Local convergence of quasi-Newton methods under metric regularity

We consider quasi-Newton methods for generalized equations in Banach spaces under metric regularity and give a sufficient condition for q-linear convergence. Then we show that the well-known Broyden update satisfies this sufficient condition in Hilbert spaces. We also establish various modes of q-superlinear convergence of the Broyden update under strong metric subregularity, metric regularity and strong metric regularity. In particular, we show that the Broyden update applied to a generalized equation in Hilbert spaces satisfies the Dennis–Moré condition for q-superlinear convergence. Simple numerical examples illustrate the results.

On Gruenhage spaces, separating σ-isolated families, and their relatives

We prove that, given a topological space X, the following conditions are equivalent. (α) X is a Gruenhage space. (β) X has a countable cover by sets of small local diameter (property SLD) by F∩G sets. (γ) X has a separating σ-isolated family M⊂F∩G. (δ) X has a one-to-one continuous map into a metric space which has a σ-isolated base of F∩G sets. Besides, we provide an example which shows Fragmentability ⇏ property SLD ⇏ the space to be Gruenhage.

Transport in magnetically ordered Pt nanocontacts

Pt nanocontacts, like those formed in mechanically controlled break junctions, are shown to develop spontaneous local magnetic order. Our density functional calculations predict that a robust local magnetic order exists in the atoms presenting low coordination, i.e., those forming the atom-sized neck. We thus find that the electronic transport can be spin polarized, although the net value of the conductance still agrees with available experimental information. Experimental implications of the formation of this new type of nanomagnet are discussed.

Ordered porous nanomaterials: the merit of small

This paper will introduce the reader to some of the “classical” and “new” families of ordered porous materials which have arisen throughout the past decades and/or years. From what is perhaps the best-known family of zeolites, which even now to this day is under constant research, to the exciting new family of hierarchical porous materials, the number of strategies, structures, porous textures, and potential applications grows with every passing day. We will attempt to put these new families into perspective from a synthetic and applied point of view in order to give the reader as broad a perspective as possible into these exciting materials.

Weighted composition operators on the predual and dual Banach spaces of Beurling algebras on Z

Let vv be a weight sequence on ZZ and let ψ,φψ,φ be complex-valued functions on ZZ such that φ(Z)⊂Zφ(Z)⊂Z. In this paper we study the boundedness, compactness and weak compactness of weighted composition operators Cψ,φCψ,φ on predual Banach spaces c0(Z,1/v)c0(Z,1/v) and dual Banach spaces ℓ∞(Z,1/v)ℓ∞(Z,1/v) of Beurling algebras ℓ1(Z,v)ℓ1(Z,v).

Electrochemical generation of oxygen-containing groups in an ordered microporous zeolite-templated carbon

Zeolite templated carbon (ZTC) was electrochemically oxidized under various conditions, and its chemistry and structural evolution were compared to those produced by conventional chemical oxidation. In both oxidation methods, a general loss of the original structure regularity and high surface area was observed with increasing amount of oxidation. However, the electrochemical method showed much better controllability and enabled the generation of a large number of oxygen functional groups while retaining the original structure of the ZTC. Unlike chemical treatments, highly microporous carbons with an ordered 3-D structure, high surface area (ranging between 1900 and 3500 m2/g) and a large number of oxygen groups (O = 11,000–3300 μmol/g), have been prepared by the electrochemical method. Some insights into the electrooxidation mechanism of carbon materials are proposed from the obtained polarization curves, using ZTC as a model carbon material.