In this paper, the solution of a moving Volterra-type screw dislocation in an orthotropic layer, bonded between two piezoelectric layers is obtained using complex Fourier transform. The dislocation solution is then employed as strain nuclei to derive singular integral equations for a medium weakened by multiple moving cracks. These equations, which are classified as, Cauchy singular equations, ...

In this paper, the analytical solution of an electric and Volterra edge dislocation in a functionally graded piezoelectric (FGP) medium is obtained by means of complex Fourier transform. The system is subjected to in-plane mechanical and electrical loading. The material properties of the medium vary exponentially with coordinating parallel to the crack. In this study, the rate of the gradual ch...

In this paper we establish a relation between the support of a function f on Ω1 ⊂ R with differentiability properties of its image Tf on Ω2 ⊂ R under a linear operator T . The classical approach requires analytic continuation of the image Tf from Ω2 into the complex domain C (theorems of Paley-Wiener type [5, 6, 7]), and therefore, could not apply to functions whose images Tf are not analytic a...

Fourier analysis is a powerful tool for many problems, and especially for solving various differential equations of interest in science and engineering. In the present paper since the utilization of Zadeh's Extension principle is quite difficult in practice, we prefer the idea of level sets in order to construct a fuzzy-valued function on a closed interval via related membership function. We de...

We report noninvasive measurements of the complex field of elastic quasimodes of a silicon wafer with chaotic shape. The amplitude and phase spatial distribution of the flexural modes are directly obtained by Fourier transform of time measurements. We investigate the crossover from real mode to complex-valued quasimode, when absorption is progressively increased on one edge of the wafer. The co...

Modern content-based image retrieval systems use different lowlevel features, like color, texture, and shape, to search in large image databases for those images which are perceptually similar to a given query image. Effective and efficient retrieval by shape similarity is still an open issue, despite the high importance of the shape feature in describing the content of an image. In this paper,...

We formalize some basic properties of Fourier series in the logic of ACL2(r), which is a variant of ACL2 that supports reasoning about the real and complex numbers by way of non-standard analysis. More specifically, we extend a framework for formally evaluating definite integrals of real-valued, continuous functions using the Second Fundamental Theorem of Calculus. Our extended framework is als...