Structure of finite, minimal nonabelian groups and triangularization

Motivated by problems concerning simultaneous triangularization, we study the structure of finite, minimal nonabelian groups. Using the structure result of Miller and Moreno we explicitly describe all irreducible representations of such groups. We illustrate the usefulness of results of this type on several examples.     

The controversy in the γγ → ρρ process: potential scattering or qqq̄q̄ resonance?

The γγ → gr⁰ ρ⁰ → 4π reaction shows a broad peak at 1.5 GeV in the (J ^P, J_z)=(2⁺, 2) channel which has no counterpart in the ρ⁺ ρ^? channel. This “resonance” is considered as a candidate for a qqq?q? state in the “s-channel”. We show, however, that it can also be explained by potential scattering of ρ⁰ ρ⁰ via the σ-exchange in the “t-channel”.     

Symbolic dynamics in investigation of quaternionic Julia sets

We focus our attention on the dynamics of the simplest quaternionic quadratic function f_Q(X) = X² + Q. The discussion can be reduced to a complex parameter Q and a three dimensional subspace. The images of quaternionic Julia sets suggest a natural decomposition. We find that it can be derived from a certain symbolic dynamics giving rise to fractal fibrations. The starting point are the equators and their preimages. If the parameter Q is real, fibrations are trivial, obtained by rotation of the complex Julia set. Repeating itineraries, on the other hand, define curves connecting periodic points.     

Note on prehomogeneous vector spaces

Let \(V\) be a complex prehomogeneous vector space under the action of a linear algebraic group \(G\) . Assume the poset of orbit closures in the Zariski topology \(\{\overline{Gx}:x\in V\}\) coincides with a (partial) flag \(V_0=0<V_1<\dots <V_k=V\) in \(V\) . Then for any Borel subgroup \(B\) of \(G\) , the poset \(\{\overline{B x}:x\in V\}\) coincides with a full flag in \(V\) .     

Direct determination of free bilirubin in serum at sub-nanomolar levels

Direct analysis of free bilirubin in human and animal blood serum samples is reported for the first time. A state-of-the-art system comprised of newly developed high-performance liquid chromatography (HPLC) on reverse-phase (RP) C18 support coupled with thermal lens spectrometric detection (TLS), based on excitation at λ = 457.9 nm by an argon laser was used for this purpose. This HPLC-TLS method enabled a baseline separation of all three structural isomers of bilirubin (XIII-α, IX-α and III-α) and the respective degradation products in isocratic mode in fewer than 7 min. The method excels in ultra-high sensitivity with limit of detection (LOD) and limit of quantitation (LOQ) of 90 pM and 250 pM, respectively. Moreover, this method also affords high precision and accuracy, with correlation coefficients R² > 0.997 over a broad linear range (0.250–150 nM) and R² = 0.9998 in a concentration range of clinical interest (0.500–25 nM). The method's boosted sensitivity enabled to streamline sample preparation to just one serum ultrafiltration step, which made qualitative evaluation of sample preparation possible for the first time. The performance of the HPLC-TLS method was assessed to have 20-fold enhanced sensitivity when compared to a comparable method incorporating HPLC coupled with diode array detector (DAD), which is also a novel method by itself, and could be applied for free bilirubin determination in patients with elevated bilirubin levels.     

Realizing irreducible semigroups and real algebras of compact operators

Let B(X) be the algebra of bounded operators on a complex Banach space X. Viewing B(X) as an algebra over R, we study the structure of those irreducible subalgebras which contain nonzero compact operators. In particular, irreducible algebras of trace-class operators with real trace are characterized. This yields an extension of Brauer-type results on matrices to operators in infinite dimensions, answering the question: is an irreducible semigroup of compact operators with real spectra realizable, i.e., simultaneously similar to a semigroup whose matrices are real?     

Densitometric DNA Analysis in Agarose Electrophoretic Gels

JPC – Journal of Planar Chromatography – Modern TLC - Agarose gel electrophoresis is a basic separation tool used in molecular biology, mostly for qualitative DNA analysis. There are...     

Bialgebra cohomology, pointed Hopf algebras, and deformations

We give explicit formulas for maps in a long exact sequence connecting bialgebra cohomology to Hochschild cohomology. We give a sufficient condition for the connecting homomorphism to be surjective. We apply these results to compute all bialgebra two-cocycles of certain Radford biproducts (bosonizations). These two-cocycles are precisely those associated to the finite dimensional pointed Hopf algebras in the recent classification of Andruskiewitsch and Schneider, in an interpretation of these Hopf algebras as graded bialgebra deformations of Radford biproducts.     

Risk management with multiple VaR constraints

We study a utility maximization problem under multiple Value-at-Risk (VaR)-type constraints. The optimization framework is particularly important for financial institutions which have to follow short-time VaR-type regulations under some realistic regulatory frameworks like Solvency II, but need to serve long-term liabilities. Deriving closed-form solutions, we show that risk management using multiple VaR constraints is more useful for loss prevention at intertemporal time instances compared with the well-known result of the one-VaR problem in Basak and Shapiro (Rev Financ Stud 14:371–405, 2001), confirming the numerical analysis of Shi and Werker (J Bank Finance 36(12):3227–3238, 2012). In addition, the multiple-VaR solution at maturity on average dominates the one-VaR solution in a wide range of intermediate market scenarios, but performs worse in good and very bad market scenarios. The range of these very bad market scenarios is however rather limited. Finally, we show that it is preferable to reach a fixed terminal state through insured intertemporal states rather than through extreme up and down movements, showing that a multiple-VaR framework induces a preference for less volatility.