Widths and optimal quadrature formulas for convolution classes

We compute Kolmogorov widths in the space L₁ for classes of periodic functions representable in the form of a kernel convolution that does not increase the number of sign changes with values in a given transposition invariant set of functions, and solve the optimization problem for quadrature formulas in these classes.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 43, No. 9, pp. 1135–1148, September, 1991.     

Two- and three-dimensional analysis of bose-einstein correlations inπ +/K+p interactions at 250 GeV/c

The NA22 data onπ ^? π ^? correlations are analyzed in terms of a number of two- and three-dimensional parametrizations (Gaussian space-time, Goldhaber, Bowler string-like, Bertsch hydrodynamical, Kopylov-Podgoretskii, etc.). Contrary to the results obtained for e⁺e^? andµp collisions, the Goldhaber parametrization, as well as string-like models, fail in describing the hadron-hadron data. Better fits are obtained in the framework of surface-emitting fireball-like models, both when including and excluding hydrodynamical expansion of nuclear matter. Our results indicate that pion radiation occurs at earlier stages of matter evolution than in nuclear collisions.     

FFT solution of the Robbins problem

An FFT method is described for the solution of Poisson's equationover a rectangular region with Robbins boundary conditions oneither one or two sides of the region, together with suitableconditions on the rest of the boundary. In contrast to earlierapplications of the FFT technique, the equations for the Fourierharmonic amplitudes do not decouple into simpler independentsystems and an effective iterative scheme is developed for thesolution of these equations. A theoretical convergence analysisis shown generally to support the results obtained from practicalcomputation. For the test problems considered the method isfound to take between 3 and 4 times the execution time for problemssoluble directly by the FFT technique.     

Coaxial Discharge and Transverse Magnetic Field

The study deals with the effect of an applied transverse magnetic field on the dynamics and parameters of the focused and expanded plasma in a coaxial discharge. The experimental results were found with a 3 kJ Plasma focus device of a Mather geometry. The discharge takes place in hydrogen gas with base pressure of 0.5 Torr. The experiments are conducted with a 10 kV bank voltage, which corresponds to 100 kA peak discharge current with rise time 8 μs. Helmholtz magnetic coils are placed outside the expansions chamber to produce a transverse magnetic field with intensity 280 G perpendicular to the plasma expanded from the coaxial electrodes. The investigations have shown that the plasma flow along the expansion chamber axis is restricted when applying the externally transverse magnetic field and the maximum axial velocity of the expanded plasma is decreased by 33%. X-ray probe has been used to measure the focused plasma electron temperature (T_e). The experimental results and the calculations showed that T_e is decreased from 2.2 keV to 800 eV with the application of a transverse magnetic field. The expanded plasma electron temperature and density have been measured by an electric double probe, the results cleared that the expanded plasma electron temperature is decreased by 2.6 times while its density is increased by 9 times, when a transverse magnetic field is applied.     

Structure and electronic spectra of 2-phenylbenzimidazoles. Quantum chemical analysis of the intramolecular hydrogen bond

Institute of High-Molecular-Weight Compounds, Russian Academy of Sciences. Leningrad State University Translated from Zhurnal Strukturnoi Khimii, Vol. 33, No. 5, pp. 20–27, September–October, 1992.     

Trimode ladar/radar transponder systems for tracking long range cooperative targets

Detection and tracking of cooperative airborne targets are very important for military and also for civilian purposes. Previous research has shown that detection and tracking LASER offer high precision but their operation range is limited to less than 40 km even in good visibility propagation conditions. For long operation ranges, high power and bulky RADAR are required which can be significantly reduced by using active transponders on the cooperative target. A trimode LADAR/RADAR/Transponder system is investigated providing optimum performances. A L band Radar with active transponder is operated for all weather long ranges up to Low Earth Orbit satellites. The L mode is switched to a Mm wave mode RADAR for operation distances lower than 350 km and to an accurate LASER mode for the final tracking steps.     

A method for investigating the orientational behaviour of fibrous particles in gaseous flow

A method is described by which the angular orientation distribution of fibrous particles carried in a gaseous stream may be investigated. The method is based upon the interpretation of the spatial intensity distribution or scattering profile of laser light scattered by individual fibres. The scattering instrument used to capture the profiles is described, and the mathematical computation required to ascertain the orientation of each particle at the measurement point is detailed. Illustrative results are given for a study of airborne micromachined silicon particles of 12 μm length and 1.0 μm by 1.5 μm cross-section. The method is currently being employed by the authors to investigate ways of improving the orientation control over nonspherical particles in systems such as aerodynamic particle sizers and particle shape classifiers, since lack of particle orientation control is known to adversely affect the measurement accuracy of both these types of instrument.