An iterative method based on boundary integrals for elliptic Cauchy problems in semi-infinite domains

In this study, we investigate the problem of reconstruction of a stationary temperature field from given temperature and heat flux on a part of the boundary of a semi-infinite region containing an inclusion. This situation can be modelled as a Cauchy problem for the Laplace operator and it is an ill-posed problem in the sense of Hadamard. We propose and investigate a Landweber-Fridman type iterative method, which preserve the (stationary) heat operator, for the stable reconstruction of the temperature field on the boundary of the inclusion. In each iteration step, mixed boundary value problems for the Laplace operator are solved in the semi-infinite region. Well-posedness of these problems is investigated and convergence of the procedures is discussed. For the numerical implementation of these mixed problems an efficient boundary integral method is proposed which is based on the indirect variant of the boundary integral approach. Using this approach the mixed problems are reduced to integral equations over the (bounded) boundary of the inclusion. Numerical examples are included showing that stable and accurate reconstructions of the temperature field on the boundary of the inclusion can be obtained also in the case of noisy data. These results are compared with those obtained with the alternating iterative method.

High-throughput manufacturing of size-tuned liposomes by a new microfluidics method using enhanced statistical tools for characterization

Microfluidics has recently emerged as a new method of manufacturing liposomes, which allows for reproducible mixing in miliseconds on the nanoliter scale. Here we investigate microfluidics-based manufacturing of liposomes. The aim of these studies was to assess the parameters in a microfluidic process by varying the total flow rate (TFR) and the flow rate ratio (FRR) of the solvent and aqueous phases. Design of experiment and multivariate data analysis were used for increased process understanding and development of predictive and correlative models. High FRR lead to the bottom-up synthesis of liposomes, with a strong correlation with vesicle size, demonstrating the ability to in-process control liposomes size; the resulting liposome size correlated with the FRR in the microfluidics process, with liposomes of 50 nm being reproducibly manufactured. Furthermore, we demonstrate the potential of a high throughput manufacturing of liposomes using microfluidics with a four-fold increase in the volumetric flow rate, maintaining liposome characteristics. The efficacy of these liposomes was demonstrated in transfection studies and was modelled using predictive modeling. Mathematical modelling identified FRR as the key variable in the microfluidic process, with the highest impact on liposome size, polydispersity and transfection efficiency. This study demonstrates microfluidics as a robust and high-throughput method for the scalable and highly reproducible manufacture of size-controlled liposomes. Furthermore, the application of statistically based process control increases understanding and allows for the generation of a design-space for controlled particle characteristics.

An iterative method for the reconstruction of a stationary flow

In this article, an iterative algorithm based on the Landweber-Fridman method in combination with the boundary element method is developed for solving a Cauchy problem in linear hydrostatics Stokes flow of a slow viscous fluid. This is an iteration scheme where mixed well-posed problems for the stationary generalized Stokes system and its adjoint are solved in an alternating way. A convergence proof of this procedure is included and an efficient stopping criterion is employed. The numerical results confirm that the iterative method produces a convergent and stable numerical solution. © 2007 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 2007

An iterative method for a Cauchy problem for the heat equation

An iterative method for reconstruction of the solution to a parabolic initial boundary value problem of second order from Cauchy data is presented. The data are given on a part of the boundary. At each iteration step, a series of well-posed mixed boundary value problems are solved for the parabolic operator and its adjoint. The convergence proof of this method in a weighted L2-space is included.

An iterative method for reconstruction of temperature

An iterative method for the reconstruction of a stationary three-dimensional temperature field, from Cauchy data given on a part of the boundary, is presented. At each iteration step, a series of mixed well-posed boundary value problems are solved for the heat operator and its adjoint. A convergence proof of this method in a weighted L 2-space is include

A Perturbed Iterative Method for a General Class of Variational Inequalities

The generalized Wiener-Hopf equation and the approximation methods are used to propose a perturbed iterative method to compute the solutions of a general class of nonlinear variational inequalities.

An Iterative Method for the Matrix Principal n-th Root

In this paper we give an iterative method to compute the principal n-th root and the principal inverse n-th root of a given matrix. As we shall show this method is locally convergent. This method is analyzed and its numerical stability is investigated.

