Studies in qualitative inorganic analysis. Part XXVI

Summary The preliminary tests for organic radicals, which are based on charring by strong heating or by hot concentrated sulphuric acid are examined. Even when both these tests are applied some organic acids escape identification. Two alternative procedures based upon oxidation of organic matter with potassium dichromate in dilute sulphuric have been examined. The first procedure involves a reduction of the dichromate ion to the distinctive green chromium(III) ion. This occurs with all organic radicals commonly encountered in qualitative inorganic analysis, except acetate and salicylate. Interference due to inorganic reducing agents is overcome by a preliminary oxidation with hydrogen peroxide. The second procedure involves decomposition of carbonates, bicarbonates, and cyanates with dilute sulphuric acid, followed by oxidation of organic matter with potassium dichromate in sulphuric acid to carbon dioxide, which is detected with lime water. Of the radicals commonly encountered in qualitative inorganic analysis only acetate gives a negative result.

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Zusammenfassung Die Vorprobe auf organische Anionen auf Grund ihrer Verkohlung durch kräftiges Erhitzen oder durch Einwirkung konz. Schwefelsäure wurde überprüft. Auch bei Anwendung beider Arbeitsweisen entziehen sich einige organische Säuren dem Nachweis. Zwei andere Verfahren auf der Grundlage der Oxydation des organischen Materials mit Kaliumbichromat in verd. Schwefelsäure wurden untersucht. Das erste führt zur Reduktion des Bichromats zu deutlich grün gefärbtem Cr(III) mit allen bei der anorganischen Analyse üblicherweise auftretenden organischen Anionen, ausgenommen Acetat und Salicylat. Störungen durch reduzierende anorganische Substanzen werden durch deren vorherige Oxydation mit Wasserstoffperoxid umgangen. Das zweite Verfahren sieht die vorherige Zersetzung anwesender Carbonate, Bicarbonate oder Cyanate mit verd. Schwefelsäure vor, wonach das organische Material mit Kaliumbichromat-Schwefelsäure zu Kohlendioxid oxydiert wird, das mit Kalklösung nachgewiesen wird. Von den in der anorganischen Analyse üblichen organischen Anionen gibt nur Acetat ein negatives Resultat.

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Résumé On examine les essais préliminaires pour radicaux organiques, fondés sur la carbonisation par chauffage à température élevée ou sur l'action de l'acide sulfurique concentré chaud. Même en appliquant ces deux modes de recherche, certains des acides organiques échappent à l'identification. On a étudié deux autres procédés susceptibles d'être utilisés. Ils reposent sur l'oxydation de la matière organique par le bichromate de potassium en milieu sulfurique dilué. Le premier met en jeu la réduction de l'ion bichromate en ion chrome-III vert caractéristique. Cette réaction se produit avec tous les radicaux organiques habituellement rencontrés en analyse minérale qualitative, sauf avec les acétates et les salicylates. On élimine l'interférence due aux agents réducteurs minéraux par oxydation préliminaire par l'eau oxygénée. Le second procédé met en jeu la décomposition des carbonates, hydrogénocarbonates et cyanates par l'acide sulfurique dilué, suivie d'une oxydation de la matière organique par le bichromate de potassium dans l'acide sulfurique, en gaz carbonique que l'on met en évidence par l'eau de chaux. Seul l'ion acétate donne un résultat négatif parmi tous les radicaux rencontrés habituellement en analyse minérale qualitative.

     

Die Phosphatbestimmung mit elektrischer Endpunktanzeige und ihre Anwendung zur Analyse organischer Substanzen. II

Zusammenfassung Nach Untersuchungen über die Einflüsse der Temperatur, organischer Lösungsmittel, und des Carbonatgehalts der Lösung wurde eine neue Vorschrift ausgearbeitet zur Phosphattitration mit Lanthanmaßlösung mit einer Endpunktanzeige mittels eines p_H-Meters. Mit einer Standardabweichung von weniger als 1% lassen sich 0,3 bis 1,5 mg P bestimmen. Die Standardabweichung bei der Phosphorbestimmung in organischen Substanzen beträgt 0,11% absolut.

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Summary Investigations of the influences of temperature, organic solvents, and the carbonate content of the solution led to the development of a new procedure for titrating phosphate with a lanthanum salt solution; the endpoint is indicated by a p_H meter. It is possible to determine 0.3 to 1.5 mg P with a standard deviation of less than 1%. The standard deviation in the determination of phosphorus in organic substances is 0.11% absolute.

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Résumé On a mis au point un nouveau mode opératoire d'après des études sur l'influence de la température, du solvant organique et de la teneur en carbonate de la solution pour titrer les phosphates par une solution étalon de lanthane avec indication du point d'équivalence sur un ph-mètre. On peut doser 0,3 à 1,5 mg de P avec un écart-type de moins de 1%. L'écart-type dans le cas du dosage du phosphore dans les substances organiques s'élève à 0,11% en valeur absolue.

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Wir danken herzlichst HerrnH. de Wit und HerrnW. Hulshof für wertvolle Mithilfe und Ausführung zahlreicher Analysen.     

Generalized-hypergeometric solutions of the biconfluent Heun equation

The Ramanujan Journal - Infinitely many cases for which two independent fundamental solutions of the biconfluent Heun equation can each be presented as an irreducible linear combination of two...     

