Über die Dehnung von Sphärenabbildungen

Ohne Zusammenfassung     

Panel The integration of voice science, voice pathology, medicine, public speaking, acting, and singing

The integration of voice science, voice pathology, medicine, public speaking, acting, and singing has been central to evolution in all fields. The Voice Foundation Symposia have played a seminal and central role in fostering integration among disciplines. The result has been an improvement in the knowledge and practice in each field. And the future promises to be even more informative and exciting.     

N.m.r. characterization of functional groups: 5—on the nature of olefinic end groups in polyisobutylenes

Proton n.m.r. signals for two types of olefinic end groups, -CH₂C(CH₃)?CH₂ (δ4.68 and δ4.87) and -CH?C(CH₃)₂ (δ5.21), have been observed in high molecular weight polyisobutylenes. Comparable amounts of both these end groups exist in commercial and laboratory prepared samples of polyisobutylenes contrary to previous reports that the former group is by far predominant. That different catalysts produce different relative concentrations of these end groups is demonstrated. Evidence for the presence of a third type of unsaturation from the -CH₂C(CH₂)?CH₂- structure is discussed.     

A Study of C5H10 radical cations by collisionally activated dissociation,charge stripping,and low energy ion-molecule reactions

C₅H₁₀ radical cations generated from a variety of olefins and cycloalkanes were investigated by collisionally activated dissociation, charge stripping, and low energy ion-molecule reactions. It has been determined that all of the isomers studied can be distinguished by charge stripping, whereas collisionally activated dissociation and the ion-molecule reactions are less informative. The radical cations from cyclopentane, methylcyclobutane and substituted cyclopropanes retain their cyclic structures for at least a fraction of the population having lifetimes in the microsecond range.     

Photoemission studies of clean and oxygen-covered Pt 6(111) × (100)

Employing the enhanced sensitivity obtained by using synchrotron radiation near the Cooper minimum for the 5d valence electrons, we have located the oxygen 2p and 2s levels for oxygen chemisorbed on a Pt 6(111) × (100) crystal. We find the oxygen 2p level located ?6 eV with a FWHM of 3 eV and the 2s at ?21.6 eV. A factor of four difference in saturation coverage is measured between temperatures of 300 and 120 K, but the position and width of the 2p level is independent of temperature. We observe also the 1b₁ orbital of weakly adsorbed H₂O molecules, which has pure O 2p parentage; from the intensity of this orbital, we are able to suggest why it is difficult to observe the oxygen 2p signal at low photon energies. In addition, we note a strong preferential attenuation in the Pt states near E_f for the adsorbed H₂O in spite of the weak nature of the bond.     

The biparticity of a graph

The biparticity β(G) of a graph G is the minimum number of bipartite graphs required to cover G. It is proved that for any graph G, β(G) = {log₂χ(G)}. In view of the recent announcement of the Four Color Theorem, it follows that the biparticity of every planar graph is 2.