Bi‐embeddability spectra and bases of spectra

We study degree spectra of structures with respect to the bi‐embeddability relation. The bi‐embeddability spectrum of a structure is the family of Turing degrees of its bi‐embeddable copies. To facilitate our study we introduce the notions of bi‐embeddable triviality and basis of a spectrum. Using bi‐embeddable triviality we show that several known families of degrees are bi‐embeddability spectra of structures. We then characterize the bi‐embeddability spectra of linear orderings and study bases of bi‐embeddability spectra of strongly locally finite graphs.     

Formalization of the “Twin Paradox” for Non-uniformly Accelerated Motions

The use of hyperbolic numbers for studying space-time geometry and trigonometry is extended for demonstrating the Frenet’s formulas in space-time. By means of this introduction the twin paradox for non-uniformly accelerated motions is formalized in a straightforward way.     

A general empiral equation for salt effects

A general quantitative treatment for salt effects by means of an empirical relationship between the observed rates k and the concentrations of added electrolyte is presented. The proposed equation has been successfully tested for a variety of processes in the literature.     

Origin of the sphere-to-rod transition in cationic micelles with aromatic counterions: specific ion hydration in the interfacial region matters

Sphere-to-rod transitions of cetyltrimethylammonium (CTA+) micelles with dichlorobenzoate counterions are remarkably substituent dependent. Simultaneous estimates of the interfacial molarities of H2O, MeOH, and Cl- and 2,6- and 3,5-dichlorobenzoate (2,6OBz and 3,5OBz) counterions were obtained by the chemical trapping method in mixed micelles of CTACl/CTA3,5OBz and CTACl/CTA2,6OBz without added salt. Increasing the CTA3,5OBz mole fraction produces a marked concurrent increase in interfacial 3,5OBz- and a decrease in interfacial H2O concentrations through the sphere-to-rod transition. No abrupt concentration changes are observed with increasing CTA2,6OBz mole fraction. Counterion-specific changes in the interfacial water concentration may be a major contributor to the delicate balance of forces governing micellar morphology.     

Expeditious access to the most easily ionized closed-shell molecule, W2(hpp)4

A new synthetic path, far superior to either of those previously available, to the W2(hpp)4 molecule (Hhpp = 1,3,4,6,7,8-hexahydro-2H-pyrimido[1,2-a]pyrimidine) is reported. The reaction of W(CO)6 with Hhpp in o-dichlorobenzene at 200 degrees C produces W2(hpp)4Cl2 in a one-pot reaction in over 90% yield. This compound is stable and easily stored for further use, and it can be efficiently reduced in a one-step reaction to the title compound W2(hpp)4.     

Entwicklung analytischer Methoden für einige biologische Abbauprodukte des Tryptophans

Zusammenfassung Es wird über Methoden für den Nachweis und die Bestimmung kleiner Mengen verschiedener Abbauprodukte des Tryptophans — auch in biologischen Flüssigkeiten —, die von zahlreichen Autoren ausgearbeitet wurden, berichtet. Hierbei handelt es sich um Kynurenin, 3-Hydroxykynurenin, Anthranilsäure und 3-Hydroxyanthranilsäure, Kynuren- und Xanthurensäure. Um das Interesse an jenen Forschungen verständlich zu machen, wird kurz hervorgehoben, daß sich die Anwendung dieser analytischen Methoden nicht auf die biologische Forschung beschränkt, sondern sich auf die Physiopathologie des Menschen ausdehnen läßt.

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Summary A report is given of methods for detecting and determining slight amounts of various degradation products of tryptophan — even in biological fluids, which were developed by various workers. Kynurenin, 3-hydroxykynurenin, anthranilic acid and 3-hydroxyanthranilic acid, kynurenic- and xanthurenic acid are included. To clarify the interest in such studies, it is briefly stressed that the application of these analytical methods is not restricted to biological studies but they can be extended to human physio-pathology.

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Résumé Communication sur les méthodes d'identification et de dosage de faibles quantités de différents produits de dégradation du tryptophane, qui ont été les objets des travaux de nombreux auteurs. Il s'agit de la kynurénine, de la 3-hydroxykynurénine, de l'acide anthranilique et de l'acide 3-hydroxyanthranilique, des acides kynurénique et xanthurénique. L'auteur indique brièvement l'intérêt de ces méthodes analytiques dont l'emploi n'est pas limité aux recherches biologiques mais peut être étendu aux recherches sur la physiopathologie de l'homme.

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Vorgetragen im Rahmen des Symposiums für angewandte Mikrochemie in Graz, 8. bis 11. April 1956.     

Preparation of annulated nitrogen-containing heterocycles via a one-pot palladium-catalyzed alkylation/direct arylation sequence

[reaction: see text] A palladium-catalyzed/norbornene-mediated sequential coupling reaction involving an aromatic sp(2) C-H functionalization as the key step is described, in which an alkyl-aryl bond and an aryl-heteroaryl bond are formed in one pot. A variety of highly substituted six- and seven-membered annulated pyrroles and pyrazoles were synthesized in a one-step process in good yields from readily accessible N-bromoalkyl pyrroles or pyrazoles and aryl iodides.     

The crystal and molecular structures of isoperezone, aminoperezone, and isoaminoperezone: a comparative study of their crystal packing

The crystal structures of isoperezone (1), aminoperezone (2), and isoaminoperezone (3) have been determined by single-crystal X-ray diffraction. Compound (1) yields orange crystals, orthorhombic space group P2₁2₁2₁ with unit cell dimensions a = 6.271(6), b = 30.373(7), c = 7.257(1) Å, and Z = 4; compound (2) yields purple crystals, orthorhombic space group P2₁2₁2₁ with unit cell dimensions a = 6.498(3), b = 7.500(1) c = 29.200(6) Å, and Z = 4; compound (3) yields purple crystals, monoclinic space group P2₁ with unit cell dimensions a = 7.354(1), b = 7.511(1), c = 13.283(1) Å, = 102,07(1)°, and Z = 2. The side chains in (1)–(3) are oriented out of the plane of the quinone ring at an angle of 124, 144, and 97°, respectively. The molecules in the crystal are held together by hydrogen-bonding networks and van der Waals interactions.     

Nucleophilic addition of phenol derivatives to methyl 1-nitrocyclopropanecarboxylates

Nucleophilic ring opening of methyl 1-nitrocyclopropanecarboxylates by phenol derivatives in the presence of Cs2CO3 is described. The reaction tolerates a variety of substituents on both the aromatic alcohol and the cyclopropane and affords the products in good yields (53-84%) and with complete preservation of the enantiomeric excess at C-4. The methodology was applied in an enantioselective synthesis of the norepinephrine reuptake inhibitor atomoxetine (Strattera).     

[U(bipy)4]: A Mistaken Case of U0?

After more than 50 years, the synthesis and electronic structure of the first and only reported “U⁰ complex” [U(bipy)₄] ( 1 ) has been reinvestigated. Additionally, its one‐electron reduced product [Na(THF)₆][U(bipy)₄] ( 2 ) has been newly discovered. High resolution crystallographic analyses combined with magnetic and computational data show that 1 and its derivative 2 are best described as highly reduced species containing mid‐to‐high‐valent uranium ligated by redox non‐innocent ligands.