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

Will Growth of Technology Lift up the Economic Status of Farmers?

As a very hot news that spread through out the state Tamilnadu, India that the formers who produced tomatos are dumped aside of road without bringing to market for domestic cooking consumption. Usually, the agricultural zaid commodities are not brings expected profit to the producers due to perishable character and gets low price at the markets in any situation. Tomato is zaid crop but it availing in all seasons and price of it will be also differing Moreover, crop in the zaid season gets very less price in the market but the level of production is high. Due to stable demand and substitute commodities are the cause for emerging low price in the market. As a remedy for this problem, recent research found that the rotten tomatos is good source to generate electricity. Hence, This empirical report brought out the real situation of zaid crop tomato in the market and plights of formers due to decreased price. Moreover, report suggests to the government that have to follow a procurement price for zaid crops also, to empower the economic status of formers followed by the execution of technology for alternative purposes

Magnetic Field Strengths in Photodissociation Regions

We measure carbon radio recombination line (RRL) emission at 5.3 GHz toward four H ii regions with the Green Bank Telescope to determine the magnetic field strength in the photodissociation region (PDR) that surrounds the ionized gas. Roshi suggests that the non-thermal line widths of carbon RRLs from PDRs are predominantly due to magneto-hydrodynamic waves, thus allowing the magnetic field strength to be derived. We model the PDR with a simple geometry and perform the non-LTE radiative transfer of the carbon RRL emission to solve for the PDR physical properties. Using the PDR mass density from these models and the carbon RRL non-thermal line width we estimate total magnetic field strengths of B ~ 100-300 µG in W3 and NGC 6334A. Our results for W49 and NGC 6334D are less well constrained with total magnetic field strengths between B ~ 200-1000 µG. H i and OH Zeeman measurements of the line of sight magnetic field strength (B_(los)), taken from the literature, are between a factor of ~ 0.5-1 of the lower bound of our carbon RRL magnetic field strength estimates. Since |B_(los)| ⩽ B, our results are consistent with the magnetic origin of the non-thermal component of carbon RRL widths

A Forecasting Study on Electricity Consumption in Indian Textile Industries: An Economic Analysis

Electricity as an important input plays a vital role from each and every economic movements for the development of the country at global level. Textile industry is not differed from this context; it provides outputs to trade at International markets. In India, textile industry is one among the important industries which supports economic development and trade balance. Hence, supply and demand for electricity in Indian textile industries are the signified economic processes to attain maximum output. Hence, the study emphasised electricity consumption and its cost which effects from consumption per unit of electricity for the Indian textile industry. This study brought out secondary data collected from various published articles and reports. It covers 30 years of forecasted data collected from 2001 to 2030 (Estimated). And data have been analysed by statistical tools such as correlation and regression. Findings of the study has highlighted that there is close relationship within and between the dependent and independent variables. Finally, the study has been concluded with effective policy recommendations with an overview of study

The Mitochondrial Ca(2+) Uniporter: Structure, Function, and Pharmacology.

Mitochondrial Ca(2+) uptake is crucial for an array of cellular functions while an imbalance can elicit cell death. In this chapter, we briefly reviewed the various modes of mitochondrial Ca(2+) uptake and our current understanding of mitochondrial Ca(2+) homeostasis in regards to cell physiology and pathophysiology. Further, this chapter focuses on the molecular identities, intracellular regulators as well as the pharmacology of mitochondrial Ca(2+) uniporter complex

Optimality criteria without constraint qualications for linear semidenite problems

We consider two closely related optimization problems: a problem of convex Semi- Infinite Programming with multidimensional index set and a linear problem of Semidefinite Programming. In study of these problems we apply the approach suggested in our recent paper [14] and based on the notions of immobile indices and their immobility orders. For the linear semidefinite problem, we define the subspace of immobile indices and formulate the first order optimality conditions in terms of a basic matrix of this subspace. These conditions are explicit, do not use constraint qualifications, and have the form of criterion. An algorithm determining a basis of the subspace of immobile indices in a finite number of steps is suggested. The optimality conditions obtained are compared with other known optimality conditions

Probing radio source environments via HI and OH absorption

We present the results of HI and OH absorption measurements towards a sample of radio sources using the Arecibo 305-m telescope and the GMRT. In total, 27 radio sources were searched for associated 21-cm HI absorption. One totally new HI absorption system was detected against the radio galaxy 3C258, while five previously known HI absorption systems, and one galaxy detected in emission, were studied with improved frequency resolution and/or sensitivity. Our sample included 17 GPS and CSS objects, 4 of which exhibit HI absorption. This detection rate of ~25% compares with a value of ~40% by Vermeulen et al. for similar sources. We detected neither OH emission nor absorption towards any of the sources that were observed at Arecibo, and estimate a limit on the abundance ratio of N(HI)/N(OH)>4x10^6 for 3C258. We have combined our results with those from other available HI searches to compile a heterogeneous sample of 96 radio sources consisting of 27 GPS, 35 CSS, 13 flat spectrum and 21 large sources. The HI absorption detection rate is highest (~45%) for the GPS sources and least for the large sources. We find HI column density to be anticorrelated with source size, as reported earlier by Pihlstr\"om et al. The HI column density shows no significant dependence on either redshift or luminosity, which are themselves strongly correlated. These results suggest that the environments of radio sources on GPS/CSS scales are similar at different redshifts. Further, in accordance with the unification scheme, the GPS/CSS galaxies have an HI detection rate of ~40% which is significantly higher than the detection rate (~20%) towards the GPS/CSS quasars. Also, the principal (strongest) absorption component detected towards GPS sources appears blue-shifted in ~65% of the cases, in agreement with the growing evidence for jet-cloud interactions.Comment: Abridged abstract, 22 pages, 21 figures, moderately revised, accepted for publication in MNRA

A saposin deficiency model in Drosophila: Lysosomal storage, progressive neurodegeneration and sensory physiological decline

Saposin deficiency is a childhood neurodegenerative lysosomal storage disorder (LSD) that can cause premature death within three months of life. Saposins are activator proteins that promote the function of lysosomal hydrolases that mediate the degradation of sphingolipids. There are four saposin proteins in humans, which are encoded by the prosaposin gene. Mutations causing an absence or impaired function of individual saposins or the whole prosaposin gene lead to distinct LSDs due to the storage of different classes of sphingolipids. The pathological events leading to neuronal dysfunction induced by lysosomal storage of sphingolipids are as yet poorly defined. We have generated and characterised a Drosophila model of saposin deficiency that shows striking similarities to the human diseases. Drosophila saposin-related (dSap-r) mutants show a reduced longevity, progressive neurodegeneration, lysosomal storage, dramatic swelling of neuronal soma, perturbations in sphingolipid catabolism, and sensory physiological deterioration. Our data suggests a genetic interaction with a calcium exchanger (Calx) pointing to a possible calcium homeostasis deficit in dSap-r mutants. Together these findings support the use of dSap-r mutants in advancing our understanding of the cellular pathology implicated in saposin deficiency and related LSDs