Change of time scale for Markov processes /

"Contract Number: AF 49(638)-617"Includes bibliographic references (leaf 20).Mode of access: Internet

Stochastic matrices with a non-trivial greatest positive root /

"Prepared for Contract No.: AF 18(603)-38"Includes biblipgraphic references (leaf 8).Mode of access: Internet

On the measurability of functions in two variables /

"Contract Number AF 49(638)-265""August, 1960"Includes bibliographic references (leaf 6).Mode of access: Internet

Meromorphic functions with small characteristic and no asymptotic values /

By the results of Fatou and Nevalinna any function F(z), meromorphic in |z| < 1, with bounded characteristic has radial limits almost everywhere. Lohwater and Piranian (Ann. Acad. Sci. Fenn. AI 239, 1957) have constructed and F(z) without radial limits and such that T(r) = 0(-log(l-r)). The object of the present note is to prove: let p(r) be a given function in [0,1), 0 < p(r) [upward arrow] [infinity sign]. Then there exists a function F(z), meromorphic in |z| < 1, such that T(r,F) ©œ< p(r) and such that if C is any continuous curve in |z| < 1, tending to |z| = 1, then the image of C by F is dense on the sphere. In particular, then, F(z) has no radial limits. The construction is of the form F(z) = ℗Ø(f(z)) where: 1) f(z) is holomorphic in |z| < 1, of slow growth, and assumes arbitrarily large values on any curve tending to |z| = 1. f is constructed as a gap Taylor series, similar to the example of Lusin Priwaloff (Ann. l'©ØEcole Norm. Sup. 1925, 147-150). 2) ℗Ø(z) is meromorphic in |z| < [infinity sign], of known growth, and such that the image by ℗Ø of any unbounded curve in |z| < [infinity sign] is dense on the sphere. ℗Ø is constructed by specifying the Riemann surface of its inverse as a covering of the sphere.February 1961.Prepared under Contract AF 49(638)-205, File No. 1.21 for Mathematical Sciences Directorate, Air Force Office of Scientific Research.Technical Note No. 3.By the results of Fatou and Nevalinna any function F(z), meromorphic in |z| < 1, with bounded characteristic has radial limits almost everywhere. Lohwater and Piranian (Ann. Acad. Sci. Fenn. AI 239, 1957) have constructed and F(z) without radial limits and such that T(r) = 0(-log(l-r)). The object of the present note is to prove: let p(r) be a given function in [0,1), 0 < p(r) [upward arrow] [infinity sign]. Then there exists a function F(z), meromorphic in |z| < 1, such that T(r,F) ©œ< p(r) and such that if C is any continuous curve in |z| < 1, tending to |z| = 1, then the image of C by F is dense on the sphere. In particular, then, F(z) has no radial limits. The construction is of the form F(z) = ℗Ø(f(z)) where: 1) f(z) is holomorphic in |z| < 1, of slow growth, and assumes arbitrarily large values on any curve tending to |z| = 1. f is constructed as a gap Taylor series, similar to the example of Lusin Priwaloff (Ann. l'©ØEcole Norm. Sup. 1925, 147-150). 2) ℗Ø(z) is meromorphic in |z| < [infinity sign], of known growth, and such that the image by ℗Ø of any unbounded curve in |z| < [infinity sign] is dense on the sphere. ℗Ø is constructed by specifying the Riemann surface of its inverse as a covering of the sphere.Mode of access: Internet

Experiments with the IBM-9900, and a discussion of an improved COMAC as suggested by these experiments, April 1961.

"AFOSR 475.""Directorate of Mathematical Sciences, Air Force Office of Scientific Research, contract no. AF 49 (638)-91."Mode of access: Internet.Photocopy (positive

Investigations on the validity of the arc-sine law /

"Contract No. AF 61(052)-42.""The research reported in this document has been sponsored by the Air Force Office of Scientific Research of the Air Research and Development Command, United States Air Force, through its European Office.""February 20, 1960."Includes bibliographic references (leaf 5).Mode of access: Internet

Problems on conformal maps of Riemannian and Kaehlerian manifolds /

"Contract Number: AF 49(638)-14""Date of Report: July 1960"Includes bibliographic references (leaf 20).Mode of access: Internet

Bayes rules for a common multiple comparisons problem and related student- t problems /

"Contract No. AF 49(638)-929""November, 1960"Includes bibliographic references (leaves 34-35).Mode of access: Internet

Series expansions of solutions of the heat equation in N dimensions /

"Contract Number: Af 49(638)-574""August, 1960"Includes bibliographic references (leaf 16).Mode of access: Internet

Properties of solutions of u'' + g(t)u 2n-1 = 0 /

"Contract No, AF 49 (638)-754""July, 1960"Includes bibliographic references (leaf 10).Mode of access: Internet