Linear and nonlinear substructured Restricted Additive Schwarz iterations and preconditioning

Iterative substructuring Domain Decomposition (DD) methods have been extensively studied, and they are usually associated with nonoverlapping decompositions. It is less known that classical overlapping DD methods can also be formulated in substructured form, i.e., as iterative methods acting on variables defined exclusively on the interfaces of the overlapping domain decomposition. We call such formulations substructured domain decomposition methods. We introduce here a substructured version of Restricted Additive Schwarz (RAS) which we call SRAS. We show that RAS and SRAS are equivalent when used as iterative solvers, as they produce the same iterates, while they are substantially different when used as preconditioners for GMRES. We link the volume and substructured Krylov spaces and show that the iterates are different by deriving the least squares problems solved at each GMRES iteration. When used as iterative solvers, SRAS presents computational advantages over RAS, as it avoids computations with matrices and vectors at the volume level. When used as preconditioners, SRAS has the further advantage of allowing GMRES to store smaller vectors and perform orthogonalization in a lower dimensional space. We then consider nonlinear problems, and we introduce SRASPEN (Substructured Restricted Additive Schwarz Preconditioned Exact Newton), where SRAS is used as a preconditioner for Newton’s method. In contrast to the linear case, we prove that Newton’s method applied to the preconditioned volume and substructured formulation produces the same iterates in the nonlinear case. Next, we introduce two-level versions of nonlinear SRAS and SRASPEN. Finally, we validate our theoretical results with numerical experiments.

     

X-ray diffraction study of the fatigue behavior of a shot-peened aluminum-lithium alloy

The effect of different shot-peening treatments on the cyclic fluctuating bending fatigue behavior of a new aluminum-lithium alloy (the 2091) has been investigated. The residual-stresses in-depth profiles have been defined just after the shot peening using mainly the X-ray diffraction method. To reach a given depth inside the material, the surface layer was removed by electro-polishing. The acquired data had to be then corrected in order to account for the redistribution of the stresses during the polishing. Furthermore, this alloy contains up to 15-percent intermetallic precipitates. Moreover, the X-rays penetrate deeply inside the material (23 m). For these reasons, a special procedure, based on a self-consistent micromechanical scheme, has been developed to correct the acquired data. The stress profiles obtained by this procedure are compared to those obtained by other mechanical experimental methods and those calculated by a theoretical shot-peening method. Shot peening improves the life of the material but the surface residual stresses are partially released during the first cycles of fatigue and are then quickly stabilized.Paper was presented at the 1994 SEM International Conference on Residual Stresses (ICRS4) held in Baltimore, MD on June 8–10.     

Stiff algebras

Consistent examples of atomic Boolean algebras with restricted types of automorphisms are constructed. In particular, the existence of an atomic Hopfian Boolean algebra of size less than 2 is shown to be consistent.Presented by V. Trnková.     

Hybrid extension of Schottky space

Part of this work was written while the author was feliow of the Graduiertenkolleg Geometrie und Mathematische Physik at the University of Bochum, Germany.     

An experimental investigation of the sources of propeller noise due to the ingestion of turbulence at low speeds

Noise radiation from a four bladed, 10 in. diameter propeller operating in air at a rotational speed of 3000 RPM and a freestream velocity of 33 ft/s was experimentally analyzed using hot-wire and microphone measurements in an anechoic wind tunnel. Turbulence levels from 0.2 to 5.5% at the propeller location were generated by square-mesh grids upstream of the propeller. Autobicoherence measurements behind the blade trailing edges near the hub and tip showed regions of high phase-coherence between the blade-passage harmonics and the broadband frequencies. Inflow turbulence reduced this coherence. By relating the fluctuation velocities in the propeller wake to the unsteady blade forces, the primary regions of tonal noise generation have been identified as the hub and tip regions, while the midspan has been identified as a region responsible for broadband noise generation. These measurements were complimented by cross-spectra between the propeller wake-flow and the measured sound. The effect of turbulence on the radiated noise level showed an overall increase of 2 dB in the broadband levels for every 1% increase in turbulence. This effect varied for different frequency bands in the acoustic spectrum.List of Symbols b ² (f _k, f _l) Bicoherence - B (k, l) Bispectrum - B Number of Blades - c Speed of Sound - C _T Thrust coefficient=T/n ²D⁴ - D Propeller diameter - E [ ] Expected value - f Frequency, Hz - G _xx (f) One sided autospectral density function. - G _xy (f) One sided cross-spectral density function - J Advance ratio, J=U/nD - j, k Fourier component indices - m Grid mesh length - M _o Rotational mach number at a radial location M _o =2nr/a _o - M _c Axial convection mach number - n Rotational speed, revolutions per second - r Propeller radial location - R Propeller radius - R _e Reynolds number - T Propeller thrust - U Freestream velocity - U _i Induced axial velocity from propeller - u, w RMS of fluctuating velocity, u=(U–u)² - X(f) Fourier transform of x(t) Symbols _xy ^/2 (f) Coherence function, - Observer angle, measured from propeller thrust direction - _f Longitudinal Eulerian dissipation length scale - _f Longitudinal Eulerian integral length scale - Air density - Blade azimuthal location This research was performed at the Hessert Center for Aerospace Research, Department of Aerospace and Mechanical Engineering, University of Notre Dame, and was sponsored by the U.S. Navy, Office of Naval Research, Arlington, Virginia under Contract No. N00014-89-J-1783. The authors would like to thank the program manager, and technical manager, Dr. E. P. Rood. The authors would also like to thank Dr. William Blake of the David Taylor Research Center and Dr. Flint O. Thomas and Dr. Huang-Chang Chu of Notre Dame for their help and comments at various stages of this research