An alternating method for Cauchy problems for Helmholtz-type operators in non-homogeneous medium

Kozlov & Maz'ya (1989, Algebra Anal., 1, 144–170) proposed an alternating iterative method for solving Cauchy problems for general strongly elliptic and formally self-adjoint systems. However, in many applied problems, operators appear that do not satisfy these requirements, e.g. Helmholtz-type operators. Therefore, in this study, an alternating procedure for solving Cauchy problems for self-adjoint non-coercive elliptic operators of second order is presented. A convergence proof of this procedure is given.

An alternating method for the stationary Stokes system

An alternating procedure for solving a Cauchy problem for the stationary Stokes system is presented. A convergence proof of this procedure and numerical results are included.

Numerical solution of an elliptic 3-dimensional Cauchy problem by the alternating method and boundary integral equations

We consider the Cauchy problem for the Laplace equation in 3-dimensional doubly-connected domains, that is the reconstruction of a harmonic function from knowledge of the function values and normal derivative on the outer of two closed boundary surfaces. We employ the alternating iterative method, which is a regularizing procedure for the stable determination of the solution. In each iteration step, mixed boundary value problems are solved. The solution to each mixed problem is represented as a sum of two single-layer potentials giving two unknown densities (one for each of the two boundary surfaces) to determine; matching the given boundary data gives a system of boundary integral equations to be solved for the densities. For the discretisation, Weinert's method [24] is employed, which generates a Galerkin-type procedure for the numerical solution via rewriting the boundary integrals over the unit sphere and expanding the densities in terms of spherical harmonics. Numerical results are included as well.

Sequential and parallel synchronous alternating iterative methods

The so-called parallel multisplitting nonstationary iterative Model A was introduced by Bru, Elsner, and Neumann [Linear Algebra and its Applications 103:175-192 (1988)] for solving a nonsingular linear system Ax = b using a weak nonnegative multisplitting of the first type. In this paper new results are introduced when A is a monotone matrix using a weak nonnegative multisplitting of the second type and when A is a symmetric positive definite matrix using a P -regular multisplitting. Also, nonstationary alternating iterative methods are studied. Finally, combining Model A and alternating iterative methods, two new models of parallel multisplitting nonstationary iterations are introduced. When matrix A is monotone and the multisplittings are weak nonnegative of the first or of the second type, both models lead to convergent schemes. Also, when matrix A is symmetric positive definite and the multisplittings are P -regular, the schemes are also convergent.

Fast reconstruction of harmonic functions from Cauchy data using integral equation techniques

We consider the problem of stable determination of a harmonic function from knowledge of the solution and its normal derivative on a part of the boundary of the (bounded) solution domain. The alternating method is a procedure to generate an approximation to the harmonic function from such Cauchy data and we investigate a numerical implementation of this procedure based on Fredholm integral equations and Nyström discretization schemes, which makes it possible to perform a large number of iterations (millions) with minor computational cost (seconds) and high accuracy. Moreover, the original problem is rewritten as a fixed point equation on the boundary, and various other direct regularization techniques are discussed to solve that equation. We also discuss how knowledge of the smoothness of the data can be used to further improve the accuracy. Numerical examples are presented showing that accurate approximations of both the solution and its normal derivative can be obtained with much less computational time than in previous works.

Automatic tuning method for the design of supplementary damping controllers for flexible alternating current transmission system devices

The design of supplementary damping controllers to mitigate the effects of electromechanical oscillations in power systems is a highly complex and time-consuming process, which requires a significant amount of knowledge from the part of the designer. In this study, the authors propose an automatic technique that takes the burden of tuning the controller parameters away from the power engineer and places it on the computer. Unlike other approaches that do the same based on robust control theories or evolutionary computing techniques, our proposed procedure uses an optimisation algorithm that works over a formulation of the classical tuning problem in terms of bilinear matrix inequalities. Using this formulation, it is possible to apply linear matrix inequality solvers to find a solution to the tuning problem via an iterative process, with the advantage that these solvers are widely available and have well-known convergence properties. The proposed algorithm is applied to tune the parameters of supplementary controllers for thyristor controlled series capacitors placed in the New England/New York benchmark test system, aiming at the improvement of the damping factor of inter-area modes, under several different operating conditions. The results of the linear analysis are validated by non-linear simulation and demonstrate the effectiveness of the proposed procedure.

A novel automated alternating current biosusceptometry method to characterization of controlled-release magnetic floating tablets of metronidazole

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

An alternating boundary integral based method for a Cauchy problem for the Laplace equation in a quadrant

We study the Cauchy problem for the Laplace equation in a quadrant (quarter-plane) containing a bounded inclusion. Given the values of the solution and its derivative on the edges of the quadrant the solution is reconstructed on the boundary of the inclusion. This is achieved using an alternating iterative method where at each iteration step mixed boundary value problems are being solved. A numerical method is also proposed and investigated for the direct mixed problems reducing these to integral equations over the inclusion. Numerical examples verify the efficiency of the proposed scheme.

A relaxation method of an alternating iterative algorithm for the Cauchy problem in linear isotropic elasticity

We propose two algorithms involving the relaxation of either the given Dirichlet data (boundary displacements) or the prescribed Neumann data (boundary tractions) on the over-specified boundary in the case of the alternating iterative algorithm of Kozlov et al. [16] applied to Cauchy problems in linear elasticity. A convergence proof of these relaxation methods is given, along with a stopping criterion. The numerical results obtained using these procedures, in conjunction with the boundary element method (BEM), show the numerical stability, convergence, consistency and computational efficiency of the proposed method.

