Weak chaos and anomalous transport: a deterministic approach

We review how transport properties for chaotic dynamical systems may be studied through cycle expansions, and show how anomalies can be quantitatively described by hierarchical sequences of periodic orbits.     

Competitive Gold‐Promoted Meyer–Schuster and oxy‐Cope Rearrangements of 3‐Acyloxy‐1,5‐enynes: Selective Catalysis for the Synthesis of (+)‐(S)‐γ‐Ionone and (−)‐(2S,6 R)‐cis‐γ‐Irone

We report a simple, highly stereoselective synthesis of (+)‐(S)‐γ‐ionone and (‐)‐(2S,6R)‐cis‐γ‐irone, two characteristic and precious odorants; the latter compound is a constituent of the essential oil obtained from iris rhizomes. Of general interest in this approach are the photoisomerization of an endo trisubstituted cyclohexene double bond to an exo vinyl group and the installation of the enone side chain through a [(NHC)Au^I]‐catalyzed Meyer–Schuster‐like rearrangement. This required a careful investigation of the mechanism of the gold‐catalyzed reaction and a judicious selection of reaction conditions. In fact, it was found that the Meyer–Schuster reaction may compete with the oxy‐Cope rearrangement. Gold‐based catalytic systems can promote either reaction selectively. In the present system, the mononuclear gold complex [Au(IPr)Cl], in combination with the silver salt AgSbF₆ in 100:1 butan‐2‐one/H₂O, proved to efficiently promote the Meyer–Schuster rearrangement of propargylic benzoates, whereas the digold catalyst [{Au(IPr)}₂(μ‐OH)][BF₄] in anhydrous dichloromethane selectively promoted the oxy‐Cope rearrangement of propargylic alcohols.     

On the structure of the automorphism group of certain automorphic loop

Automorphic loops, or A-loops, are loops in which all inner mappings are automorphisms. We investigated A-loops arising from a Lie algebra and describe their automorphism group. Also, we identify and describe their inner mapping group.     

A large displacement formulation for anisotropic beam analysis

Summary The displacement of a beam can be conveniently resolved into a roto-translational section displacement and a section warping. The correct second order approximation of the strain is deduced accounting for large displacements and thus for large rotations. On the basis of displacement method, both linear and nonlinear formulations are given: the first one leads to the elastic section properties and to the correct characterization of section warping; the second one leads to the so-called geometric section stiffness, accounting for prestress. Both formulations are general with respect to elastic material properties, thus allowing to deal with aniso-tropic and unhomogeneous cross-sections. Elastic and geometric section rigidities here proposed can then be easily used in second order problems on beam frames: either initial buckling eigenvalue analyses, either large displacement incremental analyses.

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Sommario E' conveniente scomporre lo spostamento di un punto di una trave in una rototraslazione della sezione cui appartiene e in uno spostamento che deforma la sezione (in-gobbamento). Si deduce la corretta approssimazione al second'ordine della deformazione per grandi spostamenti e quindi grandi rotazioni. Vengono presentate sia la formulazione lineare che quella non lineare, basate sul metodo degli spostamenti: dalla prima si ottengono le caratteristiche elastiche della sezione e la corretta caratterizzazione dell'ingob-bamento; dalla seconda la cosiddetta rigidezza geometrica della sezione che tiene conto dello stato di presforzo. Entrambe le formulazioni sono generali per quanto riguarda le proprietà del materiale elastico, potendosi così considerare anche sezioni anisotrope e non omogenee. Le caratteristiche di rigidezza elastica e geometrica della sezione possono quindi facilmente essere usate in problemi del second'ordine su strutture a travi: sia analisi agli autovalori della stabilità, sia analisi incrementali con grandi spostamenti.

     

w-Stability and Clifford w-Regularity of Polynomial Rings

We investigate the transfer of w-stability and Clifford w-regularity from a domain D to the polynomial ring D[X]. We show that these two properties pass from D to D[X] when D is either integrally closed or it is Mori and w-divisorial.     

Single-crystal X-ray diffraction at megabar pressures and temperatures of thousands of degrees

The most reliable information about crystal structures and their response to changes in pressure and temperature is obtained from single-crystal diffraction experiments. We have developed a methodology to perform single-crystal X-ray diffraction experiments in laser-heated diamond anvil cells and demonstrate that structural refinements and accurate measurements of the thermal equation of state of metals, oxides and silicates from single-crystal intensity data are possible in pressures ranging up to megabars and temperatures of thousands of degrees. A new methodology was applied to solve the in situ high pressure, high temperature structure of iron oxide and study structural variations of iron and aluminum bearing silicate perovskite at conditions of the Earth's lower mantle.     

Single‐crystal diffraction at the Extreme Conditions beamline P02.2: procedure for collecting and analyzing high‐pressure single‐crystal data

Fast detectors employed at third‐generation synchrotrons have reduced collection times significantly and require the optimization of commercial as well as customized software packages for data reduction and analysis. In this paper a procedure to collect, process and analyze single‐crystal data sets collected at high pressure at the Extreme Conditions beamline (P02.2) at PETRA III, DESY, is presented. A new data image format called `Esperanto' is introduced that is supported by the commercial software package CrysAlis^Pro (Agilent Technologies UK Ltd). The new format acts as a vehicle to transform the most common area‐detector data formats via a translator software. Such a conversion tool has been developed and converts tiff data collected on a Perkin Elmer detector, as well as data collected on a MAR345/555, to be imported into the CrysAlis^Pro software. In order to demonstrate the validity of the new approach, a complete structure refinement of boron‐mullite (Al₅BO₉) collected at a pressure of 19.4 (2) GPa is presented. Details pertaining to the data collections and refinements of B‐mullite are presented.     

Pyrazolo[3,4-d][1,2,3]triazolo[1,5-a]pyrimidine: a new ring system through Dimroth rearrangement

Derivatives of the new ring system pyrazolo[3,4-d][1,2,3]triazolo[1,5-a]pyrimidine were synthesized from the corresponding angular isomers, through a Dimroth rearrangement, in quantitative yields. Preliminary computational studies demonstrated that this class of compounds could be a good candidate as DNA intercalating agents.     

Chiral acetylenes as synthetic intermediates—II: Optically active 1,4-dialkylbuta-1,3-dienes: synthesis and conformational studies

The synthesis and the physical properties of some optically active 1,4-dialkylbuta-1,3-dienes are reported. The synthetic processes employed were essentially stereospecific. NMR, UV and CD spectra of these compounds provide information on the main conformation of the conjugated diene system, which was shown to be s-trans planar.