Multiple periodic solutions in impulsive hybrid neural networks with delays

The existence of multiple periodic solutions and their exponential stability are investigated for impulsive hybrid Hopfield-type neural networks with both time-dependent and distributed delays, using the Leray-Schauder fixed point theorem and Lyapunov functionals. The criteria given are easily verifiable, possess many adjustable parameters, and depend on impulses, providing flexibility for the analysis and design of delayed neural networks with impulse effects. Examples are given.     

A genetic algorithm for the unrelated parallel machine scheduling problem with sequence dependent setup times

In this work a genetic algorithm is presented for the unrelated parallel machine scheduling problem in which machine and job sequence dependent setup times are considered. The proposed genetic algorithm includes a fast local search and a local search enhanced crossover operator. Two versions of the algorithm are obtained after extensive calibrations using the Design of Experiments (DOE) approach. We review, evaluate and compare the proposed algorithm against the best methods known from the literature. We also develop a benchmark of small and large instances to carry out the computational experiments. After an exhaustive computational and statistical analysis we can conclude that the proposed method shows an excellent performance overcoming the rest of the evaluated methods in a comprehensive benchmark set of instances.     

Completion via Nearness for Metrically Generated Constructs

In this paper we will study completeness in symmetric metrically generated constructs via nearness spaces. Our approach consists in associating an appropriate regular nearness space with a given symmetric metered space. The completion theory known for regular nearness space has some convenient properties on which our completion of symmetric metered spaces will be based. This technique appears to be suitable for most symmetric metrically generated constructs and leads to a firm completion theory.      

The canonical Cauchy problem for linear systems of partial difference equations with constant coefficients over the completer-dimensional integral lattice ℕ2r

We canonically define and algorithmically solve the problem of the title. Such algorithms are of great significance for the method of finite differences for the solution of partial differential equations and for many technical applications such as image processing. In contrast to the wide (system theoretic) literature for ordinary difference equations and in spite of the great theoretical and practical significance of this problem, until now, there was no systematic theory of these systems and in particular of the corresponding Cauchy problem, let alone an algorithm. In this paper, we give both. The method consists in a transformation of this problem into a naturally associated problem which is defined over the 2r-dimensional natural number lattice ^2r (the upper quadrant in ^2r ) and for which the canonical initial value or Cauchy problem was defined and constructively solved by the second author.     

Uniformly defining valuation rings in Henselian valued fields with finite or pseudo-finite residue fields

We give a definition, in the ring language, of _Zp${\mathbb{Z}}_p$ inside _Qp${\mathbb{Q}}_p$ and of _Fp[[t]]${\mathbb{F}}_p[[t]]$ inside _Fp((t))${\mathbb{F}}_p((t))$, which works uniformly for all p   and all finite field extensions of these fields, and in many other Henselian valued fields as well. The formula can be taken existential-universal in the ring language, and in fact existential in a modification of the language of Macintyre. Furthermore, we show the negative result that in the language of rings there does not exist a uniform definition by an existential formula and neither by a universal formula for the valuation rings of all the finite extensions of a given Henselian valued field. We also show that there is no existential formula of the ring language defining _Zp${\mathbb{Z}}_p$ inside _Qp${\mathbb{Q}}_p$ uniformly for all p  . For any fixed finite extension of _Qp${\mathbb{Q}}_p$, we give an existential formula and a universal formula in the ring language which define the valuation ring.     

Local Stereology of Tensors of Convex Bodies

In this paper, we present local stereological estimators of Minkowski tensors defined on convex bodies in ? ^d . Special cases cover a number of well-known local stereological estimators of volume and surface area in ?³, but the general set-up also provides new local stereological estimators of various types of centres of gravity and tensors of rank two. Rank two tensors can be represented as ellipsoids and contain information about shape and orientation. The performance of some of the estimators of centres of gravity and volume tensors of rank two is investigated by simulation.     

Invariant subspaces for translation,dilation and multiplication semigroups

We study invariant subspaces in the context of the work of Katavolos and Power [9] and [10] when one of the semigroups considered is replaced by a discrete one. As a consequence, a rather striking connection is given with the study of the lattice of invariant subspaces of composition operators induced by automorphisms of the unit disc acting on the classical Hardy space. As a particular instance, our study concerns the lattice of invariant subspaces of those composition operators induced by hyperbolic automorphisms, and therefore with the Invariant Subspace Problem. Partially supported by Plan Nacional I+D grant no. MTM2006-06431 and Gobierno de Aragón research group Análisis Matemático y Aplicaciones, ref. DGA E-64.     

Radix representations, self-affine tiles, and multivariable wavelets

We investigate the connection between radix representations for and self-affine tilings of . We apply our results to show that Haar-like multivariable wavelets exist for all dilation matrices that are sufficiently large.

     

Confidence Regions for Local Maxima of Reconstructed Surfaces

There are several methods of surface reconstruction from a finite number of spatial data. The reconstruction is an estimate of the true surface, and it is often used to estimate topographical characteristics, e.g. to identify areas of extreme values. The uncertainty of an estimate depends both on uncertainties introduced by the reconstruction and on observation errors.We present a method to approximately evaluate the reliability of the estimates of the locations of local maxima (or minima) of the true surface. The true surface is modeled as a continuous parameter Gaussian random field, and the reliability is presented as confidence regions around the local maxima of the reconstruction.The method applies for general finite dimension of the spatial parameter, and for any reconstruction method that gives a differentiable surface with an explicit covariance function as result.