Letter, 1969 October 16, from Raymond P. Shafer to Eva Jessye

1 page, Shafer was the govenor of Pennsylvania. The Hallelujah Train is mentioned

Sidereal anisotropy of cosmic rays

The data of the ionization chamber in Yakutsk for 1954 to 1984 are analyzed. A false sidereal variation caused by the second spherical harmonic in cosmic ray distribution was found and it has the amplitude 0.020 plus or minus 0.002%. The sidereal anisotropy with a very small amplitude (not more than 0.005%) was observed to exist

Shock-Associated Noise Generation in Curved Coanda Turbulent Wall Jets

Curved three-dimensional turbulent Coanda wall jets are present in a multitude of natural and engineering applications. The mechanism by which they form a shock-cell structure is poorly understood, as is the accompanying shock-associated noise (SAN) generation. This paper discusses these phenomena from both a modeling and experimental perspective. The Method of Characteristics is used to rewrite the governing hyperbolic partial differential equations as ordinary differential equations, which are then solved numerically using the Euler predictor-corrector method. The effects of complicating factors -- such as radial expansion and streamline curvature -- on the prediction of shock-cell location are then discussed. This paper next compares the theoretical calculations of the shock-wave structure with associated schlieren flow visualization results. Related acoustical measurements are also addressed. In this way, critical flow characteristics for shock-cell formation are identified, and their influence on SAN discussed

AUDITOR\u27S ASSISTANT: A knowledge engineering tool for audit decisions

https://egrove.olemiss.edu/dl_proceedings/1039/thumbnail.jp

Ekeland’s variational principle in weak and strong systems of arithmetic

We analyze Ekeland’s variational principle in the context of reverse mathematics. We find that that the full variational principle is equivalent to Π11- CA0, a strong theory of second-order arithmetic, while natural restrictions (e.g. to compact spaces or to continuous functions) yield statements equivalent to weak König’s lemma (WKL0) and to arithmetical comprehension (ACA0). We also find that the localized version of Ekeland’s variational principle is equivalent to Π11- CA0, even when restricted to continuous functions. This is a rare example of a statement about continuous functions having great logical strength