On the stability of a class of convergence acceleration methods for power series

In this paper we study the problem of evaluating the sum of a power series whose terms are given numerically with a moderate accuracy. For a large class of divergent series a sum may be defined using analytic continuation. This sum may be estimated using the values of a finite number of terms. However, it is established here that the accuracy of this estimate will generally deteriorate if we use an ever-growing number of terms. A result on the stability of product quadrature is also obtained as a corollary of our main stability theorem.Dedicated to professor Germund Dahlquist, on the occasion of his 60th birthday     

Computing the nucleolus when the characteristic function is given implicitly: A constraint generation approach

We study a class of cooperative games that is such that the values of the characteristic function are given implicitly. A constraint generation procedure can be applied to compute the nucleolus (and related solutions) of such a game, even if the number of players is large.     

Simple models for wentzel-druyvesteyn satellite energies in soft X-ray emission spectra of molecules

Simple models for the energy displacement between Wentzel-Druyvesteyn satellites and main lines in soft X-ray emission spectra of molecules are presented. The models include effective hole-hole interaction parameters and are evaluated numerically for H₂O.     

Conformational studies on substituted purines

CNDO/2 calculations are performed on 9-methyl-8-phenyl-6-thiopurine in order to determine the molecular equilibrium conformation. The two methyl hydrogens are found to be staggered to the ortho hydrogen on the phenyl ring, and the dihedral angle between the phenyl group and the purine system was found to be equal to 30°, in good agreement with experimental data. The results are discussed in relation to other conformational analyses performed with the CNDO/2 method.     

Single-point titrations: Part II. Experimental determination of bases

An acid—base mixture is described which has linear pH response when titrated with strong base. The concentrations of the separate components in the mixture are given. Determinations of bases in the tange 0.05 M—0.25 M with a relative standard deviation of less than 0.5 % are reported. The method of preparing the mixture as well as some interferences of high salt concentrations in the sample are discussed.     

Antiaromatic Sapphyrin Isomer: Transformation into Contracted Porphyrinoids with Variable Aromaticity

Sapphyrin is a pentapyrrolic expanded porphyrin with a 22π aromatic character. Herein, we report the synthesis of a 20π antiaromatic sapphyrin isomer 1 by oxidative cyclization of a pentapyrrane precursor P₅ with a terminal β-linked pyrrole. The resulting isomer 1 , containing a mis-linked bipyrrole unit in the skeleton, exhibits a reactivity for further oxidation due to the distinct antiaromatic electronic structure, affording a fused macrocycle 2 , possessing a spiro-carbon-containing [5.6.5.6]-tetracyclic structure. Subsequent treatment with an acid afforded a weakly aromatic pyrrolone-appended N-confused corrole 3 , and thermal fusion gave a [5.6.5.7]-tetracyclic-ring-embedded 14π aromatic triphyrin(2.1.1) analog 4 . The cyclization at the mis-linked pyrrole moiety of P₅ played a crucial role in synthesizing the antiaromatic porphyrinoid susceptible to facile transformation to novel porphyrinoids with variable aromaticity.     

A note on a local effect at the Schwarzschild sphere

Passage of the Schwarzschild radius is shown to be locally measurable by a sign change in a certain scalar. In the Kerr solution this scalar changes sign at the stationary limit. This is an example of the use of a coordinate-invariant method, based on the curvature tensor and a finite number of its covariant derivatives, for investigating gravitational fields.     

Large transverse momentum particle production in αα and pp collisions at the CERN ISR

The production of charged hadrons with high p_T in αα collisions at √s=126 GeV and pp collisions at √s=31 and 63 GeV is compared, and the structure of the events associated with the high-pT particles is studied. The probability of finding associated particles close to the trigger particle increases strongly between √s=31 and 63 GeV for pp collisions. For p_T>2.5GeV/c the αα/pp cross section ratio at the same energy per nucleon is measured to be 18.7 ± 2.0, to be compared with A² = 16, and a higher associated multiplicity is observed for αα.