A Hyperbolic Non Distributive Algebra in 1 + 2 Dimensions

We introduce a non distributive algebra over the reals in 1 + 2 dimensions that contains the hyperbolic complex algebra ${\mathbb{H}_2}$ . The algebra has divisors of zero that can be avoided by introducing the necessary conditions. Under these conditions, the proposed addition and product operations satisfy group properties. More stringent restrictions sufficient to satisfy group properties separate the algebra in two subspaces. As an application, the composition of velocities in a deformed Lorentz metric is presented. In this approach, Minkowski light cones are deformed into light bipyramids.     

The hub covering flow problem

The hub covering flow problem (HCFP) seeks to find the minimal cost hub-and-spoke network by optimally locating hub nodes and assigning non-hub nodes to the hub nodes subject to a coverage constraint. The cost of establishing such a hub network is based on a fixed cost of opening hubs and the cost of transporting demand flow through the network. We also present an extension called the multi-aircraft HCFP. The results from computational experiments are presented and discussed.     

Formic acid catalyzed keto-enol tautomerizations for C2 and C3 enols: Implications in atmospheric and combustion chemistry

Enols are important species in atmospheric and combustion chemistry. However, their implications in these environments are not well established due to a lack of accurate rate constants and mechanisms to determine their fate. In this work, we investigate the formic acid catalyzed keto-enol tautomerizations converting vinyl alcohol, propen-2-ol and 1-propenol into acetaldehyde, acetone and propanal, respectively. High-level ab initio and multistructural torsional variational transition state theory calculations are performed with small-curvature tunneling corrections to obtain rate constants in the temperature range 200 K-3000 K. Tunneling is shown to be pronounced as a consequence of very narrow adiabatic potential energy curves, and indicates a need to revisit previous calculations. We show the implications of the studied reactions on the fate of enols under combustion relevant conditions by detailed kinetic modeling simulations. The yield of vinyl alcohol predicted by our calculated rate constants may be useful to lessen the underestimation of organic acids concentrations in current atmospheric models.