Impact of a cone on a thin elastic membrane

The problem of computation of parameters of motion of a thin elastic membrane under the Impact of a rigid body, was considered by various authors (see [1] together with bibliography) without, however, yielding a rational solution. This paper presents a full qualitative analysis of solution of this problem for the case of normal impact of a circular cone moving with constant velocity on an infinite elastic membrane of constant thickness. Although this is the simplest case, it is important, insofar as it brings to light the characteristic features of the problem. In the “membrane” approximation the thickness of the layer is found to be an unessential parameter, therefore the problem, as postulated by us, is self-similar and its solution is reducible to the problem for ordinary differential equations.     

Weitere Vereinfachung der Mikrobestimmung von Jod in organischen Verbindungen

Zusammenfassung Die Mikromethode zur Jodbestimmung in organischen Substanzen durch Verbrennen nachSchöniger und nachfolgende Titration mit 0,005-n Quecksilberperchlorat wird dahingehend vereinfacht, daß die Jodabsorption nach der Verbrennung anstatt mit Natronlauge direkt mit Quecksilberperchlorat erfolgt.

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Summary The micro method for determining iodine in organic materials through combustion afterSchöniger and subsequent titration with 0.005N mercuric perchlorate is modified to the extent that after the combustion the iodine is absorbed directly in mercuric perchlorate rather than in sodium hydroxide.

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Résumé On a simplifié la microméthode pour le dosage de l'iode dans les substances organiques avec combustion suivantSchöniger et titrage consécutif par le perchlorate de mercure 0,005N. L'absorption de l'iode après la combustion s'effectue directement par le perchlorate de mercure à la place de la lessive de soude.

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Riassunto La microdeterminazione dello iodio nelle sostanze organiche per combustione secondoSchöniger e successiva titolazione con perclorato di mercurio 0,005-n, è stata semplificata riprendendo direttamente il prodotto di combustione in una soluzione di perclorato di mercurio invece di una soluzione di idrato sodico.

     

ESR spectra and the behavior of substituted indophenoxyl radicals

ESR spectra and structure are compared for radicals formed from substituted indophenols by oxidation (substituents CH₃, i-C₃H₇, t-C₄H₉, t-C₅H₁₁, cyclohexyl). The unpaired electron interacts with the nitrogen and with the hydrogen in the ortho and meta positions of both benzene rings. A kinetic equation of first order with respect to the indophenol applies to the reaction of the latter with benzoyl peroxide. The loss of indophenoxyl radicals in benzene obeys an equation of second order in the radical concentration. The rate constants for radicals with various substituents indicate the radical stability, which falls greatly in going from ones with ortho-t-alkyl substituents to ones with less highly branched groups.     

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.

     

Studies in qualitative inorganic analysis. Part XXVIII

Summary Schemes for the analysis of the Copper-Tin group are reviewed. The advantages of the scheme recommended by the Midlands Association for Qualitative Analysis are discussed.

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Zusammenfassung Analysen-Schemata für die Kupfer-Zinn-Gruppe wurden besprochen. Die Vorteile des Analysenganges der Midlands Association for Qualitative Analysis werden diskutiert.

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Résumé Examen des différents processus d'analyse du groupe cuivre-étain. Discussion des avantages de la technique recommandée par la Midlands. Association pour l'analyse qualitative.

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Part XXVII: Mikrochim. Acta [Wien]1967, 389.     

On perturbations associated with the creation of lift acting on a body in a transonic stream of a dissipative gas PMM vol. 31, no. 6, 1967, pp. 1035–1049

The flow pattern of a viscous imcompressible fluid past a finite body is well known; an approximate solution of the related problem can, for example, be found in the book by Landau and Lifshits [1]. Finn [2] made a rigorous and exhaustive study of plane-parallel flows. No fundamental difficulties arise in passing from the motion of an incompressible fluid to a transonic flow of a compressible gas, however the velocity field is different, when the velocity of particles becomes critical at infinity.

The pattern of a sonic flow past a body of circular cross-section was investigated in paper [3]. This paper deals with perturbations associated with the creation of lift acting on an arbitrary body in a three-dimensional flow. When solving this problem it is necessary to consider not only the external stream, but also the laminar vortex trail because of the velocity vector transverse components becoming infinitely great, if functions defining these are formally extended into the trail area. This difficulty arises in investigations of three-dimensional flows only. The solution defining perturbation damping in an axisymmetric sonic stream of a dissipative gas has in its first approximation one singular point only, and does not contain any other singularities along the axis of symmetry [3].

The external stream pattern is essentially formed by the action of normal viscous stresses and the longitudinal component of the heat flux vector, while the distribution of gas parameters in the laminar trail is defined by tangential stresses. The conjunction of solutions valid for each of these areas makes the closure of the problem, and the determination of all necessary parameters possible.     

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...     

The crystal structure of eudesma-4(15),7(11)-dien-8α, 12-olide: a sesquiterpene lactone fromTrattinickia rhoifolia Willd

The title compound, formula C₁₅H₂₀O₂, is orthorhombic, P2₁2₁2₁ witha=8.747(2),b=12.025(3),c=12.554(3)Å,Z=4, andD _m =1.32(2)g/ml. The structural analysis shows that the compound corresponds to eudesma-4(15),7(11)-dien-8,12-olide, a sesquiterpene lactone previously isolated fromAster umbellatus but whose crystal structure was unknown.