Ludwig Levy displaying his sketch pad, showing a drawing of an older man with beard and hat.

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Aspects of tautomerism. 13. Alkaline hydrolysis of .gamma.-, .delta.-, and .epsilon.-keto esters and their desoxy analogs. Geometrical constraints on keto participation

The rates of alkaline hydrolysis of methyl &benzoylpropionate (I), methyl y-benzoylbutyrate (11) and methyll6-benzoylvalerate (In) decrease in the order I > I1 > III. Keto participation is the predominant pathway in the case of y-keto esters. Evidence has also been obtained for keto participation in the case of 6-keto esters, whereas no such evidence is available in the case of r-keto esters studied.

Artist Rafaello Busoni drawing.

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Geometrical interpretation of Inönü-Wigner contractions

The Inönü-Wigner contractions which interrelate the Lie algebras of the isometry groups of metric spaces are discussed with reference to deformations of the absolutes of the spaces. A general formula is derived for the Lie algebra commutation relations of the isometry group for anyN-dimensional metric space. These ideas are illustrated by a discussion of important particular cases, which interrelate the four-dimensional de Sitter, Poincaré, and Galilean groups.

Technicum - Drawing

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Technicum - Drawing

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Hamilton’s theory of turns and a new geometrical representation for polarization optics

Hamilton’s theory of turns for the group SU(2) is exploited to develop a new geometrical representation for polarization optics. While pure polarization states are represented by points on the Poincaré sphere, linear intensity preserving optical systems are represented by great circle arcs on another sphere. Composition of systems, and their action on polarization states, are both reduced to geometrical operations. Several synthesis problems, especially in relation to the Pancharatnam-Berry-Aharonov-Anandan geometrical phase, are clarified with the new representation. The general relation between the geometrical phase, and the solid angle on the Poincaré sphere, is established.

Influence of Geometrical Factors on the Physico-Chemical Properties of Perovskite and Layered Perovskite Oxides

A brief qualitative comparison is made of perovskite ABO sub 3 and layered perovskite ABO sub 3 and layered perovskite A sub 2 BO sub 4 oxides with special emphasis on the influence of geometrical factors on certain physico-chemical properties. The layered perovskite oxides are distinguished from three-dimensional oxides by a looser packing, frustration in three-dimensional interactions, more internal pressure on B--O bonds for small tolerance factors, and by different values of site-percolation thresholds. Their influence on electronic configurations of metal ions, stabilities and syntheses of compounds is discussed. The influence of increased anisotropy in layered oxides on localisation of charge carriers and in suppressing the onset of long-range ferromagnetic ordering is also discussed.

Influence of non-geometrical factors on intracrystalline diffusion -- Role of sorbate-zeolite interactions

Molecular dynamics simulations on Xe in NaY and Ar in NaCaA zeolite are reported. Rates of cage-to-cage crossovers in the two zeolites exhibit trends which are contrary to that expected from geometrical considerations. The results suggest the important role of the sorbate-zeolite interactions in determining the molecular sieve properties of zeolites for small sized sorbates. The results are explained in terms of the barrier height for cage-to-cage crossover in the two zeolites.

Performance analysis for geometrical attack on digital image watermarking

We present a technique for irreversible watermarking approach robust to affine transform attacks in camera, biomedical and satellite images stored in the form of monochrome bitmap images. The watermarking approach is based on image normalisation in which both watermark embedding and extraction are carried out with respect to an image normalised to meet a set of predefined moment criteria. The normalisation procedure is invariant to affine transform attacks. The result of watermarking scheme is suitable for public watermarking applications, where the original image is not available for watermark extraction. Here, direct-sequence code division multiple access approach is used to embed multibit text information in DCT and DWT transform domains. The proposed watermarking schemes are robust against various types of attacks such as Gaussian noise, shearing, scaling, rotation, flipping, affine transform, signal processing and JPEG compression. Performance analysis results are measured using image processing metrics.

