Precise Measurement of Muon Capture on the Proton

The aim of the μCap experiment is a 1% measurement of the singlet capture rate Λ _S for the basic electro-weak reaction μ + p → n + ν_μ. This observable is sensitive to the weak form-factors of the nucleon, in particular to the induced pseudoscalar coupling constant g _P . It will provide a rigorous test of theoretical predictions based on the Standard Model and effective theories of QCD. The present method is based on high precision lifetime measurements of μ⁻ in hydrogen gas and the comparison with the free μ⁺ lifetime. The μ⁻ experiment will be performed in ultra-clean, deuterium-depleted H₂ gas at 10 bar. Low density compared to liquid H₂ is chosen to avoid uncertainties due to ppμ formation. A time projection chamber acts as a pure hydrogen active target. It defines the muon stop position in 3D and detects rare background reactions. Decay electrons are tracked in cylindrical wire-chambers and a scintillator array covering 75% of 4π. This revised version was published online in August 2006 with corrections to the Cover Date.     

Energy values for the H+2 ion in superstrong magnetic fields using the adiabatic approximation

Energy values, equilibrium internuclear separations, and zero-point energies of nuclear vibrations parallel to the magnetic field are calculated for the lowest states of the H⁺₂ ion in magnetic fields B?10⁶ T (characteristic of neutron stars) using numerical wave functions that are products of Landau states and arbitrary z-dependent functions, thus improving on previous estimates of variational or LCAO type, which have been obtained in the high-field regime.     

Ein Vergleichssatz für komplexe lineare Differentialgleichungen

Ohne Zusammenfassung     

Frequency autocorrelation function of stochastically fluctuating fields caused by specific magnetic field inhomogeneities

Signal formation in NMR is due to incoherent dephasing of nuclear spins. Of particular practical importance is the situation of nuclear spins undergoing independent stochastic motion in inhomogeneous local magnetic fields, e.g., created by magnetized objects. Since it was demonstrated recently that the frequency correlation function of nuclear spins can be measured directly, a theoretical analysis of such functions is of interest. Here, we provide a numerically exact analysis of that correlation function for the inhomogeneous fields around two particular geometries: cylinders and spheres. The functional form exhibits three regimes: after an initial transient, there is an algebraic regime with a t(-d/2) time dependence (d being the space dimension), followed by an exponential cutoff due to microscopic system size effects. The main parameter controlling the range of the individual regimes is the volume fraction of the magnetized objects. In addition to our numerical analysis, which is based on eigenfunction expansions, we provide analytical results and approximations based on the generalized moment expansion.     

A method for rapid screening of interactions of pharmacologically active compounds with albumin

We determine the association constants for ligand–protein complex formation using the flow injection method. We carry out the measurements at high flow rates (F = 1 mL min⁻¹) of a carrier phase. Therefore, determination of the association constant takes only a few minutes. Injection of 1 nM of the ligand (10 μL of 1 μM concentration of the ligand solution) is sufficient for a single measurement. This method is tested and verified for a number of complexes of selected drugs (cefaclor, etodolac, sulindac) with albumin (BSA). We obtain K = 4.45 × 10³ M⁻¹ for cefaclor, K = 1.00 × 10⁵ M⁻¹ for etodolac and K = 1.03 × 10⁵ M⁻¹ for sulindac in agreement with the literature data. We also determine the association constants of 20 newly synthesized 3β- and 3α-aminotropane derivatives with potential antipsychotic activity – ligands of 5-HT_1A, 5-HT_2A and D₂ receptors with the albumin. Results of the studies reported here indicate that potential antipsychotic drugs bind weakly to the transporter protein (BSA) with K ≈ 10²–10³ M⁻¹. Our method allows measuring K in a wide range of values (10²–10⁹ M⁻¹). This range depends only on the solubility of the ligand and sensitivity of the detector.     

Empirical processes of multidimensional systems with multiple mixing properties

We establish a multivariate empirical process central limit theorem for stationary R^d-valued stochastic processes (X_i)_i≥1 under very weak conditions concerning the dependence structure of the process. As an application, we can prove the empirical process CLT for ergodic torus automorphisms. Our results also apply to Markov chains and dynamical systems having a spectral gap on some Banach space of functions. Our proof uses a multivariate extension of the techniques introduced by Dehling et al. (2009) [9] in the univariate case. As an important technical ingredient, we prove a 2pth moment bound for partial sums in multiple mixing systems.