10,084 research outputs found
Extensions by Antiderivatives, Exponentials of Integrals and by Iterated Logarithms
Let F be a characteristic zero differential field with an algebraically
closed field of constants, E be a no-new-constant extension of F by
antiderivatives of F and let y1, ..., yn be antiderivatives of E. The
antiderivatives y1, ..., yn of E are called J-I-E antiderivatives if the
derivatives of yi in E satisfies certain conditions. We will discuss a new
proof for the Kolchin-Ostrowski theorem and generalize this theorem for a tower
of extensions by J-I-E antiderivatives and use this generalized version of the
theorem to classify the finitely differentially generated subfields of this
tower. In the process, we will show that the J-I-E antiderivatives are
algebraically independent over the ground differential field. An example of a
J-I-E tower is extensions by iterated logarithms. We will discuss the normality
of extensions by iterated logarithms and produce an algorithm to compute its
finitely differentially generated subfields.Comment: 66 pages, 1 figur
Iterated Antiderivative Extensions
Let be a characteristic zero differential field with an algebraically
closed field of constants and let be a no new constants extension of .
We say that is an \textsl{iterated antiderivative extension} of if
is a liouvillian extension of obtained by adjoining antiderivatives alone.
In this article, we will show that if is an iterated antiderivative
extension of and is a differential subfield of that contains
then is an iterated antiderivative extension of .Comment: 15 pages, 0 figure
Design and development of a large diameter high pressure fast acting propulsion valve and valve actuator
The design and development of a large diameter high pressure quick acting propulsion valve and valve actuator is described. The valve is the heart of a major test facility dedicated to conducting full scale performance tests of aircraft landing systems. The valve opens in less than 300 milliseconds releasing a 46-centimeter- (18-in.-) diameter water jet and closes in 300 milliseconds. The four main components of the valve, i.e., valve body, safety shutter, high speed shutter, and pneumatic-hydraulic actuator, are discussed. This valve is unique and may have other aerospace and industrial applications
Evaluation parameters for the alkaline fuel cell oxygen electrode
Studies were made of Pt- and Au-catalyzed porous electrodes, designed for the cathode of the alkaline H2/O2 fuel cell, employing cyclic voltammetry and the floating half-cell method. The purpose was to obtain parameters from the cyclic voltammograms which could predict performance in the fuel cell. It was found that a satisfactory relationship between these two types of measurement could not be established; however, useful observations were made of relative performance of several types of carbon used as supports for noble metal catalysts and of some Au catalysts. The best half-cell performance with H2/O2 in a 35 percent KOH electrolyte at 80 C was given by unsupported fine particle Au on Teflon; this electrode is used in the Orbiter fuel cell
Congruences and Canonical Forms for a Positive Matrix: Application to the Schweinler-Wigner Extremum Principle
It is shown that a real symmetric [complex hermitian] positive
definite matrix is congruent to a diagonal matrix modulo a
pseudo-orthogonal [pseudo-unitary] matrix in [ ], for any
choice of partition . It is further shown that the method of proof in
this context can easily be adapted to obtain a rather simple proof of
Williamson's theorem which states that if is even then is congruent
also to a diagonal matrix modulo a symplectic matrix in
[]. Applications of these results considered include a
generalization of the Schweinler-Wigner method of `orthogonalization based on
an extremum principle' to construct pseudo-orthogonal and symplectic bases from
a given set of linearly independent vectors.Comment: 7 pages, latex, no figure
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