Evaporation of surfactant droplets on leaves is complicated due to the complex physical and chemical properties leaf surfaces. However, for certain surfaces which evaporation process appears follow standard constant-contact-radius or constant-contact-angle modes, it should be possible mimic droplet with both a well-chosen synthetic surface relatively simple mathematical model. Surfactant experi...

In this note, an upper bound for the sum of fractional parts certain smooth functions is given. Such sums arise naturally in numerous problems analytic number theory. The main feature here improvement term due to use Weyl’s exponential and a device used by Popov.

The Hartree-Fock-Popov theory of interacting Bose particles is developed, for modeling exciton-polaritons in semiconductor microcavities undergoing Bose-Einstein condensation. A self-consistent treatment of the linear exciton-photon coupling and of the exciton nonlinearity provides a thermal equilibrium description of the collective excitation spectrum, of the polariton energy shifts and of the...

In this paper we derive new guaranteed cost bounds for robust stability and performance with real structured uncertainty for discretetime systems. In particular. we obtain a shifted bounded real bound, a linear bound, a shifted linear bound, an inverse bound, a shifted inverse bound, and a shifted Popov bound. Several examples are used to compare these new bounds.

We briefly review a modular algorithm to perform row reduction of a matrix of Ore polynomials with coefficients in Z[t], and describe a practical implementation in Maple that improves over previous modular and fraction-free versions. The algorithm can be used for finding the rank, left nullspace, and the Popov form of such matrices.