The Matsumoto-Yor property and the structure of the Wishart distribution

This paper establishes a link between a generalized matrix Matsumoto-Yor (MY) property and the Wishart distribution. This link highlights certain conditional independence properties within blocks of the Wishart and leads to a new characterization of the Wishart distribution similar to the one recently obtained by Geiger and Heckerman but involving independences for only three pairs of block partitionings of the random matrix.In the process, we obtain two other main results. The first one is an extension of the MY independence property to random matrices of different dimensions. The second result is its converse. It extends previous characterizations of the matrix generalized inverse Gaussian and Wishart seen as a couple of distributions.We present two proofs for the generalized MY property. The first proof relies on a new version of Herz's identity for Bessel functions of matrix arguments. The second proof uses a representation of the MY property through the structure of the Wishart.     

Structure and photochemistry of 18-diazo-1,4,7,10,13,16-hexaoxacyclononadeca-17,19-dione and its sodium and potassium complexes. Control of the ground-state conformation of 2-diazo-1,3-dicarbonyl fragment via host-guest complexation

[reaction: see text] The macrocyclic 18-diazo-1,4,7,10,13,16-hexaoxacyclononadeca-17,19-dione (3-diazo-2,4-dioxo-19-crown-6, 1) readily forms complexes with potassium (2, stability constant in methanol is K(K+) = 229 +/- 25 M(-1)) and sodium ions (3, K(Na+) = 84.2 +/- 7.9 M(-1) in methanol). According to B3LYP/6-31G+(d,p) calculations and temperature-dependent 1H NMR spectroscopy, the predominant conformation of 1 has a Z,Z arrangement of the diazo and carbonyl groups. The X-ray crystal structure analysis showed that the potassium complex (2) has the same Z,Z arrangement, while the sodium analogue (2) exists in conformation with Z,E geometry of the diazodicarbonyl moiety. Direct 254 nm photolysis of diazo compounds 1-3 in methanol results in the formation of 3-methoxy-2,4-dioxo-19-crown-6 (5), the product of the insertion of corresponding alpha,alpha'-dicarbonylcarbene into the O-H bond of the solvent. The triplet-sensitized photolysis of diazomalonates 1-3 produces 2,4-dioxo-19-crown-6 (6), which is apparently formed via the triplet state of the intervening carbene.     

Synthesis of gold nanorod/single-wall carbon nanotube heterojunctions directly on surfaces

This contribution describes the synthesis of gold nanorod (Au NR)/single-wall carbon nanotube (SWCNT) heterojunctions assembled directly on Si/SiOx substrates. SWCNTs are attached to amine-functionalized Si/SiOx substrates, and Au monolayer-protected clusters (MPCs) are adsorbed to the surface of SWCNTs through hydrophobic interactions. Seed-mediated reduction of HAuCl4 with ascorbic acid in the presence of cetyltrimethylammonium bromide (CTAB) onto the Au MPCs leads to the growth of larger Au nanostructures directly on the SWCNTs. Au NRs account for 19% of the nanostructures, some of which are attached directly to the sidewall and some at the ends of the SWCNTs. Raman spectroscopic measurements of SWCNTs before and after growth of the Au nanostructures reveal that the presence of Au leads to an approximately 50-fold enhancement of the Raman scattering signal. Combining 1D nanostructures of different materials (Au and carbon in this example) is of fundamental interest and may find use in nanoelectronics, chemical sensing, electrochemical, and spectroscopy applications.     

Studies on use of differential thermal and thermogravimetric techniques for checking compositions of some drug formulations

The suitability of the differential thermal and thermogravimetric techniques for the determination of compositions of solid and soft drug formulations has been studied. A total of 117 pharmaceutical preparations have been examined, including powders, dusting powders, capsules, granulates, tablets, tablets for sucking, effervescent tablets, dragees, suppositories and ointments. Both techniques have been shown to be applicable for identification of pharmaceutical preparations. A specification has been made of thermal processes which can be employed for assaying the main components of the preparations. A rough estimate of the relative errors has been given.

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Zusammenfassung Die Eignung der differentialthermoanalytischen und thermogravimetrischen Methoden zur Bestimmung der Zusammensetzung fester und weicher ArzeneiprÄparate wurde studiert. Eine Gesamtzahl von 117 pharmazeutischen PrÄparaten, einschliesslich Pulver, Streupulver, Kapseln, Granulate, Tabletten, Saugtabletten, Brausetabletten, Dragees, Suppositorien und Salben wurde untersucht. Beide Methoden erwiesen sich als anwendbar zur Identifizierung pharmazeutischer PrÄparate. Eine Spezifizierung der zur Bestimmung der Hauptkomponenten der PrÄparate geeigneten thermischen Prozesse wurde durchgeführt. Eine grobe SchÄtzung der relativen Fehler wurde gegeben.

