Reactivity of 5,10:8,14-Disecosteroids: An unusual rearrangement of cyclodecene-1,4-dione systems to five-membered-ring spiro-γ-lactones

Upon heating in AcOH, the stereoisomeric (Z)- and (R)-6,9-dioxocyclodex-3-enyl derivatives, 5 and 6 , respectively, obtained by HgO/I₂ oxidation of 5-hydroxy-8-oxo-8,14-seco-5α-androstane-3β,17β-diyl diacetate ( 3 ), undergo an unusual intramolecular rearrangement to give the corresponding unsaturated (5R,9R)- and (5R,9S)-spiro-lactones 7 and 8 , respectively. Hydroxylation of the C?C bond in 7 and 8 , and subsequent glycol cleavage of the resulting diols 9 and 10 afforded the epimeric spiro-lactones (5R,9S)- 11 and (5R,9R)- 14 , respectively, and in both cases, the ring-D-containing fragments 12 and 13 .     

Transition metal-catalyzed intermolecular [5+2] and [5+2+1] cycloadditions of allenes and vinylcyclopropanes

Initial examples of the intermolecular Rh(I)-catalyzed [5+2] cycloaddition reaction of bifunctional allenes and vinylcyclopropanes are described. The reactions proceed with facility and in yields of up to 99% with a variety of alkyne-, ester-, styrene-, or cyano-substituents on the allene to afford the corresponding cycloadducts. In the presence of CO, the reaction proceeds to an eight-membered ring cycloadduct and its transannularly closed product, providing the first example of a three-component [5+2+1] cycloaddition with allenes.     

Improving splitless injection with electronic pressure programming

An experimental injection port has been designed for split or splitless sample introduction in capillary gas chromatography; the inlet uses electronic pressure control, in order that the column head pressure may be set from the GC keyboard, and the inlet may be used in the constant flow or constant pressure modes. Alternatively, the column head pressure may be programmed up or down during a GC run in a manner analogous to even temperature programming. Using electronic pressure control, a method was developed which used high column head pressures (high column flow rates) at the time of injection, followed by rapid reduction of the pressure to that required for optimum GC separation. In this way, high flow rates could be used at the time of splitless injection to reduce sample discrimination, while lower flow rates could be used for the separation. Using this method, up to 5 μl of a test sample could be injected in the splitless mode with no discrimination; in another experiment, 2.3 times as much sample was introduced into the column by using electronic pressure programming. Some GC peak broadening was observed in the first experiment.     

Perdeuterated Conjugated Polymers for Ultralow‐Frequency Magnetic Resonance of OLEDs

The formation of excitons in OLEDs is spin dependent and can be controlled by electron‐paramagnetic resonance, affecting device resistance and electroluminescence yield. We explore electrically detected magnetic resonance in the regime of very low magnetic fields (<1 mT). A pronounced feature emerges at zero field in addition to the conventional spin‐ Zeeman resonance for which the Larmor frequency matches that of the incident radiation. By comparing a conventional π‐conjugated polymer as the active material to a perdeuterated analogue, we demonstrate the interplay between the zero‐field feature and local hyperfine fields. The zero‐field peak results from a quasistatic magnetic‐field effect of the RF radiation for periods comparable to the carrier‐pair lifetime. Zeeman resonances are resolved down to 3.2 MHz, approximately twice the Larmor frequency of an electron in Earth's field. However, since reducing hyperfine fields sharpens the Zeeman peak at the cost of an increased zero‐field peak, we suggest that this result may constitute a fundamental low‐field limit of magnetic resonance in carrier‐pair‐based systems. OLEDs offer an alternative solid‐state platform to investigate the radical‐pair mechanism of magnetic‐field effects in photochemical reactions, allowing models of biological magnetoreception to be tested by measuring spin decoherence directly in the time domain by pulsed experiments.     

On Fundamental Domains and Volumes of Hyperbolic Coxeter–Weyl Groups

We present a simple method for determining the shape of fundamental domains of generalized modular groups related to Weyl groups of hyperbolic Kac?CMoody algebras. These domains are given as subsets of certain generalized upper half planes, on which the Weyl groups act via generalized modular transformations. Our construction only requires the Cartan matrix of the underlying finite-dimensional Lie algebra and the associated Coxeter labels as input information. We present a simple formula for determining the volume of these fundamental domains. This allows us to re-produce in a simple manner the known values for these volumes previously obtained by other methods.     

The aliasing‐phenomenon in visual terms

In a recent paper it was shown that the aliasing phenomenon, which leads to a severe identification problem in the estimation of stochastic differential equations, can be overcome by using a polygonal (or higher) approximation for the time paths of the exogenous variables. This work attempts to visualize the problem and presents several simulated trajectories of a continuous time AR(2)‐process (Ornstein‐Uhlenbeck‐process) together with the observationally equivalent structures. Furthermore it is shown that aliasing can even change the analytical properties of the time paths of the system: whereas the first component of the Ornstein‐Uhlenbeck‐process is differentiable, the trajectories of the aliasing structures are continuous, but not differentiable any more.