After reviewing the theory of elasticity, the theory of composite materials, and integral transforms
, separate chapters examine wave propagation in isotropic waveguides, laminated composites, nanostructures, smart composite structures, defective waveguides, and periodic waveguides.
Explicit solution of (4), (5) can be obtained using the method of integral transforms
 by all spatial variables (x,y,z) and not touching time argument t that is accepted as the main one.
Four such types of data that are arising in the context of current scientific research and that the project will be focusing on are: random integral transforms
, random unlabelled shapes, random flows of functions, and random tensor fields.
Trimeche, Paley-Wiener theorems for the Dunkl transform and Dunkl translation operators, Integral Transforms
Srivastava, Certain subclasses of analytic functions associated with the generalized hypergeometric function, Integral Transforms
Uniqueness theorem] If F(v) and G(v) are a new integral transforms
of f(t) and g(t) respectively, then:
Klusch, Astrophysical Spectroscopy and neutron reactions, Integral transforms
and Voigt functions, Astrophys.
6) and (7), also containing fractional derivatives, can be solved in principle by several methods, the integral transforms
technique representing a systematic, efficient and powerful tool.
Readers are assumed to have previous experience with elementary aspects of mathematical analysis including the theory of integral transforms
and Laplace and Fourier type.
Here is necessary observe that the property of the integral transforms
to the obtaining of the spectral state of the quasi-relaxation phenomena, bounded by constants or coefficients that it is compute in the corresponding energy space of signals [sigma](t), or [epsilon](t), is to say, in the space [L.
Finally, by inversing the two integral transforms
in relation (2), the transversal displacements results, having the form of a time and position function, in the case of a simple supported linear elastic bar, being in rest, actioned by a constant force [f.
Bettaieb, On Hardy's inequality for symmetric integral transforms
and analogous, App.