In this paper we give refinements of some convex and log-convex moment inequalities of the first and second order using a special kind of positive definite form. An open problem concerning eight parameter refinement of second order is also stated with some applications in Information Theory.

Regioregular poly(3-hexylthiophene)s with chain lengths varying from 5 to 100 monomers are synthesized. Poly(3-hexylthiophene)s show in solution an unexpectedly significant second-order nonlinear optical response. The increase in transition dipole moment upon oligomerisation causes the significant second-order nonlinear optical response.

This paper addresses problems of second-order cone programming important in optimization theory and applications. The main attention is paid to the augmented Lagrangian method (ALM) for such considered both exact inexact forms. Using generalized differential tools variational analysis, we formulate corresponding version sufficiency use it establish, among other results, uniform growth condition...

In this paper we review two recently suggested projection techniques for model order reduction of bilinear systems. The first one is computationally more attractive, but so far it was assumed that this method does not yield a moment-matching approximation. Here we show that the reduced-order models computed by both of the two projection techniques match multimoments of the bilinear system. This...

As a mathematically tractable example, we have investigated the stochastic dynamic problem of an irreversible second-order chemical reaction. A generalized direct-interaction approximation has been devised to close off the hierarchy of moment equations at the arbitrary moment level, and then the results of such a closure technique have been compared term-by-term with the exact moment solutions....