On the Analytic Structure of Commutative Nilmanifolds

In the classification theorems of Vinberg and Yakimova for commutative nilmanifolds, the relevant nilpotent groups have a very surprising analytic property. The manifolds are of the form $G/K = N \rtimes K/K$ where, in all but three cases, the nilpotent group $N$ has irreducible unitary representations whose coefficients are square integrable modulo the center $Z$ of $N$. Here we show that, in those three "exceptional" cases, the group $N$ is a semidirect product $N_1 \rtimes \mathbb{R}$ or $N_1 \rtimes \mathbb{C}$ where the normal subgroup $N_1$ contains the center $Z$ of $N$ and has irreducible unitary representations whose coefficients are square integrable modulo $Z$. This leads directly to explicit harmonic analysis and Fourier inversion formulae for commutative nilmanifolds

Stepwise Square Integrability for Nilradicals of Parabolic Subgroups and Maximal Amenable Subgroups

In a series of recent papers we extended the notion of square integrability, for representations of nilpotent Lie groups, to that of stepwise square integrability. There we discussed a number of applications based on the fact that nilradicals of minimal parabolic subgroups of real reductive Lie groups are stepwise square integrable. Here, in Part I, we prove stepwise square integrability for nilradicals of arbitrary parabolic subgroups of real reductive Lie groups. This is technically more delicate than the case of minimal parabolics. We further discuss applications to Plancherel formulae and Fourier inversion formulae for maximal exponential solvable subgroups of parabolics and maximal amenable subgroups of real reductive Lie groups. Finally, in Part II, we extend a number of those results to (infinite dimensional) direct limit parabolics. These extensions involve an infinite dimensional version of the Peter-Weyl Theorem, construction of a direct limit Schwartz space, and realization of that Schwartz space as a dense subspace of the corresponding $L^2$ space.Comment: The proof of Theorem 5.9 is improved, several statements are clarified, and a certain number of typographical errors are correcte

Making automated computer program documentation a feature of total system design

It is pointed out that in large-scale computer software systems, program documents are too often fraught with errors, out of date, poorly written, and sometimes nonexistent in whole or in part. The means are described by which many of these typical system documentation problems were overcome in a large and dynamic software project. A systems approach was employed which encompassed such items as: (1) configuration management; (2) standards and conventions; (3) collection of program information into central data banks; (4) interaction among executive, compiler, central data banks, and configuration management; and (5) automatic documentation. A complete description of the overall system is given

Principal Series Representations of Direct Limit Groups

We combine the geometric realization of principal series representations of the author, with the Bott--Borel--Weil Theorem for direct limits of compact groups of Natarajan, Rodriguez-Carrington and the author, obtaining limits of principal series representations for direct limits of real reductive Lie groups. We introduce the notion of weakly parabolic direct limits and relate it to the conditions that the limit representations are norm--preserving representations on a Banach space or unitary representations on a Hilbert space. We specialize the results to diagonal embedding direct limit groups. Finally we discuss the possibilities of extending the results to limits of tempered series other than the principal series.Comment: 28 page

Rates of Nuclear Reactions in Solid-Like Stars

In stellar matter as cool and dense as the interior of a white dwarf, the Coulomb energies between neighboring nuclei are large compared to the kinetic energies of the nuclei. Each nucleus is constrained to vibrate about an equilibrium position, and the motion of the nuclei in the interior of a white dwarf is similar to the motion of the atoms in a solid or liquid. We propose a solid-state method for calculating the rate at which a nuclear reaction proceeds between two identical nuclei oscillating about adjacent lattice sites. An effective potential U(r) derived by analyzing small lattice vibrations is used to represent the influence of the Coulomb fields of the lattice on the motion of the two reacting nuclei. The wave function describing the relative motion of the two reacting particles is obtained by solving the Schrödinger equation containing the effective potential U(r). From this wave function, we derive an expression for the reaction rate. The rates of the p+p and C^(12)+C^(12) reactions calculated using this solid-state method are typically 1 to 10 orders of magnitude smaller than those calculated by the method previously suggested by Cameron

Heat pipe thermal switch

A thermal switch for controlling the dissipation of heat between a body is described. The thermal switch is comprised of a flexible bellows defining an expansible vapor chamber for a working fluid located between an evaporation and condensation chamber. Inside the bellows is located a coiled retaining spring and four axial metal mesh wicks, two of which have their central portions located inside of the spring while the other two have their central portions located between the spring and the side wall of the bellows. The wicks are terminated and are attached to the inner surfaces of the outer end walls of evaporation and condensation chambers respectively located adjacent to the heat source and heat sink. The inner surfaces of the end walls furthermore include grooves to provide flow channels of the working fluid to and from the wick ends. The evaporation and condensation chambers are connected by turnbuckles and tension springs to provide a set point adjustment for setting the gap between an interface plate on the condensation chamber and the heat sink