Magnetic-Field-Dependent Electronic Relaxation of Gd3+ in Aqueous Solutions of the Complexes [Gd(H2O)8]3+, [Gd(propane-1,3-diamine-N,N,N′,N′-tetraacetate)(H2O)2]−, and [Gd(N,N′-bis[(N-methylcarbamoyl)methyl]-3-azapentane-1,5-diamine-3,N,N′-triacetate)(H2O)] of interest in magnetic-resonance imaging

EPR Spectra have been measured for aqueous solutions of a series of Gd³⁺ complexes at variable temperature and a range of magnetic fields; S-band (0.14 T), X-band (0.34 T), Q-band (1.2 T), and 2-mm-band (5.0 T). The major contribution to the observed line widths is magnetic-field-dependent and is interpreted as being due to the modulation of the zero-field splitting produced by distortion of the complexes from perfect symmetry. The transverse and longitudinal relaxation matrices for an ⁸S ion with such an interaction have been calculated using Redfield theory with vector-coupling methods, and diagonalised numerically to obtain relaxation rates and intensities for the degenerate transitions which contribute to the multiplet. The observed line width, which is inversely proportional to the magnetic field at low temperatures, is best described by the intensity-weighted mean transverse relaxation time for the four transitions with non-zero intensity. A least-squares fit of the data yields the square of the zero-field splitting tensor, Δ², and a correlation time, τ_v, with activation energy, E_v. The physical significance of these parameters and the extent of validity of the theoretical approach are considered. The parameters are used to predict the magnetic-field dependence of the longitudinal and transverse electronic relaxation times, which are discussed in the context of their relevance to ¹H-NMR relaxivity.     

Accurate determination of traces of sodium and potassium in rocks by ion exchange followed by atomic absorption spectroscopy

Sodium and potassium (5–1000 p.p.m.) in rocks such as peridotites and dunites can be determined accurately by ion-exchange separation followed by atomic absorption spectrophotometry. The samples are decomposed in sulphuric, hydrochloric and hydrofluoric acid mixtures, and after removal of hydrofluoric acid the cations are absorbed on a 90-ml column of AG50W-X8 cation-exchange resin. Vanadium and other anion-forming elements are eluted with 0.01 M nitric acid containing hydrogen peroxide. Then the alkali metals are eluted with 0.50 M nitric acid, while Mg, Mn, Ca, Ti, Al, Fe and other multivalent elements are retained by the column. The eluate fractions containing the respective alkali metals are measured directly by atomic absorption spectrophotometry against standards in 0.50 M nitric acid. Relevant elution curves, results for synthetic mixtures and for three international rock standards are presented and discussed.     

Kugo-Ojima confinement and QCD Green''s functions in covariant gauges

In Landau gauge QCD the Kugo-Ojima confinement criterion and its relations to the infrared behaviour of the gluon and ghost propagators are reviewed. It is demonstrated that the realization of this confinement criterion (which is closely related to the Gribov-Zwanziger horizon condition) results from quite general properties of the ghost Dyson-Schwinger equation. The numerical solutions for the gluon and ghost propagators obtained from a truncated set of Dyson-Schwinger equations provide an explicit example for the anticipated infrared behaviour. The results are in good agreement, also quantitatively, with corresponding lattice data obtained recently. The resulting running coupling approaches a fixed point in the infrared, (0) = 8.915/N_c. Solutions for the coupled system of Dyson-Schwinger equations for the quark, gluon and ghost propagators are presented. Dynamical generation of quark masses and thus spontaneous breaking of chiral symmetry takes place. In the quenched approximation the quark propagator functions agree well with those of corresponding lattice calculations. For a small number of light flavours the quark, gluon and ghost propagators deviate only slightly from the ones in quenched approximation. While the positivity violation of the gluon spectral function is manifest in the gluon propagator, there are no clear indications of analogous positivity violations for quarks so far.     

Spektraltheorie verwandter operationen

This is a résumé of A. Pietsch’s concept of related linear operators in the study of spectral properties and homomorphism theorems forp-bounded linear operators on Mackey-complete topological vector spaces. It turns out that many results proved by various authors in the setting of Mackey-complete topological vector spaces follow directly from the corresponding classical results by means of purely algebraic relations.     

Strong Solutions of the Navier–Stokes System in Lipschitz Bounded Domains

Let Ω be a bounded domain in ?³ with a connected Lipschitz boundary ?Ω. Consider the Navier-Stokes system.     

High energy electronic neutrino (ve) and antineutrino (ve) interactions

The total cross-sections for $\text{v}{}_{\mathrm{<mtext>e</mtext>}}\text{(}\text{v}{}_{\mathrm{<mtext>e</mtext>}}\text{)}$-nucleon scattering have been measured. A test has been made of the muon number conservation law. A limit of 2.4 GeV is found the mass of the “Georgi-Glashow type” heavy lepton