Über die Konvergenzfragen der Mondtheorie

Ohne ZusammenfassungDie vorliegende Abhandlung stel't einen Abdruck der von der mathematischnaturwissenschaftlichen Abteilung der Philosophischen Fakultät def Universität Leipzig angenommenen Inauguraldissertation dar.     

Dynamische Systeme und unitäre Matrizen

Ohne Zusammenfassung     

Über die Stetigkeit der asymptotischen Verteilungsfunktion bei inkommensurablen Partialschwingungen

Ohne Zusammenfassung     

Über die kleinen numerischen Divisoren in der Theorie der allgemeinen Störungen

Ohne ZusammenfassungInternational Education Board Fellow.     

Zur Theorie der unendlichen Differentialsysteme

Ohne Zusammenfassung     

Ein Satz über unendliche Systeme von linearen Gleichungen

Ohne Zusammenfassung     

Two-dimensional Meixner Random Vectors of Class ${mathcal{M}}_{L}$

The paper is divided into two parts. In the first part we lay down the foundation for defining the joint annihilation–preservation–creation decomposition of a finite family of not necessarily commutative random variables, and show that this decomposition is essentially unique. In the second part we show that any two, not necessarily commutative, random variables X and Y for which the vector space spanned by the identity and their annihilation, preservation, and creation operators equipped with the bracket given by the commutator forms a Lie algebra are equivalent up to an invertible linear transformation to two independent Meixner random variables with mixed preservation operators. In particular, if X and Y commute, then they are equivalent up to an invertible linear transformation to two independent classic Meixner random variables. To show this we start with a small technical condition called “non-degeneracy”.     

Preliminary studies of material surface cleaning with a multi-pulse passively Q-switched Nd:YAG laser

A multi-pulse Q-switched (MPQ) Nd:YAG laser system for surface material cleaning has been developed. Trains of pulses having total output energy of as much as 1.05 J, 10–30 pulses/train, 20–70 ns individual pulse-width, and about 100 μs whole duration were generated. Ablation threshold fluence and ablation rate for limestone substrate have been measured and compared with the theoretical calculations. Safe surface cleaning of limestone samples was demonstrated thanks to the high gap between the ablation threshold fluence of the substrate and black crust. Tests of surface cleaning for samples of stone, ceramics, and metal were performed.     

Superparamagnetic magnetite–divinylbenzene–maleic anhydride copolymer nanocomposites obtained by dispersion polymerization

Magnetite alternating copolymers divinylbenzene–maleic anhydride (DVB–MA) composites were prepared by dispersion polymerization. Because magnetite is used as a complex with oleic acid (Fe₃O₄OLA), the final hybrids show good dispersion of inorganic nanofillers in the polymer matrix. The obtained composites were analyzed by infrared absorption spectrometry, diffuse reflectance in visible light, thermogravimetry, X-ray fluorescence, X-ray diffraction, dynamic light scattering, scanning electron microscopy and vibrating sample magnetometry. The obtained results indicate the successful preparation of magnetite nanoparticles with an average size of about 23 nm dispersed in micrometer size copolymer spherical particles, which relative content can be controlled via the processing parameters. A relationship between the relative content of magnetite nanoparticles and the size of the polymer particles, with direct influence on the diffuse reflectance in the visible domain, was observed. A superparamagnetic behavior was evidenced at room temperature with a blocking temperature lower than as expected from the bulk anisotropy constant and the average size of the magnetite nanoparticles. Both the unexpected low blocking temperature and the observed low specific magnetizations were explained by a defected and poor crystalline structure of the magnetite nanoparticles, giving rise to spin disorder and diminished crystalline anisotropy constant.