We consider a piecewise analytic expanding map f : [0, 1] → [0, 1] of degree d which preserves orientation, and an analytic positive potential g : [0, 1] → R. We address the analysis of the following problem: for a given analytic potential β log g, where β is a real constant, it is well known that there exists a real analytic (with a complex analytic extension to a small complex neighborhood of...

The paper compares the features of three extensions of the notion of the Gabor’s analytic signal for 2-D signals: the analytic signals with single-quadrant spectra (AS), the quaternionic signals with quaternionic single-quadrant spectra (QS) and the monogenic signals (MS). A good platform of comparison are the polar representations of the AS and the QS and the spherical coordinate representatio...

The paper presents Leviathan, an LTL satisfiability checking tool based on a novel one-pass, treelike tableau system, which is way simpler than existing solutions. Despite the simplicity of the algorithm, the tool has performance comparable in speed and memory consumption with other tools on a number of standard benchmark sets, and, in various cases, it outperforms the other tableau-based tools.