Coupled bending-torsion vibrations of rotating blades of asymmetric aerofoil cross section with allowance for shear deflection and rotary inertia by use of the Reissner method

Theoretical natural frequencies and modal shapes of the first five modes of vibration are presented for a rotating blade of asymmetric aerofoil cross section, with allowance for shear deflection and rotary inertia. Frequency equations for a rotating blade with asymmetry in one plane are developed by using the Ritz process, in two ways: namely, by proceeding according to the Reissner method and according to the classical potential energy method. In both cases shape functions for the bending moment, shearing force, twisting moment, bending slope, elastic twist and deflection are developed in series form. The results obtained are compared with those existing in the literature; it is found that the Reissner method approach yields more rapid convergence than does the classical potential energy method.     

Synthesis, ion-exchange properties and analytical applications of stannic selenoarsenate: Comparison with other heteropolyacid salts

Summary Stannic selenoarsenate samples have been prepared by adding a mixture which is 0.05 M in sodium arsenate and 0.05 M in sodium selenite to a 0.05 M solution of stannic chloride in different volume ratios at pH 1. Its ion-exchange properties, pH titration curves and X-ray pattern were studied. Adsorption behaviour of 24 metal ions in different solvent systems has been examined. The analytical importance of this material has been demonstrated by achieving the following binary and ternary separations: Hg²⁺-Cd²⁺, Co²⁺-Fe³⁺, Cu²⁺-Fe³⁺, Hg²⁺-Zn²⁺-Al³⁺, Hg²⁺-Cu²⁺-Al³⁺, Hg²⁺-Ni²⁺-Al³⁺, Hg²⁺-Zn²⁺-Fe³⁺ and Hg²⁺-Ni²⁺-Fe³⁺. A comparison of the ion-exchange properties of this material has also been made with some other tin(IV) based ion-exchangers.

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Synthese, Ionenaustauscher-Eigenschaften und analytische Anwendungen von Zinn-Selenoarsenat: Vergleich mit anderen Heteropolysalzen

Zusammenfassung Zinn-Selenoarsenat wurde durch Mischen von 0,05 M Natriumarsenat-, 0,05 M Natriumselenitund 0,05 M Zinn(IV)-Chlorid-Lösungen bei pH 1 in verschiedenen Verhältnissen hergestellt. Die Ionenaustauscher-Eigenschaften, pH-Titrationskurven sowie Röntgendiagramme wurden untersucht und das Adsorptionsverhalten von 24 Metallionen in verschiedenen Lösungsmittelsystemen geprüft. Die analytische Verwertbarkeit wurde an Hand der folgenden Trennungsmöglichkeiten gezeigt: Hg²⁺-Cd²⁺, Co²⁺-Fe³⁺, Cu²⁺-Fe³⁺, Hg²⁺-Zn²⁺-Al³⁺, Hg²⁺-Cu²⁺-Al³⁺, Hg²⁺-Ni²⁺-Al³⁺, Hg²⁺-Zn²⁺-Fe³⁺, Hg²⁺-Ni²⁺-Fe³⁺. Vergleiche mit anderen Ionenaustauschern auf Zinn(IV)-Basis werden ebenfalls beschrieben.

     

Studies in ferrimetry

Summary We have found that ferric alum oxidises hydroxylamine quantitatively and rapidly to nitrous oxide, even at the room temperature, if 1 ml of 5% copper sulphate is used as catalyst per 50 ml of reaction mixture. The resultant ferrous salt can be determined by titration with a standard solution of sodium vanadate.     

Elastic scattering of electrons by helium atoms in high energy higher order Born approximation

The differential cross-sections forē-helium elastic scattering are calculated by using Yateshigh-energy higher order Born approximations, through 0 (K _i ^{Emphasis>−2} ) of the incident electron momentum, and comparisons have been made with the recent theoretical and experimental results.     

Time-dependent flows of rotating and stratified fluids in geometries with non-uniform cross-sections

Unsteady rotating and stratified flows in geometries with non-uniform cross-sections are investigated under Oseen approximation using Laplace transform technique. The solutions are obtained in closed form and they reveal that the flow remains oscillatory even after infinitely large time. The existence of inertial waves propagating in both positive and negative directions of the flow is observed. When the Rossby or Froude number is close to a certain infinite set of critical values the blocking and back flow occur and the flow pattern becomes more and more complicated with increasing number of stagnant zones when each critical value is crossed. The analogy that is observed in the solutions for rotating and stratified flows is also discussed.     

Polymerization of diallyl phthalate in solution by γ-radiation

The polymerization of diallyl phthalate has been studied in two solvents, benzene (G_Radical = 0.7) and chloroform (G_R = 11.2), γ-radiation being used to investigate the effect of the solvent on the rates of polymerization and also chain transfer to the solvent. Kinetic analysis shows that in benzene solution the initiating species come almost exclusively from the monomer, but in chloroform they arise only from the solvent. The latter was further confirmed from the chlorine analysis of the polymer wherein chloroform appears to have telomerized with diallyl phthalate. In neither of the solvents was high molecular weight polymer obtained. The k_p/k_t^1/2 for the polymerization of DAP was found to be 3.3 × 10^?4 and 1.17 × 10^?3 in benzene and chloroform solutions, respectively. The chain-transfer constant C_S was 11.25 × 10^?3 and 9.75 × 10^?3 for benzene and chloroform, respectively.     

Characterization of self-complementary graphs with 2-factors

Let G be a self-complementary graph (s.c.) and π its degree sequence. Then G has a 2-factor if and only if π - 2 is graphic. This is achieved by obtaining a structure theorem regarding s.c. graphs without a 2-factor. Another interesting corollary of the structure theorem is that if G is a s.c. graph of order p?8 with minimum degree at least $\text{p}\text{4}$, then G has a 2-factor and the result is the best possible.