Frequency-domain Fourier-transform terahertz spectroscopy of the single-molecule magnet (NEt4)[Mn2(5-Brsalen)2(MeOH)2Cr(CN)6

We have investigated the novel single-molecule magnet (NEt(4))[Mn(2)(5-Brsalen)(2)(MeOH)(2)Cr(CN)(6)] (1; 5-Brsalen = N,N'-ethylenebis(5-bromosalicylidene)iminato anion) using spectroscopic as well as magnetization and susceptibility measurements. Frequency-domain Fourier-transform terahertz electron paramagnetic resonance (FDFT THz-EPR) based on the generation of THz radiation from a synchrotron in combination with inelastic neutron scattering (INS) allows for the discrimination between intermultiplet and intramultiplet transitions. Together with ac/dc magnetic susceptibility measurements the obtained set of data provides a complete characterization of the lowest energetic magnetic excitations. We find that the new compound 1 exhibits much weaker intermolecular interactions than found in the closely related compound: K[Mn(2)(5-Brsalen)(2)(H(2)O)(2)Cr(CN)(6)] (2). Furthermore, two phonon lines in the vicinity of the magnetic excitations are detected.     

A Triptycene‐Based Approach to Solubilising Carbon Nanotubes and C60

We describe herein the synthesis of a triptycene‐based surfactant designed with the ability to solubilise single‐walled carbon nanotubes (SWNTs) and C₆₀ in water through non‐covalent interactions. Furthermore, an amphiphilic naphthalene‐based surfactant with the same ability to solubilise SWNTs and C₆₀ has also been prepared. The compounds synthesised were designed with either two ionic or non‐ionic tails to ensure a large number of supramolecular interactions with the solvent, thereby promoting strong solubilisation. The surfactants produced stable suspensions in which the SWNTs are dispersed and the surfactant/SWNT complexes formed are stable for more than one year. UV/Vis/NIR absorption spectroscopy, TEM and AFM were employed to probe the solubilisation properties of the dispersion of surfactants and SWNTs in water.     

Rectangular amplitudes,conformal blocks,and applications to loop models

In this paper we continue the investigation of partition functions of critical systems on a rectangle initiated in [R. Bondesan, et al., Nucl. Phys. B 862 (2012) 553–575]. Here we develop a general formalism of rectangle boundary states using conformal field theory, adapted to describe geometries supporting different boundary conditions. We discuss the computation of rectangular amplitudes and their modular properties, presenting explicit results for the case of free theories. In a second part of the paper we focus on applications to loop models, discussing in details lattice discretizations using both numerical and analytical calculations. These results allow to interpret geometrically conformal blocks, and as an application we derive new probability formulas for self-avoiding walks.     

Estimation of return values of wave height: consequences of missing observations

Extreme-value statistics is often used to estimate so-called return values (actually related to quantiles) for environmental quantities like wind speed or wave height. A basic method for estimation is the method of block maxima which consists in partitioning observations in blocks, where maxima from each block could be considered independent. Typically a block could be chosen as one year. Large portions of missing data could result in problems for estimation and seems to be an issue not highlighted in detail in the literature. The method of block maxima is here applied to real data and a related simulation study was performed, pointing out that substantially low values tend to increase the estimated return values. A plausible explanation is given by studying the redistribution of probability mass and the implications of this for the behaviours of the tails of distributions.     

The Accumulated Persistence Function,a New Useful Functional Summary Statistic for Topological Data Analysis,With a View to Brain Artery Trees and Spatial Point Process Applications

We start with a simple introduction to topological data analysis where the most popular tool is called a persistence diagram. Briefly, a persistence diagram is a multiset of points in the plane describing the persistence of topological features of a compact set when a scale parameter varies. Since statistical methods are difficult to apply directly on persistence diagrams, various alternative functional summary statistics have been suggested, but either they do not contain the full information of the persistence diagram or they are two-dimensional functions. We suggest a new functional summary statistic that is one-dimensional and hence easier to handle, and which under mild conditions contains the full information of the persistence diagram. Its usefulness is illustrated in statistical settings concerned with point clouds and brain artery trees. The supplementary materials include additional methods and examples, technical details, and the R code used for all examples.     

