Inverses of Boolean matrices

For a Boolean matrix A, a g-inverse of A is a Boolean matrix G satisfying AGA=A, and a Vagner inverse is a g-inverse which in addition satisfies GAG=G. We give algorithms for finding all g-inverses, all Vagner inverses, and all of several other types of inverses including Moore-Penrose inverses. We give a criterion for a Boolean matrix to be regular, and criteria for the various types of inverse to exist. We count the numbers of Boolean matrices having Moore-Penrose and related types of inverses.     

Interpretation of resonance cars and shpolskii spectra with calculated molecular geometries,vibrational frequencies and relative intensities: Chrysene in it's lowest excited singlet and triplet state

Coherent anti-Stokes Raman scattering (CARS) spectra of excited molecules as well as Shpolskii spectra provide information about geometry changes between ground and excited states. Vibrational frequencies and relative intensities from recently obtained CARS spectra of the chrysene S₁ and T₁ state and earlier observed Shpolskii spectra are interpreted in terms of molecular geometry and force-field changes by means of quantum-chemical consistent force field (QCFF) and Franck-Condon factor calculations. The comparison of observed and calculated relative intensities indicates a coupling between the S₁ and S₂ state enhancing some of the vibrational radiative singlet transitions both in absorption and fluorescence spectra whereas within the phosphorescence spectra proportionality to calculated Franck-Condon factors is obeyed. The T₁ state is the more loosely bound state and its geometry change is different from that of the S₁ state. The resonance CARS transitions in the S₁ state are assigned to totally symmetric vibrations getting their intensity by a coupling scheme analogous to the A term of the resonance Raman effect: the relative intensity of a transition is shown to be proportional to the Franck-Condon factor to the higher excited state and to the squared vibrational frequency. Using this relation this state can be identified by means of its finger-print-like intensity pattern.     

Une méthode polarimétrique simple pour l'étude des métaux

A simple polarimetric method for the study of metals is discussed. Modulation is obtained by means of a rotating retardation plate and information is extracted from the phase of the signal. Polarizer and analyser have fixed positions, and the system requires no optical compensator and no calibration. Systematic error due to polariser-analyser reference settings is eliminated. Also scanning of the wavelengths is possible.     

A search for charmed particles originating from the interactions of 300 GeV/c protons in emulsion nuclei

The associated production of charmed particles by the interactions of 300 GeV/c protons with complex nuclei has been sought using nuclear emulsions. The failure to observe any candidates for this process among some 60,000 interactions investigated implies, provided charmed particles lifetimes are in the range 10^?12 to 10^?14 s, a cross section for their associated production by the interactions of 300 GeV/c protons with nucleons of less than 1.5 microbarns at a 90% confidence level.     

Analyse von Hydroxysteroiden mit Hilfe der19F-NMR-Spektroskopie

Zusammenfassung Fluorresonanzsignale zeigen Änderungen der chemischen Umgebung eines Fluorkerns wesentlich empfindlicher an als Protonenresonanzsignale. Die chemischen Verschiebungen der CF₃-Singuletts trifluoracetylierter Hydroxylgruppen am Steroidgerüst sind in charakteristischer Weise von Position und Konfiguration der OH-Gruppen abhängig. Daher können Hydroxylgruppen an den C-Atomen 3, 6, 11, 12, 17 und in der Seitenkette an Ring D von Steroiden einfach und schnell mit Hilfe der¹⁹F-NMR-Spektren der Trifluoracetylderivate charakterisiert werden. Diese empfindliche Sensortechnik erlaubt Strukturbestimmungen und quantitative Analysen von Hydroxysteroidgemischen im Mikrogrammbereich.

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Analysis of hydroxy steroids by¹⁹F-NMR spectroscopyDetermination of structure and quantitative analyses of hydroxy steroid mixtures in the microgram range

Compared with proton resonance signals fluorine resonance signals depend much stronger on differences in the chemical environment of a fluorine nucleus. The¹⁹F-NMR shifts of the CF₃ singlets of trifluoroacetylated hydroxy groups on the steroidal skeleton characteristically reflect the position and configuration of OH groups on the carbons 3, 6, 11, 12, 17 and on the side chain at ring D. Therefore this sensitive technique provides a convenient tool for the structure elucidation and for quantitative analysis of mixtures of hydroxy steroids in the microgram range.

     

On 3-skein isomorphisms of graphs

It is shown that a 3-skein isomorphism between 3-connected graphs with at least 5 vertices is induced by an isomorphism. These graphs have no loops but may be infinite and have multiple edges.     

Absolute triple differential cross sections for electron impact ionization of helium: Comparison between experimental and theoretical results at 256 eV collision energy

Triple differential cross sections have been measured for electron impact ionization of helium at 256 eV collision energy, 3 eV energy of the slow outgoing electrons and scattering angles of the fast outgoing electrons of 4°, 6°, 8°, and 10°. The data have been put on absolute scale by extrapolating the generalized oscillator strength to zero momentum transfer. In this optical limit the triple differential cross sections can be normalized by using the well-known cross sections for photoionization. The experimental data are compared with results of different theoretical approaches. For nearly all calculated curves rather good agreement with the measurements is obtained for the relative shape of the binary peak, while often its absolute cross section is overestimated. Concerning the recoil peak, larger discrepancies are found with respect to both, relative shapes and cross sections. A perceptible improvement can be stated for calculations which have been performed in a distorted wave approximation and in second Born approximation.