Early transition metal dopants in cuprous oxide: To spin or not to spin

We present a trend study of a large variety of dopants at the cation site in Cu₂O (i.e. substituting Cu), focussing largely on the early 3d-, 4d-, and 5d-transition metals (TMs) in which many of them are known to be non-magnetic. We also include s-, sp- and d¹⁰-metals for comparison. We find that doping with sp-elements results in zero spin moment while dopants with a partially filled d-band show a stronger tendency to magnetize and 3d-TM dopants exhibit a larger magnetic moment than most of the 4d- and 5d-TM dopants. From this trend study, we also find a correlation between their substitution enthalpy and associated interatomic relaxations. In particular, Ti-doped Cu₂O appears to be an interesting system, given its “peculiar” ability to exhibit a spin moment when doped with a non-magnetic substituent like Ti. We also find that the interaction between two doped Ti atoms in Ti₂:Cu₂O is predominantly antiferromagnetic, and interestingly (and unexpectedly), this interaction rapidly declines as a function of inter-dopant distance, as in the case for the magnetic late-TM dopants like Co₂:Cu₂O.     

Representations for conditional expectations and applications to pricing and hedging of financial products in Lévy and jump-diffusion setting

In this article, we derive expressions for conditional expectations in terms of regular expectations without conditioning but involving some weights. For this purpose, we apply two approaches: the conditional density method and the Malliavin method. We use these expressions for the numerical estimation of the price of American options and their deltas in a Lévy and jump-diffusion setting. Several examples of applications to financial and energy markets are given including numerical examples.     

A Convenient Access to Chiral Sulfonic Acids

Neomenthyl and trans myrtanyl sulfonic acids are obtained, free from inorganic salts, starting from the corresponding chiral alcohols.