Search results for "Mellin transform."
showing 4 items of 24 documents
Fractional calculus approach to the statistical characterization of random variables and vectors
2009
Fractional moments have been investigated by many authors to represent the density of univariate and bivariate random variables in different contexts. Fractional moments are indeed important when the density of the random variable has inverse power-law tails and, consequently, it lacks integer order moments. In this paper, starting from the Mellin transform of the characteristic function and by fractional calculus method we present a new perspective on the statistics of random variables. Introducing the class of complex moments, that include both integer and fractional moments, we show that every random variable can be represented within this approach, even if its integer moments diverge. A…
Einstein-Smoluchowsky equation handled by complex fractional moments
2014
In this paper the response of a non linear half oscillator driven by α-stable white noise in terms of probability density function (PDF) is investigated. The evolution of the PDF of such a system is ruled by the so called Einstein-Smoluchowsky equation involving, in the diffusive term, the Riesz fractional derivative. The solution is obtained by the use of complex fractional moments of the PDF, calculated with the aid of Mellin transform operator. It is shown that solution can be found for various values of stability index α and for any nonlinear function of the drift term in the stochastic differential equation.
Fractional visco-elastic Timoshenko beam deflection via single equation
2015
SUMMARY This paper deals with the response determination of a visco-elastic Timoshenko beam under static loading condition and taking into account fractional calculus. In particular, the fractional derivative terms arise from representing constitutive behavior of the visco-elastic material. Further, taking advantages of the Mellin transform method recently developed for the solution of fractional differential equation, the problem of fractional Timoshenko beam model is assessed in time domain without invoking the Laplace-transforms as usual. Further, solution provided by the Mellin transform procedure will be compared with classical Central Difference scheme one, based on the Grunwald–Letni…
Primary ciliary dyskinesia assessment by means of optical flow analysis of phase-contrast microscopy images
2014
Primary ciliary dyskinesia implies cilia with defective or total absence of motility, which may result in sinusitis, chronic bronchitis, bronchiectasis and male infertility. Diagnosis can be difficult and is based on an abnormal ciliary beat frequency (CBF) and beat pattern. In this paper, we present a method to determine CBF of isolated cells through the analysis of phase-contrast microscopy images, estimating cilia motion by means of an optical flow algorithm. After having analyzed 28 image sequences (14 with a normal beat pattern and 14 with a dyskinetic pattern), the normal group presented a CBF of 5.2 +/- 1.6 Hz, while the dyskinetic patients presented a 1.9 +/- 0.9 Hz CBF. The cutoff …