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

A non-solvable extension of \Q unramified outside 7

We consider a mod 7 Galois representation attached to a genus 2 Siegel cuspforms of level 1 and weight 28 and using some of its Fourier coefficients and eigenvalues computed by N. Skoruppa and the classification of maximal subgroups of PGSp(4,p) we show that its image is as large as possible. This gives a realization of PGSp(4,7) as a Galois group over \Q and the corresponding number field provides a non-solvable extension of \Q which ramifies only at 7