A method to bypass the lack of solutions in MinSup problems under quasi-equilibrium constraints

MinSup problems with constraints described by quasi-equilibrium problems are considered in Banach spaces. The solutions set of such problems may be empty even in very good situations, so the aim of this paper is twofold. First, we determine appropriate regularizations (called inner regularizations) which allow to reach the value of the original problem. Then, among these regularizations we identify those which allow to bypass the lack of exact solutions to these problems by a suitable concept of “viscosity” solution whose existence is then proved under reasonable assumptions.     

Investigating changes in high-stakes mathematics examinations: a discursive approach

ABSTRACT

This article focuses on the theoretical-methodological question of how to identify reform-induced changes in school mathematics. The issue arose in our project The Evolution of the Discourse of School Mathematics (EDSM), in which we studied transformations in high-stakes examinations taken by students in England at the end of compulsory schooling. We have adopted a conceptualisation that draws on social semiotics and on a communicational approach, according to which school mathematics can be thought of as a discourse. Methods of comparing examinations of different years developed on the basis of this definition enable identification of subtle disparities that are nevertheless significant enough to make an important difference in students’ vision of mathematics, in their performance and, eventually, in their ability to cope with problems that can benefit from the use of mathematics. In this article, we present these methods and argue that they have wider application for comparative studies of school mathematics.     

Bilayer Networks within a Hydrogel Shell: A Robust Chassis for Artificial Cells and a Platform for Membrane Studies

The ability to make artificial lipid bilayers compatible with a wide range of environments, and with sufficient structural rigidity for manual handling, would open up a wealth of opportunities for their more routine use in real‐world applications. Although droplet interface bilayers (DIBs) have been demonstrated in a host of laboratory applications, from chemical logic to biosynthesis reaction vessels, their wider use is hampered by a lack of mechanical stability and the largely manual methods employed in their production. Multiphase microfluidics has enabled us to construct hierarchical triple emulsions with a semipermeable shell, in order to form robust, bilayer‐bound, droplet networks capable of communication with their external surroundings. These constructs are stable in air, water, and oil environments and overcome a critical obstacle of achieving structural rigidity without compromising environmental interaction. This paves the way for practical application of artificial membranes or droplet networks in diverse areas such as medical applications, drug testing, biophysical studies and their use as synthetic cells.     

Direct imaging of o-carborane molecules within single walled carbon nanotubes

Ortho-carborane molecules have been inserted into single walled carbon nanotubes (SWNTs) and imaged directly by high resolution transmission electron microscopy (HRTEM); both discrete molecules and 'zig-zag' 1D chains of o-carborane 'petit pois' were observed to pack into the tubule capillaries.     

A solid-phase route to N-cyanoamides

[reaction: see text] A new method for the solid-phase synthesis of cyanamides is described. The attachment of a secondary amine to solid support is accomplished using Merrifield resin. After functionalization, cleavage is readily achieved with cyanogen bromide to afford the desired cyanamide.     

Extended wedge covariance for wetting and filling transitions

Fluid adsorption on nonplanar and heterogeneous substrates is studied using a simple interfacial model. For systems with short-ranged forces, we find that, by tuning the local strength of the substrate potential, it is possible to find the exact equilibrium interfacial profile as a functional of the wall shape psi x. The tuning of the local substrate potential takes the form of a gauge condition theta x=+/-psi x, where theta x can be interpreted as a local effective contact angle. For wedgelike geometries with asymptotic tilt angle alpha, the midpoint interfacial height and roughness satisfy the same covariance relations previously found for simple linear wedges. For troughlike geometries satisfying the gauge condition, covariance is also found for the two-point correlation function. Predictions for more microscopic Landau and Ising models are also discussed.     

A stereospecific synthesis of vitamin A from 2,2,6-trimethyl-cyclohexanone.

An efficient synthesis of all-(E) vitamin A acetate from 2,2,6-trimethyl-cyclohexanone has been achieved via the intermediacy of 1-(9-acetoxy-3, 7-dimethyl-nona-3,5,7-trien-1-ynyl)-2,2,6-trimethyl-cyclohexanol ( 25 ), readily prepared in high yield by allylic rearrangement of tertiary propenols with glacial acetic acid. The key step in the synthesis is the transformation of 25 to the unsaturated ketone 27 (9-acetoxy-3,7-dimethyl-1-(2,6,6-trimethyl-cyclohex-1-enyl)-nona-3,5,7-trien- 2-one) using a novel vanadium(V)-catalysed rearrangement reaction. The carbonyl in 27 affords the means for the essential isomerization of the adjacent double bond to the (E) isomer and the product is readily transformed into the polyene by reduction and elimination. An overall yield of 18–31% of vitamin A acetate from 2,2,6-trimethyl-cyclohexanone has been realized.     

Detection of ammonium in geological materials by evolved gas analysis

The association of anomalously high levels of ammonium with both metallic and energy mineral deposits is of potential use in mineral exploration. Conventional geochemical methods for detecting NH₄ often provide only whole-rock NH₄ values and do not identify the specific minerals hosting NH₄. They may also lack sensitivity or be prone to interference. Evolved NH₃ analysis is shown to be capable of distinguishing between different NH₄-bearing minerals and can detect NH₄ values down to 120 ppm in rocks hosting silver-gold vein mineralization. Fully quantitative determination of NH₄ by this method is not possible as the NH₃ evolved from minerals during heating partially oxidised; however, amounts of evolved NH₃ do show a moderate positive linear correlation with NH₄ content determined by a modified Kjeldahl method.     

Effects of amine modifiers on retention and peak shape in reversed-phase high-performance liquid chromatography

A systematic evaluation of the effects of 15 different amine modifiers on the retention and peak symmetry of three solutes, a primary, a secondary, and a tertiary amine, is presented. Using automated experimentation, mobile phase combinations for each modifier over a pH range of 2.5 to 8 were investigated. The effect of changing the sodium ion concentration of the mobile phase was also examined. The importance of hydrophobic, ion exchange, and hydrogen bonding interactions as mechanisms for retention and peak symmetry of positively charged solutes is discussed.