Affine Slice for the Coadjoint Action of a Class of Biparabolic Subalgebras of a Semisimple Lie Algebra

In this article, we give a simple explicit construction of an affine slice for the coadjoint action of a certain class of biparabolic (also called seaweed) subalgebras of a semisimple Lie algebra over an algebraically closed field of characteristic zero. In particular, this class includes all Borel subalgebras.     

Ultrafast vibrational dynamics observed in higher electronic excited states of iodine using pump-UV DFWM spectroscopy

By using a combination of an initial pump pulse and a degenerate four-wave mixing process, we show that an interrogation of the vibrational dynamics occurring in different electronic states of molecules is possible. The technique is applied to iodine. The initial pump pulse is used to populate the B((3)Pi) state of molecular iodine in the gas phase. Now, by using an internal time delay in the DFWM process, which is resonant with the transition between the B state and a higher lying ion-pair state, the vibrational dynamics of the B state and the ion-pair state could be observed. States of even symmetry are investigated, which are accessed by a one photon transition from the B state. By a proper choice of the wavelengths used for the pump and DFWM beams, the dynamics of ion-pair states belonging to two different tiers are monitored.     

Multi-Component Ginzburg-Landau Theory: Microscopic Derivation and Examples

This paper consists of three parts. In part I, we microscopically derive Ginzburg–Landau (GL) theory from BCS theory for translation-invariant systems in which multiple types of superconductivity may coexist. Our motivation are unconventional superconductors. We allow the ground state of the effective gap operator \({K_{T_c}+V}\) to be n-fold degenerate and the resulting GL theory then couples n order parameters. In part II, we study examples of multi-component GL theories which arise from an isotropic BCS theory. We study the cases of (a) pure d-wave order parameters and (b) mixed (s + d)-wave order parameters, in two and three-dimensions. In part III, we present explicit choices of spherically symmetric interactions V which produce the examples in part II. In fact, we find interactions V which produce ground state sectors of \({K_{T_c}+V}\) of arbitrary angular momentum, for open sets of of parameter values. This is in stark contrast with Schrödinger operators \({-\nabla^2+V}\), for which the ground state is always non-degenerate. Along the way, we prove the following fact about Bessel functions: At its first maximum, a half-integer Bessel function is strictly larger than all other half-integer Bessel functions.     

Uniqueness of Radial Solutions for the Fractional Laplacian

We prove general uniqueness results for radial solutions of linear and nonlinear equations involving the fractional Laplacian (?Δ)^s with s ? (0,1) for any space dimensions N ≥ 1. By extending a monotonicity formula found by Cabré and Sire , we show that the linear equation has at most one radial and bounded solution vanishing at infinity, provided that the potential V is radial and nondecreasing. In particular, this result implies that all radial eigenvalues of the corresponding fractional Schrödinger operator H = (?Δ)^s + V are simple. Furthermore, by combining these findings on linear equations with topological bounds for a related problem on the upper half‐space , we show uniqueness and nondegeneracy of ground state solutions for the nonlinear equation for arbitrary space dimensions N ≥ 1 and all admissible exponents α > 0. This generalizes the nondegeneracy and uniqueness result for dimension N = 1 recently obtained by the first two authors and, in particular, the uniqueness result for solitary waves of the Benjamin‐Ono equation found by Amick and Toland .© 2016 Wiley Periodicals, Inc.     

Trapping of peroxidic intermediates with sulfur and phosphorus centered electrophiles

The trapping ability of a new peroxidic trapping agent relative to several well-established trapping agents was measured. Two different methods for this measurement were utilized. It was shown that adamantylidene adamantane reacts under the trapping conditions to give adamantylidene adamantane epoxide via a more complicated process than previously recognized and is consequently an inappropriate system to make this measurement. In contrast, the use of diethyl sulfide is straightforward and gives reliable values. © 1998 John Wiley & Sons, Inc. Heteroatom Chem 9:51–56, 1998     

Asymptotics for moist deep convection I: refined scalings and self-sustaining updrafts

Moist processes are among the most important drivers of atmospheric dynamics, and scale analysis and asymptotics are cornerstones of theoretical meteorology. Accounting for moist processes in systematic scale analyses therefore seems of considerable importance for the field. Klein and Majda (Theor Comput Fluid Dyn 20:525–551, 2006) proposed a scaling regime for the incorporation of moist bulk microphysics closures in multiscale asymptotic analyses of tropical deep convection. This regime is refined here to allow for mixtures of ideal gases and to establish consistency with a more general multiple scales modeling framework for atmospheric flows. Deep narrow updrafts, the so-called hot towers, constitute principal building blocks of larger scale storm systems. They are analyzed here in a sample application of the new scaling regime. A single quasi-one-dimensional upright columnar cloud is considered on the vertical advective (or tower life cycle) time scale. The refined asymptotic scaling regime is essential for this example as it reveals a new mechanism for the self-sustainance of such updrafts. Even for strongly positive convectively available potential energy, a vertical balance of buoyancy forces is found in the presence of precipitation. This balance induces a diagnostic equation for the vertical velocity, and it is responsible for the generation of self-sustained balanced updrafts. The time-dependent updraft structure is encoded in a Hamilton–Jacobi equation for the precipitation mixing ratio. Numerical solutions of this equation suggest that the self-sustained updrafts may strongly enhance hot tower life cycles.     

A DNA-based method for detecting homologous blood doping

Homologous (or allogeneic) blood doping, in which blood is transferred from a donor into a recipient athlete, is the easiest, cheapest, and fastest way to increase red cell mass (hematocrit) and therefore the oxygen-carrying capacity of the blood. Although thought to have been rendered obsolete as a doping strategy by the increased use of rhEPO to increased hematocrits, there is evidence that athletes are still using this potentially dangerous method to improve endurance performance. Current testing for homologous blood doping is based on identification of mixed populations of red blood cells by flow cytometry. This paper proposes that homologous blood doping could also be tested for by high-resolution qPCR-based genotyping and demonstrates that assays could be developed that would detect second populations of cells even if the “donor” blood was depleted of 99 % of the DNA-containing leukocytes. Issues of test specificity and sensitivity are discussed as well as some of the ethical considerations that would have to be addressed if athletes’ genotypes were to be used by the anti-doping authorities to prevent, or detect, the use of prohibited ergogenic practices.     

Rédei-Funktionen und das Schur'sche Problem

Ohne ZusammenfassungDie vorliegende Arbeit wurde vom Österreichischen Fonds zur Förderung der wissenschaftlichen Forschung unter dem FWF-Projekt Nr. P5452 wesentlich unterstützt.