Remarkable Nervous Perturbation

Some Remarkable Examples in Eigenvalue Perturbation Theory

We discuss the ground state energy, E(g), of some anharmonic oscillators p2 + x 2 _ 1 + P(x, g), where P(x, g) is a polynomial in x and g. Included is an example with a convergent perturbation series converging to the wrong answer and counterexamples to Dyson's argument on instability implying the divergence of perturbation theory and to the assertion that terms lower order in x to the same ord...

An Account of a Remarkable Nervous Affection

A remarkable pattern of subcortical vessel wall enhancement in granulomatous angiitis of the central nervous system.

Primary angiitis of the central nervous system (PACNS) is an idiopathic disorder. Clinical as well as radiological characteristics are nonspecific and heterogenic, making diagnosis delicate. We report an unusual pattern of extensive radial enhancement of the deep cerebral vasculature on magnetic resonance imaging (MRI) in a previously healthy 64-year-old woman. Our patient presented with a 6-mo...

Remarkable cardinals

To a large extent, the scientific work of both Peter Koepke and Philip Welch has always been inspired by Ronald Jensen’s fine structure theory and his Covering Lemma for L, the constructible universe. Cf., e.g., their joint papers [5] and [6]. In this paper we aim to play with the theme that large cardinals compatible with “V=L,” specifically: remarkable cardinals, allow us to create situations...

Remarkable Asymmetric Random Walks

There exists an asymmetric probability measure P on the real line with P n (]0; 1)+ (1=2)P n (f0g) = 1=2 for every n 2 N. P can be chosen absolutely continuous and P can be chosen to be concentrated on the integers. In both cases, P can be chosen to have moments of every order, but P can not be determined by its moments. 1 Questions and results Let P be a probability measure on the real line R,...