『莘野茗談』 : 狂歌師、平秩東作の回想記

In the late 1780s, the renowned kyōka poet Hezutsu Tōsaku (1726–1789) looked back at his life and set about notating some of his memorable experiences and the characteristics of his age. The result was a presumably unfinished zuihitsu entitled Shin’ya meidan (A Retiree’s Chat). In this piece Tōsaku presents sixteen anecdotes and opinions regarding, among other things, famous writers, poets, thinkers, and artists of the past, renowned kabuki actors, connoisseurs and courtesans in Yoshiwara, rural poets and authors, personal friends, astute monks, conditions in Ezo (Hokkaido), and the benefits of city life. This wealth of subjects supplies not just a rare glimpse into the biography of a late-eighteenth century comic poet but also an unusually personal account of cultural life in Edo

Fourier, Gauss, Fraunhofer, Porod and the Shape from Moments Problem

We show how the Fourier transform of a shape in any number of dimensions can be simplified using Gauss's law and evaluated explicitly for polygons in two dimensions, polyhedra three dimensions, etc. We also show how this combination of Fourier and Gauss can be related to numerous classical problems in physics and mathematics. Examples include Fraunhofer diffraction patterns, Porods law, Hopfs Umlaufsatz, the isoperimetric inequality and Didos problem. We also use this approach to provide an alternative derivation of Davis's extension of the Motzkin-Schoenberg formula to polygons in the complex plane.Comment: 21 pages, no figure

A stability version of H\"older's inequality

We present a stability version of H\"older's inequality, incorporating an extra term that measures the deviation from equality. Applications are given.Comment: Journal of Mathematical Analysis and Applications, Volume 343, Issue 2, Pages 842-852. This version differs from the published one in that it contains a new reference, and a trivial improvement of Corollary 3.2. fo

Optical Spectroscopy of IRAS 02091+6333

We present a detailed spectroscopic investigation, spanning four winters, of the asymptotic giant branch (AGB) star IRAS 02091+6333. Zijlstra & Weinberger (2002) found a giant wall of dust around this star and modelled this unique phenomenon. However their work suffered from the quality of the optical investigations of the central object. Our spectroscopic investigation allowed us to define the spectral type and the interstellar foreground extinction more precisely. Accurate multi band photometry was carried out. This provides us with the possibility to derive the physical parameters of the system. The measurements presented here suggest a weak irregular photometric variability of the target, while there is no evidence of a spectroscopic variability over the last four years.Comment: 5 pages, Latex, 3 tables, 4 figures, Astron. & Astrophys. - in pres

On the geometric dilation of closed curves, graphs, and point sets

The detour between two points u and v (on edges or vertices) of an embedded planar graph whose edges are curves is the ratio between the shortest path in in the graph between u and v and their Euclidean distance. The maximum detour over all pairs of points is called the geometric dilation. Ebbers-Baumann, Gruene and Klein have shown that every finite point set is contained in a planar graph whose geometric dilation is at most 1.678, and some point sets require graphs with dilation at least pi/2 = 1.57... We prove a stronger lower bound of 1.00000000001*pi/2 by relating graphs with small dilation to a problem of packing and covering the plane by circular disks. The proof relies on halving pairs, pairs of points dividing a given closed curve C in two parts of equal length, and their minimum and maximum distances h and H. Additionally, we analyze curves of constant halving distance (h=H), examine the relation of h to other geometric quantities and prove some new dilation bounds.Comment: 31 pages, 16 figures. The new version is the extended journal submission; it includes additional material from a conference submission (ref. [6] in the paper

Stability for Borell-Brascamp-Lieb inequalities

We study stability issues for the so-called Borell-Brascamp-Lieb inequalities, proving that when near equality is realized, the involved functions must be $L^1$-close to be $p$-concave and to coincide up to homotheties of their graphs.Comment: to appear in GAFA Seminar Note

Fractal curvature measures and Minkowski content for one-dimensional self-conformal sets

We show that the fractal curvature measures of invariant sets of one-dimensional conformal iterated function systems satisfying the open set condition exist, if and only if the associated geometric potential function is nonlattice. Moreover, in the nonlattice situation we obtain that the Minkowski content exists and prove that the fractal curvature measures are constant multiples of the $\delta$-conformal measure, where $\delta$ denotes the Minkowski dimension of the invariant set. For the first fractal curvature measure, this constant factor coincides with the Minkowski content of the invariant set. In the lattice situation we give sufficient conditions for the Minkowski content of the invariant set to exist, contrasting the fact that the Minkowski content of a self-similar lattice fractal never exists. However, every self-similar set satisfying the open set condition exhibits a Minkowski measurable $\mathcal{C}^{1+\alpha}$ diffeomorphic image. Both in the lattice and nonlattice situation average versions of the fractal curvature measures are shown to always exist.Comment: 36 page