Über die Existenz von freien Algebren

Ohne Zusammenfassung     

Untersuchungen über die photometrische Bestimmung von Tantal mit Pyrogallol

The optimum conditions for the photometric determination of tantalum with pyrogallol in sulphuric acid solution at 405 nm have been elaborated. The method has been checked statistically.     

Einige dielektrische Eigenschaften des gelben Bleioxyds

Zusammenfassung Es wurden einige dielektrische Eigenschaften polykristalliner gesinterter Bleioxydproben gemessen. Aus den Ergebnissen wird auf zwei Polarisationsvorgänge geschlossen, die bei niedrigen Frequenzen und Temperaturen zwischen 20–60 °C gleichzeitig die Werte der Dielektrizitätskonstante beeinflussen. Einer von ihnen ist mit dem Auftreten orientierter Bereíche verbunden, die spontane Polarisierung aufweisen, deren Sinn durch ein äusseres elektrisches Feld um 180° gedreht werden kann.     

Reactivity of α-acylated β-enamino ketones and esters: Synthesis of pyrazoles

The reactivity of the enamino compounds 4-amino-3-phenylamino(thio)carbonyl-3-penten-2-one 1 and 2 and ethyl 3-amino-2-phenylamino(thio)carbonyl-2-butyrate 7 and 8 was studied using the reaction with hydrazine hydrate and hydrazine hydrochloride to evaluate the 1,3 electrophilic center of the compounds by the formation of the pyrazole rings. The pyrazoles 3, 4, 5, 9, 11 and 13 were obtained depending on the reaction conditions employed.     

Scanning electron microscopy studies on surfaces from electrothermal atomic absorption spectrometry—I: Polycrystalline electrographite tubes with and without pyrographite coating

Morphological studies on graphite tube surfaces by scanning electron microscopy are presented for unused and corroded tubes from various endurance experiments in electrothermal AAS.Tubes always break in their center as this is the hottest part; tube thinning occurs predominantly at the outside. The inner surface of tubes coated with pyrographite is usually only slightly corroded, unless highly aggressive reagents are applied. Deposition of carbon in thin layers as well as in nodules is observed in the hot central zone.     

Domain formation and orbital ordering transition in a doped Jahn-Teller insulator

The ground state of a double-exchange model for orbitally degenerate e(g) electrons with Jahn-Teller lattice coupling and weak disorder is found to be spatially inhomogeneous near half filling. Using a real-space Monte Carlo method we show that doping the half-filled orbitally ordered insulator leads to the appearance of hole-rich disordered regions in an orbitally ordered environment. The doping driven orbital order to disorder transition is accompanied by the emergence of metallic behavior. We present results on transport and optical properties along with spatial patterns for lattice distortions and charge densities, providing a basis for an overall understanding of the low-doping phase diagram of La1 - xCaxMnO3.     

Counting arithmetical structures on paths and cycles

Let $G$ be a finite, connected graph. An arithmetical structure on $G$ is a pair of positive integer vectors $\mathbf{d},\mathbf{r}$ such that $(diag\left(\mathbf{d}\right)?A)\mathbf{r}=0$, where $A$ is the adjacency matrix of $G$. We investigate the combinatorics of arithmetical structures on path and cycle graphs, as well as the associated critical groups (the torsion part of the cokernels of the matrices $(diag\left(\mathbf{d}\right)?A)$). For paths, we prove that arithmetical structures are enumerated by the Catalan numbers, and we obtain refined enumeration results related to ballot sequences. For cycles, we prove that arithmetical structures are enumerated by the binomial coefficients $\left(\genfrac{}{}{0ex}{}{2n?1}{n?1}\right)$, and we obtain refined enumeration results related to multisets. In addition, we determine the critical groups for all arithmetical structures on paths and cycles.     

Continuous time random walks and the Cauchy problem for the heat equation

We deal with anomalous diffusions induced by continuous time random walks - CTRW in ?ⁿ. A particle moves in ?ⁿ in such a way that the probability density function u(·, t) of finding it in region Ω of ?ⁿ is given by ∫_Ωu(x, t)dx. The dynamics of the diffusion is provided by a space time probability density J(x, t) compactly supported in {t ≥ 0}. For t large enough, u satisfies the equation

$$u\left( {x,t} \right) = \left[ {\left( {J - \delta } \right)*u} \right]\left( {x,t} \right)$$

, where δ is the Dirac delta in space-time. We give a sense to a Cauchy type problem for a given initial density distribution f. We use Banach fixed point method to solve it and prove that under parabolic rescaling of J, the equation tends weakly to the heat equation and that for particular kernels J, the solutions tend to the corresponding temperatures when the scaling parameter approaches 0.