This paper reformulates a time-discontinuous finite element method (TD-FEM) based on a new class of shape functions, called complex Fourier hereafter, for solving two-dimensional elastodynamic problems. These shape functions, which are derived from their corresponding radial basis functions, have some advantages such as the satisfaction of exponential and trigonometric function fields in comple...

In this paper, the finite element analysis of two-dimensional linear viscoelastic problems is performed using quadrilateral complex Fourier elements and, the results are compared with those obtained by quadrilateral classic Lagrange elements. Complex Fourier shape functions contain a shape parameter which is a constant unknown parameter adopted to enhance approximation’s accuracy. Since the iso...

In this paper, we introduced a new way to analyze the shape using a new Fourier based descriptor, which is the smoothed derivative of the phase of the Fourier descriptors. It is extracted from the complex boundary of the shape, and is called the smoothed group delay (SGD). The usage of SGD on the Fourier phase descriptors, allows a compact representation of the shape boundaries which is robust ...

An approximation to the Fourier transform (FT) of the Kohlrausch function (stretched exponential) with shape parameter 0 < β ≤ 1 is presented by using Havriliak-Negami-like functions. Mathematical expressions to fit their parameters α, γ, and τ, as functions of β (0 < β ≤ 1 and 1 < β < 2) are given, which allows a quick identification in the frequency domain of the corresponding shape factor β....

Harmonic analysis studies the representation of functions as the linear combination of basic wave-like functions. It plays a fundamental role in the processing of time-series signals and images. Recent years have witnessed many efforts to adapt the Fourier and wavelet analysis to the domain of 3D shapes. The manifold Fourier analysis relies on the eigenfunctions of the Laplace-Beltrami operator...

we consider gabor systems generated by a gaussian function and prove certain classical results of paley and wiener on nonharmonic fourier series of complex exponentials for the gabor expansion‎. ‎in particular, we prove a version of plancherel-po ́lya theorem for entire functions with finite order of growth and use the hadamard factorization theorem to study regularity‎, ‎exactness and deficienc...

This paper introduces a novel methodology to shape boundary characterization, where a shape is modeled into a Small World complex network. It uses degree and joint degree measurements in a dynamic evolution network to compose a set of shape descriptors. The proposed shape characterization method has an efficient power of shape characterization, it is robust, noise tolerant, scale invariant and ...