Convergence behavior of interior-point algorithms

We show that most interior-point algorithms for linear programming generate a solution sequence in which every limit point satisfies the strict complementarity condition. These algorithms include all path-following algorithms and some potential reduction algorithms. The result also holds for the monotone complementarity problem if a strict complementarity solution exists. In general, the limit point is a solution that maximizes the number of its nonzero components among all solutions.Research supported in part by NSF Grant DDM-8922636, the Iowa Business School Summer Grant, and the Interdisciplinary Research Grant of the University of Iowa Center for Advanced Studies.     

Central collisions of24Mg nuclei with heavy emulsion group of nuclei (Br,Ag) at 4.5 AGeV/c momentum

Central collisions of²⁴Mg nuclei with the heavy (AgBr) group of emulsion nuclei are selected and analysed according to several selecting criteria. Theoretical calculations concerning cross sections for central events, average number of interacting protons from both projectile and target nuclei, multiplicity distributions of shower particles and dispersions, all based on the Glauber model, are performed to evaluate various criteria to select central events. The selection criterion based on the high multiplicity of total charged particles provides satisfactory agreement with the theoretical calculations.     

The use of Omega Chrome Black Blue G in chelatometric titrations

Summary The reactions of Omega Chrome Black Blue G with a large number of cations is studied. This study has shown in many cases high sensitivity limits of detection of metals. It also showed that this dye can be used as an indicator for EDTA titrations of zinc, cadmium, manganese and lead. It is also a suitable indicator for the step wise titration of calcium and magnesium in blood serum and water.     

A new and convenient synthesis of substituted benzobarrelenes

Bromination of 3-bromo-6,7-benzobicyclo [3.2.1] octa-2,6-diene at ?50°C gave anti-tribromo adduct (5) in essentially quantitative yield. The double dehydrobromination of (5) was achieved using potassium tert.- butoxide to give 2-bromo-benzobarrelene (7). Reaction of (7) with n-BuLi and subsequent quenching with CH₃I, CO₂, and dimethylformamide afforded the corresponding substituted benzobarrelenes in high yield.     

Coulomb forces in the three-body problem with application to direct nuclear reactions

Faddeev equations are considered in the case of three charged particles interacting with both separable nuclear two-body interactions and also including Coulomb forces. Modified Faddeev equations with Coulomb Green's functions are introduced. The three-body amplitudes are given into pure Coulomb and distorted-Coulomb amplitudes. Introducing a decomposition in the angular momentum states, a set of three-body integral equations is obtained. The effect of pure coulomb amplitudes is studied in direct nuclear reactions and found to give a large contribution to the cross sections. The three-body integral equations obtained are applied for direct nuclear reactions. The angular distributions for¹²C(⁶Li,d)¹⁶O,¹⁶O(⁶Li,d)²⁰Ne, and¹²C(⁶Li,α)¹⁴N transfer reactions are calculated as well as for the⁶Li elastic scattering on¹²C. From the good agreement between the theoretically calculated and experimental data, better spectroscopic factors are extracted. The effect of including Coulomb forces in the three-body problem is found to improve the results by about 16.26%.     

The (d,p) Reactions below 3.0 MeV

Excitation functions for a number of proton groups for the reactions ²³Na(d, p)²⁴Na and ²⁷Al(d, p)²⁸Al were measured in the energy range E_d = 1.5 to 3.0 MeV. The angular distributions for a number of proton groups were measured at a number of deuteron energies below 3.0 MeV for the three reactions ¹²C(d, p)¹³C, ²³Na(d, p)²⁴Na and ²⁷Al(d, p)²⁸Al. The theory of deuteron stripping reactions at incident energies below the Coulomb barrier has been considered. A closed analytical form for the differential cross-section has been obtained considering three cases according to the incident deuteron and outgoing proton energies. An attempt has been made to fit the angular distribution measurements at a number of deuterons bombarding energies accordingly.