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 $F$ be a characteristic zero differential field with an algebraically closed field of constants and let $E$ be a no new constants extension of $F$. We say that $E$ is an \textsl{iterated antiderivative extension} of $F$ if $E$ is a liouvillian extension of $F$ obtained by adjoining antiderivatives alone. In this article, we will show that if $E$ is an iterated antiderivative extension of $F$ and $K$ is a differential subfield of $E$ that contains $F$ then $K$ is an iterated antiderivative extension of $F$.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 $N\times N$ real symmetric [complex hermitian] positive definite matrix $V$ is congruent to a diagonal matrix modulo a pseudo-orthogonal [pseudo-unitary] matrix in $SO(m,n)$ [ $SU(m,n)$], for any choice of partition $N=m+n$. 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 $N$ is even then $V$ is congruent also to a diagonal matrix modulo a symplectic matrix in $Sp(N,{\cal R})$ [$Sp(N,{\cal C})$]. 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