Optical properties and g factors of GaAs quantum rods

The Hamiltonian of the zinc-blende quantum rods in the framework of eight-band effective-mass approximation in the presence of external homogeneous magnetic field is given. The electronic structure, optical properties and electron g factors of GaAs quantum rods are investigated. We found that the electron g factors are very sensitively dependent on the dimensions of the quantum rods. As some of the three dimensions increase, the electron g factors decrease. The more the dimensions increase, the more the electron g factors decrease. The dimensions perpendicular to the direction of the magnetic field affect the electron g factors more than the other dimension.     

Bitwistor and Quasitriangular Structures of Bialgebras

In this article, we first introduce the notion of a bitwistor and discuss conditions under which such bitwistor forms a bialgebra as a generalization of the well-known Radford's biproduct. Then, in order to obtain new quasitriangular bialgebras, we consider a construction called twisted tensor biproduct, which is a special case of bitwistor bialgebra, and give a necessary and sufficient condition for such twisted tensor biproduct to admit quasitriangular structures.     

Leibniz 2-Algebras and Twisted Courant Algebroids

Let Y be an integral projective curve whose singularities are of type A_k, i.e. with only tacnodes and planar (perhaps non-ordinary) cusps. Set g:= p_a(Y). Here we study the Brill - Noether theory of spanned line bundles on Y. If the singularities are bad enough, we show the existence of spanned degree d line bundles, L, with h⁰(Y, L) ≥ r + 1 even if the Brill - Noether number ρ(g, d, r) < 0. We apply this result to prove that genus g curves with certain singularities cannot be hyperplane section of a simple K3 surface S ? P ^g.     

Twisted Smash Products and L-R Smash Products for Biquasimodule Hopf Quasigroups

We consider two new algebras from an H-biquasimodule algebra A and a Hopf quasigroup H: twisted smash product A ? H and L-R smash product A?H, and find necessary and sufficient conditions for making them Hopf quasigroups. We generalize the main results in Brzeziński and Jiao [5] and Klim and Majid [9]. Moreover, if H is a cocommutative Hopf quasigroup, we prove that A ? H is isomorphic to A?H as Hopf quasigroups.