Final revised proposal to encode the Saurashtra script in the UCS

This is a proposal to encode the Saurashtra in the international character encoding standard Unicode. The script was published in Unicode Standard version 5.1 in March 2008. The Saurashtra script has been used to write the Saurashtra language, which is spoken in southern India. The language is today most often written in the Tamil script, but since the end of the 19c has been written with the Telugu, Tamil, Devanagari and Saurashtra scripts

Influence of music on the growth of koi carp, Cyprinus carpio (Pisces: Cyprindae)

An experiment was carried out to investigate the influence of music on the growth of Koi Carp (Cyprinus carpio) by subjecting the fish to music. Weekly growth in weight was recorded and used to calculate the growth rate and specific growth rate. The difference in growth between the control and experiment groups of fishes was statistically tested for significance. It was observed that the growth of fish subjected to music was significantly higher

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