A stepsize control for continuation methods and its special application to multiple shooting techniques

Summary A numerically applicable stepsize control for discrete continuation methods of orderp is derived on a theoretical basis. Both the theoretical results and the performance of the proposed algorithm are invariant under affine transformation of the nonlinear system to be solved. The efficiency and reliability of the method is demonstrated by solving three real life two-point boundary value problems using multiple shooting techniques. In two of the examples bifurcations occur and are significantly marked by sharp changes in the stepsize estimates.     

Mixed ligand complexes of ruthenium(III), rhodium(III) and iridium(III) with dipicolinic acid and some monobasic bidentate nitrogen,oxygen donor ligands

The trivalent ruthenium, rhodium and iridium complexes of dipicolinic acid and its mixed ligand complexes with several nitrogen, oxygen donor molecules, of types: Na[M(dipic)₂]·2H₂O and [M(dipic)(N-O)]·nH₂O (where M = Ru(III), Rh(III) or Ir(III); dipicH₂ = dipicolinic acid; NOH represents different nitrogen, oxygen donor molecules, viz., picolinic acid, nicotinic acid, isonicotinic acid, glycine, aminophenol, o- or p-aminobenzoic acid), have been synthesized and characterised on the basis of elemental analyses, electrical conductance, magnetic susceptibility measurements and spectral (electronic and infrared) data. The parent dipicolinic acid complexes are found to have a six-coordinate pseudooctahedral structure, whereas for mixed ligand complexes, a polymeric six-coordinate structure has been assigned. Various ligand field and nephelauxetic parameters have also been evaluated.     

Hyperfine structure in Iodine at the 612-nm and 640-nm helium-neon laser wavelengths

The hyperfine structure of iodine-127 at 612 nm and 640 nm is observed by saturated absorption in a gas cell placed within a He-Ne laser cavity modified to operate at these wavelengths. At 612 nm, all the 21 components of the strong R 47 9-2 line lie within the laser gain profile, and the resulting saturated absorption peaks have a contrast of 10% at a gas pressure of 3 Pa.     

An X-ray double-crystal method utilizing non-parallel setting for measuring local lattice mismatches between epitaxial films and substrates

An X-ray topographic method utilizing non-parallel (+,-) setting for measuring lattice mismatches between epitaxial films and substrates is reported. This method gives quantitative as well as topographical information on lattice distortions in a distorted crystal and allows us to study any reflection from various crystals, in which the fractional variation of lattice spacing, δd/d, is of the order of 10^-4?10^-5. Examples of applications are lattice mismatches between epitaxial magnetic garnet films and (111) gadolinium garnet (GGG) substrates. The spacing of the epitaxial film was slightly larger along the [111] direction than that of the substrate and the apparent crystal symmetry of the epitaxial film is rhombohedral.     

An automatic electrometer ranging circuit for a spark-source mass-spectrometer

An auto-ranging circuit which accommodates the erratic nature of the electrometer output signals from a spark-source mass-spectrometer is described briefly.     

Synthese eines verbrückten π-allyl-chinolin-palladiumchlorid-komplexes

Chloro[N-3′5′-η-(4′-methylpentenyl)quinoline-2]palladium was synthesized; the NMR-spectrum of this compound is helpful in distinguishing the cis/trans-isomers of other non-bridged π-allyl-base-palladium chloride complexes.     

Peptides—XXXV: Synthesis of the 17–26 fragment of a lysozyme analogue

The fully protected 17–26 fragment of a lysozyme analogue has been synthesised. A fragment condensation approach has been employed using the protected subfragments 17–19, 20–22 and 23–26. In the synthesis of the subfragments the use of the diphenylphosphinyl mixed anhydride method has been demonstrated.     

Characterizations of spaces by embeddings in βX

In this paper we obtain characterizations of metrizable spaces, paracompact M-spaces, Moore spaces and semimetrizable spaces in terms of the way those spaces are embedded in their Stone-?ech compactification. In addition, we give an internal characterization of paracompact M-spaces which we use in the proof of the embedding characterization.     

Endor frequencies of randomly oriented triplets by electron spin echo spectroscopy

ENDOR frequencies of randomly oriented triplets have been measured from the fast Fourier transform of electron spin echo envelope modulation. Important experimental conditions are low temperatures, high microwave power and long phase memory time in a proper form of solvent. The technique is exemplified by using diphenylmethylenes in rigid glasses, polycrystalline forms and single crystals of benzophenones.