Gyrokinetic theory is used to investigate the effect of the polarization drift on magnetic island evolution. Three regimes are found. For island phase velocities between the ion- and electric-drift velocities, the polarization current is shown to be stabilizing. For phase velocities between the electric- and electron-drift velocities, the island emits drift waves. This results in a radiative dr...

In this short discussion, we point out that it is apparently as easy to be fooled by robustness as it is to be fooled by randomness. Our objective is to bring to the attention of applied ecologists that radius-of-stability robustness models are models of local robustness. As such, these models are utterly unsuitable for the treatment/management of a severe uncertainty characterized by a vast un...

We prove the `p-spectral radius formula for n-tuples of commuting Banach algebra elements. This generalizes results of [6], [7] and [10]. Let A be a Banach algebra with the unit element denoted by 1. Let a = (a1, . . . , an) be an n-tuple of elements of A. Denote by σ(a) the Harte spectrum of a, i.e. λ = (λ1, . . . , λn) / ∈ σ(a) if and only if there exist u1, . . . , un, v1, . . . , vn ∈ A suc...

The curve is the most basic design element to determine shapes and silhouettes of industrial products and works for shape designers and it is inevitable for them to make it aesthetic and attractive to improve the total quality of the shape design. If we can find an equation of aesthetic curves, it is expected that the quality of the curve design improves drastically because we can use it as a s...

We show that binary microlensing events with three well-measured peaks (two caustic crossings plus a cusp approach) can yield determinations of both the projected Einstein radius r̃E and the angular Einstein radius θE, and so the lens mass M = c2(4G)−1r̃EθE. To a certain extent, rotation of the binary can mimic the effects of parallax, but should often be possible to disentangle parallax from rot...

We show that the joint spectral radius of a set of matrices is strictly increasing as a function of the data in the sense that if a set of matrices is contained in the relative interior of the convex hull of an irreducible set of matrices, then the joint spectral radius of the smaller set is strictly smaller than that of the larger set. This observation has some consequences in the theory of ti...

A precision aspheric artefact is measured in 3D by a commercially available nano-measuring machine (NMM) integrated with a contact inductive sensor as the probe. The mathematics of 3D compensation of the error caused by the probe radius is derived. The influence of the probe radius measurement uncertainty on the compensation errors for the 3D measurements is discussed. If the calibration uncert...

Preoperative three-dimensional planning methods have been described extensively. However, transferring the virtual plan to the patient is often challenging. In this report, we describe the management of a severely malunited distal radius fracture using a patient-specific plate for accurate spatial positioning and fixation. Twenty months postoperatively the patient shows almost painless reconstr...