As an example from amore extensive investigation, the binding analysis of the mixture PtSnM (M = undetermined mole number) is described. A phase becomes stable when a lattice-like correlation of the valence electrons (with cell b) and a lattice-like correlation of the peripheral core electrons of Pt (cell e) are in an energetically favourable commensurability to the crystal cell a and to one an...

Bayesian clinical trial designs offer the possibility of a substantially reduced sample size, increased statistical power, and reductions in cost and ethical hazard. However when prior and current information conflict, Bayesian methods can lead to higher than expected Type I error, as well as the possibility of a costlier and lengthier trial. This motivates an investigation of the feasibility o...

In this paper, we prove that a normal subgroup N of an n-dimensional crystallographic group Γ determines a geometric fibered orbifold structure on the flat orbifold En/Γ, and conversely every geometric fibered orbifold structure on En/Γ is determined by a normal subgroup N of Γ, which is maximal in its commensurability class of normal subgroups of Γ. In particular, we prove that En/Γ is a fiber...

Abstract In this chapter, we collect some information on various constructions of manifolds, orbifolds, and their covers. Notably, discuss the notions fiber product (in sense Thurston) compositum manifolds over a common developable orbifold, difference with set-theoretic product, connected components Galois covers, normal closure cover, relation between commensurability, arithmeticity, existenc...

Frequentists and Bayesians disagree about the soundness of performing calculations based, in an important part, on prior information. The disagreement goes back to a basic philosophical how conceptualize meaning probability. As frequentists use term differently, there is incommensurability. However, this incommensurability need not imply empirical It possible for be, simultaneously, commensurab...

The current debate over the ‘identity crisis' in the field of information systems has led to increasing calls from a number of researchers for the development of a common ‘intellectual core’ and common set of related methodologies. Currently the consensus seems to be that researchers in the field of information systems typically adhere to one or another broad schools of thought. There is debate...

Introducing artificial pinning centers is a well established strategy to trap quantum vortices and increase the maximal magnetic field and applied electric current that a superconductor can sustain without dissipation. In case of spatially periodic pinning, a clear enhancement of the superconducting critical current arises when commensurability between the vortex configurations and the pinning ...