LP-Abschätzungen und klassische Lösungen für nichtlineare Wellengleichungen II

This paper deals with the global classical solvability of the Cauchy problem for nonlinear wave equations of higher order of the following form where denotes the Laplacian, a real constant, m a positive integer, and f the nonlinearity. Using results of the first part [6] concerning estimations for the kernel of the associated integral equation a priori estimates for certain L^P-norms of the local regular solution are established for higher space dimensions and for a class of nonlinearities satisfying certain growth and positivity conditions. This leads to completely regular solutions by means of the Sobolev embedding theorems.     

Organometallic complex compounds,part 6(1). Property-specific ligand control of stability and reactivity of (1,3-dimethyl-η3-allyl)methylnickel-ligand complexes. Separation of electronic and steric effects

Summary The property-specific ligand control of 28 ligands on the decomposition temperatures in solution, measured by d.t.a. of a four-coordinate nickel(II)-complex is reported. A quantitative separation of electronic and steric effects by a multilinear regression analysis (75% electronic and 25% steric influence for the chosen ligands) is presented. The controlling effect of the selectivity on the decomposition (fraction of the C-C-linked product) (25 P-ligands) leads to an electronic: steric ratio of the property-specific ligand control of 5545 for the chosen ligands. An increase in the relative acceptor character of the P-ligands relatively destabilizes the complexes and thereby favours formation of a C-C-bond. An increase in steric hindrance also favours C-C-bond formation. A method for revising the steric parameter of P-ligands is presented and is used to correct the -value of (PhCH₂)₃P is corrected to 135°. SCCC-MO-calculations for testing the chemical reasoning of the separated electronic and steric ligand property control are shown.     

Novel rhenium chelate system derived from dimercaptosuccinic acid for the selective labeling of biomolecules

This work is part of an effort to develop chelating agents for stable binding and easy conjugation of Re-188 to biologically interesting structures. Starting from the well-known in vivo stability of [(188)ReO(DMSA)(2)](-), we want to exploit this coordination system for the design of (188)ReO(V) chelates, which are stable toward reoxidation to perrhenate and toward ligand exchange under all conditions of radiopharmaceutical development. Therefore, a new type of tetradentate ligand has been synthesized by bridging two molecules of N,N'-diisobutyl-2,3-dimercaptosuccinamide with N-(3-aminopropyl)propane-1,3-diamine. The resulting stereoisomeric tetrathiolato S(4) ligand of composition ((i)()Bu)(2)N(O)C-C(SH)-C(SH)-C(O)NH-(CH(2))(3)-NH-(CH(2))(3)-NHC(O)-C(SH)-C(SH)-C(O)N((i)Bu)(2) forms anionic five-coordinate oxorhenium(V) complexes by a ligand-exchange reaction of NBu(4)[ReOCl(4)] in methanol. In the absence of a base, the compounds were isolated as "betaine", [ReO(S(4))], with the protonated nitrogen of the bridge serving as an internal "counterion". Two representatives have been fully characterized in both the solid and solution states and found to adopt the expected square-pyramidal coordination geometry. The equatorial plane is formed by four thiolate sulfur atoms, whereas the oxygen occupies the apical position. The orientation of the metal oxo group is exo in relation to the carbamido groups in both isomers. Both complexes are stereoisomeric regarding the junction of the triamine chain.     

Emission,Emissionslebensdauer und Absorption von [Cr urea6]X3-Einkristallen

Emission and absorption polarization spectra as well as emission lifetimes between room temperature and 5 °K have been measured of [Cr urea₆]X₃ single crystals, where X stands for ClO ₄ ^– , J^–, NO ₃ ^– , Br^–, Cl^–, F^–, and X₃ for JSO ₄ ^3– . The strong temperature dependence of the fluorescence/phosphorescence-ratios, and of the emission lifetimes is discussed. The differences between the spectra as well as the emission lifetimes of the various salts can be attributed to an anion dependent trigonal perturbation.

Die Autoren danken dem Verband der Chemischen Industrie für finanzielle Unterstützung dieser Arbeit.     

Time decay for nonlinear wave equations in two space dimensions

The Cauchy Problem for the equation u_tt–u+|u|^p–1u=0 (x², t>0, >1) is studied. Smooth Cauchy data is prescribed, and no smallness condition is imposed. For >5, it is shown that the maximum amplitude of such a wave decays at the expected rate t^–1/2 as t. For 1+8<5, the maximum amplitude still decays, but at a slower rate. These results are then used to demonstrate the existence of the scattering operator when >_o, where _o is the root of the cubic equation ³-2²-7-8=0; thus _o4.15.Alfred P. Sloan Research Fellow     

En route to coordination chemistry under confined conditions in a porous capsule: Pr3+ with different coordination shells

The highly charged nanocontainer capsule of the type [pentagon]12[linker]30 identical with [(Mo)Mo5O21(H2O)6]12[Mo2O4(SO4)]30 with 20 nanosized pores and channels allows the entrance of cations like Pr3+: the latter are positioned at two different sites and have two different coordination shells, corresponding to a coordination chemistry under confined conditions; a fascinating aspect is that capsule encapsulated water shells fixed by hydrogen bonds act formally as polydentate ligands.     

On the rotordynamic stability of two-pole synchronous electric machinery considering different load cases

This paper discusses stationary rotordynamics of synchronous electric machinery, considering different load cases. The model comprises the electrical operation in a rigid network and in an isolated condition. The mechanical part is modelled as a Laval Rotor (Jeffcott Rotor) with a noncircular shaft, accounting for both static- and dynamic rotor eccentricities. The results show, that the machine's electrical operation may influence the occurence of mechanical vibrations significantly and therefore demonstrate the importance of analysing the electromechanical interaction. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Bifurcation behaviour and limit cycles of a compliant seal-rotor system

This contribution discusses the non-linear dynamic behaviour of a rotor system equipped with a compliant seal. The investigated model consists of a Laval-Rotor and a stiff seal ring which is visco-elastically supported. The fluid forces stemming from the turbulent incompressible lubricant film are accounted for by the non-linear Muszynska model. The added compliance leads to an improved stability behaviour of the steady state. Within the post-critical regime the additional compliance gives rise to bifurcations of the stationary vibration: Hopf bifurcations lead to limit cycles which can loose their stability via Neimark-Sacker bifurcations. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Tannin-Mordant Coloration with Matcha (camelia sinensis) and Iron(II)-Lactate on Human Hair Tresses

The aim of this work was to optimize our natural hair dyeing system which we described in our previous work and to compare with other dyeing systems. Therefore, we investigated concentration limits of matcha and mordant and compared this new dyeing method with commercial permanent systems on the market. Completely unpigmented hair tresses were dyed with matcha powder (camelia sinensis) and iron(II)-lactate. To investigate the wash fastness and concentration limits, the differently dyed hair tresses were spectrophotometrically measured. The comparison of the damage potential for which cysteic acid is an indicator was measured by NIR. The concentration of matcha and mordant are responsible for the intensity of the color results. The higher the matcha or the mordant concentration, the darker the color results of the dyed hair tresses. Hair damage of matcha mordant dyeing is comparable with results of commercial permanent hair coloration systems. Moreover, the results of wash fastness of matcha mordant dyed hair tresses is comparable and even better by tendency to permanent colored hair tresses.