The Segal--Bargmann transform for odd-dimensional hyperbolic spaces

We develop isometry and inversion formulas for the Segal--Bargmann transform on odd-dimensional hyperbolic spaces that are as parallel as possible to the dual case of odd-dimensional spheres.Comment: To appear in Mathematic

Coherent states for a 2-sphere with a magnetic field

We consider a particle moving on a 2-sphere in the presence of a constant magnetic field. Building on earlier work in the nonmagnetic case, we construct coherent states for this system. The coherent states are labeled by points in the associated phase space, the (co)tangent bundle of S^2. They are constructed as eigenvectors for certain annihilation operators and expressed in terms of a certain heat kernel. These coherent states are not of Perelomov type, but rather are constructed according to the "complexifier" approach of T. Thiemann. We describe the Segal--Bargmann representation associated to the coherent states, which is equivalent to a resolution of the identity.Comment: 23 pages. To appear in Journal of Physics A, Special Issue on Coherent State

Influence of structure and material research on advanced launch systems' weight, performance, and cost Summary report, May 25, 1965 - Jun. 30, 1967

Influence of structure and materials research on weight, performance, and cost of advanced launch vehicle system

The Segal-Bargmann transform for noncompact symmetric spaces of the complex type

We consider the generalized Segal-Bargmann transform, defined in terms of the heat operator, for a noncompact symmetric space of the complex type. For radial functions, we show that the Segal-Bargmann transform is a unitary map onto a certain L^2 space of meromorphic functions. For general functions, we give an inversion formula for the Segal-Bargmann transform, involving integration against an "unwrapped" version of the heat kernel for the dual compact symmetric space. Both results involve delicate cancellations of singularities.Comment: 28 pages. Minor corrections made. To appear in J. Functional Analysi

One Controller at a Time (1-CAT): A mimo design methodology

The One Controller at a Time (1-CAT) methodology for designing digital controllers for Large Space Structures (LSS's) is introduced and illustrated. The flexible mode problem is first discussed. Next, desirable features of a LSS control system design methodology are delineated. The 1-CAT approach is presented, along with an analytical technique for carrying out the 1-CAT process. Next, 1-CAT is used to design digital controllers for the proposed Space Based Laser (SBL). Finally, the SBL design is evaluated for dynamical performance, noise rejection, and robustness

Formation of Supermassive Black Holes by Direct Collapse in Pregalactic Halos

We describe a mechanism by which supermassive black holes can form directly in the nuclei of protogalaxies, without the need for seed black holes left over from early star formation. Self-gravitating gas in dark matter halos can lose angular momentum rapidly via runaway, global dynamical instabilities, the so-called "bars within bars" mechanism. This leads to the rapid buildup of a dense, self-gravitating core supported by gas pressure - surrounded by a radiation pressure-dominated envelope - which gradually contracts and is compressed further by subsequent infall. These conditions lead to such high temperatures in the central region that the gas cools catastrophically by thermal neutrino emission, leading to the formation and rapid growth of a central black hole. We estimate the initial mass and growth rate of the black hole for typical conditions in metal-free halos with T_vir ~ 10^4 K, which are the most likely to be susceptible to runaway infall. The initial black hole should have a mass of <~20 solar masses, but in principle could grow at a super-Eddington rate until it reaches ~ 10^4-10^6 solar masses. Rapid growth may be limited by feedback from the accretion process and/or disruption of the mass supply by star formation or halo mergers. Even if super-Eddington growth stops at \~10^3-10^4 solar masses, this process would give black holes ample time to attain quasar-size masses by a redshift of 6, and could also provide the seeds for all supermassive black holes seen in the present universe.Comment: 11 pages, 2 figures, Monthly Notices of the Royal Astronomical Society, in press. Minor revision

LOGSIM programmer's manual

A programmer's manual is reported for a Logic Simulator (LOGSIM) computer program that is a large capacity event simulator with the capability to accurately simulate the effects of certain unknown states, rise and fall times, and floating nodes in large scale metal oxide semiconductor logic circuits. A detailed description of the software with flow charts is included within the report

Advanced expander test bed program

The Advanced Expander Test Bed (AETB) is a key element in NASA's Space Chemical Engine Technology Program for development and demonstration of expander cycle oxygen/hydrogen engine and advanced component technologies applicable to space engines as well as launch vehicle upper stage engines. The AETB will be used to validate the high-pressure expander cycle concept, investigate system interactions, and conduct investigations of advanced mission focused components and new health monitoring techniques in an engine system environment. The split expander cycle AETB will operate at combustion chamber pressures up to 1200 psia with propellant flow rates equivalent to 20,000 lbf vacuum thrust. Contract work began 27 Apr. 1990. During 1992, a major milestone was achieved with the review of the final design of the oxidizer turbopump in Sep. 1992