Influence of operational and geometrical parameters on the performance of twin thermoacoustic prime mover

Thermoacoustics is the interaction between heat and sound, which are useful in designing heat engines and heat pumps. Research in the field of thermoacoustics focuses on the demand to improve the performance which is achieved by altering operational, geometrical and fluid parameters. The present study deals with improving the performance of twin thermoacoustic prime mover, which has gained the significant importance in the recent years for the production of high amplitude sound waves. The performance of twin thermoacoustic prime mover is evaluated in terms of onset temperature difference, resonance frequency and pressure amplitude of the acoustic waves by varying the resonator length and charge pressures of fluid medium nitrogen. DeltaEC, the free simulation software developed by LANL, USA is employed in the present study to simulate the performance of twin thermoacoustic prime mover. Experimental and simulated results are compared and the deviation is found to be within 10%.

MRT Letter: Experimental Verification of Vectorial Theory to Determine Field at the Geometrical Focus of a Cylindrical Lens

We provide experimental evidence supporting the vectorial theory for determining electric field at and near the geometrical focus of a cylindrical lens. This theory provides precise distribution of field and its polarization effects. Experimental results show a close match (approximate to 95% using (2)-test) with the simulation results (obtained using vectorial theory). Light-sheet generated both at low and high NA cylindrical lens shows the importance of vectorial theory for further development of light-sheet techniques. Potential applications are in planar imaging systems (such as, SPIM, IML-SPIM, imaging cytometry) and spectroscopy. Microsc. Res. Tech. 77:105-109, 2014. (c) 2014 Wiley Periodicals, Inc.

A novel method for studying the buckling of nanotubes considering geometrical imperfections

Buckling of nanotubes has been studied using many methods such as molecular dynamics (MD), molecular mechanics, and continuum-based shell theories. In MD, motion of the individual atoms is tracked under applied temperature and pressure, ensuring a reliable estimate of the material response. The response thus simulated varies for individual nanotubes and is only as accurate as the force field used to model the atomic interactions. On the other hand, there exists a rich literature on the understanding of continuum mechanics-based shell theories. Based on the observations on the behavior of nanotubes, there have been a number of shell theory-based approaches to study the buckling of nanotubes. Although some of these methods yield a reasonable estimate of the buckling stress, investigation and comparison of buckled mode shapes obtained from continuum analysis and MD are sparse. Previous studies show that the direct application of shell theories to study nanotube buckling often leads to erroneous results. The present study reveals that a major source of this error can be attributed to the departure of the shape of the nanotube from a perfect cylindrical shell. Analogous to the shell buckling in the macro-scale, in this work, the nanotube is modeled as a thin-shell with initial imperfection. Then, a nonlinear buckling analysis is carried out using the Riks method. It is observed that this proposed approach yields significantly improved estimate of the buckling stress and mode shapes. It is also shown that the present method can account for the variation of buckling stress as a function of the temperature considered. Hence, this can prove to be a robust method for a continuum analysis of nanosystems taking in the effect of variation of temperature as well.

Size Effect and Geometrical Effect of Polycrystals and Thin Film/Substrate System in Micro-indentation Test

Micro-indentation test at scales on the order of sub-micron has shown that the measured hardness increases strongly with decreasing indent depth or indent size, which is frequently referred to as the size effect. Simultaneously, at micron or sub-micron scale, the material microstructure size also has an important influence on the measured hardness. This kind of effect, such as the crystal grain size effect, thin film thickness effect, etc., is called the geometrical effect by here. In the present research, in order to investigate the size effect and the geometrical effect, the micro-indentation experiments are carried out respectively for single crystal copper and aluminum, for polycrystal aluminum, as well as for a thin film/substrate system, Ti/Si3N4. The size effect and geometrical effect are displayed experimentally. Moreover, using strain gradient plasticity theory, the size effect and the geometrical effect are simulated. Through comparing experimental results with simulation results, length-scale parameter appearing in the strain gradient theory for different cases is predicted. Furthermore, the size effect and the geometrical effect are interpreted using the geometrically necessary dislocation concept and the discrete dislocation theory. Member Price: $0; Non-Member Price: $25.00