Normalized Ricci flow on Riemann surfaces and determinants of Laplacian

In this note we give a simple proof of the fact that the determinant of Laplace operator in smooth metric over compact Riemann surfaces of arbitrary genus $g$ monotonously grows under the normalized Ricci flow. Together with results of Hamilton that under the action of the normalized Ricci flow the smooth metric tends asymptotically to metric of constant curvature for $g\geq 1$, this leads to a simple proof of Osgood-Phillips-Sarnak theorem stating that that within the class of smooth metrics with fixed conformal class and fixed volume the determinant of Laplace operator is maximal on metric of constant curvatute.Comment: a reference to paper math.DG/9904048 by W.Mueller and K.Wendland where the main theorem of this paper was proved a few years earlier is adde

Research to develop and define concepts for reliable control sensors - The solid state rate sensors Final report

Solid state device for sensing angular rate by detecting presence of coriolis force

Noncontacting device to indicate deflection of turbopump internal rotating parts

Phase 2 (development) which was concluded for the ultrasonic Doppler device and the light-pipe-reflectance device is reported. An ultrasonic Doppler breadboard system was assembled which accurately measured runout in the J-2 LOX pump impeller during operation. The transducer was mounted on the outside of the pump volute using a C-clamp. Vibration was measured by conducting the ultrasonic wave through the volute housing and through the fluid in the volute to the impeller surface. The impeller vibration was also measured accurately using the light-pipe probe mounted in an elastomeric-gland fitting in the pump case. A special epoxy resin developed for cryogenic applications was forced into the end of the fiber-optic probe to retain the fibers. Subsequently, the probe suffered no damage after simultaneous exposure to 2150 psi and 77 F. Preliminary flash X-radiographs were taken of the turbine wheel and the shaft-bearing-seal assembly, using a 2-megavolt X-ray unit. Reasonable resolution and contrast was obtained. A fast-neutron detector was fabricated and sensitivity was measured. The results demonstrated that the technique is feasible for integrated-time measurements requiring, perhaps, 240 revolutions to obtain sufficient exposure at 35,000 rpm. The experimental verification plans are included

Noncontacting devices to indicate deflection and vibration of turbopump internal rotating parts

Published report discusses feasibility of ultrasonic techniques; neutron techniques; X-radiography; optical devices; gamma ray devices; and conventional displacement sensors. Use of signal transmitters in place of slip rings indicated possible improvement and will be subject of futher study

Metamaterials for light rays: ray optics without wave-optical analog in the ray-optics limit

Volumes of sub-wavelength electromagnetic elements can act like homogeneous materials: metamaterials. In analogy, sheets of optical elements such as prisms can act ray-optically like homogeneous sheet materials. In this sense, such sheets can be considered to be metamaterials for light rays (METATOYs). METATOYs realize new and unusual transformations of the directions of transmitted light rays. We study here, in the ray-optics and scalar-wave limits, the wave-optical analog of such transformations, and we show that such an analog does not always exist. Perhaps, this is the reason why many of the ray-optical possibilities offered by METATOYs have never before been considered.Comment: 10 pages, 3 figures, references update

Filler bar heating due to stepped tiles in the shuttle orbiter thermal protection system

An analytical study was performed to investigate the excessive heating in the tile to tile gaps of the Shuttle Orbiter Thermal Protection System due to stepped tiles. The excessive heating was evidence by visible discoloration and charring of the filler bar and strain isolation pad that is used in the attachment of tiles to the aluminum substrate. Two tile locations on the Shuttle orbiter were considered, one on the lower surface of the fuselage and one on the lower surface of the wing. The gap heating analysis involved the calculation of external and internal gas pressures and temperatures, internal mass flow rates, and the transient thermal response of the thermal protection system. The results of the analysis are presented for the fuselage and wing location for several step heights. The results of a study to determine the effectiveness of a half height ceramic fiber gap filler in preventing hot gas flow in the tile gaps are also presented

The Conference on High Temperature Electronics

The status of and directions for high temperature electronics research and development were evaluated. Major objectives were to (1) identify common user needs; (2) put into perspective the directions for future work; and (3) address the problem of bringing to practical fruition the results of these efforts. More than half of the presentations dealt with materials and devices, rather than circuits and systems. Conference session titles and an example of a paper presented in each session are (1) User requirements: High temperature electronics applications in space explorations; (2) Devices: Passive components for high temperature operation; (3) Circuits and systems: Process characteristics and design methods for a 300 degree QUAD or AMP; and (4) Packaging: Presently available energy supply for high temperature environment

Attorneys and the California Athlete Agencies Act: The Toll of the Bill

Agents have become a rising force in the sports industry. Their increased role in contract negotiations has brought with it increased scandal. The authors analyze the problems with the regulations promulgated by the various player associations as well as the California Athlete Agencies Act. The authors focus on the efforts of the California Legislature to alleviate these problems by amending the Act with Senate Bill 11 this year. The authors applaud the amendment and state that, with more involvement by the player associations, the sports industry will be much improved