The weakness of being cohesive,thin or free in reverse mathematics

Informally, a mathematical statement is robust if its strength is left unchanged under variations of the statement. In this paper, we investigate the lack of robustness of Ramsey’s theorem and its consequence under the frameworks of reverse mathematics and computable reducibility. To this end, we study the degrees of unsolvability of cohesive sets for different uniformly computable sequence of sets and identify different layers of unsolvability. This analysis enables us to answer some questions of Wang about how typical sets help computing cohesive sets.     

Sard theorems for Lipschitz functions and applications in optimization

We establish a “preparatory Sard theorem” for smooth functions with a partially affine structure. By means of this result, we improve a previous result of Rifford [17, 19] concerning the generalized (Clarke) critical values of Lipschitz functions defined as minima of smooth functions. We also establish a nonsmooth Sard theorem for the class of Lipschitz functions from R^d to R^p that can be expressed as finite selections of C^k functions (more generally, continuous selections over a compact countable set). This recovers readily the classical Sard theorem and extends a previous result of Barbet–Daniilidis–Dambrine [1] to the case p > 1. Applications in semi-infinite and Pareto optimization are given.     

Chemiluminescent probe for the in vitro detection of protease activity

A strategy involving the use of a self-immolative linker has been investigated for the chemiluminescent sensing of proteases. The reactive linker enabled the release of a 1,2-dioxetane light precursor. As a proof of principle, caspase-3, a key peptidase involved in apoptosis has been targeted. An in vitro assay has been carried out and proved the decomposition of the linker and the selectivity for caspase-3.     

The influence of halide-mediated oxidation on algae-born adhesives

Adhesive materials extracted from the brown algae Fucus Serratus were studied. These adhesives are composed of cross-linked alginate and polyphenols oxidized in the presence of KI or KBr. All formulations were capable of adhering to a variety of surfaces, however the adhesion properties were influenced by the halide used. SAXS and TEM experiments revealed that oxidized polyphenols self-assemble into chain-like objects, irrespective of the oxidation conditions. Yet, slight differences in the aggregate size were detected. QCM-D results showed that the kinetics of the oxidation was faster with iodide than with bromide. Moreover, oxidation with iodide generates stiffer networks, suggesting that the interaction between the alginate and the polyphenol could be the cause of the reduced adhesion.     

Characterization of a sCMOS‐based high‐resolution imaging system

The detection system is a key part of any imaging station. Here the performance of the novel sCMOS‐based detection system installed at the ID17 biomedical beamline of the European Synchrotron Radiation Facility and dedicated to high‐resolution computed‐tomography imaging is analysed. The system consists of an X‐ray–visible‐light converter, a visible‐light optics and a PCO.Edge5.5 sCMOS detector. Measurements of the optical characteristics, the linearity of the system, the detection lag, the modulation transfer function, the normalized power spectrum, the detective quantum efficiency and the photon transfer curve are presented and discussed. The study was carried out at two different X‐ray energies (35 and 50 keV) using both 2× and 1× optical magnification systems. The final pixel size resulted in 3.1 and 6.2 µm, respectively. The measured characteristic parameters of the PCO.Edge5.5 are in good agreement with the manufacturer specifications. Fast imaging can be achieved using this detection system, but at the price of unavoidable losses in terms of image quality. The way in which the X‐ray beam inhomogeneity limited some of the performances of the system is also discussed.     

Stochastic Cahn–Hilliard equation with singular nonlinearity and reflection

We consider a stochastic partial differential equation with logarithmic (or negative power) nonlinearity, with one reflection at 0 and with a constraint of conservation of the space average. The equation, driven by the derivative in space of a space–time white noise, contains a bi-Laplacian in the drift. The lack of the maximum principle for the bi-Laplacian generates difficulties for the classical penalization method, which uses a crucial monotonicity property. Being inspired by the works of Debussche and Zambotti, we use a method based on infinite dimensional equations, approximation by regular equations and convergence of the approximated semigroup. We obtain existence and uniqueness of a solution for nonnegative initial conditions, results on the invariant measures, and on the reflection measures.     

MIL-96, a porous aluminum trimesate 3D structure constructed from a hexagonal network of 18-membered rings and mu3-oxo-centered trinuclear units

A new aluminum trimesate Al12O(OH)18(H2O)3(Al2(OH)4)[btc]6.24H2O, denominated MIL-96, was synthesized under mild hydrothermal conditions (210 degrees C, 24 h) in the presence of 1,3,5-benzenetricarboxylic acid (trimesic acid or H3btc) in water. Hexagonal crystals, allowing a single-crystal XRD analysis, are grown from a mixture of trimethyl 1,3,5-benzenetricarboxylate (Me3btc), HF, and TEOS. The MIL-96 structure exhibits a three-dimensional (3D) framework containing isolated trinuclear mu3-oxo-bridged aluminum clusters and infinite chains of AlO4(OH)2 and AlO2(OH)4 octahedra forming a honeycomb lattice based on 18-membered rings. The two types of aluminum groups are connected to each other through the trimesate species, which induce corrugated chains of aluminum octahedra, linked via mu2-hydroxo bonds with the specific -cis-cis-trans- sequence. The 3D framework of MIL-96 reveals three types of cages. Two of them, centered at the special positions 0 0 0 and 2/3 1/3 1/4, have estimated pore volumes of 417 and 635 A3, respectively, and encapsulate free water molecules. The third one has a smaller pore volume and contains disordered aluminum octahedral species (Al(OH)6). The solid-state NMR characterization is consistent with crystal structure and elemental and thermal analyses. The four aluminum crystallographic sites are resolved by means of 27Al 3QMAS technique. This product is able to sorb both carbon dioxide and methane at room temperature (4.4 mmol.g(-1) for CO2 and 1.95 mmol.g(-1) for CH4 at 10 bar) and hydrogen at 77 K (1.91 wt % under 3 bar).     

Synthesis and applications of copillar[5]arene dithiols

Abstract

A novel copillar[4+1]arene incorporating alkylthiol substituents was synthesised in three steps and structurally characterised as the first example of a pillar[n]arene to incorporate two terminal thiols on the same aromatic ring. The macrocycle was attached to gold electrodes through a standard dipping technique. Cyclic voltammetry demonstrated selectivity for Li⁺ over other alkali metal cations. The copillar[4+1]arene was also used as a capping agent in the preparation of 3 nm gold nanoparticles.