Harmonic Analysis On Heisenberg Nilmanifolds

In these lectures we plan to present a survey of certain aspects of harmonic analysis on a Heisenberg nilmanifold Gammakslash}H-n. Using Weil-Brezin-Zak transform we obtain an explicit decomposition of L-2 (Gammakslash}H-n) into irreducible subspaces invariant under the right regular representation of the Heisenberg group. We then study the Segal-Bargmann transform associated to the Laplacian on a nilmanifold and characterise the image of L-2 (GammakslashH-n) in terms of twisted Bergman and Hermite Bergman spaces.

The third post-Newtonian gravitational wave polarizations and associated spherical harmonic modes for inspiralling compact binaries in quasi-circular orbits

The gravitational waveform (GWF) generated by inspiralling compact binaries moving in quasi-circular orbits is computed at the third post-Newtonian (3PN) approximation to general relativity. Our motivation is two-fold: (i) to provide accurate templates for the data analysis of gravitational wave inspiral signals in laser interferometric detectors; (ii) to provide the associated spin-weighted spherical harmonic decomposition to facilitate comparison and match of the high post-Newtonian prediction for the inspiral waveform to the numerically-generated waveforms for the merger and ringdown. This extension of the GWF by half a PN order (with respect to previous work at 2.5PN order) is based on the algorithm of the multipolar post-Minkowskian formalism, and mandates the computation of the relations between the radiative, canonical and source multipole moments for general sources at 3PN order. We also obtain the 3PN extension of the source multipole moments in the case of compact binaries, and compute the contributions of hereditary terms (tails, tails-of-tails and memory integrals) up to 3PN order. The end results are given for both the complete plus and cross polarizations and the separate spin-weighted spherical harmonic modes.

Micro-treatment options for components of organic fraction of MSW in residential areas

There is a growing interest in management of MSW through micro-treatment of organic fraction of municipal solid wastes (OFMSW) in many cities of India. The OFMSW fraction is high (> 80%) in many pockets within South Indian cities like Bangalore, Chikkamagalur, etc. and is largely represented by vegetable, fruit, packing and garden wastes. Among these, the last three have shown problems for easy decomposition. Fruit wastes are characterized by a large pectin supported fraction that decomposes quickly to organic acids (becomes pulpy) that eventually slow down anaerobic and aerobic decomposition processes. Paper fraction (newsprint and photocopying paper) as well as paddy straw (packing), bagasse (from cane juice stalls) and tree leaf litter (typical garden waste and street sweepings) are found in reasonably large proportions in MSW. These decompose slowly due to poor nutrients or physical state. We have examined the suitability of these substrates for micro-composting in plastic bins by tracking decomposition pattern and physical changes. It was found that fruit wastes decompose rapidly to produce organic acids and large leachate fraction such that it may need to be mixed with leachate absorbing materials (dry wastes) for good composting. Leaf litter, paddy straw and bagasse decompose to the tune of 90, 68 and 60% VS and are suitable for composting micro-treatment. Paper fractions even when augmented with 10% leaf compost failed to show appreciable decomposition in 50 days. All these feedstocks were found to have good biological methane potential (BMP) and showed promise for conversion to biogas under a mixed feed operation. Suitability of this approach was verified by operating a plug-flow type anaerobic digester where only leaf litter gathered nearby (as street sweepings) was used as feedstock. Here only a third of the BMP was realized at this scale (0.18 m(3) biogas/kg VS 0.55 m(3)/kg in BMP). We conclude that anaerobic digestion in plug-flow like digesters appear a more suitable micro-treatment option (2-10 kg VS/day) because in addition to compost it also produces biogas for domestic use nearby.

Resource recovery potential from secondary components of segregated municipal solid wastes

Fermentable components of municipal solid wastes (MSW) such as fruit and vegetable wastes (FVW), leaf litter, paddy straw, cane bagasse, cane trash and paper are generated in large quantities at various pockets of the city. These form potential feedstocks for decentralized biogas plants to be operated in the vicinity. We characterized the fermentation potential of six of the above MSW fractions for their suitability to be converted to biogas and anaerobic compost using the solid-state stratified bed (SSB) process in a laboratory study. FVW and leaf litter (papermulberry leaves) decomposed almost completely while paddy straw, sugarcane trash, sugarcane bagasse and photocopying paper decomposed to a lower extent. In the SSB process between 50-60% of the biological methane potential (BMP) could be realized. Observations revealed that the SSB process needs to be adapted differently for each of the feedstocks to obtain a higher gas recovery. Bagasse produced the largest fraction of anaerobic compost (fermentation residue) and has the potential for reuse in many ways.

Space-Vector-Based Hybrid Pulsewidth Modulation Techniques for Reduced Harmonic Distortion and Switching Loss

Novel switching sequences can be employed in spacevector-based pulsewidth modulation (PWM) of voltage source inverters. Differentswitching sequences are evaluated and compared in terms of inverter switching loss. A hybrid PWM technique named minimum switching loss PWM is proposed, which reduces the inverter switching loss compared to conventional space vector PWM (CSVPWM) and discontinuous PWM techniques at a given average switching frequency. Further, four space-vector-based hybrid PWM techniques are proposed that reduce line current distortion as well as switching loss in motor drives, compared to CSVPWM. Theoretical and experimental results are presented.

