Lacunary Fourier series and a qualitative uncertainty principle for compact Lie groups

We define lacunary Fourier series on a compact connected semisimple Lie group G. If f is an element of L-1 (G) has lacunary Fourier series and f vanishes on a non empty open subset of G, then we prove that f vanishes identically. This result can be viewed as a qualitative uncertainty principle.

Star formation in giant extragalactic H II regions

Star formation properties in Giant Extragalactic H II Regions (GEHRs) are investigated using optical photometry and evolutionary population synthesis models. Photometric data in $BVR$ bands and in the emission line of H-alpha are obtained by CCD imaging at Vainu Bappu Observatory, Kavalur. Aperture photometry is performed for 180 GEHRs in galaxies NGC 1365, 1566, 2366, 2903, 2997, 3351, 4303, 4449, 4656 and 5253. Thirty six of these GEHRs having published spectroscopic data are studied for star formation properties. The population synthesis model is constructed based on Maeder's stellar evolutionary and Kurucz stellar atmosphere models, to synthesize observational quantities of embedded clusters in GEHRs. The observed H-alpha luminosity is a measure of the number of massive stars while the contribution to BVR bands is from intermediate mass (5-15 solar mass) stars when the cluster is young and from evolving supergiants when the cluster is old (age >/= 6~Myr). Differential reddening between gas and embedded stars is essential to constrain the dereddened cluster colors within the range of youngest clusters. Obscuring dust closely associated with gas, which is distributed in filaments and clumps, as in the case of 30 Doradus, is the most likely configuration giving rise to net reduction of extinction towards stars. The fraction of the stellar photons escaping the nebula unattenuated is estimated to be 50%. GEHRs are rarely found to be simple systems containing stars from single generation. In the present sample such regions in addition to being older than 3~Myr, have their Lyman continuum luminosity reduced by as much as 60%, compared to the observed $B$ band luminosity for a normal IMF. The missing ionizing photons may be escaping the nebula, leading to the ionization of extra-H II region ionized medium. Co-existence of young (age stars producing ionizing photons) and old populations (~10~Myr; Red Supergiants) is found to be common in GEHRs. The emission and continuum knots are seen spatially separated (40-100 pc) on CCD images in NGC 2997, 4303 and 4449 and may be direct evidences for the co-existence of young and old populations in giant star forming complexes. Triggering of star formation from earlier bursts is the most likely cause of new generation of stars, and may be a common phenomenon in GEHRs. Spatial separation between the young and old stars (~30 pc) had been earlier reported in 30 Doradus. Thus GEHRs in nearby galaxies share many of the properties shown by 30 Dor, the nearest GEHR. (SECTION: Dissertation Summaries)

A compact proof of Fisher�s Fundamental Theorem for multiple loci

A systematic method is formulated to carry out theoretical analysis in a multilocus multiallele genetic system. As a special application, the Fundamental Theorem of Natural Selection is proved (in the continuous time model) for a multilocus multiallele system if all pairwise linkage disequilibria are zero.

Flat connections, geometric invariants and energy of harmonic functions on compact Riemann surfaces

A geometric invariant is associated to the space of fiat connections on a G-bundle over a compact Riemann surface and is related to the energy of harmonic functions.

Photolysis of arene chromium tricarbonyl complexes in presence of amine-boranes: Observation of sigma-borane complexes in solution

Activation of the B-H sigma-bond of amine-boranes on the chromium(0) center of arene chromium tricarbonyl complexes (eta(6)-arene) Cr(CO)(3) (arene = fluorobenzene, 1a; benzene, 1b and mesitylene, 1c) has been studied. Photolysis of 1b in presence of ammonia-borane (H3N center dot BH3, AB) and tert-butylamine-borane ((BuH2N)-Bu-t center dot BH3, TBAB) resulted in H-2 evolution and precipitation of a BNHx polymer. On the other hand, photolysis in the presence of trimethylamine-borane (Me3N center dot BH3, TMAB) resulted in the formation of a sigma-borane complex (2) along with Cr(CO)(5)(eta(1)-HBH2 center dot NMe3) (3). The sigma-borane complexes (eta(6)-arene) Cr-( CO)(2)(eta(1)-HBH2 center dot NMe3) (arene = fluorobenzene, 2a; benzene, 2b and mesitylene, 2c) were characterized in solution by H-1, B-11, and C-13 NMR spectroscopy. Electron withdrawing substituents on the arene ring provide the more stable sigma-borane moiety in this series of complexes. (C) 2011 Elsevier B.V. All rights reserved.

Parallel implementation of alternate quadrant interlocking factorisation method on star topology

This paper discusses the parallel implementation of the solution of a set of linear equations using the Alternative Quadrant Interlocking Factorisation Methods (AQIF), on a star topology. Both the AQIF and LU decomposition methods are mapped onto star topology on an IBM SP2 system, with MPI as the internode communicator. Performance parameters such as speedup, efficiency have been obtained through experimental and theoretical means. The studies demonstrate (i) a mismatch of 15% between the theoretical and experimental results, (ii) scalability of the AQIF algorithm, and (iii) faster executing AQIF algorithm.

