Solvability and limit bicharacteristics

SOLVABILITY OF FREE PRODUCTS, CAYLEY GRAPHS AND COMPLEXES

In this paper, we verify the solvability of free product of finite cyclic groups with topological methods. We use Cayley graphs and Everitt methods to construct suitable 2-complexes corresponding to the presentations of groups and their commutator subgroups. In particular, using these methods, we prove that the commutator subgroup of $mathbb{Z}_{m}*mathbb{Z}_{n}$ is free of rank $(m-1)(n-1)$ fo...

Group Solvability

Reaching the betz limit experimentally and numerically

The Betz theory expresses that no horizontal axis wind turbine can extract more than 16/27 (59.3%) of the kinetic energy of the wind. The factor 16/27 (0.593) is known as the Betz limit. Horizontal Axis wind turbine designers try to improve the power performance to reach the Betz limit. Modern operational wind turbines achieve at peak 75% to 80% of the Betz limit. In 1919, Albert Betz used an a...

Linearity, Non-determinism and Solvability

We study the notion of solvability in the resource calculus, an extension of the λ-calculus modelling resource consumption. Since this calculus is non-deterministic, two different notions of solvability arise, one optimistic (angelical, may) and one pessimistic (demoniac, must). We give a syntactical, operational and logical characterization for the may-solvability and only a partial characteri...

Solvability of HornSAT and CNFSAT

This article describes the solvability of HornSAT and CNFSAT. Unsatisfiable HornCNF have partially ordered set that is made by causation of each clauses. In this partially ordered set, Truth value assignment that is false in each clauses become simply connected space. Therefore, if we reduce CNFSAT to HornSAT, we must make such partially ordered set in HornSAT. But CNFSAT have correlations of e...