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Marinoschi G.,Institute of Mathematical Statistics and Applied Mathematics of the Romanian Academy | Marinoschi G.,Simion Stoilow Institute of Mathematics of the Romanian Academy
Journal of Biological Dynamics | Year: 2013

We study a model, motivated by a bioremediation process, describing a cross-diffusion movement of a bacteria population b attracted by a chemoattractant signal c, in a nonhomogeneous stratified medium with n layers. We assume that this reaction-diffusion process is characterized by a low rate of degradation and a low diffusion coefficient of the chemoattractant, expressed in the model by a small parameter ε{lunate}. The model consists of n systems of nonlinear parabolic equations with transmission conditions between layers. We prove a global-in-time solution for the asymptotic model setup with respect to the small parameter of the problem, for arbitrarily large initial data. Next, we deal with the control problem focusing mainly on the reduction of the chemoattractant concentration, by acting upon the initial distribution of the bacteria population b0. To this end, we prove the existence of a solution to the control problem and determine the optimality conditions. © 2013 The Author(s). Published by Taylor & Francis. Source


Jayswa A.,Birla Institute of Technology | Stancu-Minasian I.M.,Institute of Mathematical Statistics and Applied Mathematics of the Romanian Academy
Proceedings of the Romanian Academy Series A - Mathematics Physics Technical Sciences Information Science | Year: 2010

We introduce new classes of generalized convex n-set functions that we call d-weak strictly pseudoquasi type-I univex, d-strong pseudo-quasi type-I univex and d-weak strictly pseudo type-I univex functions. We focus on multiobjective subset programming problem. Sufficient optimality conditions are obtained under the assumptions involving such functions. Duality results are also established for Mond-Weir and general Mond-Weir type dual problems in which the functions involved satisfy appropriate generalized d-type-I univexity conditions. The results obtained in this paper present a refinement and improvement of previously known results in the literature. Source


Beldiman M.,Institute of Mathematical Statistics and Applied Mathematics of the Romanian Academy
Proceedings of the Romanian Academy Series A - Mathematics Physics Technical Sciences Information Science | Year: 2013

Some types of equilibrium problems and systems of equilibrium problems on cones are studied. For these, we obtain equivalence results and prove, using a fixed - point theorem of Chowdury and Tan, existence results. Source


Ionescu V.,Institute of Mathematical Statistics and Applied Mathematics of the Romanian Academy
Proceedings of the Romanian Academy Series A - Mathematics Physics Technical Sciences Information Science | Year: 2011

We give a new proof concerning the complete positivity of the Boolean product of contractive, completely positive maps between C*-Algebras (see [9]). This is inspired by a technique due to M. Bozejko, M. Leinert and R. Speicher from [6] and uses an extension of a W.L.Paschke and E. Stormer's criterion for the positivity of a matrix over a C*-Algebra[13] [18]. Source


Barbu T.,Romanian Academy of Sciences | Marinoschi G.,Institute of Mathematical Statistics and Applied Mathematics of the Romanian Academy
International Journal of Control | Year: 2016

We propose a technique for image denoising by solving a nonconvex optimal control problem with the state and controller connected on a manifold described by a nonlinear elliptic equation. The existence of a control able to denoise an initial blurred image is proved and the optimality conditions are determined by a passing to the limit technique in an appropriate approximating problem, involving the Legendre–Fenchel relations. An algorithm constructed on the basis of the theoretical results is developed and numerical simulations are provided. © 2016 Informa UK Limited, trading as Taylor & Francis Group Source

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