Reflection of plane waves under initial stresses at a free surface

The paper deals with the phenomenon of reflection of plane elastic waves in a free surface when the medium is initially stressed. It has been shown analytically that the reflected P and SV waves depend on initial stresses present in the medium. The numerical values of reflection coefficients for different initial stresses and the angle of incidence have been calculated by the Computer I.C.L. 1901-A and the results are given in the form of graphs. Many interesting results are found in the paper which are not seen in an initially stress-free medium.     

Perturbed iterative solution of nonlinear equations with applications to fluid dynamics

In this work a technique has been developed to solve a set of nonlinear equations with the assumption that a solution exists. The algorithm involves nonlinear Gauss-Seidel iteractions and at each iteration the value of the iterate is added to a predetermined perturbation parameter which is computed in terms of quantities already known. This perturbation parameter has two properties: (i) it determines the mode of convergence, that means it shows how many more computations are required so that convergence may be achieved, and (ii) it accelerates the rate of convergence. The algorithm is computationally simple. Several nonlinear equations have been studied. The results seem to be encouraging.     

7-iodo 8-hydroxy quinoline 5-sulphonic acid (Ferron) as a colloidal electrolyte

Summary Electrical conductance studies have been performed to investigate the nature of aqueous solutions of 7-iodo 8-hydroxy quinoline 5-sulphonic acid (Ferron). The reagent has been found to behave as a colloidal electrolyte and does not obeyBeer's law in concentrated solutions. The curve between the square root of concentration and equivalent conductance is not linear and resembles those of colloidal electrolytes. The temperature of zero conductance has also been determined to be –32 C. The temperature coefficient per degree centrigrade per 100 of the conductance at 35 C ranges between 1.56 and 1.72.

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Zusammenfassung Elektrische Leitfähigkeitsuntersuchungen wurden an wä\rigen Lösungen von Ferron (7-Jod-8-hydroxyquinolin-5-sulfonsäure) durchgefÜhrt, um die Natur dieser Lösungen aufzuklären. Das Reagenz benimmt sich wie ein kolloider Elektrolyt und folgt nicht demBeerschen Gesetz in konzentrierten Lösungen. Der Zusammenhang zwischen Leitfähigkeit und Quadratwurzel aus Konzentration ist nicht linear und ähnelt dem kolloider Elektrolyte. Die Temperatur der Leifähigkeit 0 liegt bei –32 C. Der Temperaturkoeffizient in Prozenten der Leitfähigkeit bei 35 C liegt zwischen 1,56 und 1,72.

     

Statistical proofs of some matrix results

Using statistical arguments, proofs of some results in matrix theory are provided. Most of the proofs use results in linear statistical models and multivariate analysis. Some new results are also obtained in the process. In particular, several inequalities involving parallel sum of matrices are obtained.     

Spectrophotometric determination of vanadium and niobium: Xylenol orange as a chromogenic reagent

Summary The formation of red coloured chelates of vanadium(V) and niobium(V) with xylenol orange (DCAC) having _max at 490 nm (at p_H 5.0) and 530 nm (at p_H 5.5) have been reported. The colour formation has been applied to the spectrophotometric determination of metal ions. The colour has been found to be stable between p_H 3.5–6.5 and 2.0–7.0 respectively. The sensitivity of the reagent is 0.051g/cm² of vanadium and 0.093g/cm² of niobium. Maximum colour intensity has been found for Nb-DCAC chelate at p_H 5.5 whereas no appreciable change has been found for V-DCAC chelate between p_H 4.5 and 6.5.

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Zusammenfassung Über die Bildung rot gefärbter Chelate von Vanadin und Niob mit Xylenolorange wurde berichtet. Deren Absorptionsmaxima liegen bei 490 nm (p_H 5,0) bzw. bei 530 nm (p_H 5,5). Die Farbreaktion wurde für die Bestimmung der beiden Metalle verwendet. Die Farbe ist zwischen p_H 3,5 und 6,5 bzw. zwischen p_H 2,0 und 7,0 stabil. Die Empfindlichkeit für Vanadin beträgt 0,051g/cm², für Niob 0,093g/cm². Die Farbe des Niobchelates erreicht bei p_H 5,5 ein Maximum, während die des Vanadinchelates zwischen p_H 4,5 und 6,5 keine wesentlichen Änderungen erkennen läßt.