Physicochemical studies on the gelation of hen egg yolk; separation of gelling protein components from yolk plasma

A study of the component(s) in egg yolk responsible for gelation of yolk on freezing and thawing has shown that granule-free yolk plasma, obtained by high-speed centrifugation of yolk, has the capacity to gel. As with the whole yolk, gelation of yolk plasma on freezing and thawing could be inhibited by additives such as sugars, sodium chloride, proteolytic enzymes, and phospholipase-A. Phospholipase-C, which induces gelation of whole yolk at room temperature, has a similar effect on yolk plasma. Yolk plasma has been separated into aggregating (gelling) and soluble fractions by delipidation, using formic acid. Each of these fractions consists of three or four protein components, as observed by gel filtration, ultracentrifugation, and agar electrophoresis. The proteins are glycoproteins and contain bound hexoses, hexosamine, and sialic acid. The gelation of yolk has been attributed to the interactions between protein molecules following disruption of lipid-protein bonds.

The protein components of elastoidin

Not all elastoidin samples from different species of sharks show a high content of tryptophan in contrast to one specimen from an unidentified species examined in our earlier study. There may be considerable species-dependent variation in tryptophan content and analytical artefacts may have occurred. Available analyses for tyrosine in different specimens of fibres also suggest the possibility that the variation in tyrosine content is also species-dependent. Elastoidin, from Galeoscerdo cuveir (Tiger Shark) and another unidentified species, on treatment with formic acid yielded three fractions A,B and C. On the basis of analytical data it appears that specimens of elastoidin containing no (or little) tryptophan may yield fraction B through the solubilization of fraction A by formic acid. C fractions from two specimens of fibres were collagenous in nature. C fractions have been further purified in this study by charcoal treatment which removes a tyrosine-rich contaminant, to yield collagens with only approx. 2–4 residues of tyrosine per assumed mol. wt. of 360000. In the collagen from the unidentified species glucose and galactose were present in the ratio of 2:5; some glucosamine was also present.

Anthranilic acid oxidase system of Tecoma stans—II. : Studies on the properties of a purified anthranilic acid oxidase system and its separation into different enzymic components

An enzyme system which catalysed the conversion of anthranilic acid to catechol has been purified 20-fold from a cell-free leaf extract of Tecoma stans. The optimum substrate concentration was 10−3 M and optimum temperature for the reaction was 45°. The presence of a multi-enzyme system was inferred from inhibition studies. The formation of catechol was inhibited by Mg2+, Zn2+, and Co2+ ions, whereas anthranilic acid disappearance was not affected to the same extent. The effect of metal chelating agents like EDTA, cyanide and pyrophosphate showed a similar trend. PCMB inhibited catechol formation but had no effect on anthranilic acid disappearance. The reaction was not inhibited by catalase, nor was it activated by peroxide-donating systems. This ruled out the possibility of peroxidative type of reaction. The overall reaction is markedly activated by NADPH and THFA. This multi-enzyme was separated into three different components, by fractionation with Alumina Cγ and calcium phosphate gels. The overall reaction catalysed by these components can be represented as anthranilic acid→3-hydroxy anthranilic acid→o-aminophenol→catechol.

Experimental studies on the wear of engine components

Wear studies of engine components of high-speed diesel engines running under various operating conditions are presented. Tests were conducted under controlled conditions over long periods. The results of the various tests are discussed and attempts have been made to examine the effects of engine operating variables and the quality of the lubricating oil on the wear of engine components.

Harmonic and anharmonic oscillations of a cylindrical plasma in the presence of a uniform axial magnetic field and a steady axial current

In the present note we have studied the harmonic and anharmonic oscillations of cylindrical plasma using Lagrangian formalism. In order to study the harmonic oscillations, the equations are linearized and the resulting equation for the displacement has been numerically solved. For situations present in thermonuclear reactors, the presence of axial magnetic field is found necessary to make the periods of oscillation to become comparable with the time required for the thermonuclear reactions to set in. A detailed analysis of the anharmonic oscillations reveals that the significant interaction is between the first and the second mode. The fundamental period of anharmonic oscillation is more than the corresponding period of harmonic oscillations by 9·2%. Graphs have been drawn for the amplitudes of relative variations in density and magnetic field and of the time-varying part of anharmonic oscillation.

Principle of a Dual Current Source Converter for AC Motor Drives

The principle of operation of a dual current source converter is briefly explained. The combination of two single current source converters (SCSC) to form a ``dual (duplex) current source converter'' (DCSC) is proposed. The DCSC is shown to have the following merits: 1) it retains all the advantages of the SCSC; 2) it reduces the harmonic content of the current waveform considerably; and 3) since the load current is shared equally between two current source converters, ratings of the individual components employed in the circuit are considerably lowered. A DCSC can be an attractive choice for sophisticated large horsepower drives where a good performance of the drive rather than cost is a prime factor. An open-loop control scheme employing the DCSC for an ac motor drive has been successfully implemented in the laboratory. Oscillograms of the improved load current waveforms are shown.

Second harmonic generation in some donor-acceptor ethylenes—I

We report the absorption spectra, oscillator strengths, ground state and excited state dipole moments, and molecular second order polarizability coefficients (βCT) due to donor—acceptor charge transfer in four trisubstituted ethylenes, namely 1,1-bisdimethylamino-2-nitroethylene, 1,1-bispyrolidino-2-nitroethylene, 1,1-bispiperidino-2-nitroethylene and 1,1-bismorpholino-2-nitroethylene. The results are compared with that of trans-N,N-dimethylamino-nitroethylene, which has a large βCT. The powder second harmonic generation (SHG) intensity of all these molecules is also measured and only 1,1-bispiperidino-2-nitroethylene is found to possess an efficiency of 20% of that of urea under the same conditions. The SHG efficiency of this compound and deficiency in the other molecules in the powdered state is discussed in terms of their arrangements in the unit cell. The crystal structure of the active molecule is also presented and the structure—property relationship is critically examined in all these molecules.