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Marinoschi G.,Institute of Mathematical Statistics and Applied Mathematics
AIP Conference Proceedings | Year: 2011

We consider a nonlinear diffusion parabolic equation with transport in which the coefficient of time derivative u vanishes on a subset of positive measure of the space domain. The aim of the paper is to identify this coefficient on the basis of known data for the solution. © 2011 American Institute of Physics.

Iannelli M.,University of Trento | Marinoschi G.,Institute of Mathematical Statistics and Applied Mathematics
Mathematical Methods in the Applied Sciences | Year: 2013

The basic linear model for describing an age structured population spreading in a limited habitat is considered with the purpose of investigating an approximation procedure based on parabolic regularization. In fact, a viscosity model is introduced by considering an appropriate approximating regularized parabolic problem and it is proved that the sequence of the approximating solutions tends to the solution to the original problem. The advantage of this approach is that it leads to the numerical solution of a parabolic problem that has more stable solutions than the hyperbolic-parabolic original problem and avoids the restrictions (compatibility conditions) needed to treat the latter. Moreover, for the solution of the approximating problem, it is possible to take advantage of established software packages dedicated to parabolic problems. Some examples of the approach are provided using COMSOL Multiphysics. Copyright © 2012 John Wiley & Sons, Ltd. Copyright © 2012 John Wiley & Sons, Ltd.

Agapie A.,University of Bucharest | Agapie M.,Tarleton State University | Rudolph G.,TU Dortmund | Zbaganu G.,Institute of Mathematical Statistics and Applied Mathematics
IEEE Transactions on Cybernetics | Year: 2013

Evolutionary algorithms (EAs) are random optimization methods inspired by genetics and natural selection, resembling simulated annealing. We develop a method that can be used to find a meaningful tradeoff between the difficulty of the analysis and the algorithms' efficiency. Since the case of a discrete search space has been studied extensively, we develop a new stochastic model for the continuous n-dimensional case. Our model uses renewal processes to find global convergence conditions. A second goal of the paper is the analytical estimation of the computation time of EA with uniform mutation inside the (hyper)-sphere of volume 1, minimizing a quadratic function. © 2013 IEEE.

Popescu D.,Institute of Mathematical Statistics and Applied Mathematics
Proceedings of the Romanian Academy Series A - Mathematics Physics Technical Sciences Information Science | Year: 2010

I consider a great lipid vesicle filled with an aqueous solution of a solute, for which its membrane is impermeable. Because of the mechanical tension induced by the osmotic flow, the vesicle swells up to a critical size, triggering a transient lipidic pore when it is introduced into a hypotonic aqueous medium. In this paper, we will obtain the differential equations of the vesicle dynamics, which is in fact a periodic process due to osmotic gradient and transbilayer pore appearance. We will also analyse the characteristic parameters of this process: swelling time, pore lifetime, number of cycles, the length time of vesicle activity, material quantity leaked out during a cycle. In the end, we present the condition to design a n-cycles working vesicle and propose some biotechnological applications.

Agapie A.,Academy of Economic Studies Bucharest | Agapie A.,Institute of Mathematical Statistics and Applied Mathematics
International Journal of Computer Mathematics | Year: 2010

The evolutionary algorithms discussed in this paper do not use crossover, nor mutation. Instead, they estimate and evolve a marginal probability distribution, the only distribution responsible for generating new populations of chromosomes. So far, the analysis of this class of algorithms was confined to proportional selection and additive decomposable functions. Dropping both assumptions, we consider here truncation selection and non-separable problems with polynomial number of distinct fitness values. The emergent modelling is half theoretical - with respect to selection, completely characterized by stochastic calculus - and half empirical - concerning the generation of new individuals. For the latter operator, we sample the chromosomes arbitrarily, one for each selected level of fitness. That is the break-symmetry point, making the difference between the finite and infinite population cases, and ensuring the convergence of the model.

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