Understanding singularities in Cartan's and NSF geometric structures

In this work we establish a relationship between Cartan's geometric approach to third order ODEs and the 3-dim Null Surface Formulation (NSF). We then generalize both constructions to allow for caustics and singularities that necessarily arise in these formalisms.Comment: 22 pages, 2 figure

Synthesis and characterization of a tetrathia[7]helicenebased rhenium(I) complex

Tetrathia[7]helicenes (7-TH), formed by thiophene and benzene rings ortho-fused in an alternating fashion, are emerging as one of the most popular class of chiral helical-shaped molecules, thanks to their peculiar electronic and chiroptical properties suitable for manifold applications in different areas of science.1 In particular, transition metal-based 7-TH systems are an extremely appealing class of complexes, in which the coordination of metals with the \uf070-helical ligand, bearing appropriate coordinating functionalities, provides original chiral architectures. Indeed, the effective functionalization of the \uf061-position(s) of the terminal thiophene ring(s) of the 7-TH scaffold allows the introduction of a variety of substituents, including those with efficient coordinating ability (e.g. cyano2, phosphane3, phosphine oxide4). For example, Rh(I)5 and Au(I)6 complexes based on 7-TH phosphanes have been successfully used in the homogenous transition metal catalysis. In our ongoing studies on 7-TH-based organometallic complexes, we have focused on a novel field of investigation concerning the development of rhenium-based polynuclear complexes containing 7-TH phosphine oxide ligands. In this communication, we describe the synthesis and the characterization of a novel dinuclear rhenium(I) complex (Figure 1), along with the elucidation of its tridimensional structure by single crystal X-ray diffraction studies

Study of the deactivation of a commercial catalyst for ethylbenzene dehydrogenation to styrene

The catalytic performance and characteristics of an industrial catalyst, fresh and spent, i.e. downloaded from an industrial reactor after a normal lifetime cycle, were compared. Some different causes of catalyst deactivation, such as loss or redistribution of promoters, active phase modification, Fe 3+ reduction, coke deposition on catalyst surface and physical modifications, were evidenced by means of several techniques. All the mentioned causes of deactivation showed strictly interconnected and concurred to the decrease of conversion. However, the key factors leading to irreversible deactivation showed potassium migration towards the inner part of the extrudate particle, its agglomeration into concentrated spots and its volatilisation from the surface, together with the progressive Fe3+ reduction to Fe 2+. These modifications led to the enhancement of coking activity and to the loss of mechanical properties, so making deactivation irreversible

Solid-state Nonlinear Optical Properties of Mononuclear Copper(II) Complexes with Chiral Tridentate and Tetradentate Schiff Base Ligands

Salen-type metal complexes have been actively studied for their nonlinear optical (NLO) properties, and push-pull compounds with charge asymmetry generated by electron releasing and withdrawing groups have shown promising results. As a continuation of our research in this field and aiming at solid-state features, herein we report on the synthesis of mononuclear copper(II) derivatives bearing either tridentate N2O Schiff bases L(a-c)- and pyridine as the forth ancillary ligand, [Cu(La-c)(py)](ClO4) (1a-c), or unsymmetrically-substituted push-pull tetradentate N2O2 Schiff base ligands, [Cu(5-A-5'-D-saldpen/chxn)] (2a-c), both derived from 5-substituted salicylaldehydes (sal) and the diamines (1R,2R)-1,2-diphenylethanediamine (dpen) and (1S,2S)-1,2-diaminocyclohexane (chxn). All compounds were characterized through elemental analysis, infrared and UV/visible spectroscopies, and mass spectrometry in order to guarantee their purity and assess their charge transfer properties. The structures of 1a-c were determined via single-crystal X-ray diffraction studies. The geometries of cations of 1a-c and of molecules 2a-c were optimized through DFT calculations. The solid-state NLO behavior was measured by the Kurtz-Perry powder technique @1.907 µm. All chiral derivatives possess non-zero quadratic electric susceptibility (χ(2)) and an efficiency of about 0.15-0.45 times that of standard urea

Square-tiled cyclic covers

A cyclic cover of the complex projective line branched at four appropriate points has a natural structure of a square-tiled surface. We describe the combinatorics of such a square-tiled surface, the geometry of the corresponding Teichm\"uller curve, and compute the Lyapunov exponents of the determinant bundle over the Teichm\"uller curve with respect to the geodesic flow. This paper includes a new example (announced by G. Forni and C. Matheus in \cite{Forni:Matheus}) of a Teichm\"uller curve of a square-tiled cyclic cover in a stratum of Abelian differentials in genus four with a maximally degenerate Kontsevich--Zorich spectrum (the only known example found previously by Forni in genus three also corresponds to a square-tiled cyclic cover \cite{ForniSurvey}). We present several new examples of Teichm\"uller curves in strata of holomorphic and meromorphic quadratic differentials with maximally degenerate Kontsevich--Zorich spectrum. Presumably, these examples cover all possible Teichm\"uller curves with maximally degenerate spectrum. We prove that this is indeed the case within the class of square-tiled cyclic covers.Comment: 34 pages, 6 figures. Final version incorporating referees comments. In particular, a gap in the previous version was corrected. This file uses the journal's class file (jmd.cls), so that it is very similar to published versio

Improvements in cytological preparations for fluorescent in situ hybridization in Passiflora

Cytological preparations for the fluorescent in situ hybridization (FISH) technique require cytoplasm-free metaphases, with well-spread chromosomes, for the localization of DNA sequences and chromosome mapping. We tested various procedures for FISH analysis of Passiflora cacaoensis, P. gardneri and hybrid F₁ progeny of P. gardneri x P. gibertii. Two treatments with four enzymes and three incubation times were compared. The material was treated with 1.0 M HCl before enzymatic digestion. The following criteria were used to determine the quality of the metaphases: a) lack or presence of cytoplasm; b) well-spread chromosomes or with overlap; c) complete or incomplete chromosome number (2n). The enzyme Pectinex(®) SP ULTRA gave the best performance, with the shortest incubation time. The best results were observed after 30 min of incubation; more than 70% of the metaphases did not have large amounts of cytoplasm or overlapping chromosomes, and about 75% maintained the chromosome number. FISH was carried out using a 45S rDNA probe (pTa71) labeled with biotin and detected with fluorescein isothiocyanate. Sites with strong staining and without nonspecific signals were observed. Our methodological adaptations allowed the preparation of metaphase slides of high quality for the FISH technique, with less time required for the preparation of samples.Fil: Souza, M. M.. Universidade Estadual de Santa Cruz. Departamento de Ciências Biológicas; BrasilFil: Urdampilleta, Juan Domingo. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Córdoba. Instituto Multidisciplinar de Biología Vegetal (p). Grupo Vinculado Centro de Relevamiento y Evaluacion de Recursos Agricolas y Naturales; ArgentinaFil: Forni Martins, E. R.. Universidade Estadual de Campinas. Instituto de Biologia. Departamento de Biologia Vegetal; Brasi

The Origin of the σ-Hole in Halogen Atoms: a Valence Bond Perspective

A detailed Valence Bond-Spin Coupled analysis of a series of halogenated molecules is here reported, allowing to get a rigorous ab initio demonstration of the qualitative models previously proposed to explain the origin of halogen bonding. The concepts of σ-hole and negative belt observed around the halogen atoms in the electrostatic potential maps are here interpreted by analysis of the relevant Spin Coupled orbitals