On false branch points of incompressible branched immersions

We prove that a branched immersion of a surface with boundary into a differentiable manifold has no false branch points (in fact, no ramified points) if the immersion induces an isomorphism of fundamental groups and some other natural hypotheses are satisfied. This result has immediate applications to Plateau's problem.Work done while the first author was a visiting member of the Max-Planck-Institut für Mathematik at Bonn. Both authors acknowledge the support of Max-Planck-Institut für Mathematik, Bonn and Schwerpunkt Geometrie at Mathematisches Institut, University of Heidelberg     

Schwingungsspektren und Kraftkonstanten von Hexamethyldisilan,Hexaphenyldisilan und 1,1,1-Trimethyl-2,2,2-triphenyldisilan

The Raman and infrared spectra of (CH₃)₃SiSi(CH₃)₃ (I), (CD₃)₃SiSi(CD₃)₃, (C₆H₅)₃SiSi(C₆H₅)₃ (II), (CH₃)₃SiSi(C₆H₅)₃ (III), and (CD₃)₃SiSi(C₆H₅)₃ are reported. Assignments are based on symmetry G ₃₆ ⁺ (free internal rotation) forI, D_3d forII, and C_3v forIII. Normal coordinate treatment has been done using some simplifications in the phenyl coordinates. The SiSi stretching force constant inI amounts to 1,65 N/cm. In compoundsII andIII strong vibrational coupling is elucidated byPED calculations.     

1-Alkoxy-2-azaallenyl-komplexe von chrom und wolfram

The successive reaction of (CO)₆M with Na[NCR₂¹] and [Et₃O]BF₄ yields (CO)₅M[C(NCR₂¹)OEt] (II: M = Cr; III: M = W; CR₂¹ = C(C₆H₄Br-p)₂ (a), CPh₂ (b), C(C₆H₄OMe-p)₂ (c), C(C₆H₄)₂O (d), CBu₂^tt (e)). Hexacarbonyltungsten, (CO)₆W, reacts with Na[NCPh₂] and MeOSO₂F to give (CO)₅W[C(NCPh₂) OMe] (IV). X-Ray analysis of IIe shows that: (1) the CNC fragment is almost linear (171.7°); (2) the two NC bond lengths are equal within experimental error; and (3) the O,C,Cr,N plane is perpendicular to the C(Me₃),C,N,C(Me₃) plane (90.0°). Therefore compounds II–IV are best described as 1-alkoxy-2-azaallenyl complexes.     

Automatisches Verfahren zur Bestimmung des Bleioxidgehalts von Grauoxid durch Messung der L?sungsw?rme

Zusammenfassung Für das zur Herstellung von Bleibatterien verwendete Grauoxid (bestehend aus einem feinteiligen Gemisch von ca. 60 bis 90% Bleioxid, PbO, und einem Rest metallischem Blei) wurde ein Verfahren zur kontinuierlichen bzw. quasikontinuierlichen, automatischen Bestimmung des PbO-Gehaltes an den Fertigungsanlagen benötigt. Eine schnelle Analyse mit vergleichsweise geringem Aufwand war durch Messung der Lösungswärme bei Behandlung einer abgewogenen Menge Grauoxid mit verd. Essigsäure möglich. Unter technisch bequem realisierbaren Bedingungen wurden Temperaturerhöhungen von einigen Grad erhalten. Der Einfluß verschiedener Arbeitsbedingungen, der verschiedenen PbO-Modifikationen und der Teilchengröße und -form wurde untersucht. Zur Zeit wird eine für die Fertigung bestimmte, automatische Apparatur aufgebaut, die bei einer Analysenfolge von 1 min die Bestimmung mit einer Standardabweichung unter ±1% durchzuführen gestattet.

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Automatic procedure for the determination of the lead oxide content of gray oxides by measurement of the heat of solution

A continuous or semicontinuous automatic method for the determination of the lead oxide content was needed in the manufacturing process of gray oxides (a fine particle mixture of about 60 to 90% lead oxide, PbO, and metallic lead, used in manufacturing lead batteries).A rapid determination with comparatively small effort was possible by measuring the heat of solution of a weighed amount of gray oxides treated with acetic acid. Temperature rise of a few degrees could be reached under technically realisable conditions. The influence of different working conditions, of the particle size and shape and of the PbO modifications were investigated. An automatic apparatus for the determination is at present being built and will give one determination per minute with a standard deviation of less than ±1%.

     

Infrared intensities of the external modes of crystalline nitrous oxide

The absorption intensities of two infrared active lattice modes of crystalline N₂O have been measured. Both the frequencies and intensities of the external modes of N₂O have been found to be very similar to those of CO₂, and most of the differences between the spectra of CO₂ and N₂O can be explained by the differences in the quadrupole moments.     

New minimal geodesics in the group of symplectic diffeomorphisms

We compute the Hofer distance for a certain class of compactly supported symplectic diffeomorphisms of ²ⁿ. They are mainly characterized by the condition that they can be generated by a Hamiltonian flow _H ^t which possesses only constantT-periodic solutions for 0 <T 1. In addition, we show that on this class Hofer's and Viterbo's distances coincide.     

Surgery on 3-manifolds with \mathbb{S} 1-actions

We study the topological structure of all 3-manifolds obtained by surgery along principal fibers of a closed orientable -manifold. As a consequence, we give alternative proofs of some classical results due to W. Heil and L. Moser. Moreover, we completely specify the Seifert invariants for the considered manifolds. Finally we classify the manifolds obtained by surgery along certain Seifert links and determine geometric presentations of their fundamental groups.Work performed under the auspices of C.N.R. (National Research Council) of Italy and partially supported by Ministero della Ricerca Scientifica e Tecnologica within the projects Geometria Reale e Complessa and Topologia.