Convergence Properties and Fixed Points of Two General Iterative Schemes with Composed Maps in Banach Spaces with Applications to Guaranteed Global Stability

This paper investigates the boundedness and convergence properties of two general iterative processes which involve sequences of self-mappings on either complete metric or Banach spaces. The sequences of self-mappings considered in the first iterative scheme are constructed by linear combinations of a set of self-mappings, each of them being a weighted version of a certain primary self-mapping on the same space. The sequences of self-mappings of the second iterative scheme are powers of an iteration-dependent scaled version of the primary self-mapping. Some applications are also given to the important problem of global stability of a class of extended nonlinear polytopic-type parameterizations of certain dynamic systems.

A New Type of Coincidence and Common Fixed Point Theorem with Applications

Coincidence and common fixed point theorems for a class of 'Ciric-Suzuki hybrid contractions involving a multivalued and two single-valued maps in a metric space are obtained. Some applications including the existence of a common solution for certain class of functional equations arising in a dynamic programming are also discussed..

An approach version of fuzzy metric spaces including an ad hoc fixed point theorem

In this paper, inspired by two very different, successful metric theories such us the real view-point of Lowen's approach spaces and the probabilistic field of Kramosil and Michalek's fuzzymetric spaces, we present a family of spaces, called fuzzy approach spaces, that are appropriate to handle, at the same time, both measure conceptions. To do that, we study the underlying metric interrelationships between the above mentioned theories, obtaining six postulates that allow us to consider such kind of spaces in a unique category. As a result, the natural way in which metric spaces can be embedded in both classes leads to a commutative categorical scheme. Each postulate is interpreted in the context of the study of the evolution of fuzzy systems. First properties of fuzzy approach spaces are introduced, including a topology. Finally, we describe a fixed point theorem in the setting of fuzzy approach spaces that can be particularized to the previous existing measure spaces.

DNA extraction from formalin-fixed Franciscana tissues

The present paper reports the extraction of DNA from formalin-fixed Pontoporia blainvillei tissues. Following the Vachot and Monerot (1996) protocol, fragmented DNA (300-700bp) was extracted from more than 95% of liver and muscle samples. DNA yield in liver samples was significantly higher than in muscle samples (4.574 ± 1.169mg DNA/mg versus 0.808 ± 0.297mg DNA/mg). Similar results were obtained from nine other species of cetaceans and five species of pinnipeds. It is of special interest to have a method that allows the utilisation of museum specimens not originally preserved for genetic studies, which may include rarely available, declining or extinct species. SPANISH: El presente trabajo reporta la extracción de ADN a partir de tejidos formolizados de Pontoporia blainvillei. Siguiendo el protocolo de Vachot y Monerot (1996) se pudo extraer ADN degradado (300-700pb) en más del 95% de las muestras de hígado y músculo analizadas. El rendimiento en ADN fue significativamente mayor en muestras de hígado que en muestras de músculo (4.574 ± 1.169mg DNA/mg tejido húmedo versus 0.808 ± 0.297mg DNA/mg tejido húmedo). Resultados similares se obtuvieron en otras nueve especies de Cetáceos y cinco de Pinnípedos. Resulta de gran interés contar con un método que permita la utilización de especímenes depositados en museos y que no hayan sido originalmente colectados para estudios genéticos, incluyendo especies de difícil obtención, en franca declinación o extintas.

BEHAVIOUR OF FIXED CANTILEVER WALLS SUBJECT TO LATERAL SHAKING.

A programme of research on the seismic behaviour of retaining walls has been under way at Cambridge since 1981. Centrifuge tests have presently been conducted both on cantilever walls and isolated mass walls, retaining dry sands of varying grading and density. This paper is devoted to the modelling of fixed-base cantilever walls retaining Leighton Buzzard (14/25) sand of relative density 99% with a horizontal surface level with the crest of the wall. The base of the centrifuge container was used to fix the walls, and to provide a rigid lower boundary for the sand. No attempt was made to inhibit the propagation of compression waves from the side of the container opposite the inside face of the model wall. The detailed analysis of dynamic deflections and bending moments was made difficult by the anelastic nature of reinforced concrete, and the difficulty of measuring bending strains thereon. A supplementary programme of well-instrumented tests on Dural walls of similar stiffness, including the modelling of models, was therefore carried out. Refs.

Application of the fixed point method for solution in time stepping finite element analysis using the inverse vector Jiles-Atherton model

An implementation of the inverse vector Jiles-Atherton model for the solution of non-linear hysteretic finite element problems is presented. The implementation applies the fixed point method with differential reluctivity values obtained from the Jiles-Atherton model. Differential reluctivities are usually computed using numerical differentiation, which is ill-posed and amplifies small perturbations causing large sudden increases or decreases of differential reluctivity values, which may cause numerical problems. A rule based algorithm for conditioning differential reluctivity values is presented. Unwanted perturbations on the computed differential reluctivity values are eliminated or reduced with the aim to guarantee convergence. Details of the algorithm are presented together with an evaluation of the algorithm by a numerical example. The algorithm is shown to guarantee convergence, although the rate of convergence depends on the choice of algorithm parameters. © 2011 IEEE.