It is shown that a lossless first-order optical system whose real symplectic ray transformation matrix can be diagonalized and has only unimodular eigenvalues is similar to a separable fractional Fourier transformer in the sense that the ray transformation matrices of the unimodular system and the separable fractional Fourier transformer are related by means of a similarity transformation. More...

Rotational transformation based on coordinate rotation in Fourier space is a useful technique for simulating wave field propagation between nonparallel planes. This technique is characterized by fast computation because the transformation only requires executing a fast Fourier transform twice and a single interpolation. It is proved that the formula of the rotational transformation mathematical...

The purpose is to formulate a Fourier transformation for the space of functionals, as an infinitesimal meaning. We extend R to ( ∗R) under the base of nonstandard methods for the construction. The domain of a functional is the set of all internal functions from a ∗-finite lattice to a ∗-finite lattice with a double meaning. Considering a ∗-finite lattice with a double meaning, we find how to tr...

This paper uses as starting point the transformation matrix defined in the homogeneous space that associates the points of a 2D plane (that represents the model) with those of another 2D space (the image one), this transformation characterizing the camera capture process. This transformation (an homography from 2D to 2D) is coming from previous work and is used within the scope of the SimulFoot...

We present a scalable 2D Galerkin spectral element method solution to the linearized potential flow radiation problemfor wave induced forcing of floating offshore structure. The pseudo-impulsive formulation problem is solved in time-domain using Gaussian displacement signal tailored discrete resolution. added mass and damping coefficients are then obtained via Fourier transformation. used discr...

To accurately reconstruct the three-dimensional (3D) surface of dynamic objects, we proposed a wrapped phase extraction method for spatiotemporal analysis based on 3D wavelet transform (WT). Our uses 2D spatial fringe image combined with time dimension and forms sequence. The encoded sequence’s information was extracted by WT complex Morlet wavelet, improved extraction’s accuracy using characte...

We derive the I transformation, an iterative sequence transformation that is useful for the convergence acceleration of certain Fourier series. The derivation is based on the concept of hierarchical consistency in the asymptotic regime. We show that this sequence transformation is a special case of the J transformation. Thus, many properties of the I transformation can be deduced from the known...