Backtracking of a sphere slowing down in a viscous compressible fluid

It is shown on the basis of the linearized Navier-Stokes equations that a sphere set in motion by a sudden impulse, and slowing down in a viscous compressible fluid, can temporarily reverse its velocity at a late stage of the motion before finally slowing down with a positive velocity. For the effect to occur, the fluid needs to be sufficiently compressible, and the bulk viscosity needs to be sufficiently small relative to the shear viscosity. More generally, the velocity decays nonmonotonically, without necessarily passing through zero. The results are derived from the frequency-dependent friction coefficient, and hold for general boundary condition on the surface of the sphere.     

Concentrated electrolyte solutions at high temperatures and pressures

A survey is given of recent experimental results obtained from high-temperature, high-pressure investigations with water, aqueous solutions, and ionic fluids. Data on the static dielectric constant of water to 550°C and 5 kbar are given and discussed with respect to their relation to water structure. Infrared and Raman spectra of HDO in pure water have been obtained to 400°C and 4 kbar, which give information on hydrogen bonding. Xe–H₂O and CO₂–H₂O mixtures were investigated in the infrared. Ni(II) and Cu(II) complexes were investigated by absorption spectroscopy in aqueous solutions of high chloride content to 350°C and 2–6 kbar. The gas-liquid critical point of ammonium chloride was found at 880°C and 1635 bars. This fluid appears to be predominantly ionic even in the critical region. The possibility of converting pure polar fluids such as ammonia and water into concentrated ionic solutions by self-ionization at very high pressures is mentioned.This paper was presented at the symposium, The Physical Chemistry of Aqueous Systems, held at the University of Pittsburgh, Pittsburgh, Pennsylvania, June 12–14, 1972, in honor of the 70th birthday of Professor H. S. Frank.     

Determination of stainless steel constituents in plastics

Summary Instrumental neutron activation analysis (INAA), atomic absorption spectrometry (AAS), and X-ray fluorescence analysis (XRF) were tested for the determination of the abrasion effect in plastics processing equipment. As optimal solution measurement of Fe by XRF in cylindrical samples was found.     

Diene synthesis with 2-pyrones and 2-pyridones XIV. 1,4-Cycloadducts of 1-alkyl-2-pyridones with N-phenylmaleinimide and maleinimide

1-Alkyl-2-pyridones react with N-phenylmaleinimide and maleinimide stereoselectively via the scheme of the diene synthesis to give imides of 8-alkyl-8-azabicyclo[2.2.2]-4-octen-7-one-1,2-dioic acid. 3-Unsubstituted 2-pyridones form adducts with an endo configuration, whereas 1,3-dimethyl-2-pyridone gives an exo adduct under the same conditions. The endo- and exo-bridge adducts readily undergo retrograde diene disintegration on heating.     

Low temperature absorption spectra of TcO 4 − and ReO 4 − in KClO4

The low temperature spectra of TcO ₄ ^– and ReO ₄ ^– both show two band systems with pronounced vibrational structures. The bands are identified as¹ A ₁¹ T ₂ transitions. No other bands are observed with certainty. It seems likely that the KClO₄ crystals contain KReO₄ crystallites. They are therefore not pure mixed crystals. It is concluded that the virtual orbital (2e) used in the construction of the low lying states resembles an atomic nd orbital more and more when going from n=3, Mn to n=5, Re.

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Zusammenfassung Die Tieftemperaturspektren von TcO ₄ ^– und ReO ₄ ^– zeigen beide zwei Bandensysteme mit ausgeprägten Schwingungsstrukturen. Die Banden werden als ¹ A ₁¹ T ₂-Übergänge identifiziert. Keine anderen Banden werden mit Sicherheit beobachtet. Es scheint wahrscheinlich, daß die KClO₄-Kristalle KReO₄-Kristallite enthalten und deswegen keine reinen Mischkristalle sind. Es wird geschlossen, daß das virtuelle Orbital (2e), welches zur Konstruktion der tiefliegenden Zustände gebraucht wird, in der Reihe n=3, Mn bis n=5, Re immer weitgehender einem nd-Atomorbital ähnelt.

