Imbedding problem with non-Abelian kernel of order p4

This paper considers the imbedding problem for numerical fields and p-groups with nonabelian kernel of order p⁴, two generators and , and defining relations =1, ^p=1, [,,]=1, and [,,]= 1. For p=2 and almost always for odd p, the Hasse principle is valid, and the problem is solvable if and only if all related local problems are solvable. Counterexamples in which the Hasse principle is not valid are constructed for some exceptional cases.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova Akademii Nauk SSSR, Vol. 175, pp. 46–62, 1989.     

State and degree of polarization along single-polarization optical fibres with random perturbations

A numerical study of the state and degree of polarization along single-polarization fibres has been carried out on the basis of Müller-Stokes matrix approach and the mode coupling centre model. The general quasimonochromatic case is considered. Correspondence between polarization holdingh-parameter and the mode coupling centres' parameters has been established. The spectral average process has been considered and a novel criterion has been proposed. Expressions for the degree of polarization along the fibre have been derived for the cases of guided mode excitation and nonpolarized input. The degree of polarization has been shown to tend to a saturation level which depends on theh-parameter, the differential mode attenuation gD and the coherence lengthL in the fibre.     

Temperature and magnetic field dependent correlations in the singlet ground state system CsFeBr3

The magnetic excitations in CsFeBr₃ have been measured with inelastic scattering of cold neutrons to high precision at 80 mK. The fact that the lowest frequency mode softens with decreasing temperature but stabilizes at 0.11 THz below 2.5 K is the indication that CsFeBr₃ remains a SGS system forT0.From dispersion curves measured earlier in a magnetic field along the chain axis experimental intensities were derived and in turn correlation lengths. Correlation lengths were also calculated using the new parameters for exchange and anisotropy. The experimental results and the calculations both show that the correlation lengths increase for increasing magnetic field, flatten off around the phase transformation at 4.1 Tesla with a maximum of about 35 Å and then decrease again for higher fields. No critical phenomena connected with this phase transformation could be detected.The Mirror Mode published earlier was found to be of spurious origin due to double scattering. It does not exist.     

The deformation of103Nb

Tie half-lives of 8 low lying levels of¹⁰³Nb have been determined at the fission-product separator JOSEF. A B-- triple-coincidence method was used which consists in a measurement of the time delay between the feeding of the levels through the B^– decay of¹⁰³Zr and their decay, in coincidence with a tagging ray, with plastic, BaF₂ and Ge detectors, respectively. Most of the investigated levels are members of the three known rotational bands based on the ground state and the 164 and 248 keV levels. The deformation B_q=0.31(3) of¹⁰³Nb could be deduced from the half-life data. The half-lives are well reproduced through calculations in the frame of the Nilsson model.The authors thank Dr. T. Seo for valuable advise in connection with the Nilsson-model calculations.     

Nonlinear forecasting and iterated function systems

The theory of dynamical forecasting can be extended to iterated function systems. An unordered set of iterates may be sufficient to construct a simulation of the unknown dynamics. The underlying dynamical system may be nondeterministic: A random element may be allowed in the dynamics, and retrieved by our proposed procedures. A first application of these extensions pertains to the reconstruction of fractal attractors, and allows us to solve the so-called inverse problem in Iterated Functions Systems.     

Theoretical analysis of pulse development in a colliding pulse mode-locked dye laser

The pulse development in colliding pulse mode-locked dye lasers is analysed theoretically. The chosen parameters belong to a c.w. argon laser pumped linear resonator arrangement with rhodamine 6G in ethylene glycol as gain medium and DODCI (3,3-diethyloxadicarbocyanine iodide) in ethylene glycol as saturable absorber. The pulse shortening and pulse broadening effects in the laser oscillator are investigated. The steady-state pulse duration is determined by equal pulse broadening and pulse shortening within a single resonator round-trip. The detuning of the absorber jet out of the middle position of the resonator is considered. Multiple transits through the resonator are simulated to study the influence of various resonator and dye parameters on the pulse development and the background signal suppression. Fast relaxations within theS ₁ andS ₀-state of DODCI are necessary for sufficient background suppression to obtain femtosecond pulse trains.     

Interferometric phase measurements of average field cubeE ω 2 E 2ω *

The method of interferometric measurements of the field cube evolutionE ² E ₂ ^* due to propagation in air and other media was investigated experimentally by the use of a pair of nonlinear crystals. A gas cell with variable pressure turned out to be the most convenient among different methods of changing the phase of the field cube. The phase shift by rad of the field cube in passing through the focus was demonstrated experimentally.     

Gyromagnetic ratios of low-lying rotational states in156, 158, 160Gd

Transient-field precessions were measured simultaneously for levels in the ground-state bands of^{156, 158, 160}Gd as ions of these nuclei traversed a thin polarized Fe foil. Relative g-factors of levels up to 6 ₁ ⁺ were deduced, those of the 4 ₁ ⁺ levels being determined with greatest precision. In contrast with the conclusions of the recent report by Alzner et al. [1], our results are consistent with g(4 ₁ ⁺ ) having the same value in all three isotopes and imply g(2 ₁ ⁺ )=g(4 ₁ ⁺ ) in¹⁵⁶Gd, consistent with nuclear structure models.     

Theoretical evidence for di-molecular rotational behaviour in the hypernuclei ∑ 8 Li and ∑ 8 Be

We have performed microscopic cluster studies of light∑-hypernuclei based on effective nucleon-nucleon and two different sigma-nucleon interactions. Our calculation confirms a bound 0⁺ state in _∑ ⁴ He and _∑ ⁴ H, but reveals no evidence for levels in other partial waves. We have investigated the _∑ ⁸ Li and _∑ ⁸ Be hypernuclei in a microscopic 3-cluster approach. For both hypernuclei, our calculation shows that the lowest levels in the partial wavesJ=0–4 are bound or quasibound states of collective nature and show a strong α _∑ ⁴ H and α + _∑ ⁴ He clustering. These levels form a sequence of states which can be well interpreted as arising from a rotatingα+ _∑ ⁴ H orα+ _∑ ⁴ He di-molecule. Our results are compared to those of similar studies for lightΛ-hypernuclei which do not show evidence for this kind of collective degrees of freedom.