In his seminal work of 1981, A M Cormack has established that Radon transforms defined on two remarkable families of curves in the plane are invertible and admit explicit inversion formulas via circular harmonic decomposition. A sufficient condition for finding larger classes of curves enjoying the same property is given in this paper. We show that these generalized Cormack’s curves are given b...

 sinx x if x 6= 0 1 otherwise This function is important in many areas of computing science, approximation theory, and numerical analysis. For example, it is used in interpolation and approximation of functions, approximate evaluation of transforms (e.g. Hilbert, Fourier, Laplace, Hankel, and Mellon transforms as well as the fast Fourier transform). It is used in finding approximate solutions ...

A simple, processable precursor to mullite can be synthesized in quantities of 100 g in a few hours by direct reaction of silica, aluminum hydroxide, and triethanolamine in ethylene glycol. To delineate a processing window whereby precursor shapes can be transformed into mullite, the chemical and phase microstructural evolution of this precursor on pyrolysis to selected temperatures in air is f...

Although wave optics is the standard method of analyzing systems composed of a sequence of lenses separated by arbitrary distances, it is often easier and more intuitive to ascertain the function and properties of such systems by tracing a few rays through them. Determining the location, magnification or scale factor, and field curvature associated with images and Fourier transforms by tracing ...

The starting point for this paper is the well known equivalence between convolution filtering with a rescaled Gaussian and the solution of the heat equation. In the first chapters we analyze the equivalence between multiscale convolution filtering, linear smoothing methods based on continuous wavelet transforms and the solutions of linear diffusion equations. I.e. we determine a wavelet ψ, resp...

Modelling stochastic systems has many important applications. Normal form coordinate transforms are a powerful way to untangle interesting long term macroscale dynamics from detailed microscale dynamics. We explore such coordinate transforms of stochastic differential systems when the dynamics has both slow modes and quickly decaying modes. The thrust is to derive normal forms useful for macros...

The starting point for this paper is the well known equivalence between convolution filtering with a rescaled Gaussian and the solution of the heat equation. In the first sections we analyze the equivalence between multiscale convolution filtering, linear smoothing methods based on continuous wavelet transforms and the solutions of linear diffusion equations. I.e. we determine a wavelet ψ, resp...

Abstract This work introduces a new integral transform for functions of exponential order called “NE transform”. We prove some properties NE -transform. Also, applications the NE- to find solution ordinary linear equation are given. The relationships with well-known transforms characterized by identities. study this transform. Then we compare it few exiting in Laplace family such as Laplace, Su...

This paper addresses the critical issue of the development of intelligent or assisting tools for the scientist who is working in the initial problem formulation and mathematical model representation stage of research. In particular, examples of that representation in fluid dynamics and instability theory are discussed. The creation of a mathematical model that is ready for application of certai...

We utilize the Bellman function technique to prove a bilinear dimension-free inequality for the Hermite operator. The Bellman technique is applied here to a non-local operator, which at first did not seem to be feasible. As a consequence of our bilinear inequality one proves dimension-free boundedness for the Riesz-Hermite transforms on L with linear growth in terms of p. A feature of the proof...