Analysis of hashing with chaining in the prime area

The expected performance of hashing with chaining in the prime area is analyzed. The method analyzed is briefly characterized as hashing with chaining of overflow records in the prime storage area, using one or several noncoalescing chains per bucket, and with random search for empty space. The analysis is asymptotic, and it is assumed that deletions do not occur. Simple closed formulas cannot be obtained, except in the case of bucket size one, but numerical results are readily computed. The expected performance compares favorably with that of other methods for handling overflow records.     

A comparison of some algorithms for the nonlinear least squares problem

The problem of minimizing a sum of squares of nonlinear functions is studied. To solve this problem one usually takes advantage of the fact that the objective function is of this special form. Doing this gives the Gauss-Newton method or modifications thereof. To study how these specialized methods compare with general purpose nonlinear optimization routines, test problems were generated where parameters determining the local behaviour of the algorithms could be controlled. The order of 1000 test problems were generated for testing three algorithms: the Gauss-Newton method, the Levenberg-Marquardt method and a quasi-Newton method.     

Convergence acceleration by means of numerical quadrature

By regarding a series as a Stieltjes integral to which classical numerical methods are applied, very accurate expressions for the sum are obtained. Convergence and stability are investigated in some cases of practical importance. When certain conditions are satisfied, realistic and strict error bounds for the sum can be found. Some generalizations are also indicated.     

Racematspaltung von (±)-5-äthyl-1-(3,4-dimethoxyphenyl)-6,7-dimethoxy-4-methyl-5H-2,3-benzodiazepin und anomales chiroptisches verhalten der enantiomeren

A process has been developed for resolving 1 , and the anomalous behaviour of the specific rotation of the enantiomers has been studied. It was shown that this is due to the shift in the conformational equilibrium la ? Ib , and not to an epimerization at C-5.     

Diffusion in phases with several components and sublattices

Diffusion in multicomponent alloys is discussed in order to extend earlier treatments to phases with sublattices. Both a phenomenological approach and some physical models are applied. Care is taken so that the driving forces and the fluxes are chosen in a way obeying the requirements of irreversible thermodynamics. The Onsager reciprocal relation will thus be obeyed. Two kinds of models have been considered, exchange between two atoms and exchange between an atom and a vacancy.For phases with several sublattices a number of difficulties arise and only a few cases of great practical importance are considered. The connection between practical diffusion coefficients and phenomenological coefficients is given. The use of different concentration variables in Fick's second law is discussed.     

Vibration-vibration energy transfer in gaseous HBr

The vibration-vibration energy transfer of HBr gas initially excited to the first vibrational state has been observed. Collisional pumping to the V = 2 level is measured by monitoring the fluorescence of the 2−1 transition. The rate constant for the process: HBr(V=0) + HBr(V=2) → 2HBr(V=1) is found to be 1.4×10⁵ sec⁻¹ torr⁻¹.     

Interpretation of electron spectra I. Spectra of furan,pyrrole and cyclopentadiene,studied with HAM/3

The interpretation of spectra of molecules by use of semi-empirical methods, of which SPINDO is an example, is usually possible for only one property of the molecule. If several properties of the molecules are used in the parametrization process the resulting method will have a more general applicability. This possibility is illustrated by the use of HAM/3 to interpret ionization energies, excitation energies and electron affinities of furan, pyrrole and cyclopentadiene.