Luminescence properties of Ba2NaNb5O15 crystals activated with Sm, Eu, Tb or Dy ions

Single crystals of Ba₂NaNb₅O₁₅ (BNN) singly doped with Sm³⁺, Eu³⁺, Tb³⁺ or Dy³⁺ have been grown by means of the flux growth method. Their visible emission and excitation spectra and the decay profiles of the luminescence have been measured at room temperature. All spectral features are significantly inhomogeneously broadened in consequence of the structural disorder of the host and of the doping mechanisms. The analysis of the observed spectra allows formulating an hypothesis about the site occupancy of the active ions in the BNN lattice.     

Diffeomorphic vs Isotopic Links in Lens Spaces

Links in lens spaces may be defined to be equivalent by ambient isotopy or by diffeomorphism of pairs. In the first case, for all the combinatorial representations of links, there is a set of Reidemeister-type moves on diagrams connecting isotopy equivalent links. In this paper, we provide a set of moves on disk, band and grid diagrams that connects diffeo-equivalent links: there are up to four isotopy equivalent links in each diffeo-equivalence class. Moreover, we investigate how the diffeo-equivalence relates to the lift of the link in the 3-sphere: in the particular case of oriented primitive-homologous knots, the lift completely determines the knot class in L(p, q) up to diffeo-equivalence, and thus only four possible knots up to isotopy equivalence can have the same lift.     

Rates of C-S bond cleavage in tert-alkyl phenyl sulfide radical cations

[reaction: see text] Radical cations of tert-alkyl phenyl sulfides 1-4 have been generated photochemically in MeCN in the presence of the N-methoxyphenanthridinium cation (MeOP(+)), and the rates of C-S bond cleavage have been determined by laser flash photolysis.     

Time irregularity of generalized Ornstein–Uhlenbeck processes

This Note is concerned with the properties of solutions to a linear evolution equation perturbed by a cylindrical Lévy process. It turns out that solutions, under rather weak requirements, do not have a càdlàg modification. Some natural open questions are also stated.     

A note on scale functions and the time value of ruin for Lévy insurance risk processes

We examine discounted penalties at ruin for surplus dynamics driven by a general spectrally negative Lévy process; the natural class of stochastic processes which contains many examples of risk processes which have already been considered in the existing literature. Following from the important contributions of [Zhou, X., 2005. On a classical risk model with a constant dividend barrier. North Am. Act. J. 95-108] we provide an explicit characterization of a generalized version of the Gerber-Shiu function in terms of scale functions, streamlining and extending results available in the literature.     

Securitizing and tranching longevity exposures

We consider the problem of optimally designing longevity risk transfers under asymmetric information. We focus on holders of longevity exposures that have superior knowledge of the underlying demographic risks, but are willing to take them off their balance sheets because of capital requirements. In equilibrium, they transfer longevity risk to uninformed agents at a cost, where the cost is represented by retention of part of the exposure and/or by a risk premium. We use a signalling model to quantify the effects of asymmetric information and emphasize how they compound with parameter uncertainty. We show how the cost of private information can be minimized by suitably tranching securitized cashflows, or, equivalently, by securitizing the exposure in exchange for an option on mortality rates. We also investigate the benefits of pooling several longevity exposures and the impact on tranching levels.     

Hausdorff measures of subgroups of \mathbb{R }/\mathbb{Z } and \mathbb{R }

For a sequence $\underline{u}=(u_n)_{n\in \mathbb{N }}$ of integers, let $t_{\underline{u}}(\mathbb{T })$ be the group of all topologically $\underline{u}$ -torsion elements of the circle group $\mathbb{T }:=\mathbb{R }/\mathbb{Z }$ . We show that for any $s\in ]0,1[$ and $m\in \{0,+\infty \}$ there exists $\underline{u}$ such that $t_{\underline{u}}(\mathbb{T })$ has Hausdorff dimension $s$ and $s$ -dimensional Hausdorff measure equal to $m$ (no other values for $m$ are possible). More generally, for dimension functions $f,g$ with $f(t)\prec g(t), f(t)\prec \!\!\!\prec t$ and $g(t)\prec \!\!\!\prec t$ we find $\underline{u}$ such that $t_{\underline{u}}(\mathbb{T })$ has at the same time infinite $f$ -measure and null $g$ -measure.