Convergence of the Lasserre Hierarchy of SDP Relaxations for Convex Polynomial Programs without Compactness

The Lasserre hierarchy of semidefinite programming (SDP) relaxations is an effective scheme for finding computationally feasible SDP approximations of polynomial optimization over compact semi-algebraic sets. In this paper, we show that, for convex polynomial optimization, the Lasserre hierarchy with a slightly extended quadratic module always converges asymptotically even in the face of non-compact semi-algebraic feasible sets. We do this by exploiting a coercivity property of convex polynomials that are bounded below. We further establish that the positive definiteness of the Hessian of the associated Lagrangian at a saddle-point (rather than the objective function at each minimizer) guarantees finite convergence of the hierarchy. We obtain finite convergence by first establishing a new sum-of-squares polynomial representation of convex polynomials over convex semi-algebraic sets under a saddle-point condition. We finally prove that the existence of a saddle-point of the Lagrangian for a convex polynomial program is also necessary for the hierarchy to have finite convergence.Comment: 17 page

Collimation of extragalactic radio jets in compact steep spectrum and larger sources

We study the collimation of radio jets in the high-luminosity Fanaroff-Riley class II sources by examining the dependence of the sizes of hotspots and knots in the radio jets on the overall size of the objects for a sample of compact steep-spectrum or CSS and larger-sized objects. The objects span a wide range in overall size from about 50 pc to nearly 1 Mpc. The mean size of the hotspots increases with the source size during the CSS phase, which is typically taken to be about 20 kpc, and the relationship flattens for the larger sources. The sizes of the knots in the compact as well as the larger sources are consistent with this trend. We discuss possible implications of these trends. We find that the hotspot closer to the nucleus or core component tends to be more compact for the most asymmetric objects where the ratio of separations of the hotspots from the nucleus, r_d > 2. These highly asymmetric sources are invariably CSS objects, and their location in the hotspot size ratio - separation ratio diagram is possibly due to their evolution in an asymmetric environment. We also suggest that some soures, especially of lower luminosity, exhibit an asymmetry in the collimation of the oppositely-directed radio jets.Comment: MNRAS in press, 9 pages and 3 figures, MNRAS LaTe

Mass of the black hole in the Seyfert 1.5 galaxy H 0507+164 from reverberation mapping

We present the results of our optical monitoring campaign of the X-ray source H 0507+164, a low luminosity Seyfert 1.5 galaxy at a redshift z = 0.018. Spectroscopic observations were carried out during 22 nights in 2007, from the 21 of November to the 26 of December. Photometric observations in the R-band for 13 nights were also obtained during the same period. The continuum and broad line fluxes of the galaxy were found to vary during our monitoring period. The R-band differential light curve with respect to a companion star also shows a similar variability. Using cross correlation analysis, we estimated a time delay of 3.01 days (in the rest frame), of the response of the broad H-beta line fluxes to the variations in the optical continuum at 5100 angstroms. Using this time delay and the width of the H-beta line, we estimated the radius for the Broad Line Region (BLR) of 2.53 x 10^{-3} parsec, and a black hole mass of 9.62 x 10^{6} solar mass.Comment: 7 pages, 8 figures, Accepted for publication in MNRA

‘Beauty Lies In The Eyes Of The Beholder’: Why And How Island Tourists Look At SMTE Websites

This research examined the information needs of small and medium tourism enterprise (SMTE) customers sampled from two popular island destinations in the Indian Ocean. It also identified their motivations and inhibitions in using the Internet. A study of the website navigation behavior showed that the appeal mix and multimedia mix features were accessed more than the offering mix features. The association between the tourism products bought online and the purchase motivations was mapped using correspondence analysis. The online buyers of „accommodation‟ and „attractions‟ were motivated by transactional objectives while the „access‟ and auxiliary product buyers by informational uses