An alternating boundary integral based method for a Cauchy problem for the Laplace equation in semi-infinite regions

We consider a Cauchy problem for the Laplace equation in a two-dimensional semi-infinite region with a bounded inclusion, i.e. the region is the intersection between a half-plane and the exterior of a bounded closed curve contained in the half-plane. The Cauchy data are given on the unbounded part of the boundary of the region and the aim is to construct the solution on the boundary of the inclusion. In 1989, Kozlov and Maz'ya [10] proposed an alternating iterative method for solving Cauchy problems for general strongly elliptic and formally self-adjoint systems in bounded domains. We extend their approach to our setting and in each iteration step mixed boundary value problems for the Laplace equation in the semi-infinite region are solved. Well-posedness of these mixed problems are investigated and convergence of the alternating procedure is examined. For the numerical implementation an efficient boundary integral equation method is proposed, based on the indirect variant of the boundary integral equation approach. The mixed problems are reduced to integral equations over the (bounded) boundary of the inclusion. Numerical examples are included showing the feasibility of the proposed method.

Ultra-thin films of alternating semi-interpenetrating layers of a conducting polymer with thermosetting phenolic resins for sensor application

In this work a new method for crosslinking ultra-thin films with potential applications in sensor systems is proposed. The films were produced by layer-by-layer (LbL) assembly using a conducting polymer, poly(o-ethoxyaniline) (POEA), alternated with a thermosetting resin, novolac-type phenolformaldehyde (PF), crosslinked by a simple thermal treatment. The PF resin served as both alternating and crosslinking agents. The films were characterized by Fourier transform infrared (FTIR) and ultraviolet-visible (UV-Vis) spectroscopy, thermogravimetry (TG), desorption, doping/dedoping cycling and electrical measurements. The results showed that film architecture and crosslinking degree can be controlled by the conditions used for film deposition (number of bilayers, polymer concentration, pH, and deposition time), and crosslinking time. Moreover, this approach offers several advantages such as fast curing time and low cost, indicating that these films can be used to produce sensors with improved stability.

Inhibition of motor cortex excitability with 15 Hz transcranial alternating current stimulation (tACS)

There remains a lack of solid evidence showing whether transcranial stimulation with weak alternating current (transcranial alternating current stimulation, tACS) can in fact induce significant neurophysiological effects. Previously, a study in which tACS was applied for 2 and 5 min with current density = 0.16-0.25 A/m(2) was unable to show robust effects on cortical excitability. Here we applied tACS at a significantly higher current density (0.80 A/m(2)) for a considerably longer duration (20 min) and were indeed able to demonstrate measurable changes to cortical excitability. Our results show that active 15 Hz tACS of the motor cortex (electrodes placed at C3 and C4) significantly diminished the amplitude of motor evoked potentials and decreased intracortical facilitation (ICF) as compared to baseline and sham stimulation. In addition, we show that our method of sham tACS is a reliable control condition. These results support the notion that AC stimulation with weak currents can induce significant changes in brain excitability; in this case, 15 Hz tACS led to a pattern of inhibition of cortical excitability. We propose that tACS may have a dampening effect on cortical networks and perhaps interfere with the temporal and spatial summation of weak subthreshold electric potentials. (C) 2010 Elsevier Ireland Ltd. All rights reserved.

Phase 3 randomized trial on larynx preservation comparing sequential vs alternating chemotherapy and radiotherapy.

BACKGROUND: Both induction chemotherapy followed by irradiation and concurrent chemotherapy and radiotherapy have been reported as valuable alternatives to total laryngectomy in patients with advanced larynx or hypopharynx cancer. We report results of the randomized phase 3 trial 24954 from the European Organization for Research and Treatment of Cancer. METHODS: Patients with resectable advanced squamous cell carcinoma of the larynx (tumor stage T3-T4) or hypopharynx (T2-T4), with regional lymph nodes in the neck staged as N0-N2 and with no metastasis, were randomly assigned to treatment in the sequential (or control) or the alternating (or experimental) arm. In the sequential arm, patients with a 50% or more reduction in primary tumor size after two cycles of cisplatin and 5-fluorouracil received another two cycles, followed by radiotherapy (70 Gy total). In the alternating arm, a total of four cycles of cisplatin and 5-fluorouracil (in weeks 1, 4, 7, and 10) were alternated with radiotherapy with 20 Gy during the three 2-week intervals between chemotherapy cycles (60 Gy total). All nonresponders underwent salvage surgery and postoperative radiotherapy. The Kaplan-Meier method was used to obtain time-to-event data. RESULTS: The 450 patients were randomly assigned to treatment (224 to the sequential arm and 226 to the alternating arm). Median follow-up was 6.5 years. Survival with a functional larynx was similar in sequential and alternating arms (hazard ratio of death and/or event = 0.85, 95% confidence interval = 0.68 to 1.06), as were median overall survival (4.4 and 5.1 years, respectively) and median progression-free interval (3.0 and 3.1 years, respectively). Grade 3 or 4 mucositis occurred in 64 (32%) of the 200 patients in the sequential arm who received radiotherapy and in 47 (21%) of the 220 patients in the alternating arm. Late severe edema and/or fibrosis was observed in 32 (16%) patients in the sequential arm and in 25 (11%) in the alternating arm. CONCLUSIONS: Larynx preservation, progression-free interval, and overall survival were similar in both arms, as were acute and late toxic effects.