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.Growth rate, Audio recordings, Sound Cyprinus carpio

SDP Duals without Duality Gaps for a Class of Convex Minimax Programs

In this paper we introduce a new dual program, which is representable as a semi-definite linear programming problem, for a primal convex minimax programming model problem and show that there is no duality gap between the primal and the dual whenever the functions involved are SOS-convex polynomials. Under a suitable constraint qualification, we derive strong duality results for this class of minimax problems. Consequently, we present applications of our results to robust SOS-convex programming problems under data uncertainty and to minimax fractional programming problems with SOS-convex polynomials. We obtain these results by first establishing sum of squares polynomial representations of non-negativity of a convex max function over a system of SOS-convex constraints. The new class of SOS-convex polynomials is an important subclass of convex polynomials and it includes convex quadratic functions and separable convex polynomials. The SOS-convexity of polynomials can numerically be checked by solving semi-definite programming problems whereas numerically verifying convexity of polynomials is generally very hard