Compact steep-spectrum sources from the S4 sample

We present the results of 5-GHz observations with the VLA A-array of a sample of candidate Compact Steep Spectrum sources (CSSs) selected from the S4 survey. We also estimate the symmetry parameters of high-luminosity CSSs selected from different samples of radio sources, and compare these with the larger sources of similar luminosity to understand their evolution and the consistency of the CSSs with the unified scheme for radio galaxies and quasars. The majority of CSSs are likely to be young sources advancing outwards through a dense asymmetric environment. The radio properties of CSSs are found to be consistent with the unified scheme, in which the axes of the quasars are observed close to the line of sight, while radio galaxies are observed close to the plane of the sky.Comment: accepted for publication in mnras; 8 pages, figure 1 with 21 images, and two additional figures; 2 table

Socio-economic Impact Assessment of Livelihood Security in Agriculture, Animal Husbandry and Aquaculture on the Tsunami-hit Lands of Andaman

Indian subcontinent is highly vulnerable to major natural disasters such as earthquakes, cyclones, floods, droughts, landslides and bushfires. Tsunami, which is a recent addition to this list, had occurred in the early morning of 26th December 2004, after a massive earthquake of 9.2 magnitude on the Richter scale in Andaman & Nicobar islands, resulting in the submergence of large area of farmland, and subsequent drying up of water bodies. It caused moisture stress for the standing crops, livestock and fisheries and affected the livelihood of the people to a large extent. In this context, the present study has been carried out to make the socio-economic impact assessment of livelihood security in agriculture, animal husbandry and aquaculture on the tsunami-hit lands of Andaman. Data have been collected from 150 sample respondents and the survey has been conducted for two periods, pre-tsunami and post-tsunami. The results have indicated that tsunami has ravaged the households, standing crops, farm inputs such as seed, feed and implements, livestock and poultry population, their sheds, fish ponds, etc., thereby affecting the basic livelihood security of the people in Andaman. The rehabilitation measures taken by the government and NGOs have improved their livelihoods by reviving agriculture considerably in the subsequent years and by creating employment opportunities in various farm and non-farm activities. The paper has suggested creating profitable livelihood security to vulnerable sections of the society in the existing socio-economic penury with holistic intervention of the community, government and NGOs.Agricultural and Food Policy,

Early detection of lung involvement in rheumatoid arthritis patients

AIM OF THE STUDY: The Aim of the study was to assess the early involvement of lung in Rheumatoid Arthritis patients. METHODS AND MATERIALS: For this study, 40 normal control group in the age group between 25-55 years and 40 patients with Rheumatoid Arthritis of <5 yrs duration as study group were selected as per American Association Criteria of Rheumatology. This Study was conducted at Research Laboratory, Department of Physiology, Thanjavur Medical College, Thanjavur. The Study group was from the Thanjavur Medical College & Hospital, Thanjavur. Patients with Diabetes Mellitus, Alcoholism, Neuropathy, Chronic Tuberculosis, Carcinoma lung, Metabolic disorders and other connective tissue disorders were excluded. Informed written consent were obtained from the patients of Thanjavur Medical College & Hospital.Ethical committee approval obtained before starting the study. In this study, FVC, FEV 1, FEV 1/FVC, MVV and PEFR were compared and statistically analyzed. RESULTS: The results showed statistically significantly reduced pulmonary function parameters FEV₁, FVC, MVV & PEFR (P<0.05). However FEV₁/FVC (%) was mildly increased which was not statistically significant in Rheumatoid arthritis patients. CONCLUSION: The result of the present study shows that there is a decrease in pulmonary function in Rheumatoid arthritis patients when compared with healthy controls

Effect of Neat Sardine Oil with Varies Blends on the Performance and Emission Characteristics of Diesel Engine

This study investigates the performance and emission characteristics of a diesel engine which is fuelled with neat sardine oil and diesel. A single cylinder four stroke diesel engine was used for the experiments at various load and speed of 1500 rpm. An AVL5 gas analyzer and a smoke meter were used for the measurements of exhaust gas emission. The results showed that break thermal efficiency is decreased and CO (Carbon-monoxide), HC (Hydro-Carbon) in the exhaust is increased when fuelled with neat sardine oil compared to diesel except NOx (Nitrogen Oxide). The future scope of the work is to do some modification (e.g may be engine, piston or values) in the engine to get better performance in same blending ratio