Modular frames for Hilbert C*-modules and symmetric approximation of frames

We give a comprehensive introduction to a general modular frame construction in Hilbert C*-modules and to related modular operators on them. The Hilbert space situation appears as a special case. The reported investigations rely on the idea of geometric dilation to standard Hilbert C*-modulesover unital C*-algebras that admit an orthonormal Riesz basis. Interrelations and applications to classical linear frame theory are indicated. As an application we describe the nature of families of operators {S_i} such that SUM_i S*_iS_i=id_H, where H is a Hilbert space. Resorting to frames in Hilbert spaces we discuss some measures for pairs of frames to be close to one another. Most of the measures are expressed in terms of norm-distances of different kinds of frame operators. In particular, the existence and uniqueness of the closest (normalized) tight frame to a given frame is investigated. For Riesz bases with certain restrictions the set of closetst tight frames often contains a multiple of its symmetric orthogonalization (i.e. L\"owdin orthogonalization).Comment: SPIE's Annual Meeting, Session 4119: Wavelets in Signal and Image Processing; San Diego, CA, U.S.A., July 30 - August 4, 2000. to appear in: Proceedings of SPIE v. 4119(2000), 12 p

Vitis vinifera (Vitales: Vitaceae) as a Reproductive Host of Spissistilus festinus (Hemiptera: Membracidae).

Feeding by the three-cornered alfalfa hopper, Spissistilus festinus (Say) (Hemiptera: Membracidae) results in girdling of grapevine petioles and shoots. Its significance as an economic pest of grape has increased since it was shown to transmit Grapevine red blotch virus (GRBV) in a greenhouse study. However, the status of grapevines as a reproductive host for S. festinus remained undetermined. Adult S. festinus were caged onto three regions of the grapevines: apical shoot, green shoot, and dormant cane. Their ability to reproduce was determined by weekly destructive sampling for 7 wk. Successful oviposition and nymphal emergence were observed on apical and green shoots, but not on dormant canes. However, insect development beyond the second nymphal instar did not occur. Knowledge of S. festinus reproduction on grapevines will be an important consideration in designing management guidelines to minimize the spread of GRBV in vineyards

Transition from adiabatic inspiral to plunge into a spinning black hole

A test particle of mass mu on a bound geodesic of a Kerr black hole of mass M >> mu will slowly inspiral as gravitational radiation extracts energy and angular momentum from its orbit. This inspiral can be considered adiabatic when the orbital period is much shorter than the timescale on which energy is radiated, and quasi-circular when the radial velocity is much less than the azimuthal velocity. Although the inspiral always remains adiabatic provided mu << M, the quasi-circular approximation breaks down as the particle approaches the innermost stable circular orbit (ISCO). In this paper, we relax the quasi-circular approximation and solve the radial equation of motion explicitly near the ISCO. We use the requirement that the test particle's 4-velocity remain properly normalized to calculate a new contribution to the difference between its energy and angular momentum. This difference determines how a black hole's spin changes following a test-particle merger, and can be extrapolated to help predict the mass and spin of the final black hole produced in finite-mass-ratio black-hole mergers. Our new contribution is particularly important for nearly maximally spinning black holes, as it can affect whether a merger produces a naked singularity.Comment: 9 pages, 6 figures, final version published in PRD with minor change

Research reports: 1991 NASA/ASEE Summer Faculty Fellowship Program

The basic objectives of the programs, which are in the 28th year of operation nationally, are: (1) to further the professional knowledge of qualified engineering and science faculty members; (2) to stimulate an exchange of ideas between participants and NASA; (3) to enrich and refresh the research and teaching activities of the participants' institutions; and (4) to contribute to the research objectives of the NASA Centers. The faculty fellows spent 10 weeks at MSFC engaged in a research project compatible with their interests and background and worked in collaboration with a NASA/MSFC colleague. This is a compilation of their research reports for summer 1991

Research reports: 1990 NASA/ASEE Summer Faculty Fellowship Program

Reports on the research projects performed under the NASA/ASEE Summer Faculty Fellowship Program are presented. The program was conducted by The University of Alabama and MSFC during the period from June 4, 1990 through August 10, 1990. Some of the topics covered include: (1) Space Shuttles; (2) Space Station Freedom; (3) information systems; (4) materials and processes; (4) Space Shuttle main engine; (5) aerospace sciences; (6) mathematical models; (7) mission operations; (8) systems analysis and integration; (9) systems control; (10) structures and dynamics; (11) aerospace safety; and (12) remote sensin

1992 NASA/ASEE Summer Faculty Fellowship Program

For the 28th consecutive year, a NASA/ASEE Summer Faculty Fellowship Program was conducted at the Marshall Space Flight Center (MSFC). The program was conducted by the University of Alabama and MSFC during the period June 1, 1992 through August 7, 1992. Operated under the auspices of the American Society for Engineering Education, the MSFC program, was well as those at other centers, was sponsored by the Office of Educational Affairs, NASA Headquarters, Washington, DC. The basic objectives of the programs, which are the 29th year of operation nationally, are (1) to further the professional knowledge of qualified engineering and science faculty members; (2) to stimulate and exchange ideas between participants and NASA; (3) to enrich and refresh the research and teaching activities of the participants' institutions; and (4) to contribute to the research objectives of the NASA centers