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Résumé On a étudié l'utilité des techniques ATD et TG pour déterminer la composition des préparations pharmaceutiques solides et molles. On a soumis à l'examen un total de 117 préparations pharmaceutiques comprenant des poudres, des talcs, des capsules, des granulats, des tablettes, des tablettes à sucer, des tablettes effervescentes, des dragées, des suppositoires et des onguents. Les deux techniques se sont montrées applicables à l'identification des préparations pharmaceutiques. On a effectué une spécification des processus thermiques qui se prÊtent au dosage des composants essentiels des préparations. On a donné une évaluation approximative des erreurs relatives.

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Thermoanalytical assessment of the quality of edible and technical oils

An investigation of the thermal decomposition of fish oils and motor lubricating oils resulted in the elaboration of a new method, which, by utilizing the relationship between the temperatures of mass losses and the changes in the cnemical composition due to the oxidative and hydrolytic decomposition of fish oils and to the processes occuring in lubricating oils in the course of their service in the oils system of combustion engines, allows estimations of the physicochemical properties of these oils.

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Zusammenfassung In Zusammenhang mit der Ausarbeitung einer neuen Methode, die die Abschätzung der physikalisch-chemischen Eigenschaften von Fischölen und Motorschmierölen ermöglicht, wurde eine Untersuchung über die thermische Zersetzung dieser Öle durchgeführt. Als Grundlage dafür diente der Zusammenhang zwischen der Masseverlusttemperatur und der mit der oxidativen bzw. hydrolytischen Zersetzung von Fischölen und den Alterungsprozessen von Motorschmierölen in Verbrennungsmotoren in Verbindung stehenden Veränderung der chemischen Zusammensetzung.

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Thermal analysis of binary and ternary systems of salicylic acid,sodium salicylate and sodium hydrogen carbonate

The thermal decompositions of binary and ternary systems of salicylic acid, monosodium salicylate, disodium salicylate and sodium hydrogen carbonate were studied by thermogravimetry and differential thermal analysis. The possibility was shown of analyzing systems involving components which react with each other upon heat treatment. Use can be made of results of this work to follow the course and extent of the reaction employed in the commercial method of manufacturing sodium salicylate and to check declared compositions of salicylate mixtures.

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Zusammenfassung Die thermische Zersetzung binärer und ternärer Systeme, die Salicylsäure, Mononatriumsalicylat, Dinatriumsalicylat und Natriumhydrocarbonat enthalten, wurde untersucht. Die Möglichkeit der Analyse von Systemen, deren Komponenten bei Hitzebehandlung miteinander reagieren, wurde gezeigt. Die Ergebnisse dieser Arbeit gestatten den Verlauf und das Ausmaß der Reaktionen zu untersuchen, welche bei dem Herstellungsverfahren von handelsüblichen Natriumsalicylat ablaufen und die deklarierte Zusammensetzung von Salicylatmischungen zu prüfen.

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Résumé Etude par thermogravimétrie et analyse thermique différentielle de la décomposition thermique de systèmes binaires et ternaires constitués d' acide salicylique salicylate monosodique, de salicylate disodique et d'hydrogénocarbonate de sodium. On montre la possibilité d'analyser des systèmes dont les composants réagissent entre eux lors du traitement thermique. Les résultats de cette étude permettent de suivre le déroulement et le degré d'avancement de la réaction utilisée dans le procédé commercial de fabrication du salicylate de sodium et de contrôler la composition déclarée des mélanges de salicylates.

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Strategy for the synthesis of polymeric supports with hydrazone linkers for solid-phase alkylation of ketones and aldehydes

A new approach to polymeric supports useful for the immobilization of aldehydes and ketones via hydrazone linkers is reported. The new strategy gives supports with better properties and is effective for the synthesis of all supports previously used for the alkylation of ketones anchored as hydrazones. In contrast to other approaches, the new strategy also provided a polymer with an economical C2 spacer linker. The supports were used for immobilization of ketones 3-pentanone, acetone, N-benzylpiperidone, and aldehydes hexanal and 3-phenylpropanal in the form of their hydrazones. The polymer-supported hydrazones were subjected to alpha-alkylation (LDA/RX) followed by acidic, reductive, or oxidative cleavage/workup procedures to provide alpha-alkylated aldehydes or ketones as well as corresponding primary amines, alcohols, nitriles or acids.     

Optically active imidazole N-oxides derived from l-prolinamine1

Starting with (S)-1-benzylprolinamine and α-hydroxyimino ketones, enantiomerically pure bisheterocyclic imidazole N-oxides bearing the (S)-configured N-benzyl(pyrrolidin-2-yl)methyl residue were prepared. These N-oxides reacted with 2,2,4,4-tetramethylcyclobutane-1,3-dithione to give the corresponding optically active imidazole-2-thione derivatives via a sulfur transfer reaction. Reduction of the N-oxides with Raney-nickel led to deoxygenation, whereas catalytic hydrogenation (Pd/C) in ethanol occurred with simultaneous deoxygenation and debenzylation, leading to optically active 1-(pyrrolidin-2-yl)methyl-1H-imidazoles. Alkylation of the prepared imidazole N-oxides and their respective imidazoles with butyl and hexyl bromide and subsequent anion exchange gave optically active N-alkoxy- and N-alkylimidazolium tetrafluoroborates, respectively, with the properties of ‘room temperature ionic liquids’.