Weak type (1, 1) inequalities of maximal convolution operators

In this paper we study the behavior of the constants which appear in the weak type (1, 1) inequalities for maximal convolution operators by means of discrete methods. One of the first applications of these techniques will give us a very simple proof of the ergodic theorem. We also present partial results in order to investigate the best constant in the weak type (1, 1) inequality for the Hardy-Littlewood centered maximal operator in dimension one. In dimension bigger than one we also obtain some lower bounds for that constant.     

Metric foliations and curvature

We prove a rigidity theorem for Riemannian fibrations of flat spaces over compact bases and give a metric classification of compact four-dimensional manifolds of nonnegative curvature that admit totally geodesic Riemannian foliations.     

Transition-metal-templated synthesis of rotaxanes and catenanes: From small molecules to polymers

This article provides an overview of the fundamental principles of the synthesis of metallocatenanes and metallorotaxanes. It also describes the synthesis and properties of electronic conducting polymers—polypyrrole and polythiophene—built around metallocatenanes and metallorotaxanes. The particular properties of this new class of polymers, including the possibility of transmetallation reactions being performed with them and the observation of electronic coupling between the metal centers and the conducting matrix, are discussed. © 2003 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 41: 3470–3477, 2003     

Infinitely renormalizable diffeomorphisms of the disk at the boundary of chaos

We show that, among area contracting embeddings of the 2-disk, infinitely renormalizable maps with a bounded geometry either have positive topological entropy or correspond to a cascade of period doubling.

     

Magnetic silica colloids for catalysis

Monodisperse magnetizable colloidal silica particles in a stable dispersion have been functionalized with a homogeneous catalyst: a PCP–pincer Pd-complex. In a proof-of-principle experiment we demonstrate the catalytic activity of the colloids in a C–C bond formation reaction. Advantages of the magnetic silica carriers are the large surface-to-volume ratio and the easy recovery by magnetic separation. After magnetic separation, the catalyst-loaded particles are readily redispersed for further use.     

A hybrid genetic algorithm-heuristic for a two-dimensional orthogonal packing problem

In this paper we address a two-dimensional (2D) orthogonal packing problem, where a fixed set of small rectangles has to be placed on a larger stock rectangle in such a way that the amount of trim loss is minimized. The algorithm we propose hybridizes a placement procedure with a genetic algorithm based on random keys. The approach is tested on a set of instances taken from the literature and compared with other approaches. The computation results validate the quality of the solutions and the effectiveness of the proposed algorithm.     

Should Epstein strip arrangement be changed?

The paper describes effect of texture on the anisotropy of magnetic properties and shows that an Epstein strip arrangement including strips cut in a direction 45° to the rolling direction gives property values that are closer to the average values than the traditional RD+TD arrangement.     

Consequences of magnetic aging for iron losses in electrical steels

Electrical steels, when submitted to operation, present continuous decrease of their magnetic properties, depending on the carbon content. This effect is attributed to the increase of the size of carbides, a process also known as coarsening or Ostwald Ripening. Loss separation can offer a better understanding of this phenomenon. Experimental results show that all effect of aging is inside the hysteresis loss component, with the excess losses unaffected. The carbon content in electrical steels should be less than 25 ppm to avoid magnetic aging.     

On γ-hyperelliptic Numerical Semigroups

This work was realized while the author was ICTP (Trieste - Italy) with a grant from the International Atomic Energy Agency and UNESCO.