Some new filters inspired in quantum models are used as edge detectors in infrared images. In this case, Bessel, Hermite and Morse filters will be applied to detect edges and fibrillar structures in infrared images. The edge detectors will be built by the Laplacian of the mentioned quantum filters. Furthermore, using curvature operators, curvature detectors and amplifiers of contrast will be constructed to analyze infrared images. The quantum filter prototyping will be done using computer algebra software, specifically Maple and its package, ImageTools. The quantum filters will be applied to infrared images using the technique of convolutions and blurred derivatives. It is expected that designed quantum filters will be useful for analysis and processing of infrared images. As future investigations, we propose to design plugins with the quantum filters that can be incorporated into the program ImageJ, which will facilitate the use of the quantum filters for the infrared image processing.
Some special functions of the mathematical physics are using to obtain a mathematical model of the propagation of airborne diseases. In particular we study the propagation of tuberculosis in closed rooms and we model the propagation using the error function and the Bessel function. In the model, infected individual emit pathogens to the environment and this infect others individuals who absorb it.
The evolution in time of the concentration of pathogens in the environment is computed in terms of error functions. The evolution in time of the number of susceptible individuals is expressed by a differential equation that contains the error function and it is solved numerically for different parametric simulations. The evolution in time of the number of infected individuals is plotted for each numerical simulation. On the other hand, the spatial distribution of the pathogen around the source of infection is represented by the Bessel function K0.
The spatial and temporal distribution of the number of infected individuals is computed and plotted for some numerical simulations. All computations were made using software Computer algebra, specifically Maple. It is expected that the analytical results that we obtained allow the design of treatment rooms and ventilation systems that reduce the risk of spread of tuberculosis.
The dynamics of shrinking drug-loaded microspheres were studied using a diffusion equation in spherical coordinates
and with a radially modulated diffusivity. A movable boundary condition that represents the shrinking was incorporated
using an approximation based on the Laplace transform. The resulting diffusive problem with radially modulated
diffusivity was solved using Laplace transform techniques with the Bromwich integral, the residue theorem and special
functions. Analytical solutions in the form of infinity series of special functions were derived for the general case of
shrinking microspheres and for the particular case with exponential shrinking. All computations were made using
computer algebra, specifically Maple. Some numerical simulations were made in the case of microspheres with
exponential shrinking. The analytical results were used to derive the effective constant time for the shrinking
microsphere. As future line of investigation, it is proposed the analysis of models with boundary condition that shows
the memory effect. It is expected that the obtained analytical results could be very important in pharmaceutical
engineering.
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