Incremental-angle and angular velocity estimation using a star sensor

A method is described for estimating the incremental angle and angular velocity of a spacecraft using integrated rate parameters with the help of a star sensor alone. The chief advantage of this method is that the measured stars need not be identified, whereas the identification of the stars is necessary in earlier methods. This proposed estimation can be carried out with all of the available measurements by a simple linear Kalman filter, albeit with a time-varying sensitivity matrix. The residuals of estimated angular velocity by the proposed spacecraft incremental-angle and angular velocity estimation method are as accurate as the earlier methods. This method also enables the spacecraft attitude to be reconstructed for mapping the stars into an imaginary unit sphere in the body reference frame, which will preserve the true angular separation of the stars. This will pave the way for identification of the stars using any angular separation or triangle matching techniques applied to even a narrow field of view sensor that is made to sweep the sky. A numerical simulation for inertial as well as Earth pointing spacecraft is carried out to establish the results.

Possible conversion of a neutron star to a quark star in the presence of high magnetic field

Recent results and data suggest that high magnetic fields in neutron stars (NS) strongly affect the characteristics (radius, mass) of the star. Such stars are even separated into a class known as magnetars, for which the surface magnetic field is greater than 10(14) G. In this work we discuss the effect of such a high magnetic field on the phase transition of a NS to a quark star (QS). We study the effect of magnetic field on the transition from NS to QS including the magnetic-field effect in the equation of state (EoS). The inclusion of the magnetic field increases the range of baryon number densities for which the flow velocities of the matter in the respective phase are finite. The magnetic field helps in initiation of the conversion process. The velocity of the conversion front, however, decreases due to the presence of the magnetic field, as the presence of the magnetic field reduces the effective pressure (P). The magnetic field of the star is decreased by the conversion process, and the resultant QS has lower magnetic field than the initial NS.

An Improved Compact Compliant Mechanism for an External Pipe-Crawler

An external pipe-crawling device presented in this paper aids the inspection of pipes in hazardous environments and areas inaccessible to humans. The principal component of our design, which uses inchworm type motion, is a compliant ring mechanism actuated using shape memory alloy (SMA) wire. It was fabricated and tested and was reported in our earlier work. But this device had a drawback of low crawling speed (about 1 mm/min) owing to the delay in heating and cooling of the SMA strips in the linear actuation. Additionally, that design also had the difficulties of mounting on pipes with closed ends, large radial span, and the need for housing for electrical insulation and guiding of the SMA wire. In this paper we present a compact design that overcomes the difficulties of the earlier design. In particular, we present a compact compliant mechanism with two halves so as to enable mounting and un-mounting on any closed or open pipe. Another feature is the presence of insulation and guiding of the SMA wire without housing. This design results in a reduction of the radial span of the ring from 22 mm to 12 mm, and the stiffness of the mechanism and the SMA wire are matched. An SMA helical spring is to used in the place of an SMA strip to increase the crawling speed of the device. A microcontroller-based circuitry is also fitted to cyclically.activate the SMA wires and springs.

Continous Time Sigma-Delta Modulator Employing a Novel Comparator Architecture

A novel comparator architecture is proposed for speed operation in low voltage environment. Performance comparison with a conventional regenerative comparator shows a speed-up of 41%. The proposed comparator is embedded in a continuous time sigma-delta ADC so as to reduce the quantizer delay and hence minimizes the excess loop delay problem. A performance enhancement of 1dB in the dynamic range of the ADC is achieved with this new comparator. We have implemented this ADC in a standard single-poly 8-Metal 0.13 mum UMC process. The entire system operates at 1.2 V supply providing a dynamic range of 32 dB consuming 720 muW of power and occupies an area of 0.1 mm2.

Hexa-arm star shaped hydrazone derivatives from hexakis(4-formylphenoxy)-cyclotriphosphazene core

A series of novel hexasubstituted cyclophosphazene hydrazones [N(3)P(3)(-OC(6)H(4)-p-CH=N-NH-C(O)-C(6)H(4)-p-X)(6)] (X = H, Br, Cl, F, OH, OCH(3), CH(3), NO(2), NH(2)) were prepared by a sixfold condensation reaction of [N(3)P(3)(-OC(6)H(4)-p-CHO)(6)] with para-substituted benzoic hydrazides [NH(2)-NH-C(O)-C(6)H(4)-p-X] with excellent yields (91-98%). The structures of the compounds were confirmed by elemental analysis, FT-IR, (1)H, (13)C, (31)P, 2D-HSQC NMR and mass spectrometry (MALDI-TOF). All the synthesized cyclophosphazene hydrazones exhibit high thermal stability. The crystal structure of a homogeneously substituted hexakis(4-formylphenoxy)-cyclotriphosphazene was determined by X-ray diffraction analysis. The compound crystallizes in the monoclinic system, space group P2(1)/n with a = 16.558(3) angstrom, b = 10.250(2) angstrom, c = 23.429(5) angstrom, alpha = gamma = 90.00 degrees, beta = 90.461(4)degrees, V = 3976.5(14) angstrom(3) and Z = 4. The R value is 0.0823 for 4290 observed reflections. The conformations of the 4-formylphenoxy-groups are different at the three phosphorus atoms. (C) 2011 Elsevier B.V. All rights reserved.