Newton–Hensel Interpolation Lifting

The main result of this paper is a new version of Newton-Hensel lifting that relates to interpolation questions. It allows one to lift polynomials in ℤ[x] from information modulo a prime number p ≠ 2 to a power p^k for any k, and its originality is that it is a mixed version that not only lifts the coefficients of the polynomial but also its exponents. We show that this result corresponds exactly to a Newton--Hensel lifting of a system of 2t generalized equations in 2t unknowns in the ring of p-adic integers ℤ_p. Finally, we apply our results to sparse polynomial interpolation in ℤ[x].     

XPS investigations of the electrochemical double layer on silver in alkaline chloride solutions

The electrochemical double layer on Ag in alkaline NaCl solutions was examined ex situ with X-ray photoelectron spectroscopy (XPS). The specimens were removed from the electrolyte with hydrophobic surfaces and under potential control. The potential dependent surface concentrations of the adsorbed anions (Cl⁻, OH⁻), cations (Na⁺), the surface excess charge and the amount of adsorbed water were determined and compared to the results obtained for acidic NaCl solutions. The distinct differeness found between both electrolytes were discussed in terms of a specific adsorption of hydroxide ions in the basic Cl⁻-electrolyte; i.e., the OH⁻-surface concentration has to be considered for a proper determination of the cationic excess charge and the potential of zero charge. In addition, the initial stages of silver (1) oxide formation were examined with XPS.     

Comparison of Physical and Photophysical Properties of Monometallic and Bimetallic Ruthenium(II) Complexes Containing Structurally Altered Diimine Ligands

The physical and photophysical properties of a series of monometallic, [Ru(bpy)(2)(dmb)](2+), [Ru(bpy)(2)(BPY)](2+), [Ru(bpy)(Obpy)](2+) and [Ru(bpy)(2)(Obpy)](2+), and bimetallic, [{Ru(bpy)(2)}(2)(BPY)](4+) and [{Ru(bpy)(2)}(2)(Obpy)](4+), complexes are examined, where bpy is 2,2'-bipyridine, dmb is 4,4'-dimethyl-2,2'-bipyridine, BPY is 1,2-bis(4-methyl-2,2'-bipyridin-4'-yl)ethane, and Obpy is 1,2-bis(2,2'-bipyridin-6-yl)ethane. The complexes display metal-to-ligand charge transfer transitions in the 450 nm region, intraligand pi --> pi transitions at energies greater than 300 nm, a reversible oxidation of the ruthenium(II) center in the 1.25-1.40 V vs SSCE region, a series of three reductions associated with each coordinated ligand commencing at -1.3 V and ending at approximately -1.9 V, and emission from a (3)MLCT state having energy maxima between 598 and 610 nm. The Ru(III)/Ru(II) oxidation of the two bimetallic complexes is a single, two one-electron process. Relative to [Ru(bpy)(2)(BPY)](2+), the Ru(III)/Ru(II) potential for [Ru(bpy)(2)(Obpy)](2+) increases from 1.24 to 1.35 V, the room temperature emission lifetime decreases from 740 to 3 ns, and the emission quantum yield decreases from 0.078 to 0.000 23. Similarly, relative to [{Ru(bpy)(2)}(2)(BPY)](4+), the Ru(III)/Ru(II) potential for [{Ru(bpy)(2)}(2)(Obpy)](4+) increases from 1.28 to 1.32 V, the room temperature emission lifetime decreases from 770 to 3 ns, and the room temperature emission quantum yield decreases from 0.079 to 0.000 26. Emission lifetimes measured in 4:1 ethanol:methanol were temperature dependent over 90-360 K. In the fluid environment, emission lifetimes display a biexponential energy dependence ranging from 100 to 241 cm(-)(1) for the first energy of activation and 2300-4300 cm(-)(1) for the second one. The smaller energy is attributed to changes in the local matrix of the chromophores and the larger energy of activation to population of a higher energy dd state. Explanations for the variations in physical properties are based on molecular mechanics calculations which reveal that the Ru-N bond distance increases from 2.05 ? (from Ru(II) to bpy and BPY) to 2.08 ? (from Ru(II) to Obpy) and that the metal-to-metal distance increases from approximately 7.5 ? for [{Ru(bpy)(2)}(2)(Obpy)](4+) to approximately 14 ? for [{Ru(bpy)(2)}(2)(BPY)](4+).     

Studies of delocalized electron bonding

A calculation of the ethane barrier is made using a six-electron model in which all single exchange interactions are included. A barrier of 0.6 Kcal. per mole favoring the staggered configuration is calculated. The wave function is used to calculate the NMR proton spin-spin coupling constants, which are found to be at variance with the experimental values. The factors which influence these calculated results are discussed.

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Zusammenfassung Die Potentialschwelle für die innere Rotation des Äthans wird mit einem Sechselektronen-modell unter Einschluß aller Austauschintegrale berechnet. Man erhält eine Schwelle von 0,6 kcal/Mol zugunsten der trans-Konfiguration. Die mit der Eigenfunktion berechneten magnetischen Spin-Spin-Kopplungskonstanten der Protonen weichen von den experimentellen Werten ab. Die die berechneten Werte beeinflussenden Faktoren werden diskutiert.

