Asymmetries in semi-leptonic hyperon decay

Based on the thermodynamic model for particle production, inclusive two-particle correlations are studied. The model is used to study integrated correlations R⁽²⁾(s) and rapidity correlations at accelerator and ISR energies.Particle production is described via the formation of clusters called fireballs. The average mass of these clusters changes as $\text{s}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext><mtext>w</mtext>}}\text{exp}\text{(? |η|ν), (0 ? ν, w ? 1)}$ with the primary energy s and fireball rapidity η. The model produces in the limiting cases the same correlations as the multiperipheral model (with w = 0) and the diffractive excitation model (with w = 1) but contains also all intermediate cases (0 < w < 1) in which fireballs increasing in mass and number are formed. The average number of fireballs produced is also calculated. At ISR energies integrated correlations R⁽²⁾ and rapidity correlations are very different in the cases $\text{w = 0,}\text{1}\text{2}\text{and}\text{1}$. Therefore, experimental data at high energy on R⁽²⁾(s) or on rapidity correlations will allow one to determine the parameter w. Measurements of these different quantities should result in a consistent picture for the production of fireballs.     

Uniform approximation with rational functions having negative poles

A general theory of uniform approximation with rational functions having negative poles is developed. An existence theory is given and local characterization and uniqueness results are developed. Algorithms for computing these approximants are given, together with numerical results.     

A unified approach to direct and inverse boundary layer solutions

A unified approach is presented for solving the two-dimensional incompressible boundary layer equations. Solutions are obtained for direct and inverse options using the same equation formulation by a simple interchange of boundary conditions. A modified form of the mechul function scheme obtains inverse solutions with specification of transformed wall shear, skin friction coefficient or displacement thickness distributions. Direct solutions may be obtained without altering the block tridiagonal structure of the system by simply requiring no corrections on the streamwise pressure gradient parameter. Fourth-order spline discretization approximates normal derivatives with two- and three-point backward differences approximating streamwise derivatives, yielding a fully implicit solution method. The resulting spline/finite difference equations are solved by Newton-Raphson iteration together with partial pivoting. The results of the study demonstrate the importance of proper linearization of all equations. The successful use of spline discretization is also tied to the use of strong two-point boundary conditions at the wall for cases involving reversed flow. Numerical solutions are presented for several non-similar flows and compared with published results.     

Convergence and perturbation resilience of dynamic string-averaging projection methods

We consider the convex feasibility problem (CFP) in Hilbert space and concentrate on the study of string-averaging projection (SAP) methods for the CFP, analyzing their convergence and their perturbation resilience. In the past, SAP methods were formulated with a single predetermined set of strings and a single predetermined set of weights. Here we extend the scope of the family of SAP methods to allow iteration-index-dependent variable strings and weights and term such methods dynamic string-averaging projection (DSAP) methods. The bounded perturbation resilience of DSAP methods is relevant and important for their possible use in the framework of the recently developed superiorization heuristic methodology for constrained minimization problems.     

Laser-microprobe elemental determinations with an optical multichannel detection system

The results obtained when a laser microprobe is adapted to imaging detectors for multiwavelength detection are described. Detectors evaluated are a silicon-intensified target vidicon and a second-generation photodiode array. Data are presented to illustrate how the combined system can be used to monitor both surface and depth profiles of elemental content of a variety of sample types including a ruby rod and ceramic material with blemishes, electrical capacitors, integrated circuits, and surface-coated electrical conductors. It is also shown how the gating capability of the intensified vidicon can be used to monitor time-dependent changes in the several nanosecond range during the laser microprobe excitation process. Detection limits obtained with both detectors are in the range 2–500 ppm depending on the element, the wavelength used, the matrix, and other variables. The uncertainty associated with the measurement step can be improved by a factor of 2–3 by using ratios of spectral lines. Principal limitations of the laser microprobe method are the nonlinear response of intensity vs. concentration and the resulting need for reference materials with matrices similar to samples for calibration purposes.     

Synthesis of 2-diphenylphosphinoyl-3,5-(diaryl)-3,4-dihydro-2H-thiopyrans by the reaction of a bis[(diphenylphosphinoyl)methyl]sulfide with chalcones

The NaH-promoted tandem Michael addition/intramolecular Horner-Wittig reaction of bis(diphenylphosphinoylmethyl)sulfide with chalcones afforded 3,4-dihydro-2H-thiopyrans 3a-l in 78-88% yield.