Existence of many ergodic absolutely continuous invariant measures for piecewise-expandingC 2 chaotic transformations in ℝ2 on a fixed number of partitions

Let Ω be a region in ℝⁿ and letp = P_i ) _i ^1m , be a partition ofΩ into a finite number of closed subsets having piecewise C² boundaries of finite(n - 1 )dimensional measure. Let τ:Ω→Ω be piecewise C² onP where, τ_i = τ|p_i is aC ² diffeomorphism onto its image, and expanding in the sense that there exists α > 1 such that for anyi = 1, 2,...,m ‖Dτ_i ^-1 ‖ < α^-1, where Dτ_i ^-1 is the derivative matrixτ _i ^- 1 and |‖·‖ is the Euclidean matrix norm. By means of an example, we will show that the simple bound of one-dimensional dynamics cannot be generalized to higher dimensions. In fact, we will construct a piecewise expanding C² transformation on a fixed partition with a finite number of elements in ℝ², but which has an arbitrarily large number of ergodic, absolutely continuous invariant measures     

Structure elucidation and 1H/13C NMR spectral assignments of four trabectedin related compounds

This article presents the structure elucidation of four new compounds, formed during the hemisynthetic preparation of trabectedin, an anti-tumor natural product from Ecteinascidia turbinata. We report herein on the use of UV, MS and NMR spectroscopic data along with (1)H and (13)C spectral assignments obtained by means of 1D and 2D homo- and heteronuclear NMR techniques.     

Efficient approach for the detection and identification of new androgenic metabolites by applying SRM GC‐CI‐MS/MS: a methandienone case study

Identification of anabolic androgenic steroids (AAS) is a vital issue in doping control and toxicology, and searching for metabolites with longer detection times remains an important task. Recently, a gas chromatography chemical ionization triple quadrupole mass spectrometry (GC‐CI‐MS/MS) method was introduced, and CI, in comparison with electron ionization (EI), proved to be capable of increasing the sensitivity significantly. In addition, correlations between AAS structure and fragmentation behavior could be revealed. This enables the search for previously unknown but expected metabolites by selection of their predicted transitions. The combination of both factors allows the setup of an efficient approach to search for new metabolites. The approach uses selected reaction monitoring which is inherently more sensitive than full scan or precursor ion scan. Additionally, structural information obtained from the structure specific CI fragmentation pattern facilitates metabolite identification. The procedure was demonstrated by a methandienone case study. Its metabolites have been studied extensively in the past, and this allowed an adequate evaluation of the efficiency of the approach. Thirty three metabolites were detected, including all relevant previously discovered metabolites. In our study, the previously reported long‐term metabolite (18‐nor‐17β‐hydroxymethyl,17α‐methyl‐androst‐1,4,13‐trien‐3‐one) could be detected up to 26 days by using GC‐CI‐MS/MS. The study proves the validity of the approach to search for metabolites of new synthetic AAS and new long‐term metabolites of less studied AAS and illustrates the increase in sensitivity by using CI. Copyright © 2016 John Wiley & Sons, Ltd.     

Microstructural impact of anodic coatings on the electrochemical chlorine evolution reaction

Sol-gel Ru(0.3)Sn(0.7)O(2) electrode coatings with crack-free and mud-crack surface morphology deposited onto a Ti-substrate are prepared for a comparative investigation of the microstructural effect on the electrochemical activity for Cl(2) production and the Cl(2) bubble evolution behaviour. For comparison, a state-of-the-art mud-crack commercial Ru(0.3)Ti(0.7)O(2) coating is used. The compact coating is potentially durable over a long term compared to the mud-crack coating due to the reduced penetration of the electrolyte. Ti L-edge X-ray absorption spectroscopy confirms that a TiO(x) interlayer is formed between the mud-crack Ru(0.3)Sn(0.7)O(2) coating and the underlying Ti-substrate due to the attack of the electrolyte. Meanwhile, the compact coating shows enhanced activity in comparison to the commercial coating, benefiting from the nanoparticle-nanoporosity architecture. The dependence of the overall electrode polarization behaviour on the local activity and the bubble evolution behaviour for the Ru(0.3)Sn(0.7)O(2) coatings with different surface microstructure are evaluated by means of scanning electrochemical microscopy and microscopic bubble imaging.     

[BuN(CH2CH2)3NBu]3[Pb5I16] · 4 DMF – ein Iodoplumbat mit nahezu D5h‐symmetrischem Anion

[BuN(CH₂CH₂)₃NBu]₃[Pb₅I₁₆] · 4 DMF – an Iodoplumbate Anion with approximately D _5h Symmetry The star‐shaped anion of [BuN(CH₂CH₂)₃NBu]₃‐[Pb₅I₁₆] · 4 DMF ( 1 ) consists of a cyclic arrangement of five PbI₆ octahedra sharing one common I atom in the centre of an almost planar Pb₅ ring. Compound 1 crystallizes in space group P2₁ with a = 1657.2(1), b = 2029.2(1), c = 1773.6(1) pm, β = 113.238(8)°, Z = 2.     

Diastereoselective Strategies towards Thia[n]helicenes

In the present study, we have investigated different strategies for diastereoselective synthesis of thia[n]helicenes. We describe the introduction of different chiral auxiliaries at various positions and investigated their effect in the photocyclization reaction. Different chiral groups were placed at the sterically hindered position of the helical core and their interactions with various solvents and metals like copper were investigated. The use of Cu^I salts has led to high diastereoselectivity in the photocyclization process and we were successful in obtaining the thia[5]helicene in enantiomerically pure form in good yield. The single diastereomer obtained was characterized by X‐ray crystallography. From the study of the barrier of racemization of these thia[5]helicenes, the stability was found to be comparable to unsubstituted tetrathia[7]helicenes and substituted diazadithia[7]helicenes. This approach provides an easy access to enantiopure helicenes.     

E2(CN)2 (E = S, Se) and related compounds

A synthetic, spectroscopic, and theoretical study of Ex(CN)2 (E = S, Se; x = 1-3) is described. The X-ray structures of Se2(CN)2 and Se3(CN)2 have been determined. Se2(CN)2 crystallizes in a chiral space group with the CN groups approximately gauche.     

A Geometric characterization of the perfect Suzuki-Tits ovoids

We characterize in a geometrical way those Suzuki-Tits ovoids which are defined over a perfect fieidK (or equivalently living inside a self polar symplectic quadrangle). We simplify our axioms in the particular cases that (1) the associated Suzuki group has exactly two orbits in the set of lines ofPG(3,K), and (2) the ovoid is finite.Senior Research Associate at the Belgian National Fund for Scientific Research