Boundary-value problems for an elliptic equation with complex coefficients and a certain moment problem

Elliptic systems of two second-order equations, which can be written as a single equation with complex coefficients and a homogeneous operator, are studied. The necessary and sufficient conditions for the connection of traces of a solution are obtained for an arbitrary bounded domain with a smooth boundary. These conditions are formulated in the form of a certain moment problem on the boundary of a domain; they are applied to the study of boundary-value problems. In particular, it is shown that the Dirichlet problem and the Neumann problem are solvable only together. In the case where the domain is a disk, the indicated moment problem is solved together with the Dirichlet problem and the Neumann problem. The third boundary-value problem in a disk is also investigated.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 45, No. 11, pp. 1476–1483, November, 1993.     

The effect of radiofrequency modulation of 57Fe hyperfine interaction by rotating magnetic field

The effect of ⁵⁷Fe hyperfine interaction radiofrequency (rf) modulation by external rotating magnetic field was studied in thin Permalloy foil by means of Mössbauer spectroscopy. The rf effect was investigated as a function of intensity for several rf field frequencies. The experiments show that the external rotating rf field causes considerable changes in the hyperfine pattern. The obtained spectra are in disagreement with those obtained by Perlow [Phys. Rev. 172 (1968) 319]. They also are inconsistent with magnetostriction hypothesis. Proceeding from the Mössbauer spectrum analysis one may conclude that the magnetization of investigated foil changes its direction in a complex manner. However, the undertaken experiments show that the essential number of Mössbauer nuclei experience the rotating magnetic field influence.     

Two Coulomb waves theory for direct excitation

A theoretical model of Dewangan, in which the total scattering wave function is approximated by a distorted wave containing two Coulomb wave functions, is discussed and its relation with the Brauner-Briggs-Klar model for ionization is examined. An important feature of the theory is that it includes a second Born amplitude naturally and in addition, contains, albeit approximately, both real and imaginary parts of all higher order Born terms. The theory is applied to study the 1s→2s excitation of hydrogen by electrons in the energy range 54.4 to 400eV. The differential and integral cross sections predicted by the theory are compared with the results of other theories and experimental data at 54.4eV and a good agreement is found.     

Strain of an anisotropic monolith during the excavation of minerals

We solve the problem of the normal and transverse shear in an anisotropic monolith during the excavation of a stratum of solid mineral. It is shown that the stress perturbation field in the rock is due to the whole extent of the excavated portion of the stratum. We study way in which the friction that arises between the interacting rock of the roof and the floor influences the strain and stress fields as the front of the excavation evolves, and also the influence of the extent of the excavated portion of the rock stratum on the magnitude of the accumulated tangential displacements. Three figures. Translated fromTeoreticheskaya i Prikladnaya Mekhanika, No. 25, 1995, pp. 62–69.     

Weakly symmetric spaces in dimension five

We prove that every five-dimensional simply connected naturally reductive space is weakly symmetric in the sense of A.Selberg [11]. (For dimension less than five it was shown in [1] by a different method). We also show that the converse holds for all dimensions not greater than five.Supported by the grant GACR 201/93/0469Supported by a National Research Project of the M. U. R. S. T (Italy).     

Parallel Algorithm for Unconstrained Optimization Based on Decomposition Techniques

We present a numerical implementation of the parallel gradient distribution (PGD) method for the solution of large-scale unconstrained optimization problems. The proposed parallel algorithm is characterized by a parallel phase which exploits the portions of the gradient of the objective function assigned to each processor; then, a coordination phase follows which, by a synchronous interaction scheme, optimizes over the partial results obtained by the parallel phase. The parallel and coordination phases are implemented using a quasi-Newton limited-memory BFGS approach. The computational experiments, carried out on a network of UNIX workstations by using the parallel software tool PVM, show that parallelization efficiency was problem dependent and ranged between 0.15 and 8.75. For the 150 problems solved by PGD on more than one processor, 85 cases had parallelization efficiency below 1, while 65 cases had a parallelization efficiency above 1.     

Photodiffraction in InGaAs/InGaAsP multiple quantum wells enclosed in a microcavity

We report new results on the diffraction properties of photoinduced gratings in InGaAs/InGaAsP MQW structures. The original feature of this device is that the QWs are enclosed in an asymmetric Fabry–Perot microcavity in order to increase the diffraction efficiency. We observe oscillations in the diffraction efficiency due to resonant effects in the microcavity. The experimental spectra are compared with theory. Diffraction efficiency at 1.55 μm attains a maximum value of 2.7% at a write beam fluence of 260 μ J cm⁻², and then decreases at higher fluences. We explain this phenomenon by an absorption saturation at high excitation.