25 research outputs found
Identities between field-equations in the general field theory of Schouten and van Dantzig and certain results in the theories of legendre and confluent hypergeometric functions
The general field- theory of Schouten and van Dantzig forms
an important step in the solution of the unification problem of
the gravitational and electromagnetic phenomena in Physics.
This theory depends on the use of a projective geometry employing five homogeneous coordinates. In the first part of this
thesis an attempt is made to make a contribution to this unified
field- theory by finding the identical relations between the
field- equations in this theory. We have also shown the connection between these identities and the identities found by
Professor E.T. Whittaker between the field- equations of Einstein's
general relativity.In the second part of the thesis we first develop certain
series and integral properties of Legendre functions in a direction, which has received little attention till now. The import -
á.nce of the properties of Rₘ -functions developed towards the end
of the second part may be seen from the following remark of
Professor E.T. Whittaker in his well -known paper (The Bulletin of
the American Yathematical Society, volume 10, [1903 -04,] page 133)
in which he defines the function Wᵣ,ₘ (3):"There are other members of the family of functions Wᵣ,ₘ (3) which have not been noticed, but which give promise of interesting properties. Among these may be mentioned the families of functions for which rn, = 0 and those for which m = 1/2 ".The Rₘ -functions considered correspond to the case m = 1/2, the associated differential equation having arisen recently in the theory of turbulence in researches of W. Tollmien and Th. von Kármán and also in the wave- mechanical theory of the
α -particles by Theodor Sexl
Microwave device investigations
Several tasks were active during this report period: (1) noise modulation in avalanche-diode devices; (2) schottky-barrier microwave devices; (3) intermodulation products in IMPATT diode amplifiers; (4) harmonic generation using Read-diode varactors; and (5) fabrication of GaAs Schottky-barrier IMPATT diodes
On uniformization of Burnside's curve
Main objects of uniformization of the curve are studied: its
Burnside's parametrization, corresponding Schwarz's equation, and accessory
parameters. As a result we obtain the first examples of solvable Fuchsian
equations on torus and exhibit number-theoretic integer -series for
uniformizing functions, relevant modular forms, and analytic series for
holomorphic Abelian integrals. A conjecture of Whittaker for hyperelliptic
curves and its hypergeometric reducibility are discussed. We also consider the
conversion between Burnside's and Whittaker's uniformizations.Comment: Final version. LaTeX, 23 pages, 1 figure. The handbook for elliptic
functions has been moved to arXiv:0808.348
Comparative needs in child abuse education and resources: perceptions from three medical specialties
Temperature dependence of ionization rates in AlxGa1-xAs
The ionization rates in AlxGa1-xAs have been measured in a temperature range from 77[deg]K to 373[deg]K for samples with various Al content. The results showed that the ionization rates decrease with both the Al content and temperature at a given electric field. A deviation from exp(1/E2) field dependence is observed for the sample with the highest Al content at lower temperatures. By fitting the data into the modified Baraff's plot, [lambda], the optical phonon mean free path was determined at four different temperatures. Assuming [lambda] = [lambda]0 tanh ([epsilon]r/2kT), [lambda]0, the high-energy low-temperature asymptotic limit of the mean free path was evaluated. The temperature dependence of [lambda] and the compositional dependence of [lambda]0 are discussed.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/33625/1/0000133.pd
On some definite integrals involving Legendre functions
This article does not have an abstract