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In this study, the solution of the Neumann problem associated with the CR Yamabe operator on a subset Ω\Omega of the CR manifold S3{{\mathbb{S}}}^{3} bounded by the Clifford torus Σ\Sigma is discussed. The Yamabe-type problem of finding a contact form on Ω\Omega which has zero Tanaka-Webster scalar curvature and for which Σ\Sigma has a constant pp-mean curvature is also discussed.

A muskox neonate ( Ovibos moschatus ) that died of starvation was diagnosed with congenital lenticular anomalies that included spherophakia and hypermature cataract associated with probable lens-induced lymphocytic uveitis and neutrophilic keratitis. Impaired sight as a result of cataract and associated inflammation likely contributed to abandonment and starvation, although maternal death cannot be excluded definitively. Ocular lesions, such as congenital cataracts and spherophakia in neonates, may be important factors affecting survival in free-ranging animals.

Critical acoustical systems operating in complex environments contaminated with disturbances and noise offer an extreme challenge when excited by out-of-the-ordinary, impulsive, transient events that can be undetected and seriously affect their overall performance. Transient impulse excitations must be detected, extracted, and evaluated to determine any potential system damage that could have been imposed; therefore, the problem of recovering the excitation in an uncertain measurement environment becomes one of multichannel deconvolution. Recovering a transient and its initial energy has not been solved satisfactorily, especially when the measurement has been truncated and only a small segment of response data is available. The development of multichannel deconvolution techniques for both complete and incomplete excitation data is discussed, employing a model-based approach based on the state-space representation of an identified acoustical system coupled to a forward modeling solution and a Kalman-type processor for enhancement and extraction. Synthesized data are utilized to assess the feasibility of the various approaches, demonstrating that reasonable performance can be achieved even in noisy environments.

Spectral estimation is a necessary methodology to analyze the frequency content of noisy data sets especially in acoustic applications. Many spectral techniques have evolved starting with the classical Fourier transform methods based on the well-known Wiener-Khintchine relationship relating the covariance-to-spectral density as a transform pair culminating with more elegant model-based parametric techniques that apply prior knowledge of the data to produce a high-resolution spectral estimate. Multichannel spectral representations are a class of both nonparametric, as well as parametric, estimators that provide improved spectral estimates. In any case, classical nonparametric multichannel techniques can provide reasonable estimates when coupled with peak-peaking methods as long as the signal levels are reasonably high. Parametric multichannel methods can perform quite well in low signal level environments even when applying simple peak-picking techniques. In this paper, the performance of both nonparametric (periodogram) and parametric (state-space) multichannel spectral estimation methods are investigated when applied to both synthesized noisy structural vibration data as well as data obtained from a sounding rocket flight. It is demonstrated that for the multichannel problem, state-space techniques provide improved performance, offering a parametric alternative compared to classical methods.

Dynamic testing of large flight vehicles (rockets) is not only complex, but also can be very costly. These flights are infrequent and can lead to disastrous effects if something were to fail during the flight. The development of sensors coupled to internal components offers a great challenge in reducing their size, yet still maintaining their precision. Sounding rockets provide both a viable and convenient alternative to the more costly vehicular flights. Some of the major objectives are to test various types of sensors for monitoring components of high interest as well as investigating real-time processing techniques. Signal processing presents an extreme challenge in this noisy multichannel environment. The estimation and tracking of modal frequencies from vibrating structures is an important set of features that can provide information about the components under test; therefore, high resolution multichannel spectral processing is required. The application of both single channel and multichannel techniques capable of producing reliable modal frequency estimates of a vibrating structure from uncertain accelerometer measurements is discussed.

Monitoring mechanical systems operating in uncertain environments contaminated with both environmental disturbances and noise lead directly to low signal-to-noise-ratios, creating an extremely challenging processing problem, especially in real-time. In order to estimate the performance of a particular system from uncertain vibrational data, it is necessary to identify its unique resonant (modal) frequency signature. The monitoring of structural modes to determine the condition of a device under investigation is essential, especially if it is a critical entity of an operational system. The development of a model-based scheme capable of the on-line tracking of the inherent structural modal frequencies by applying both constrained subspace identification techniques to extract the modal frequencies and state estimation methods to track the evolution is discussed. An application of this approach to a cylindrical structural device (pipe-in-air) is analyzed based on theoretical simulations along with controlled validation experiments, including injected anomalies illustrate the approach and performance. Statistics are gathered to bound potential processors for real-time performance employing these constrained techniques.

Juvenile red snapper settle across several complex habitats, which function as nurseries for young fish. Little is known about their life history or feeding biomechanics during this time. However, recent studies have shown higher growth rates for juveniles located on mud habitats adjacent to low profile reefs, perhaps because of varied prey availability and abundance. To further investigate the habitat needs of juvenile red snapper and test hypotheses of feeding development, individuals were collected from a low profile shell ridge and adjacent mud areas on Freeport Rocks, TX, USA, and divided into three size classes (< or = 3.9, 4.0-5.9, > or = 6.0 cm SL). Output from a dynamic lever model suggested an ontogenetic shift in feeding morphology. Biomechanical modeling also predicted that off-ridge juveniles would have slower, stronger jaws compared with on-ridge juveniles. Kinematic profiles obtained from actual feeding events validated the models' predictive ability. Analysis of prey capture events demonstrated that on-ridge juveniles exhibited larger jaw displacements than off-ridge juveniles. Shape analysis was used to further investigate habitat effects on morphology. Off-ridge juveniles differed from on-ridge juveniles in possessing a deeper head and body. Results from model simulations, kinematic profiles, behavioral observations and shape analysis all compliment the conclusion that on-ridge juveniles exhibited more suction feeding behavior, whereas off-ridge juveniles used more biting behavior. Habitat disparity and possibly available prey composition generated variations in juvenile feeding biomechanics and behavior that may affect recruitment.

A residual negative free-air and Bouguer anomaly of at least 80 milligals, superimposed on a broader high, occurs over the Galápagos Islands The axis of the anomaly trends roughly east and plunges eastward. Thus, a low-density mass in the crust or upper mantle must underlie the archipelago. This anomaly may be caused by thermal expansion over a crust-mantle " hot spot".