Über ganze Functionen vonm Systemen von jen Unbestimmten

Ohne Zusammenfassung     

Counting lattice animals: A parallel attack

A parallel algorithm for the enumeration of isolated connected clusters on a regular lattice is presented. The algorithm has been implemented on 17 RISC-based workstations to calculate the perimeter polynomials for the plane triangular lattice up to clustersizes=21. New data for perimeter polynomials D_s up toD ₂₁, total number of clustersg _s up tog ₂₂, and coefficientsb _r in the low-density series expansion of the mean cluster size up tob ₂₁ are given.     

Relaxation phenomena and nuclear magnetic resonance of116In(T 1/2=14s) produced by capture of polarized neutrons in the indium III–V compounds

Polarized¹¹⁶In nuclei have been produced by capture of polarized thermal neutrons in several In compounds. At temperaturesT below 77 °K and magnetic field strengthsH ₀ of several kOe, asymmetries of a few percent of the β^? decay of the¹¹⁶In ground state could be observed in polycrystalline InP, InAs and InSb, thus indicating the nuclear polarization. Nuclear magnetic resonance signals have been measured with the result for the magnetic moment μ _i (¹¹⁶In)=2.7723 (10) nm (uncorrected). β^? decay asymmetry and spin lattice relaxation timeT ₁ have been studied as a function ofH ₀ andT. The effect ofH ₀ is to decouple the hyperfine interaction caused by the capture-γ recoil process. However,H ₀ has no influence uponT ₁, which demonstrates the absence of nuclear relaxation due to paramagnetic impurities.T ₁ is determined by quadrupolar relaxation. A quadrupole momentQ(¹¹⁶In)=0.09 (2) b was calculated by comparison of the¹¹⁶In relaxation rates with those of the stable¹¹⁵In isotope in the same compounds. Above 30 °K the temperature dependence of 1/T ₁ agrees with a recent theoretical investigation. Below 30 °K the relaxation rate shows an anomalous behaviour, which can be explained by resonance modes due to recoil lattice defects.     

On Fatou's Lemma in several dimensions

Probability Theory and Related Fields -     

Diffraction of light by supersonic waves: The solution of the raman-nath equations

The partial differential equation associated with the system of difference-differential equations of Raman-Nath for the amplitudes of the diffracted light-waves is solved exactly by the method of the separation of the variables. The solution is presented as a double infinite series containing the Fourier coefficients of the even periodic Mathieu functions with periodπ and the corresponding eigenvalues. Considering this solution as a Laurent series in one of the variables, the Laurent coefficients immediately give the exact expressions for the amplitudes of the diffracted light-waves, from which the formulae for the intensities are calculated. The connection between the Raman-Nath method and Brillouin’s Mathieu function method has thus been achieved.