We develop a fast method for solving the one-dimensional wave equation based on geometrical optics. From geometrical optics (e.g., Fourier integral operator theory or WKB approximation) it is known that high-frequency waves split into forward and backward propagating parts, each propagating with the wave speed, with amplitude that is slowly changing depending on the medium coefficients, under t...

Equations are described to derive the true anterior chamber dimensions of an eye from a photograph of its optical section. If the surface of the eye is assumed to be spherical, the three-dimensional coordinates of rays emanating from the anterior chamber to a camera can be transformed to two-dimensional coordinates on a plane, which contains rays both inside and outside of the "eye." The actual...

Biometrics identification methods proved to be very efficient, more natural and easy for users than traditional methods of human identification. In fact, only biometrics methods truly identify humans, not keys and cards they posses or passwords they should remember. The future of biometrics leads to passive physiological methods based on images of such parts of human body as face and ear. The a...

We develop a method, based on Darboux’ and Liouville’s works, to find first integrals and/or invariant manifolds for a physically relevant class of dynamical systems, without making any assumption on these elements’ form. We apply it to three dynamical systems: Lotka–Volterra, Lorenz and Rikitake. I. HISTORICAL OVERVIEW. In, Roger Liouville and A. Tresse developed a method for deciding whether ...

Over the last years, the demand for high strength and low weight materials, such as fabric-reinforced plastics, has grown in the aeronautical industry. By decreasing the production cost with short production cycle times and increasing reproducibility by automation, fabric-reinforced plastics are becoming increasingly better economical competitors to other construction materials such as for exam...

In the paper the main attention is paid to conditions on algebras from a given variety Θ which provide coincidence of their algebraic geometries. The main part here play the notions mentioned in the title of the paper.

Abstract Liouville’s equation on phase space in geometrical optics describes the evolution of an energy distribution through optical system, which is discontinuous across interfaces. The Galerkin spectral element method conservative and can achieve higher order convergence locally, making it a suitable for this equation. When dealing with interfaces space, non-local boundary conditions arise. B...