It is shown that any convolution operator in the time domain can be represented exactly as a multiplication operator in the time-scale (wavelet) domain. The Mellin transform gives a one-to-one correspondence between frequency filters (system functions) and scale filters (multiplication operators in the scale domain), subject to the convergence of the defining integrals. The usual wavelet recons...

This paper presents an algorithm that uses visual information to achieve the homing of an autonomous agent inside a previously visited environment. An image grabbed at the target position is compared with the currently perceived one to determine the relative position of the robot and of its target. Only particular regions of the image, called Visual References, are taken into account. A Visual ...

We revisit the American put and call option valuation problems. We derive analytical formulas for the option prices and approximate ordinary differential equations for the optimal exercise boundaries. Numerical simulations yield accurate option prices and comparable computational speeds when benchmarked against the binomial method for calculating option prices. Our approach is based on the Mell...

Dirichlet series and Fourier series can both be used to encode sequences of complex numbers an , n ∈ N. Dirichlet series do so in a manner adapted to the multiplicative structure of N, whereas Fourier series reflect the additive structure of N. Formally at least, the Mellin transform relates these two ways of representing sequences. In this paper, we make sense of the Mellin transform of period...

Central and local limit theorems are derived for the number of distinct summands in integer partitions, with or without repetitions, under a general scheme essentially due to Meinardus. The local limit theorems are of the form of Cramér-type large deviations and are proved by Mellin transform and the two-dimensional saddle-point method. Applications of these results include partitions into posi...

This paper introduces variations on the template matching theme that extend its usefulness by providing invariance to mean intensity-level variations, certain geometric transformations and partial obscura-tions of the target object in the image. First order statistics of the pixel by pixel diierences between the template and the image are used as a match measure in order to provide invariance t...