Analogues of Weyl's formula for reduced enveloping algebras

In this note we study simple modules for a reduced enveloping algebra U_chi(g) in the critical case when chi element of g^* is ``nilpotent''. Some dimension formulas computed by Jantzen suggest modified versions of Weyl's dimension formula, based on certain reflecting hyperplanes for the affine Weyl group which might be associated to Kazhdan--Lusztig cells.Comment: AMS-LaTeX, 10 pages, 2 figure

Thermal fatigue performance of integrally cast automotive turbine wheels

Fluidized bed thermal fatigue testing was conducted on 16 integrally cast automotive turbine wheels for 1000-10,000 (600 sec total) thermal cycles at 935/50 C. The 16 wheels consisted of 14 IN-792 + 1% Hf and 2 gatorized AF2-1DA wheels; 6 of the IN-792 + Hf wheels contained crack arrest pockets inside the blade root flange. Temperature transients during the thermal cycling were measured in three calibration tests using either 18 or 30 thermocouples per wheel. Thermal cracking based on crack length versus accumulated cycles was greatest for unpocketed wheels developing cracks in 8-13 cycles compared to 75-250 cycles for unpocketed wheels. However, pocketed wheels survived up to 10,000 cycles with crack lengths less than 20 mm, whereas two unpocketed wheels developed 45 mm long cracks in 1000-2000 cycles

Thermal fatigue and oxidation data of TAZ-8A and M22 alloys and variations

Thermal fatigue and oxidation data were obtained on 36 specimens, representing 18 distinct variations (including the base systems) of TAZ-8A and M22 alloys. Double-edge wedge specimens for these systems were cycled between fluidized beds maintained at 1088 C and 316 C with a 180 s immersion in each bed. The systems included alloys TAZ-8A, M22, and 16 variations of these alloys. Each alloy variation consisted of a unique composition with an alternation in the percentage of carbon (C1 and C2), molydenum (M1 and M2), tungsten (W1 and W2), columbium (CB1, CB2, and CB3), tantalium (T1, T2, and T3), or boron (B1, B2, and B3) present. All of the alloys showed little weight change due to oxidation compared with other alloys previously tested in fluidized beds. Only both C1 alloy variation specimens survived 3500 cycles without cracking in the small radius, although substantial cracks were present, emanating from the end notches which were used for holding the specimens

Motion Planning for Optimal Information Gathering in Opportunistic Navigation Systems

Motion planning for optimal information gathering in an opportunistic navigation (OpNav) environment is considered. An OpNav environment can be thought of as a radio frequency signal landscape within which a receiver locates itself in space and time by extracting information from ambient signals of opportunity (SOPs). The receiver is assumed to draw only pseudorange-type observations from the SOPs, and such observations are fused through an estimator to produce an estimate of the receiver’s own states. Since not all SOP states in the OpNav environment may be known a priori, the receiver must estimate the unknown SOP states of interest simultaneously with its own states. In this work, the following problem is studied. A receiver with no a priori knowledge about its own states is dropped in an unknown, yet observable, OpNav environment. Assuming that the receiver can prescribe its own trajectory, what motion planning strategy should the receiver adopt in order to build a high-fidelity map of the OpNav signal landscape, while simultaneously localizing itself within this map in space and time? To answer this question, first, the minimum conditions under which the OpNav environment is fully observable are established, and the need for receiver maneuvering to achieve full observability is highlighted. Then, motivated by the fact that not all trajectories a receiver may take in the environment are equally beneficial from an information gathering point of view, a strategy for planning the motion of the receiver is proposed. The strategy is formulated in a coupled estimation and optimal control framework of a gradually identified system, where optimality is defined through various information-theoretic measures. Simulation results are presented to illustrate the improvements gained from adopting the proposed strategy over random and pre-defined receiver trajectories.Aerospace Engineering and Engineering Mechanic

A Technique for Determining the Carrier Phase Differences between Independent GPS Receivers during Scintillation

A method for recovering the carrier phase differences between pairs of independent GPS receivers has been developed and demonstrated in truth-model simulations. This effort is in support of a project that intends to image the disturbed ionosphere with diffraction tomography techniques using GPS measurements from large arrays of receivers. Carrier phase differential GPS techniques, common in surveying and relative navigation, are employed to determine the phase relationships between the receivers in the imaging array. Strategies for estimating the absolute carrier phase disturbances at each receiver are discussed. Simulation results demonstrate that the system can rapidly detect the onset of scintillation, identify one non-scintillating reference signal, and recover the carrier phase differences accurate to 0.1 cycles.Aerospace Engineering and Engineering Mechanic

Data-Driven Generalized Integer Aperture Bootstrapping for Real-Time High Integrity Applications

A new method is developed for integer ambiguity resolution in carrier-phase differential GPS (CDGPS) positioning. The method is novel in that it is (1) data-driven, (2) generalized to include partial ambiguity resolution, and (3) amenable to a full characterization of the prior and posterior distributions of the three-dimensional baseline vector that results from CDGPS. The technique is termed generalized integer aperture bootstrapping (GIAB). GIAB improves the availability of integer ambiguity resolution for high-integrity, safety-critical systems. Current high-integrity CDGPS algorithms, such as EPIC and GERAFS, evaluate the prior risk of position domain biases due to incorrect integer ambiguity resolution without further validation of the chosen solution. This model-driven approach introduces conservatism which tends to reduce solution availability. Common data-driven ambiguity validation methods, such as the ratio test, control the risk of incorrect ambiguity resolution by shrinking an integer aperture (IA), or acceptance region. The incorrect fixing risk of current IA methods is determined by functional approximations that are inappropriate for use in safety-of-life applications. Moreover, generalized IA (GIA) methods incorrectly assume that the baseline resulting from partial ambiguity resolution is zero mean. Each of these limitations is addressed by GIAB, and the claimed improvements are validated by Monte Carlo simulation. The performance of GIAB is then optimized by tuning the integer aperture size to maximize the prior probability of full ambiguity resolution. GIAB is shown to provide higher availability than EPIC for the same integrity requirements.Aerospace Engineering and Engineering Mechanic

Economic Determinants of Participation in Physical Activity and Sport

This paper examines the economic determinants of participation in physical activity by developing and analyzing a consumer choice model of participation and by testing the predictions of this model using data drawn from the Behavioral Risk Factor Surveillance Survey (BRFSS). Both emphasize that individuals face two distinct decisions: (1) should I participate in sport?; and (2) how much time should I spend participating in sport? The evidence highlights the importance of selectivity. The economic factors that affect these two decisions work in opposite directions; factors that increase the likelihood of participation generally decrease the amount of time spent participating.physical activity, time allocation, health production

Development of a realistic stress analysis for fatigue analysis of notched composite laminates

A finite element stress analysis which consists of a membrane and interlaminar shear spring analysis was developed. This approach was utilized in order to model physically realistic failure mechanisms while maintaining a high degree of computational economy. The accuracy of the stress analysis predictions is verified through comparisons with other solutions to the composite laminate edge effect problem. The stress analysis model was incorporated into an existing fatigue analysis methodology and the entire procedure computerized. A fatigue analysis is performed upon a square laminated composite plate with a circular central hole. A complete description and users guide for the computer code FLAC (Fatigue of Laminated Composites) is included as an appendix