The classical Whitney formula relates the algebraic number of self-intersections of a generic plane curve to its winding number. We generalize it to an innnite family of identities, expressing the winding number in terms of the internal geometry of a plane curve. This enables us to split the Whit-ney formula by some characteristic of double points. It turns out, that only crossings of a very sp...

Although great effort is made in clinical trials to demonstrate statistical superiority of one intervention vs. another, insufficient attention is paid regarding the clinical relevance or clinical significance of the observed outcomes. Effect sizes are not always reported. Available absolute effect size measures include Cohen's d, area under the curve, success rate difference, attributable risk...

solute transport processes are affected by soil pore water velocity distribution. pore size distribution, which can be used to infer pore water velocity distribution, can be estimated from a soil water retention curve (n). in this study, a solute breakthrough curve was simulated using soil hydraulic parameters in four different soils. to evaluate the proposed model, predictions were compared to...

In this paper we describe moving frames and differential invariants for curves in two different |1|-graded parabolic manifolds G/H, G = O(p + 1, q + 1) and G = O(2m, 2m), and we define differential invariants of projective-type. We then show that, in the first case, there are geometric flows in G/H inducing equations of KdV-type in the projective-type differential invariants when proper initial...

BACKGROUND In patients with atrioventricular nodal re-entrant tachycardia, modifications of the antegrade atrioventricular nodal function curve caused by catheter ablation of the so-called slow pathway are heterogeneous, but have not yet been systematically evaluated. AIM To test the hypothesis that successful treatment is independent of specific electrophysiological modifications of atrioven...

Justification Logic provides an axiomatic description of justifications and delegates the question of their nature to semantics. In this note, we address the conceptual issue of the logical type of justifications: we argue that justifications in the logical setting are naturally interpreted as sets of formulas which leads to a class of epistemic models that we call modular models. We show that ...