Domination spaces and factorization of linear and multilinear summing operators

[EN] It is well known that not every summability property for multilinear operators leads to a factorization theorem. In this paper we undertake a detailed study of factorization schemes for summing linear and nonlinear operators. Our aim is to integrate under the same theory a wide family of classes of mappings for which a Pietsch type factorization theorem holds. Our construction includes the cases of absolutely p-summing linear operators, (p, sigma)-absolutely continuous linear operators, factorable strongly p-summing multilinear operators, (p(1), ... , p(n))-dominated multilinear operators and dominated (p(1), ... , p(n); sigma)-continuous multilinear operators.Supported by the Ministerio de Economia y Competitividad (Spain) under Grant MTM2015-66823-C2-2. Supported by the Ministerio de Economia y Competitividad (Spain) under Grant MTM2012-36740-C02-02.Achour, D.; Dahia, E.; Rueda, P.; Sánchez Pérez, EA. (2016). Domination spaces and factorization of linear and multilinear summing operators. Quaestiones Mathematicae. 39(8):1071-1092. https://doi.org/10.2989/16073606.2016.1253627S1071109239

Laser smoothing of sub-micron grooves in hydroxyl-rich fused silica

Nano- to micrometer-sized surface defects on UV-grade fused silica surfaces are known to be effectively smoothed through the use of high-temperature localized CO{sub 2} laser heating, thereby enhancing optical properties. However, the details of the mass transport and the effect of hydroxyl content on the laser smoothing of defective silica at submicron length scales is still not completely understood. In this study, we examine the morphological evolution of sub-micron, dry-etched periodic surface structures on type II and type III SiO{sub 2} substrates under 10.6 {micro}m CO{sub 2} laser irradiation using atomic force microscopy (AFM). In-situ thermal imaging was used to map the transient temperature field across the heated region, allowing assessment of the T-dependent mass transport mechanisms under different laser-heating conditions. Computational fluid dynamics simulations correlated well with experimental results, and showed that for large effective capillary numbers (N{sub c} > 2), surface diffusion is negligible and smoothing is dictated by capillary action, despite the relatively small spatial scales studied here. Extracted viscosity values over 1700-2000K were higher than the predicted bulk values, but were consistent with the surface depletion of OH groups, which was confirmed using confocal Raman microscopy

Surface Aggregation of Urinary Proteins and Aspartic Acid-Rich Peptides on the Faces of Calcium Oxalate Monohydrate Investigated by In Situ Force Microscopy

The growth of calcium oxalate monohydrate in the presence of Tamm-Horsfall protein (THP), osteopontin, and the 27-residue synthetic peptides (DDDS)6DDD and (DDDG)6DDD (D = aspartic acid, S = serine, and G = glycine) was investigated via in situ atomic force microscopy. The results show that these four growth modulators create extensive deposits on the crystal faces. Depending on the modulator and crystal face, these deposits can occur as discrete aggregates, filamentary structures, or uniform coatings. These proteinaceous films can lead to either the inhibition of or an increase in the step speeds (with respect to the impurity-free system), depending on a range of factors that include peptide or protein concentration, supersaturation, and ionic strength. While THP and the linear peptides act, respectively, to exclusively increase and inhibit growth on the \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\left( {\bar{1}01} \right)$$\end{document} face, both exhibit dual functionality on the (010) face, inhibiting growth at low supersaturation or high modulator concentration and accelerating growth at high supersaturation or low modulator concentration. Based on analyses of growth morphologies and dependencies of step speeds on supersaturation and protein or peptide concentration, we propose a picture of growth modulation that accounts for the observations in terms of the strength of binding to the surfaces and steps and the interplay of electrostatic and solvent-induced forces at the crystal surface

Entropy of Molecular Binding at Solvated Mineral Surfaces

We present thermodynamic integration simulations for the binding of mannose and methanoic acid onto the {10.4} calcite surface producing free energy of binding values of −2.89 and −1.64 kJ mol–1, respectively. We extract the entropy of binding from vacuum-based simulations and use these values to determine the entropy of binding for surface water molecules which is ∼6 J mol–1 K–1

Re-branding Abu Dhabi: From oil giant to energy titan

This article presents a case study of Abu Dhabi\u27s \u27energy re-branding\u27 since 2005 when it declared its intention to transform itself from an oil exporter to a total energy giant that also embraces alternative (renewable and nuclear) energy. The first part of the article identifies the benefits of this policy for Abu Dhabi\u27s external diplomacy but argues that the real driver is the emirate\u27s domestic gas shortage and its effects on economic diversification and political legitimacy. The second part of the article discusses the motivations and interactions of local and foreign agents by focusing on the implementation of alternative energy platforms. It therefore provides a rare glimpse of the policy-making process in Abu Dhabi. The final part of the article examines the extent to which energy re-branding may be linked to a process by the government to reiterate, reinterpret and repudiate Emirati identity in order to enhance regime legitimacy in the twenty-first century. © 2012 Macmillan Publishers Ltd

Tuning hardness in calcite by incorporation of amino acids

Structural biominerals are inorganic/organic composites that exhibit remarkable mechanical properties. However, the structure–property relationships of even the simplest building unit—mineral single crystals containing embedded macromolecules—remain poorly understood. Here, by means of a model biomineral made from calcite single crystals containing glycine (0–7 mol%) or aspartic acid (0–4 mol%), we elucidate the origin of the superior hardness of biogenic calcite. We analysed lattice distortions in these model crystals by using X-ray diffraction and molecular dynamics simulations, and by means of solid-state nuclear magnetic resonance show that the amino acids are incorporated as individual molecules. We also demonstrate that nanoindentation hardness increased with amino acid content, reaching values equivalent to their biogenic counterparts. A dislocation pinning model reveals that the enhanced hardness is determined by the force required to cut covalent bonds in the molecules

Lawson criterion for ignition exceeded in an inertial fusion experiment

For more than half a century, researchers around the world have been engaged in attempts to achieve fusion ignition as a proof of principle of various fusion concepts. Following the Lawson criterion, an ignited plasma is one where the fusion heating power is high enough to overcome all the physical processes that cool the fusion plasma, creating a positive thermodynamic feedback loop with rapidly increasing temperature. In inertially confined fusion, ignition is a state where the fusion plasma can begin "burn propagation" into surrounding cold fuel, enabling the possibility of high energy gain. While "scientific breakeven" (i.e., unity target gain) has not yet been achieved (here target gain is 0.72, 1.37 MJ of fusion for 1.92 MJ of laser energy), this Letter reports the first controlled fusion experiment, using laser indirect drive, on the National Ignition Facility to produce capsule gain (here 5.8) and reach ignition by nine different formulations of the Lawson criterion