Matrix algebras in Quasi-Newton methods for unconstrained minimization

Summary.  In this paper a new class of quasi-Newton methods, named ℒQN, is introduced in order to solve unconstrained minimization problems. The novel approach, which generalizes classical BFGS methods, is based on a Hessian updating formula involving an algebra ℒ of matrices simultaneously diagonalized by a fast unitary transform. The complexity per step of ℒQN methods is O(n log n), thereby improving considerably BFGS computational efficiency. Moreover, since ℒQN's iterative scheme utilizes single-indexed arrays, only O(n) memory allocations are required. Global convergence properties are investigated. In particular a global convergence result is obtained under suitable assumptions on f. Numerical experiences [7] confirm that ℒQN methods are particularly recommended for large scale problems. Received December 30, 2001 / Revised version received December 20, 2001 / Published online November 27, 2002 Mathematics Subject Classification (1991): 65K10 Correspondence to: P. Zellini     

A new reverse mode light shutter from silica-dispersed liquid crystals

Nanoparticle dispersions in liquid crystalline materials at low concentrations allow both investigating the formation of defects in liquid crystal (LC) and enhancing the light-scattering properties of LC optical devices. Reverse mode LC dispersions are LC devices, which look like transparent in their OFF state, when no electric field is applied, and opaque in their ON state. In this paper, a new reverse mode device, formed by a dispersion of a LC mixture in a silica nanoparticle crosslinked network, is presented. The morphology and the electro-optical properties of these silica nanoparticle/LC composites were investigated for two different LC mixtures with a negative dielectric anisotropy. The observed transmittances and relaxation times were found to depend strongly on the silica amount and chemical–physical properties of LC used in the sample preparation.     

Gold nanoparticles stabilized by modified halloysite nanotubes for catalytic applications

A highly sustainable prototype of a flow system based on gold nanoparticles (4.2 nm) supported on thiol‐functionalized halloysite nanotubes (HNTs) was developed for catalytic applications. The catalytic performances were evaluated using the reduction of 4‐nitrophenol to 4‐aminophenol as a model system. Under the best experimental conditions (0.0001 mol%, 1.97 × 10^?8 mg of Au nanoparticles), an impressive apparent turnover frequency value up to 2 204 530 h^?1 was achieved and the halloysite‐based catalyst showed full recyclability even after ten cycles. The high catalytic activity confirms the importance of the use of HNTs as support for Au nanoparticles that can exert a synergistic effect both as medium for transfer of electrons from borohydride ions to 4‐nitrophenol and by modulating interfacial electron transfer dynamics. With the application of flow technology, the obtained heterogeneous HNT@Au catalyst was fully recovered and reused for at least one month.     

Evidence of electron wave function delocalization in CdSe/CdS asymmetric nanocrystals

We studied the delocalization of electron wave function in asymmetric CdSe/CdS nanocrystals, consisting of a spherical CdSe dot embedded in an elongated CdS shell, by means of a pump–probe technique. By comparing the transient spectra obtained upon pumping the band edge transition of the CdSe in CdSe/CdS heterostructure and in a bare CdSe dot, we observed the delocalization of electron wave function at the CdSe/CdS interface.     

Dots in rods as polarized single photon sources

We report the evidence of a polarized single photon flux from a colloidal nanoparticle. We analyze, by time and polarization resolved spectroscopy measurements, the polarization behavior of a single CdSe/CdS core/shell dot in rod, achieving a polarization ratio at room temperature of ∼75% and a lifetime of the excited state of ∼11 ns.     

An abstract characterization of Thompson’s group F

We show that Thompson’s group F is the symmetry group of the ‘generic idempotent’. That is, take the monoidal category freely generated by an object A and an isomorphism A ? A→A; then F is the group of automorphisms of A.     

Leibniz rules and reality conditions

An analysis is made of reality conditions within the context of non-commutative geometry. We show that if a covariant derivative satisfies a given left Leibniz rule then a right Leibniz rule fixes the reality condition for the covariant derivative itself. We show also that the map which determines the right Leibniz rule must satisfy the braid equation if the extension of the covariant derivative to tensor products is to satisfy the reality condition. Received: 6 June 2000 / Published online: 9 August 2000     

Universality of the string picture in lattice gauge systems

We test the conjecture that the infrared behaviour of gauge theories is described by an effective string picture by analyzing the Monte Carlo data of five different three- and four-dimensional lattice gauge systems, SU(2) and SU(3) included. We find that there is a unique string of fermionic type which fits well to the whole set of analyzed data.