methoxyphenylamino)boronium hexafluoridophosphate acetonitrile hemisolvate, [Fe(C₅H₅)(C₂₂H₂₀BN₃O)]PF₆·0.5CH₃CN, (IIIb), and 1,1′‐bis[(2,2′‐bipyridyl)(cyanomethyl)boronium]ferrocene bis(hexafluoridophosphate), [Fe(C₁₇H₁₄BN₃)₂](PF₆)₂, (IVb). The asymmetric unit of (IIIb) contains two independent cations with very similar conformations. The B atom has a distorted tetrahedral coordination in all four structures. The cyclopentadienyl rings of (Ib), (IIa) and (IIIb) are approximately eclipsed, while a bisecting conformation is found for (IVb). The N—H groups of (IIa) and (IIIb) are shielded by the ferrocenyl and tert‐butyl or phenyl groups and are therefore not involved in hydrogen bonding. The B—N(amine) bond lengths are shortened by delocalization of π‐electrons. In the cations with an amine substituent at boron, the B—N(bipyridyl) bonds are 0.035 (3) Å longer than in the cations with a methylene C atom bonded to boron. A similar lengthening of the B—N(bipyridyl) bonds is found in a survey of related cations with an oxy group attached to the B atom.