Facile preparation of fluorovinylene aryl ether telechelic polymers with dual functionality for thermal chain extension and tandem crosslinking

New fluorovinylene aromatic ether polymers, possessing dual reactivity, have been successfully prepared via the step-growth polymerization of commercial bis(trifluorovinyl) aromatic ethers and bisphenols.     

Improved synthesis of substituted 6,7-dihydroxy-4-quinazolineamines: tandutinib, erlotinib and gefitinib

The synthesis of three substituted 6,7-dihydroxy-4-quinazolineamines: tandutinib (1), erlotinib (2) and gefitinib (3) in improved yields is reported. The intermediates were characterized by NMR and the purities determined by HPLC.     

Resonance splitting in gyrotropic ring resonators

We present the theoretical concept of an optical isolator based on resonance splitting in a silicon ring resonator covered with a magneto-optical polymer cladding. For this task, a perturbation method is derived for the modes in the cylindrical coordinate system. A polymer magneto-optical cladding causing a 0.01 amplitude of the off-diagonal element of the dielectric tensor is assumed. It is shown that the derived resonance splitting of the clockwise and counterclockwise modes increases for smaller ring radii. For the ring with a radius of approximately 1.5μm, a 29GHz splitting is demonstrated. An integrated optical isolator with a 10μm geometrical footprint is proposed based on a critically coupled ring resonator.     

The optimal execution strategy of employee stock options

In this paper, we develop an optimal execution strategy for employee stock options by means of the fluid model, in which a voluntary turnover is considered. We show that the value function is the viscosity solution of the Hamilton-Jacobi-Bellman variational inequality and prove the uniqueness of the viscosity solution. Finally, we present numerical illustrative examples and numerical solutions of optimal strategies which are computed by the finite difference method.     

Cycle factors in strongly connected local tournaments

A digraph without loops, multiple arcs and directed cycles of length two is called a local tournament if the set of in-neighbors as well as the set of out-neighbors of every vertex induces a tournament. A digraph is 2-connected if the removal of an arbitrary vertex results in a strongly connected digraph.In 2004 and 2005, Li and Shu investigated the structure of strongly connected, but not 2-connected tournaments. Using their structural results they were able to give sufficient conditions for a strongly connected tournament T to have complementary cycles or a k-cycle factor, i.e. a set of k vertex disjoint cycles that span the vertex set of T.Inspired by the articles of Li and Shu we develop in this paper the structure necessary for a strongly connected local tournament to be not cycle complementary. Using this structure, we are able to generalize and transfer various results of Li and Shu to the class of local tournaments.