Volatility skews and extensions of the Libor market model

The paper considers extensions of the Libor market model to markets with volatility skews in observable option prices. The family of forward rate processes is expanded to include diffusions with non-linear forward rate dependence, and efficient techniques for calibration to quoted prices of caps and swaptions are discussed. Special emphasis is put on generalized CEV processes for which closed-form expressions for cap and swaption prices are derived. Modifications of the CEV process which exhibit more appealing growth and boundary characteristics are also discussed. The proposed models are investigated numerically through Crank–Nicholson finite difference schemes and Monte Carlo simulations.     

On Frobenius splitting of orbit closures of spherical subgroups in flag varieties

Let H denote a spherical subgroup within a semisimple algebraic group G. In this paper we study the closures of the finitely many H-orbits in the flag variety of G. Using the language of Frobenius splitting we provide a criterion for these closures to have nice geometric and cohomological properties. We then show how the criterion applies to the spherical subgroups of minimal rank studied by N. Ressayre. Finally, we also provide applications of the criterion to orbit closures which are not multiplicity-free in the sense defined by M. Brion.     

Linearly polarized, single-mode spontaneous emission in a photonic nanowire

We introduce dielectric elliptical photonic nanowires to funnel efficiently the spontaneous emission of an embedded emitter into a single optical mode. Inside a wire with a moderate lateral aspect ratio, the electromagnetic environment is largely dominated by a single guided mode, with a linear polarization oriented along the ellipse major axis. The resulting monomode spontaneous emission is maintained over a broad wavelength range, a key asset of this 1D photonic structure. Our theoretical analysis is completed by an experimental study of GaAs elliptical photonic wires with embedded InAs quantum dots. In particular, the fraction of collected photons with the desired linear polarization can exceed 95%.     

A first low‐resolution difference Fourier map of phosphorus in a membrane protein from near‐edge anomalous diffraction

Crystal diffraction of three membrane proteins (cytochrome bc₁ complex, sarcoplasmic reticulum Ca²⁺ ATPase, ADP‐ATP carrier) and of one nucleoprotein complex (leucyl tRNA synthetase bound to tRNAleu, leuRS:tRNAleu) was tested at wavelengths near the X‐ray K‐absorption edge of phosphorus using a new set‐up for soft X‐ray diffraction at the beamline ID01 of the ESRF. The best result was obtained from crystals of Ca²⁺ ATPase [adenosin‐5′‐(β,γ‐methylene) triphosphate complex] which diffracted out to 7 Å resolution. Data were recorded at a wavelength at which the real resonant scattering factor of phosphorus reaches the extreme value of ?20 electron units. The positions of the four triphosphates of the monoclinic unit cell of the ATPase have been obtained from a difference Fourier synthesis based on a limited set of anomalous diffraction data.     

Asymmetric Transfer Hydrogenation of Ketones Catalyzed by Amino Acid Derived Rhodium Complexes: On the Origin of Enantioselectivity and Enantioswitchability

Amino acid based thioamides, hydroxamic acids, and hydrazides have been evaluated as ligands in the rhodium‐catalyzed asymmetric transfer hydrogenation of ketones in 2‐propanol. Catalysts containing thioamide ligands derived from L ‐valine were found to selectively generate the product with an R configuration (95 % ee), whereas the corresponding L ‐valine‐based hydroxamic acids or hydrazides facilitated the formation of the (S)‐alcohols (97 and 91 % ee, respectively). The catalytic reduction was examined by performing a structure–activity correlation investigation with differently functionalized or substituted ligands and the results obtained indicate that the major difference between the thioamide and hydroxamic acid based catalysts is the coordination mode of the ligands. Kinetic experiments were performed and the rate constants for the reduction reactions were determined by using rhodium–arene catalysts derived from amino acid thioamide and hydroxamic acid ligands. The data obtained show that the thioamide‐based catalyst systems demonstrate a pseudo‐first‐order dependence on the substrate, whereas pseudo‐zero‐order dependence was observed for the hydroxamic acid containing catalysts. Furthermore, the kinetic experiments revealed that the rate‐limiting steps of the two catalytic systems differ. From the data obtained in the structure–activity correlation investigation and along with the kinetic investigation it was concluded that the enantioswitchable nature of the catalysts studied originates from different ligand coordination, which affects the rate‐limiting step of the catalytic reduction reaction.