Anharmonicity in polyatomic molecules: The problem of phase coincidence and applications to the CH-stretching overtone spectrum of benzene

A previous analysis of the first six members of the CH-stretching overtone spectrum of benzene in terms of local oscillators is reexamined (1). The importance of the choice of relative phases in the transformation from normal modes to local modes is elucidated. The theory is recast in a form more consistent with the limitations indicated by this analysis. The frequencies of all eight members of the CH-stretching overtone spectrum of benzene are calculated on this basis and excellent agreement with experiment is obtained.     

Assessment of the state of order of hydroxyl groups and of molecular segments in hydrocellulose

Through a study of the selective distribution of substituents introduced into hydrocellulose from reaction with N,N-diethylaziridinium chloride, the change in selective availability of hydroxy groups at C-2, C-3, and C-6 has been followed as a function of duration of hydrolysis to form the hydrocellulose. The hydrocellulose formed at a particular duration of hydrolysis showed maximum selective availability of hydroxyl groups; this was found to coincide with minimum moisture regain and minimum breadth at half height for 101 , 101, and 002 peaks in x-ray diffractograms. These points are discussed in terms of the structures of the hydrocelluloses at various stages of hydrolysis and in terms of the sequence of changes which is now associated with the conversion of fibrous cotton to “exemplar hydrocellulose,” i.e., the hydrocellulose having the highest degree of crystalline order, and subsequently, to less highly ordered hydrocelluloses.     

Models of a Consumer Product Market

Aggregate models of the United Kingdom razor blade market are discussed. During one prolonged period when the market was dominated by two major brands, approximately equivalent in terms of quality, price and distribution, a model based on advertising expenditures alone was remarkably accurate at predicting short-term movements of a brand's market share in periods of both growth and decline. An optimum decay rate of advertising effectiveness was identified. The value of consumer promotions could be estimated from the deviations they produced from the model. To cover longer periods and to encompass brands of widely differing qualities and prices a more complex model was necessary. This has been successful in following long-term trends of market shares of all brands and has contributed towards understanding the market structure. It has shed light on the value of a multi-brand policy and has enabled a retrospective evaluation to be made of the effect of a period of production capacity limitation on market share growth.     

Substituent effects and stereochemical mechanisms for substitution reactions of 18F for halogen atoms in CF3X, (CH3)3−n CHnX,and CH3X

No thermal substitutions of ¹⁸F for X (X  halogen atom) are observed with CF₃X and (CH₃)_3?nCH_nX substrates in excess SF₆. The absence of thermal yield increasing with weaker CX bond energies, as found with CH₃X substrates, is attributed to the much larger mass versus H of F and CH₃ substituents. The thermal substitution of ¹⁸F/X in CH₃X molecules probably occurs by an inversion mechanism.     

Flow rates of polymer solutions through porous disks as a function of solute. I. method

A method for studying the thickness of adsorbed polymer films, based on the reduction in effective cross section for liquid flow caused by the deposition of such a film on the interior of a capillary, is described. A sintered disk is used instead of a single capillary to raise the flow rate to an easily measured level, to avoid the difficulties of obtaining or fabricating the extremely fine capillaries which would be required, and to eliminate the extreme precautions needed to prevent plugging of a single capillary. Techniques for characterizing the sintered disks are presented. When applied to benzene solutions of stearic acid and of polystyrene, film thicknesses of 30 and 312 A., respectively, were obtained. This is in good agreement with present knowledge of fatty acid adsorption, and suggests that the polymer is adsorbed in a highly extended configuration. The application of this method to solutions of poly(vinyl acetate), poly(methyl methacrylate), and polystyrene in several solvents at various temperatures is described in a following paper.     

Research into teacher knowledge: a stimulus for development in mathematics teacher education practice

In this paper, we document some developments in teacher education practice at one university, brought about by reflection on research into mathematics teacher knowledge. The authors are three members of the Cambridge-based research team who developed the Knowledge Quartet (KQ), a theory of mathematics teacher knowledge, with a focus on classroom situations in which this knowledge is applied. At the same time as being researchers, the authors were elementary mathematics teacher education instructors. They found that the KQ research brought about new awareness of the importance of some components of mathematics didactics, as well as providing new tools for undertaking some aspects of their teacher educator role. The paper explores some of these awarenesses and tools in detail.     

Estimating Arterial Cyclic Strain from the Spacing of Endothelial Nuclei

Experimental Mechanics - The non-uniform distribution of atherosclerosis within the arterial system is widely attributed to variation in haemodynamic wall shear stress. It may also depend on...