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.     

Certificates of infeasibility via nonsmooth optimization

An important aspect in the solution process of constraint satisfaction problems is to identify exclusion boxes which are boxes that do not contain feasible points. This paper presents a certificate of infeasibility for finding such boxes by solving a linearly constrained nonsmooth optimization problem. Furthermore, the constructed certificate can be used to enlarge an exclusion box by solving a nonlinearly constrained nonsmooth optimization problem.     

Short Syntheses of some ‘Decalin‐1,8‐diones’ and their Derivatives: Breaking the Pretended Symmetry

A cheap synthesis of the so‐called ‘decalin‐1,8‐diones’ started with the conjugate (1,4‐) addition of cyclohex‐2‐en‐1‐one derivatives to the γ‐position of the dilithium derivative (buta‐1,3‐diene‐1,1‐bis(olate)) of crotonic acid. Hydrogenation of these ‘1,4‐γ’ adducts and final cyclization afforded the enol tautomers of decalin‐1,8‐diones. Nucleophilic substitutions at these 3‐oxoenols by NH₃ or primary amines created only monoamino products (namely, 3‐oxoenamines) whose reactions with OPCl₃ yielded dihydro(1,3,2)oxazaphosphinin‐2‐one derivatives. The two regioisomers of a trimethyl‐3‐oxoenamine served as models for the constitutional assignments of the two rapidly interconverting (hence, individually NMR‐invisible), tautomeric trimethyl‐3‐oxoenols. Such methyl substitutions served to break the ‘pretended’ symmetry of ‘decalin‐1,8‐dione’. Hydrazine and 3‐oxoenols furnished oxygen‐free indazole derivatives whose N?H bonds exchanged with t_1/2=ca. 0.00035 s at ca. ?58(9) °C.