The dose dependence of 45 keV V+ and Bi+Ion sputtering yield of copper

The sputtering yield of 45 keV V⁺ ions on copper is found to decrease with increasing dose even for very large doses, whilst the yield of 45 keV Bi⁺ ions on copper increases with increasing dose until approximately ten times the projected range of the Bi⁺ ions has been sputtered away. The fate of the incoming V⁺ and Bi⁺ ions was investigated. A radiotracer technique showed that vanadium accumulated on the target surface, whilst bismuth diffused into the target, as was seen by means of Rutherford-scattering of light ions.     

Convex conservation laws with discontinuous coefficients. existence,uniqueness and asymptotic behavior

Existence and uniqueness is proved, in the class of functions satisfying a wave entropy condition, of weak solutions to a conservation law with a flux function that may depend discontinuously on the space variable. The large time limit is then studied, and explicit formulas for this limit is given in the case where the initial data as well as the x dependency of the flux vary periodically. Throughout the paper, front tracking is used as a method of analysis. A numerical example which illustrates the results and method of proof is also presented.     

On the pricing and hedging of volatility derivatives

The paper considers the pricing of a range of volatility derivatives, including volatility and variance swaps and swaptions. Under risk-neutral valuation closed-form formulae for volatility-average and variance swaps for a variety of diffusion and jump-diffusion models for volatility are provided. A general partial differential equation framework for derivatives that have an extra dependence on an average of the volatility is described. Approximate solutions of this equation are given for volatility products written on assets for which the volatility process fluctuates on a timescale that is fast compared with the lifetime of the contracts, analysing both the 'outer' region and, by matched asymptotic expansions, the 'inner' boundary layer near expiry.     

Poverty,inequality and mathematics performance: the case of South Africa’s post-apartheid context

South Africa’s recent history of apartheid, its resultant high levels of poverty and extreme social and economic distance between rich and poor continue to play-out in education in complex ways. The country provides a somewhat different context for exploring the relationship between SES and education than other countries. The apartheid era only ended in 1994, after which education became the vehicle for transforming society and a political rhetoric of equity and quality education for all was prioritized. Thus education focused on redressing inequalities; and major curriculum change, with on-going revisions, was attempted. In this sense engagement with SES and education became foregrounded in policy, political discourse and research literature. Yet for all the political will and rhetoric little has been achieved and indicators are that inequality has worsened in mathematics education, where it is particularly pronounced. This paper proposes that continued research confirming poverty–underachievement links, which suggest an inevitability of positive correlations, is unhelpful. Instead we should explore issues of disempowerment and agency, constraints and possibilities, and the complex interplay of factors that create these widely established national statistics while simultaneously defying them in particular local contexts. Such research could shift the focus from a discourse of deficit and helplessness towards a discourse of possibilities in the struggle for equity and quality education for all.     

Developing Bicatalytic Cascade Reactions: Ruthenium-catalyzed Hydrogen Generation From Methanol

A novel state-of-the-art bicatalytic system for hydrogen generation from aqueous methanol at low temperature and base concentration is described. Applying two molecularly defined ruthenium complexes A and B3 for methanol dehydrogenation at the same time under the same conditions, a synergistic effect is observed. This behavior is explained by the increase of the dehydrogenation of formic acid, which is formed as an intermediate, by the second catalyst B3 .     

Linear Tetraphenylmethane‐Based Thioether Oligomers Stabilising an Entire Gold Nanoparticle by Enwrapping

The design and synthesis of a novel linear thioether‐based ligand subunit with a tetraphenylmethane core used in the stabilisation of gold nanoparticles (AuNPs) are presented. Mono‐, tri, penta‐ and heptamers of the ligand have been synthesised and used to stabilise AuNPs by enwrapping. With the exception of the monomer, all ligands provide reliable long‐term stability and redispersibility for the coated nanoparticles in common organic solvents. Despite variation of the oligomer length, all stable particles were of the same size within error tolerance (1.16±0.32 nm for the trimer, 1.15±0.30 nm for the pentamer, 1.17±0.34 nm for the heptamer), as investigated by transmission electron microscopy (TEM). These findings suggest that not only the number of sulfur atoms in the ligand, but also its bulkiness play a crucial role in stabilising the AuNPs. These findings are supported by thermogravimetric analysis (TGA), showing that AuNPs stabilised by the penta‐ or heptamer are passivated by a single ligand. Thermal stability measurements suggest a correlation between ligand coverage and thermal stability, further supporting these findings.     

Multi-Phase Quadrature Domains and a Related Minimization Problem

In this paper we introduce the multi-phase version of the so-called Quadrature Domains (QD), which refers to a generalized type of mean value property for harmonic functions. The well-established and developed theory of one-phase QD was recently generalized to a two-phase version, by one of the current authors (in collaboration). Here we introduce the concept of the multi-phase version of the problem, and prove existence as well as several properties of such solutions. In particular, we discuss possibilities of multi-junction points.     

Second‐Generation Fluorescent Quadracyclic Adenine Analogues: Environment‐Responsive Probes with Enhanced Brightness

Fluorescent base analogues comprise a group of increasingly important molecules for the investigation of nucleic acid structure, dynamics, and interactions with other molecules. Herein, we report on the quantum chemical calculation aided design, synthesis, and characterization of four new putative quadracyclic adenine analogues. The compounds were efficiently synthesized from a common intermediate through a two‐step pathway with the Suzuki–Miyaura coupling as the key step. Two of the compounds, qAN1 and qAN4, display brightnesses (εΦ_F) of 1700 and 2300, respectively, in water and behave as wavelength‐ratiometric pH probes under acidic conditions. The other two, qAN2 and qAN3, display lower brightnesses but exhibit polarity‐sensitive dual‐band emissions that could prove useful to investigate DNA structural changes induced by DNA–protein or –drug interactions. The four qANs are very promising microenvironment‐sensitive fluorescent adenine analogues that display considerable brightness for such compounds.