A nonconvex approach to low‐rank matrix completion using convex optimization

This paper deals with the problem of recovering an unknown low‐rank matrix from a sampling of its entries. For its solution, we consider a nonconvex approach based on the minimization of a nonconvex functional that is the sum of a convex fidelity term and a nonconvex, nonsmooth relaxation of the rank function. We show that by a suitable choice of this nonconvex penalty, it is possible, under mild assumptions, to use also in this matrix setting the iterative forward–backward splitting method. Specifically, we propose the use of certain parameter dependent nonconvex penalties that with a good choice of the parameter value allow us to solve in the backward step a convex minimization problem, and we exploit this result to prove the convergence of the iterative forward–backward splitting algorithm. Based on the theoretical results, we develop for the solution of the matrix completion problem the efficient iterative improved matrix completion forward–backward algorithm, which exhibits lower computing times and improved recovery performance when compared with the best state‐of‐the‐art algorithms for matrix completion. Copyright © 2016 John Wiley & Sons, Ltd.     

Development and characterisation of an XeCl excimer laser-generated soft-X-ray plasma source and its applications

Summary A large-aperture, long-pulse XeCl excimer laser has been used to generate a soft-X-ray plasma source. Several laser optical configurations have been employed to optimise X-ray emission, including positive-branch unstable resonators and injection by seeding the gain region of the laser with a small commercial excimer laser, resulting in power densities in the range 10¹²–10¹⁴ W cm⁻². The characteristics of the plasma source for each different laser configuration and for different target materials are investigated. The most suitable source conditions (spectral energy distribution, time duration, etc.) for specific applications are discussed. Supported by the Royal Society, UK. Supported by INFM, Italy.     

Pulsed X-ray diode with a long-lifetime plasma cathode

6 shots, the X-ray dose, uniformity, and ionisation rate values guarantee an effective preionisation of excimer laser discharges. Owing to both the long lifetime and the substantial absence of maintenance, this X-ray diode seems suitable to preionise commercial gas lasers, such as excimer and TEA CO₂ lasers. Received: 28 August 1998 / Revised version: 16 November 1998 / Published online: 24 February 1999     

A novel oxidative side-chain transformation of α-amino acids and peptides by methyltrioxorhenium/H2O2 system

N-Boc derivatives of Met, Cys, and Trp, the properties of which resemble those of the respective amino acid residues present in proteins, are efficiently oxidized by methyltrioxorhenium and H₂O₂. A high regioselectivity for the oxidation of these residues when embedded into peptides was also found.     

The Meyer-Schuster rearrangement: a new synthetic strategy leading to prostaglandins and their drug analogs, Bimatoprost and Latanoprost

Gold(I) mediated Meyer-Schuster rearrangement for the installation of the ‘lower’ side chain of prostaglandins and their analogs has been developed. This Au-mediated rearrangement, featuring a low catalyst loading and mild reaction conditions, has been demonstrated to be an efficient alternative to the standard Horner-Wadsworth-Emmons reaction in prostaglandin chemistry. Moreover, the present results provide a new synthetic process leading to pharmacologically active prostanoids: Latanoprost and Bimatoprost, that continue to hold key positions in the anti-glaucoma drug market.     

Scattering by small defects in the neighbourhood of a fluid-solid interface

The scattering of incident plane elastic waves by a varietyof different defects that lie upon a fluid-solid interface isconsidered here using matched asymptotic expansions. The expansionscheme is developed in terms of a parameter , the ratio of typicaldefect length scale to a typical wavelength of the incidentfield, taken to be small. Three different canonical situations occur and these are illustratedvia three specific examples treated here: a rigid strut, anedge crack, and a rigid strip. In each case the leading-ordermatching is performed to identify the leading-order contributionof the defect to the acoustic field in the far field. In particular,each defect is identified with a source of dipole response ininterfacial stress of displacement. It is shown in the limit as s<<s1 that in the inner problemsthe fluid and solid pieces uncouple in a particularly convenientmanner allowing analytical solutions to be deduced. These arethen matched with appropriate outer solutions.     

Conventional and modified Schwarzschild objective for EUV lithography: design relations

The design criteria of a Schwarzschild-type optical system are reviewed in relation to its use as an imaging system in an extreme ultraviolet lithography setup. Both the conventional and the modified reductor imaging configurations are considered, and the respective performances, as far as the geometrical resolution in the image plane is concerned, are compared. In this connection, a formal relation defining the modified configuration is elaborated, refining a rather naïve definition presented in an earlier work. The dependence of the geometrical resolution on the image-space numerical aperture for a given magnification is investigated in detail for both configurations. So, the advantages of the modified configuration with respect to the conventional one are clearly evidenced. The results of a semi-analytical procedure are compared with those obtained from a numerical simulation performed by an optical design program. The Schwarzschild objective based system under implementation at the ENEA Frascati Center within the context of the Italian FIRB project for EUV lithography has been used as a model. Best-fit functions accounting for the behaviour of the system parameters vs. the numerical aperture are reported; they can be a useful guide for the design of Schwarzschild objective type optical systems.     

Further comparisons between the conventional and the modified Schwarzschild objectives

The performance of the modified Schwarzschild objective configuration in comparison with the ordinary configuration is further investigated, completing the analysis presented in a previous work, which was concerned with the trend of the image-plane resolution against the numerical aperture. Here, we compare the third-order aberration coefficients in both configurations, illustrating the dependence of each coefficient on both the on-axis object position and the numerical aperture. This conveys the tolerances of the two configurations to lateral and mirrors’ axial misalignments. Also, the nonconcentric mirror configuration is considered and the relative performance confronted with that of the modified configuration. PACS 42.15.Eq; 42.82.Cr     

Mobility of ions in fluid Kr at various densities

We report measurements of mobility of positive and negative ions in fluid Kr at various densities. The experimental results are discussed with the Langevin theory. Comparison between self-diffusion of ions is made.     

B and collider physics: Working group report

This report summarises the work done during WHEPP-6 (Institute of Mathematical Sciences, Chennai, India, Jan 3–15, 2000) in Working group on ‘B and collider physics’.