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Nachwuchsstipendiat, Schweizerischer Nationalfonds.     

Purine N-oxides—XLI : The 3-acyloxypurine 8-substitution reaction: On the mechanism of the reaction

The 3-acyloxypurine 8-substitution reaction involves elimination of the 3-acyloxy group and nucleophilic substitution at C-8 to yield 8-substituted xanthines or guanines. In aqueous solutions the reaction of 3-acetoxyxanthine proceeds slowly below pH 2, but is greatly accelerated with an increase of the pH from 3 to 7. It is proposed that the slow reaction involves heterolytic cleavage of the 3-acetoxy moiety from 3-acetoxyxanthine to yield a nitrenium ion at N-3 followed by intermolecular nucleophilic substitution of the incipient carbonium ion at the allylic C-8 position, also the most probable mechanism in polar aprotic solvents. The beginning of the fast reaction coincides with the beginning of ionization of the imidazole hydrogen of 3-acetoxyxanthine. It is proposed that this ionization induces a similar but more rapid departure of the 3-acetoxy group from the anion of 3-acetoxyxanthine to produce dehydroxanthine. The latter, upon protonation, yields the same reactive carbonium ion at C-8 that is formed in the slow reaction. Some reduction of 3-acetoxyxanthine to xanthine accompanies the fast reaction. That reduction has the characteristics of a free-radical mediated reaction. It is proposed that reduction results from a homolytic cleavage of the NO bond in the 3-acetoxyxanthine anion to produce a radical-anion, which abstracts hydrogen from water to yield xanthine. These reaction mechanisms and possible alternatives are evaluated.     

Studies in sesquiterpenes—LVI: Isolongifolene (part 7): mechanism of rearrangement of longifolene to isolongifolene—II

The question of possible neutral intermediates which may lie on the reaction pathway in going from longifolene to isolongifolene has been investigated using BF₃·Et₂O-AcOD and D₃PO₄-dioxane, as reagents. It has been found that longicyclene is not an obligatory intermediate. The mode of cleavage of cyclopropane ring in longicyclene has been investigated.     

Dialkylindiumacetate R2InOOCCH3 (R = CH3, C2H5) Darstellung,Eigenschaften und Struktur

Dialkylindium Acetates R₂InOOCCH₃ (R = CH₃, C₂H₅). Preparation, Properties, and Structure. Dimethyl- and diethylindium acetate were prepared and the vibrational spectra (IR and RAMAN ) discussed. The X-ray structure determination shows that diethylindium acetate belongs to the orthorhombic space group Pnma. The unit cell with lattice constants a = 8.40, b = 7.41, c = 15.13 Å contains four molecules. Each indium atom forms with an acetate group a planar four-membered ring. The indium-oxygen distance within such a ring is only a little shorter than the distance of this oxygen to the indium of the next neighboured ring. Indium has therefore the coordination number six.     

Ab initio SCF Calculation of the Fluoronium Ion: Geometry,electronic structure and vibrational constants

An ab initio SCF calculation of 42 points of the energy hypersurface of the fluoronium ion is presented using a contracted F(5s/3p), H(2s) gaussian basis set. In its equilibrium structure a bond length of 1.812 a.u. and a HFH bond angle of 127.2° are predicted. The calculated vibrational frequencies for H₂F⁺, HDF⁺, and D₂F⁺ are in good agreement with the experimental data.     

On an Asymptotics of the Number of Representations of a Pair of Integers by Quadratic and Linear Forms with Congruential Condition

Mathematical Notes - Asymptotic formulas with remainder for the number of representations of a pair of integers by quadratic and linear forms with a congruential condition are proved.