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.     

Some observations concerning the direct titration of nitrite with cerium(IV)

Direct titration of nitrite with cerium (IV), with ferroin as indicator, is shown to give satisfactory results if the acidity is kept between 0.033 and 0.055M at the end-point. Loss of nitrous acid owing to volatilization and decomposition is discussed. From 10 to 60 mg of sodium nitrite can be estimated with a standard deviation of 5 mug and an average error of 0.2%.     

Alkenenitriles: Zn-Cu promoted conjugate additions of alkyl iodides in water

[reaction: see text] A new silica-supported zinc-copper matrix dramatically promotes conjugate additions of alkyl iodides to alkenenitriles in water. Acyclic and cyclic nitriles react with functionalized alkyl iodides, overcoming the previous difficulty of performing conjugate additions to disubstituted alkenenitriles with nonstabilized carbon nucleophiles. Conjugate additions with omega-chloroalkyl iodides generate cyclic nitriles primed for cyclization, collectively providing one of the few annulation methods for cyclic alkenenitriles.     

A note on the solution of a class of functional equations

On the basis of fixed point theorems for linear topological spaces the authors prove existence theorems for the solutions of functional equations that arise in Dynamic Programming.     

The effect of molecular weight on the separation of semiconducting single‐walled carbon nanotubes using poly(2,7‐carbazole)s

The use of selective interactions between conjugated polymers and single‐walled carbon nanotubes has emerged as a promising method for the separation of nanotubes by electronic type. Although much attention has been devoted to investigating polyfluorenes and their ability to disperse semiconducting carbon nanotubes under specific conditions, other polymer families, such as poly(2,7‐carbazole)s, have been relatively overlooked. Poly(2,7‐carbazole)s have been shown to also preferentially interact with semiconducting carbon nanotubes, however a detailed investigation of polymer parameters, such as molecular weight, has not been performed. We have prepared seven different molecular weights of a poly(2,7‐carbazole), from short chain oligomers to high molecular weight polymers, and have investigated their effectiveness at dispersing semiconducting single‐walled carbon nanotubes. Although all polymer chain lengths were able to efficiently exfoliate carbon nanotube bundles using a mild dispersion protocol, only polymers above a certain threshold molecular weight (M_n ～ 27 kDa) were found to exhibit complete selectivity for semiconducting nanotubes, with no observable signals from metallic species. Additionally, we found the quality of separation to be strongly dependent on the ratio of polymer to carbon nanotube. Contrary to previous reports, we have found that an excess of poly(2,7‐carbazole) leads to incomplete removal of metallic carbon nanotubes. © 2015 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2015 , 53, 2510–2516     

A Validated Chiral LC Method for the Separation and Quantification of (S,R,S)-Enantiomer and (R,R,R)-Isomer of Aprepitant

A new and accurate chiral liquid chromatographic method has been developed for the separation and quantification of (S,R,S)-enantiomer (unwanted enantiomer) and (R,R,R)-isomer (key intermediate) of aprepitant in bulk drug and formulation samples of apprepitant. The elution time was approximately 20 min using an immobilized amylose-based chiral stationary phase (Chiralpak-IA). The mobile phase was n-hexane and ethanol (90:10, v/v) and was delivered at a flow rate of 1.0 mL min^?1. Detection was carried out with a wavelength set to 220 nm. The resolution factor between enantiomers was found to be greater than five. Limit of detection for both (S,R,S) enantiomer and (R,R,R) isomer of aprepitant was 0.035 µg, and limit of quantification for both (S,R,S) enantiomer and (R,R,R) isomers of aprepitant was 0.1 µg, for a 10 µL injection. The developed method showed excellent linearity (r > 0.999) for both isomers. When the method was applied to bulk drug samples and in pharmaceutical formulations recoveries were obtained ranging from 97.2 to 103.1%. Aprepitant sample solutions were found to be stable when characterized over a period of 48 h.