Acceleration of Convergence in Dontchev’s Iterative Method for Solving Variational Inclusions

2000 Mathematics Subject Classification: 47H04, 65K10.

A new scheduling method for enhanced quality of experience in LTE systems

In this paper a new approach to the resource allocation and scheduling mechanism that reflects the effect of user's Quality of Experience is presented. The proposed scheduling algorithm is examined in the context of 3GPP Long Term Evolution (LTE) system. Pause Intensity (PI) as an objective and no-reference quality assessment metric is employed to represent user's satisfaction in the scheduler of eNodeB. PI is in fact a measurement of discontinuity in the service. The performance of the scheduling method proposed is compared with two extreme cases: maxCI and Round Robin scheduling schemes which correspond to the efficiency and fairness oriented mechanisms, respectively. Our work reveals that the proposed method is able to perform between fairness and efficiency requirements, in favor of higher satisfaction for the users to the desired level. © VDE VERLAG GMBH.

Biomarkers of Nitrosative Stress: Development and validation of a new analytical method for 3-Nitrotyrosine quantification

Background: The nitration of tyrosine residues in proteins is associated with nitrosative stress, resulting in the formation of 3-nitrotyrosine (3-NT). 3-NT levels in biological samples have been associated with numerous physiological and pathological conditions. For this reason, several attempts have been made in order to develop methods that accurately quantify 3-NT in biological samples. Regarding chromatographic methods, they seem to be very accurate, showing very good sensibility and specificity. However, accurate quantification of this molecule, which is present at very low concentrations both at physiological and pathological states, is always a complex task and a target of intense research. Objectives: We aimed to develop a simple, rapid, low-cost and sensitive 3-NT quantification method for use in medical laboratories as an additional tool for diagnosis and/or treatment monitoring of a wide range of pathologies. We also aimed to evaluate the performance of the HPLC-based method developed here in a wide range of biological matrices. Material and methods: All experiments were performed on a Hitachi LaChrom Elite® HPLC system and separation was carried out using a Lichrocart® 250-4 Lichrospher 100 RP-18 (5μm) column. The method was further validated according to ICH guidelines. The biological matrices tested were serum, whole blood, urine, B16 F-10 melanoma cell line, growth medium conditioned with the same cell line, bacterial and yeast suspensions. Results: From all the protocols tested, the best results were obtained using 0.5% CH3COOH:MeOH:H2O (15:15:70) as the mobile phase, with detection at wavelengths 215, 276 and 356 nm, at 25ºC, and using a flow rate of 1 mL/min. By using this protocol, it was possible to obtain a linear calibration curve (correlation coefficient = 1), limits of detection and quantification in the order of ng/mL, and a short analysis time (<15 minutes per sample). Additionally, the developed protocol allowed the successful detection and quantification of 3-NT in all biological matrices tested, with detection at 356 nm. Conclusion: The method described in this study, which was successfully developed and validated for 3-NT quantification, is simple, cheap and fast, rendering it suitable for analysis in a wide range of biological matrices.

Exact and numerical solutions for diffusio-reaction equations with convection term

Esta dissertação estuda essencialmente dois problemas: (A) uma classe de equações unidimensionais de reacção-difusão-convecção em meios não uniformes (dependentes do espaço), e (B) um problema elíptico não-linear e paramétrico ligado a fenómenos de capilaridade. A Análise de Perturbação Singular e a dinâmica de Hamilton-Jacobi são utilizadas na obtenção de expressões assimptóticas para a solução (com comportamento de frente) e para a sua velocidade de propagação. Os seguintes três métodos de decomposição, Adomian Decomposition Method (ADM), Decomposition Method based on Infinite Products (DIP), e New Iterative Method (NIM), são apresentados e brevemente comparados. Adicionalmente, condições suficientes para a convergência da solução em série, obtida pelo ADM, e uma aplicação a um problema da Telecomunicações por Fibras Ópticas, envolvendo EDOs não-lineares designadas equações de Raman, são discutidas. Um ponto de vista mais abrangente que unifica os métodos de decomposição referidos é também apresentado. Para subclasses desta EDP são obtidas soluções numa forma explícita, para diferentes tipos de dados e usando uma variante do método de simetrias de Bluman-Cole. Usando Teoria de Pontos Críticos (o teorema usualmente designado mountain pass) e técnicas de truncatura, prova-se a existência de duas soluções não triviais (uma positiva e uma negativa) para o problema elíptico não-linear e paramétrico (B). A existência de uma terceira solução não trivial é demonstrada usando Grupos Críticos e Teoria de Morse.