The problem of reflection and refraction of elastic waves due to an incident quasi-primary $(qP)$ wave at a plane interface between two dissimilar nematic elastomer half-spaces has been investigated. The expressions for the phase velocities corresponding to primary and secondary waves are given. It is observed that these phase velocities depend on the angle of propagation of the elastic waves. The reflection and refraction coefficients corresponding to the reflected and refracted waves, respectively, are derived by using appropriate boundary conditions. The energy transmission of the reflected and refracted waves is obtained, and the energy ratios and the reflection and refraction coefficients are computed numerically.

In this paper we introduce an insurance ruin model with an adaptive premium rate, henceforth referred to as restructuring/refraction, in which classical ruin and bankruptcy are distinguished. In this model the premium rate is increased as soon as the wealth process falls into the red zone and is brought back to its regular level when the wealth process recovers. The analysis is focused mainly on the time a refracted Lévy risk process spends in the red zone (analogous to the duration of the negative surplus). Building on results from [11] and [16], we identify the distribution of various functionals related to occupation times of refracted spectrally negative Lévy processes. For example, these results are used to compute both the probability of bankruptcy and the probability of Parisian ruin in this model with restructuring.

Near sea surface radio frequency (RF) refraction is four dimensional (4D) and can significantly impact the performance of radar systems. The refractivity field is dictated by the vertical thermodynamic structure of the constantly evolving marine atmospheric boundary layer (MABL). Logistical and budgetary restraints on meteorological measurements over water to capture the spatio-temporal structure of refractivity fields influencing radar performance have limited the knowledge of how and why radar performance is azimuth, range, and time dependent. Rapidly increasing computer processing speeds and decreasing memory capacity costs have supported the horizontal and vertical resolution requirements for mesoscale numerical weather prediction (NWP) models to resolve the thermodynamic structure in the MABL. Once modeled, refractivity structure is easily calculated from the thermodynamic structure. Mesoscale NWP models coupled with modern parabolic equation radar performance models can support the prediction of 4D radar performance in challenging non-homogeneous, near surface refractivity fields at the time and location of the modeler's choice. The NWP modeling presented in this paper demonstrates how large-scale offshore flow of warm and dry air over colder seas produces strong near surface RF trapping. Large land-sea temperature differences can produce near shore sea breezes and surface-based ducts. This paper describes modeled radar performance in such a complex ducting structure over the Persian Gulf during large-scale northwest atmospheric flow. The refractivity field was resolved by the Coupled Ocean/ Atmosphere Mesoscale Prediction System (COAMPS® is a registered trademark of the Naval Research Laboratory) and the notional radar performance was modeled by the advanced refractive effects prediction system (AREPS). The results indicate strong spatial and wavelength-dependent enhancements and degradations in radar performance relative to a standard atmosphere.

This study elucidated the complicated phenomena of wave refraction and diffraction around a circular island due to random incident waves traveling with a current. Various combinations of random incident wave and current conditions were used to investigate the wave height distributions around a circular island numerically and experimentally. Numerical calculations were carried out based on the theory derived by Lin & Hsu [1]. According to the results, it shows that numerical calculations can predict experimental data quantitatively well.

The eyes of eighteen female sheep (Ovis aries) were refracted and details of inter ocular distance, pupil size, shape and fundus presence recorded. The sheep eyes generally possessed very low hyperopia with little astigmatism, such physiological optics being expected to produce a well focused retinal image for objects in the middle and long distance. No evidence was found for accommodation, which would have produced a well focused ocular image for near objects. A further 10 sheep had their monocular and binocular visual fields measured. The estimated visual field suggests the existence of at least binocular vision, if not the presence of stereopsis. Given the lack of accommodation and a wide inter-ocular distance, it is likely that some degree of stereopsis exists in the animal's middle and long distance vision, but is absent in near vision. These findings support those taken from the animal's neurophysiology and observations of its visually guided behaviour.