On $\Delta$-Transforms

On ∆ - Transforms

Any set of two legs in a Gough–Stewart platform sharing an attachment is defined as a ∆component. This component links a point in the platform (base) to a line in the base (platform). Thus, if the two legs, which are involved in a ∆ component, are rearranged without altering the location of the line and the point in their base and platform local reference frames, the singularity locus of the Go...

On Euler Transforms

provided that d>, instead of being subject to both restrictions (1), is subject only to the second of those restrictions and to the assumption that the integral (7) is convergent at every x>0 (but not necessarily at 2c = 0). By the "natural" topology on Ece is meant that defined by the Helly convergence of monotone functions. Proof of (3). It is readily verified from (1) and (2) that, as *—»oo,...

A note on the comparison between Laplace and Sumudu transforms

Multiscaled Wavelet Transforms, Ridgelet Transforms, and Radon Transforms on the Space of Matrices

Let Mn,m be the space of real n × m matrices which can be identified with the Euclidean space R. We introduce continuous wavelet transforms on Mn,m with a multivalued scaling parameter represented by a positive definite symmetric matrix. These transforms agree with the polar decomposition on Mn,m and coincide with classical ones in the rank-one case m = 1. We prove an analog of Calderón’s repro...

\Delta \Delta \Delta