Capillary Wave Theory of Adsorbed Liquid Films and the Structure of the Liquid-Vapor Interface

In this paper we try to work out in detail the implications of a microscopic theory for capillary waves under the assumption that the density is given along lines normal to the interface. Our study provides interface Hamiltonians for adsorbed films in a variety of systems, and shows that the corrections to the classical capillary wave spectrum are of the same order as the surface tension. This implies that it is possible, at least in principle, to measure them in x-ray surface scattering experiments. Interestingly, our study also sheds some light on the nature of the liquid-vapor interface in the absence of external fields and allows us to reconcile the Fisk-Widom scaling hypothesis with capillary wave theory.Comment: Revised version, 51 pages, 4 figure

Clifford, William Kingdon

W.K. Clifford’s famous 1876 essay The Ethics of Belief contains one of the most memorable lines in the history of philosophy: "it is wrong always, everywhere, and for anyone, to believe anything upon insufficient evidence." The challenge to religious belief stemming from this moralized version of evidentialism is still widely discussed today

Toroidal and Klein bottle boundary slopes

Let M be a compact, connected, orientable, irreducible 3-manifold and T' an incompressible torus boundary component of M such that the pair (M,T') is not cabled. By a result of C. Gordon, if S and T are incompressible punctured tori in M with boundary on T' and boundary slopes at distance d, then d is at most 8, and the cases where d=6,7,8 are very few and classified. We give a simplified proof of this result (or rather, of its reduction process), based on an improved estimate for the maximum possible number of mutually parallel negative edges in the graphs of intersection of S and T. We also extend Gordon's result by allowing either S or T to be an essential Klein bottle. to the case where S or T is a punctured essential Klein bottle.Comment: Preliminary version, updated. We use a new approach that yields a stronger conclusion. 28 pages, 18 figure

Classification of Triadic Chord Inversions Using Kohonen Self-organizing Maps

In this paper we discuss the application of the Kohonen Selforganizing Maps to the classification of triadic chords in inversions and root positions. Our motivation started in the validation of Schönberg´s hypotheses of the harmonic features of each chord inversion. We employed the Kohonen network, which has been generally known as an optimum pattern classification tool in several areas, including music, to verify that hypothesis. The outcomes of our experiment refuse the Schönberg´s assumption in two aspects: structural and perceptual/functional

Sceptical Theism and the Paradox of Evil

Given plausible assumptions about the nature of evidence and undercutting defeat, many believe that the force of the evidential problem of evil depends on sceptical theism’s being false: if evil is..