α-Mellin Transform and One of Its Applications

MSC 2010: 35R11, 44A10, 44A20, 26A33, 33C45

On the probability density function of the product of Rayleigh distributed random variables

In this paper we investigate the distribution of the product of Rayleigh distributed random variables. Considering the Mellin-Barnes inversion formula and using the saddle point approach we obtain an upper bound for the product distribution. The accuracy of this tail-approximation increases as the number of random variables in the product increase.

Ergodic capacity and outage performance of amplify-and-forward protocols

This thesis analyses the performance bounds of amplify-and-forward relay channels which are becoming increasingly popular in wireless communication applications. The statistics of cascaded Nakagami-m fading model which is a major obstacle in evaluating the outage of wireless networks is analysed using Mellin transform. Furthermore, the upper and the lower bounds for the ergodic capacity of the slotted amplify-and-forward relay channel, for finite and infinite number of relays are derived using random matrix theory. The results obtained will enable wireless network designers to optimize the network resources, benefiting the consumers.

An example in Beurling's theory of generalised primes

In this paper we prove some connections between the growth of a function and its Mellin transform and apply these to study an explicit example in the theory of Beurling primes.

Krätzel Function as a Function of Hypergeometric Type

2000 Mathematics Subject Classification: 33C60, 33C20, 44A15

Fractional Calculus of P-transforms

MSC 2010: 44A20, 33C60, 44A10, 26A33, 33C20, 85A99

Towards automatic power line detection for a UAV surveillance system using pulse coupled neural filter and an improved Hough transform

Spatial information captured from optical remote sensors on board unmanned aerial vehicles (UAVs) has great potential in automatic surveillance of electrical infrastructure. For an automatic vision-based power line inspection system, detecting power lines from a cluttered background is one of the most important and challenging tasks. In this paper, a novel method is proposed, specifically for power line detection from aerial images. A pulse coupled neural filter is developed to remove background noise and generate an edge map prior to the Hough transform being employed to detect straight lines. An improved Hough transform is used by performing knowledge-based line clustering in Hough space to refine the detection results. The experiment on real image data captured from a UAV platform demonstrates that the proposed approach is effective for automatic power line detection.