We formulate the notion of typical boundedness of torsion on a family of abelian varieties defined over number fields. This means that the torsion subgroups of elements in the family can be made uniformly bounded by removing from the family all abelian varieties defined over number fields of degree lying in a set of arbitrarily small density. We show that for each fixed g, torsion is typically bounded on the family of all g-dimensional CM abelian varieties. We show that torsion is not typically bounded on the family of all elliptic curves, and we establish results -some unconditional and some conditional -on typical boundedness of torsion of elliptic curves for which the degree of the j-invariant is fixed.

Motivated by the conjectures from Castro, et al. in 2011, in this paper we use integer programming formulations for computing the domination number, the 2-packing number and the independent domination number of Fibonacci cubes and Lucas cubes for n ≤ 13.

In this paper we show how the star complement technique can be used to reprove the result of Wilbrink and Brouwer that the strongly regular graph with parameters (57, 14, 1, 4) does not exist.

2 by three planes. The advantage of our approach is that it can be applied on other more complicated questions of the similar nature.

A Slurry Bubble Column Reactor (SBCR) is a gas-liquid-solid reactor in which the finely divided solid catalyst is suspended in the liquid by the rising gas bubbles. SBCR offers many advantages over fixed-bed type reactors such as: 1) improved heat transfer and mass transfer; 2) isothermal temperature profile is maintained; and 3) relatively low capital and operating cost. Fischer-Tropsch Synthesis (FTS) takes place in a SBCR where the synthesis gas is converted on catalysts suspended as fine particles in a liquid. The synthesis gas flows in a bubble phase through the catalyst/wax suspension. The volatile products are removed with unconverted gases, and the liquid products are separated from the suspension. A gas distributor located in the bottom of the reactor produces the bubbles in the reactor.A considerable interest has been expressed in using the SBCR to carry out FTS particularly for the conversion of stranded natural gas into liquids. Currently, the Center for Applied Energy Research (CAER) is utilizing a Prototype Integrated Process Unit (PIPU) system for scale-up research of the FTS. The purpose of this study was to compare the performance and activity decline of a precipitated Fe/K Fischer Tropsch Synthesis (FTS) catalyst in a revamped slurry bubble column reactor (SBCR) to that of previous CSTR and SBCR runs using the same catalyst and operating conditions. The activity decline measured in the revamped SBCR system was shown to be similar to that of the CSTR experiments. The apparent activity decline in a previous SBCR run was due a transient startup effect from the slurry filtration system.