Numerical solutions to singular ϕ-Laplacianwith Dirichlet boundary conditions

In this note we are concerned with numerical solutions to Dirichlet problem $$[\phi(u')]' =f(x) \quad \mbox{in} [\alpha, \beta]; \quad u(\alpha)=A, \; u(\beta)=B, $$ where \(\phi :(-\eta , \eta ) \to \mathbb {R}\) \((\eta <+ \infty )\) is an increasing diffeomorphism with \(\phi '(y)\geq d >0\) for all \(y\in (-\eta , \eta )\) . The obtained algorithm combines the shooting method with Euler’s method and it is convergent whenever the problem is solvable. We provide numerical experiments confirming the theoretical aspects.     

Family constraining of iterative algorithms

In constraining iterative processes, the algorithmic operator of the iterative process is pre-multiplied by a constraining operator at each iterative step. This enables the constrained algorithm, besides solving the original problem, also to find a solution that incorporates some prior knowledge about the solution. This approach has been useful in image restoration and other image processing situations when a single constraining operator was used. In the field of image reconstruction from projections a priori information about the original image, such as smoothness or that it belongs to a certain closed convex set, may be used to improve the reconstruction quality. We study here constraining of iterative processes by a family of operators rather than by a single operator.     

Hilbert geometry for convex polygonal domains

We prove in this paper that the Hilbert geometry associated with an open convex polygonal set is Lipschitz equivalent to the Euclidean plane.     

Surface and electrochemical analysis for the understanding of TiO2 nanopores/nanotubes changes in post‐elaboration treatment

The electrochemical stability of TiO₂ nanoarchitecture fabricated in fluoride electrolyte presented in this paper is related to 2D and 3D geometries that present a shift from nanopores toward nanotubes. The fabrication conditions involve a 60 V applied voltage for 2 hours of anodizing in order to create the ordered structures, in a mixture of low‐water glycerol electrolyte and fluoride. With the use of different ultrasonication times, a variety of nanotubes/nanopores were observed. The surface interfacial aspects were investigated mainly by surface microscopy and hydrophilic/hydrophobic balance for the grown structures ultrasonicated at various periods of time. The electrochemical behavior of the nanotube‐structured surface was performed by potentiodynamic evaluation and electrochemical impedance spectroscopy in a simulated body fluid solution. As a most important result, all surface analysis and electrochemical data interpretation permitted the proposition of a model for elaboration of different nanostructures from nanopores to nanotubes. These different surface nanoarchitectures were obtained as a result of ultrasonication at various periods of time. Copyright © 2010 John Wiley & Sons, Ltd.     

Ueber die Trennung und Bestimmung von Nickel und Kobalt

Ohne Zusammenfassung     

Block-Projections Algorithms with Blocks Containing Mutually Orthogonal Rows and Columns

In this paper we present an algorithm which, for a given (sparse) matrix, constructs a partition of its set of row-indices, such that each subset of this partition (except the last one obtained) contains indices which correspond to mutually orthogonal rows. We then use such decompositions in some classes of block-projections methods, previously extended by the author to general inconsistent linear least-squares problems. Numerical experiments on an inconsistent and rank-deficient least-squares model problem are described in the last section of the paper.