Local existence of solutions to the Euler–Poisson system,including densities without compact support

Local existence and well posedness for a class of solutions for the Euler Poisson system is shown. These solutions have a density ρ which either falls off at infinity or has compact support. The solutions have finite mass, finite energy functional and include the static spherical solutions for $\gamma =\frac{6}{5}$. The result is achieved by using weighted Sobolev spaces of fractional order and a new non-linear estimate which allows to estimate the physical density by the regularised non-linear matter variable. Gamblin also has studied this setting but using very different functional spaces. However we believe that the functional setting we use is more appropriate to describe a physical isolated body and more suitable to study the Newtonian limit.     

Über die Kleinsche Theorie der algebraischen Gleichungen

Ohne Zusammenfassung     

Transformations of isomeric naphthopyranones. The synthesis of substituted β-naphthyl-α,β-dehydro-α-amino acid derivatives

The opening of the pyranone ring in 2H-naphtho[1,2-b]pyran-2-one derivative (1) and 3H-naphtho[2,1-b]-pyran-3-one derivatives 8 and 20 with nucleophiles afforded 3-(naphthyl-1)- and 3-(naphthyl-2)propenoates (substituted β-naphthyl-α,β-dehydro-α-amino acid derivatives) 7, 13, 14, 15, 24 , and 35 .     

Meso-Tetraphenylporphyrin Dimer Derivative as a Potential Photosensitizer in Photodynamic Therapy

Abstract— Studies on the synthesis, preliminary in vivo biological activity, singlet oxygen and fluorescence yields of a di-meric porphyrin (Dl) are described. The pharmacokinetic behavior and photodynamic properties of the dimer Dl were examined in Balb/c mice bearing an MS-2 fibrosarcoma. Compound Dl shows a high selectivity for tumor localization (tumor/peritumoral tissue ratios of dye concentration ranging between ca 100 and 140 at 24 h after drug administration of 5.0-1.0 mg kg_-1 into DL-AL-dipalmitoylphosphatidylcholine liposomes). The photo-therapeutic efficiency of dimer Dl was evaluated by following the growth curves of fibrosarcoma irradiated with red light (600-700 nm) with a total dose of 400 J cm_-2, at 24 h after intravenous injection. Photodynamic therapy-treated tumors showed a significant delay in growth as compared to untreated control mice. The results obtained suggest that the porphyrin dimer Dl may be a promising candidate for further use in PDT experiments.     

Darstellung und Kristallstruktur von Niob-Tantal-Nitridphasen (Nb,Ta)N∼1

Preparation and Crystal Structures of Niobium-Tantalum-Nitride Phases (Nb, Ta)N_～1 Ta? Nb alloys with graduated composition are nitrided with NH₃ at 1100–1450°C. The mononitrides formed are investigated by X-ray diffraction. Their nitrogen content is evaluated by chemical analysis. Seven Ta? Nb nitride phases are observed. Depending on the temperature, the phases appear in a strictly defined sequence along the variation of the Ta:Nb relation. Corresponding to this sequence, the density (formula volume) of this nitride phases varies.     

Sintering and crystallization of titanium-containing lead borate glasses

The sintering and crystallization of glass powders with chemical composition 47 PbO—38 B₂O₃—15 TiO₂ (mole %) was investigated under non-isothermal conditions by shrinkage measurements, differential thermo-analysis (DTA), X-ray diffraction (XRD), dielectric measurement and positron annihilation (Doppler broadening). The correlation between changes of macroscopic properties and positron annihilation results recommends this method for the detection of structural changes in glasses.     

Synthesis and characterization of a helical step‐ladder polyarylene

A helical step‐ladder polyarylene incorporating chiral (R)‐2,2′‐dioctoxy‐1,1′‐binaphthyl units was synthesized for the first time. The first step involved the preparation of a precursor poly(arylene ketone) via a palladium‐mediated Suzuki‐type cross‐coupling reaction with the aid of microwave heating. Two polymer‐analog reaction steps, the reduction of the keto groups to tertiary alcohol functionalities and subsequent intramolecular Friedel–Crafts cyclization, gave a step‐ladder polymer ( 6 ) in good yields with reasonable mean average molecular weights greater than 13,000. The regioselective cyclization pattern in the α position of the naphthalene core was confirmed by a comparison of the NMR data of the polymer with those of the corresponding model ladder oligomers, 12 and 13 , and also a single‐crystal structure of 13 . The optical spectra of the oligomers and polymers indicated that there was little electronic interaction across the binaphthyl units. The circular dichroism spectrum of 6 exhibited a strong bisignate Cotton effect in the π–π* absorption region of the planar chromophores, which reflected the strong exciton coupling within the helical polymer chain. © 2006 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 44: 5533–5545, 2006     

Über Systeme hyperkomplexer Zahlen

Ohne Zusammenfassung     

Über die Dichte der Summe zweier Mengen. deren eine von positiver Dichte ist

Ohne Zusammenfassung