A uniqueness theorem for functions in the extended Selberg class

Recently, we proved that every finite dimensional Alexandrov space is strongly locally Lipschitz contractible. In the present paper, we consider the set \(\mathcal M\) of all isometry classes of Alexandrov spaces of curvature \(\ge -1\) and of fixed dimension having upper diameter bound and lower volume bound, and prove that there exists a constant \(N\) depending on the parameters determining \(\mathcal M\) such that every space in \(\mathcal M\) can be covered by at most \(N\) strongly Lipschitz contractible balls. Also, we prove that there exists a constant \(N^\prime \) depending on \(\mathcal M\) such that every space in \(\mathcal M\) can be covered by at most \(N^\prime \) strongly Lipschitz contractible and convex regions.     

Approximation by Penultimate Extreme Value Distributions

In certain cases the distribution of the normalized maximum of a sample can be better approximated by a sequence of different extreme value distributions than by the final one. We show that these cases are somewhat restricted and that the possible improvement is not spectacular.     

Rates of Convergence for Bivariate Extremes

Under a second order regular variation condition, rates of convergence of the distribution of bivariate extreme order statistics to its limit distribution are given both in the total variation metric and in the uniform metric.     

Domain wall effects in neutron depolarisation in Co-Cr films

The height and stripe width of the domains in Co-Cr films of 300 nm thickness is determined from angle-dependent 3-D neutron depolarisation. The effect on the data due to Bloch walls and due to domain walls identical with column boundaries is discussed. The maximum wall thickness derived is ≈ 2 and ≈ 30 nm, respectively.     

Physical properties of 3-methyl-N-butylpyridinium tetracyanoborate and 1-butyl-1-methylpyrrolidinium tetracyanoborate and ternary LLE data of [3-mebupy]B(CN)4 with an aromatic and an aliphatic hydrocarbon at T = 303.2 K and 328.2 K and p = 0.1 MPa

Several physical properties were determined for the ionic liquids 3-methyl-N-butylpyridinium tetracyanoborate ([3-mebupy]B(CN)₄) and 1-butyl-1-methylpyrrolidinium tetracyanoborate ([1-mebupyr]B(CN)₄), viz. liquid density, viscosity, surface tension, thermal stability, and heat capacity over the temperature range from 283.2 K to 475.2 K and at 0.1 MPa. The density and the surface tension were well correlated with linear equations and the viscosity with a Vogel–Fulcher–Tamman equation. The IL [3-mebupy]B(CN)₄ is stable up to a temperature of 480 K and the IL [1-mebupyr]B(CN)₄ up to a temperature of 548 K.Ternary data for the systems {(benzene + n-hexane), or (toluene + n-heptane), or (p-xylene + n-octane + [3-mebupy]B(CN)₄)} were determined at T = 303.2 K and 328.2 K and p = 0.1 MPa. All experimental data were well correlated with the NRTL model. The values of the experimental and calculated aromatic/aliphatic selectivity are in good agreement with each other. The LLE data of [1-mebupyr]B(CN)₄ were only measured in a 10 vol% aromatic feed for the three systems.     

Estimating extreme bivariate quantile regions

When simultaneously monitoring two possibly dependent, positive risks one is often interested in quantile regions with very small probability p. These extreme quantile regions contain hardly any or no data and therefore statistical inference is difficult. In particular when we want to protect ourselves against a calamity that has not yet occurred, we need to deal with probabilities p?<?1/n, with n the sample size. We consider quantile regions of the form {(x, y)?∈?(0, ∞?)²: f(x, y)?≤?β}, where f, the joint density, is decreasing in both coordinates. Such a region has the property that it consists of the less likely points and hence that its complement is as small as possible. Using extreme value theory, we construct a natural, semiparametric estimator of such a quantile region and prove a refined form of consistency. A detailed simulation study shows the very good statistical performance of the estimated quantile regions. We also apply the method to find extreme risk regions for bivariate insurance claims.     

Cyano-containing ionic liquids for the extraction of aromatic hydrocarbons from an aromatic/aliphatic mixture

Ionic liquids can replace conventional solvents in aromatic/aliphatic extractions, if they have higher aromatic distribution coef- ficients and higher or similar aromatic/aliphatic selectivities. Also physical properties, such as density and viscosity, must be taken into account if a solvent is applied in an industrial extraction process. Cyano-containing ionic liquids have a lower den- sity than the benchmark solvent sulfolane and a higher viscosity. Sulfolane is from a hydrodynamic point of view a better sol- vent than ionic liquids for the aromatic/aliphatic extraction. The most suitable ionic liquids for the extraction of aromatic hy- drocarbons from a mixture of aromatic and aliphatic hydrocarbons are [bmim]C(CN)3, [3-mebupy]N(CN)2, [3-mebupy]C(CN)3, [3-mebupy]B(CN)4 and [mebupyrr]B(CN)4. They have factors of 1.2-2.3 higher mass-based distribution coefficients than sul- folane and a similar or higher, up to a factor of 1.9 higher, aromatic/aliphatic selectivity than sulfolane. The IL [3-mebupy]N(CN)2 is a better extractant for the separation of toluene from a mixture of toluene/n-heptane in a pilot plant Ro- tating Disc Contactor (RDC) than sulfolane.     

Imaging cytoplasmic cAMP in mouse brainstem neurons

Background  

cAMP is an ubiquitous second messenger mediating various neuronal functions, often as a consequence of increased intracellular Ca²⁺ levels. While imaging of calcium is commonly used in neuroscience applications, probing for cAMP levels has not yet been performed in living vertebrate neuronal tissue before.