A new proof of a Nordgren, Rosenthal and Wintrobe Theorem on universal operators

A striking result by Nordgren, Rosenthal and Wintrobe states that the Invariant Subspace Problem is equivalent to the fact that any minimal invariant subspace for a composition operator Cφ induced by a hyperbolic automorphism φ of the unit disc D acting on the classical Hardy space H² is one dimensional. We provide a completely different proof of Nordgren, Rosenthal and Wintrobe’s Theorem based on analytic Toeplitz operators

A hyperbolic universal operator commuting with a compact operator

A Hilbert space operator is called universal (in the sense of Rota) if every operator on the Hilbert space is similar to a multiple of the restriction of the universal operator to one of its invariant subspaces. We exhibit an analytic Toeplitz operator whose adjoint is universal in the sense of Rota and commutes with a non-trivial, quasinilpotent, injective, compact operator with dense range, but unlike other examples, it acts on the Bergman space instead of the Hardy space and this operator is associated with a `hyperbolic' composition operator

Grillparzer\u27s Erny and Lessing\u27s Emilia

Similarities between Grillparzer\u27s Erny in Ein treuer Diener seines Herrn and Lessing\u27s Emilia Galotti have already been suggested, albeit somewhat incidentally. In his edition of Grillparzer\u27s works, Rudolf Franz comments on Erny\u27s exclamation in Act II when she discovers Otto waiting for her. ... And when Erny stabs herself at the end of Act III, Franz remarks: Der Ausgang Ernys erinnert an den der Emilia Galotti und an dessen Vorbild, den Tod der Virginia; jedoch ist die Notlage Ernys zwingender als die der Lessingschen Heldin (IV, 388). But such annotations, while suggestive, hardly exhaust the similarities, nor do they penetrate to the crux of possible problems

Type-Casting in Carl Zuckmayer\u27s \u3cem\u3eThe Devil\u27s General\u3c/em\u3e

In his autobiography A Part of Myself, Carl Zuckmayer records the reactions to the first performance of The Devil\u27s General. On the day after the premiere on 14 December 1946 in Zürich, Zuckmayer met Carl Jakob Burckhardt, about whose judgment he writes: He was the first to tell me what I afterwards heard from countless Germans: that was what it was like - the way I had presented it in this play; that I had captured the truth which cannot be found in documents, only in literature, and which cannot be delineated with hatred, but only with love

A Meta-Analysis for Laboratory Diagnostics for Coccidioidomycosis

Coccidioidomycosis, commonly referred to as Valley Fever, is a fungal infection found in arid regions of the southwestern United States and Mexico. Infection occurs through inhalation of airborne spores from Coccidioides species, Coccidioides immitis and/or Coccidioides posadasii, and proceeds in both pulmonary and disseminated fashions. Approximately 60% of patients with coccidioidomycosis remain asymptomatic, while 40% will experience symptoms. Within the literature, there are no papers that summarize sensitivity and specificity values between different tests; therefore, this paper presents sensitivity and specificity results across different tests and companies (Meridian, IMMY, and MiraVista)

Finite Blaschke Products as Compositions of Other Finite Blaschke Products

These notes answer the question "When can a finite Blaschke product $B$ be written as a composition of two finite Blaschke products $B_1$ and $B_2$, that is, $B=B_1\circ B_2$, in a non-trivial way, that is, where the order of each is greater than 1." It is shown that a group can be computed from $B$ and its local inverses, and that compositional factorizations correspond to normal subgroups of this group. This manuscript was written in 1974 but not published because it was pointed out to the author that this was primarily a reconstruction of work of Ritt from 1922 and 1923, who reported on work on polynomials. It is being made public now because of recent interest in this subject by several mathematicians interested in different aspects of the problem and interested in applying these ideas to complex analysis and operator theory.Comment: 22 page

The manufacture of Portland cement

The principal characteristics which, in the process of manufacture, sharply and clearly distinguish Portland cement from Limes, Hydraulic Limes, and other Hydraulic cements, are the necessity for carefully proportioning and finely grinding the raw materials to insure a homogenous [sic] mixture, and the extremely high temperature at which it must be burned in order to insure a sound a trustworthy product --page 1

The effects of temperature upon cement mortar

Probably no material in use by the Engineering profession at the present time has been subjected to more careful and rigid tests by expert Engineers than our hydraulic cements, both natural and artificial. While the manufacturer and use of cements in America is of comparatively recent origin, this industry is fast assuming enormous proportions, and the use of cement is fast displacing many of our more common building materials. Its use in our more important structures has created an increasing demand for the best quality of cements, and the manufacturers have not been slow to comply with this demand --page 1