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Résumé La barrière de potentiel de la rotation intramoléculaire de léthane est calculée à l'aide d'un modèle à 6 électrons et tenant compte de toutes les interactions d'échange. On la calcule à 0,6 kcal/mole en faveur de la configuration trans. Avec la fonction d'onde sont calculées les constantes de couplage magnétique des spins protoniques; elles sont en désaccord avec les valeurs expérimentales. Les facteurs influençant ces résultats sont discutés.

     

A stereocontrolled synthesis of delta-trans-tocotrienoloic acid

[reaction: see text] A concise stereoselective total synthesis of a naturally occurring polymerase beta inhibitor, delta-trans-tocotrienoloic acid (2), is described. The key step in the synthesis is an acid-catalyzed cyclodehydration reaction. Additionally, this report corrects a previously reported structural assignment, defines the absolute stereochemistry of 2, and defines key structural requirements for polymerase beta inhibition.     

A simple class ofU(N) Racah coefficients and their application

Using permutation group techniques, a general expression is derived for the special class ofU(N) Racah coefficients for which the representations [f ¹] and [f ³] in the recoupling matrix for [f ¹]×[f ²]×[f ³][f] are either both totally antisymmetric or both totally symmetric. For the totally antisymmetric case further specialization gives a simple expression for aU(N) Racah coefficient which is needed in taking the average of the product of operators over the states of an irreducible representation ofU(N), where this result can be useful in the study of identical fermion systems by spectral distribution methods.Supported by the US National Science Foundation.     

Radiochemische Versuche zur Optimierung der Extraktionschromatographie mit Polytrifluormonochloräthylen (Voltalef) als Träger

Zusammenfassung Für eine mit Tributylphosphat (TBP) beladene extraktionschromatographische Kolonne von Polytrifluormonochloräthylen (Voltalef) als Träger wurden die optimalen Arbeitsbedingungen bei der Elution von Zn-65 mit HCl bestimmt. Das Kolonnenverhalten wurde in Abhängigkeit von Trägermaterial, Beladung mit TBP, Fließgeschwindigkeit, Temperatur, Verteilungskoeffizient und Belastung der Säule mit dem Metallsalz durch die Bestimmung der effektiven Höhe eines theoretischen Bodens (H) untersucht.Voltalef 300 PL und Voltalef 300 UF erwiesen sich als ausgezeichnete Trägermaterialien für die Extraktionschromatographie mit TBP als stationäre Phase. Unter optimalen Elutionsbedingungen ergab sich für die Bodenhöhe H ein Wert von 0,15 mm.

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Radiochemical attempts at the optimalization of the extraction chromatography with polytrifluoromonochlorethylene (Voltalef) as carrier

Summary The optimal working conditions in the elution of Zn-65 with HCl were determined for an extraction chromatographic column made of polytrifluoroethylene (Voltalef) and charged with tributyl phosphate. The columnar behavior was studied in dependance of the carrier material, charging of the column with TBP, flow velocity, temperature, distribution coefficient and charging of the column with the metal salt through the determination of the effective height of a theoretical floor level (H).Voltalef 300 Pl and Voltalef 300 UF proved themselves to be excellent carrier materials for the extraction chromatography with TBP as stationary phase. Under optimal elution conditions a value of 0.15 mm was found for the floor level.

     

Über die quantitative Extrahierbarkeit des Germaniumtetrabromids mit Äther

Zusammenfassung Da ein früher angewandter Analysengang für kleine Mengen Germanium (ausgenommen bei Verwendung eines radioaktiven Germaniumisotops) nicht quantitativ verläuft, wurde eine neue Methode zur Abtrennung des Germaniums ausgearbeitet. Sie beruht auf der kontinuierlichen Extraktion des Germaniumtetrabromids aus 6-n Bromwasserstoffsäure mit Äther, aus dem das Germaniumtetrabromid sodann mit Wasser ausgezogen und photometrisch mit Phenylfluoron bestimmt wird. Diese Methode wurde mit Erfolg auf eine Zinkblende, deren Germaniumgehalt auf Grund der radioaktiven Messung 0,037% Ge betrug, angewendet, wobei im Mittel 0,036% Ge gefunden wurden.

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Summary Since a previously used analytical procedure for small amounts of germanium (except when a radioactive isotope of germanium was employed) does not proceed quantitatively, a new method was worked out for isolating the germanium. It is based on the continuous extraction of germanium tetrabromide from 6N hydrobromic acid with ether, from which the germanium tetrabromide can then be extracted with water and determined photometrically whith phenylfluorone. This method was applied successfully to a zinc blende, whose germanium content was 0.037% (as determined by radioactive measurement). An average of 0.036% germanium was found.

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Résumé La méthode analytique exposée antérieurement ne permet pas la détermination quantitative de petites quantités de germanium (sauf lorsqu'on emploie un isotope radioactif de ce métal). On a mis au point une méthode nouvelle pour isoler ce métal. Elle est basée sur l'extraction continue, par l'éther, du tétrabromure de germanium de l'acide bromhydrique 6 N; on extrait ensuite le tétrabromure de l'éther par l'eau et détermine le métal photométriquement par la phénylfluorone. Cette méthode a été appliquée avec succès àla blende (ZnS) contenant 0,037% de germanium (déterminé par mesure radioactive). On a trouvé un taux moyen de 0,036%.