Abstract: Heterogenous data about the prognostic impact of atrial fibrillation (AF) in patients with ventricular tachyarrhythmias exist. Therefore, this study evaluates this impact of AF in patients presenting with ventricular tachyarrhythmias. 1,993 consecutive patients presenting with ventricular tachyarrhythmias (i.e. ventricular tachycardia and fibrillation (VT, VF)) on admission at one institution were included (from 2002 until 2016). All medical data of index and follow-up hospitalizations were collected during the complete follow-up period for each patient. Statistics comprised univariable Kaplan-Meier and multivariable Cox regression analyses in the unmatched consecutive cohort and after propensity-score matching for harmonization. The primary prognostic endpoint was long-term all-cause mortality at 2.5 years. AF was present in 31% of patients presenting with index ventricular tachyarrhythmias on admission (70% paroxysmal, 9% persistent, 21% permanent). VT was more common (67% versus 59%; p = 0.001) than VF (33% versus 41%; p = 0.001) in AF compared to non-AF patients. Long-term all-cause mortality at 2.5 years occurred more often in AF compared to non-AF patients (mortality rates 40% versus 24%, log rank p = 0.001; HR = 1.825; 95% CI 1.548-2.153; p = 0.001), which may be attributed to higher rates of all-cause mortality at 30 days, in-hospital mortality and mortality after discharge (p

In this thesis, the Order Completion Method for nonlinear partial differential equation, in the setting of convergence spaces, is interpreted in terms of the algebraic theory of gen- eralised functions. In particular, certain spaces of generalised functions that are involved in the construction of generalised solutions for nonlinear partial differential equations through the Order Completion Method are identi ed with a differential chain of algebras of generalise functions. By so doing, the generalised solutions for smooth nonlinear partial differential equation obtained through Order Completion Method are interpreted as chain generalised solutions. Moreover, the mentioned differential chain is shown to be related to the Rosinger's chain of nowhere dense algebras of generalised functions. This leads to an interpretation of the existence result for the solution of smooth nonlinear partial differ- ential equations obtained through the order completion method in the chain of nowhere dense algebras. Using techniques introduced by Verneave, we construct a chain of almost everywhere algebras of generalised functions and show how the chain of algebras of generalised func- tions associated with the order completion method is related to this chain of almost everywhere algebras of generalised functions. We also discuss the embedding of the dis- tributions into the chain of almost everywhere algebras of generalised functions. We further show that the generalised solutions of nonlinear partial differential equations ob- tained through the order completion method corresponds to a chain generalised solution in the chain of nowhere dense algebras of generalized functions. Finally, using the theory of chains of algebras of generalized functions, we construct algebras of generalised functions that can handle certain types of singularities occurring on sets of rst Baire category, so called, space-time foam algebras.