We introduce the concept of pseudo S-asymptotically periodic functions and study some of the qualitative properties of functions of this type. In addition, we discuss the existence of pseudo S-asymptotically periodic mild solutions for abstract neutral functional differential equations. Some applications involving ordinary and partial differential equations with delay are presented.2010 Mathematics subject classification: primary 35B15; secondary 34K40, 34K30, 47D06.
We study the existence and uniqueness of solutions, and the wellposedness of a general class of second order abstract differential equations with state‐dependent delay. Some examples related to partial differential equations with state‐dependent delay are presented.
The image reconstruction using the EIT (Electrical Impedance Tomography) technique is a nonlinear and ill-posed inverse problem which demands a powerful direct or iterative method. A typical approach for solving the problem is to minimize an error functional using an iterative method. In this case, an initial solution close enough to the global minimum is mandatory to ensure the convergence to the correct minimum in an appropriate time interval. The aim of this paper is to present a new, simple and low cost technique (quadrant-searching) to reduce the search space and consequently to obtain an initial solution of the inverse problem of EIT. This technique calculates the error functional for four different contrast distributions placing a large prospective inclusion in the four quadrants of the domain. Comparing the four values of the error functional it is possible to get conclusions about the internal electric contrast. For this purpose, initially we performed tests to assess the accuracy of the BEM (Boundary Element Method) when applied to the direct problem of the EIT and to verify the behavior of error functional surface in the search space. Finally, numerical tests have been performed to verify the new technique.
Physics has played a fundamental role in medicine sciences, specially in imaging diagnostic. Currently, image reconstruction techniques are already taught in Physics courses and there is a growing interest in new potential applications. The aim of this paper is to introduce to students the electrical impedance tomography, a promising technique in medical imaging. We consider a numerical example which consists in finding the position and size of a non-conductive region inside a conductive wire. We review the electrical impedance tomography inverse problem modeled by the minimization of an error functional. To solve the boundary value problem that arises in the direct problem, we use the boundary element method. The simulated annealing algorithm is chosen as the optimization method. Numerical tests show the technique is accurate to retrieve the non-conductive inclusion. Keywords: electrical impedance tomography, boundary element method, simulated annealing algorithm, inverse problem, optimization.A física tem tido um papel fundamental nas ciências médicas, especialmente em diagnósticos por imagem. Atualmente, as técnicas de reconstrução de imagem já são ensinadas nos curso de Física e existe um crescente interesse em possíveis novas aplicações. O objetivo deste trabalhoé apresentar aos alunos a tomografia de impedância elétrica, uma promissora técnica de imageamento em medicina. Para isso, consideramos um exemplo numérico que consiste em encontrar a posição e o tamanho de uma região não condutora no interior de um fio condutor. Nós revisamos o problema inverso da tomografia de impedância elétrica modelado pela minimização de um funcional de erro. Para resolver o problema de valor de contorno que surge no problema direto, nós usamos o método dos elementos de contorno. O algoritmo de recozimento simulado foi escolhido como método de otimização. Testes numéricos mostram que a técnicaé precisa para encontrar a inclusão não condutora. Palavras-chave: tomografia de impedância elétrica, método dos elementos de contorno, algoritmo de recozimento simulado, problema inverso, otimização.
The formal calibration procedure of a phase fraction meter is based on registering the outputs resulting from imposed phase fractions at known flow regimes. This can be straightforwardly done in laboratory conditions, but is rarely the case in industrial conditions, and particularly for on-site applications. Thus, there is a clear need for less restrictive calibration methods regarding to the prior knowledge of the complete set of inlet conditions. A new procedure is proposed in this work for the on-site construction of the calibration curve from total flown mass values of the homogeneous dispersed phase. The solution is obtained by minimizing a convenient error functional, assembled with data from redundant tests to handle the intrinsic ill-conditioned nature of the problem. Numerical simulations performed for increasing error levels demonstrate that acceptable calibration curves can be reconstructed, even from total mass measured within a precision of up to 2%. Consequently, the method can readily be applied, especially in on-site calibration problems in which classical procedures fail due to the impossibility of having a strict control of all the input/output parameters
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