The diminishing segment process

Let Ξ₀=[−1,1], and define the segments Ξ_n recursively in the following manner: for every n=0,1,…, let Ξ_n+1=Ξ_n∩[a_n+1−1,a_n+1+1], where the point a_n+1 is chosen randomly on the segment Ξ_n with uniform distribution. For the radius ρ_n of Ξ_n, we prove that n(ρ_n−1/2) converges in distribution to an exponential law, and we show that the centre of the limiting unit interval has arcsine distribution.     

Horoball packings and their densities by generalized simplicial density function in the hyperbolic space

The aim of this paper is to determine the locally densest horoball packing arrangements and their densities with respect to fully asymptotic tetrahedra with at least one plane of symmetry in hyperbolic 3-space $\overline{\mathbf{H}}^{3}$ extended with its absolute figure, where the ideal centers of horoballs give rise to vertices of a fully asymptotic tetrahedron. We allow horoballs of different types at the various vertices. Moreover, we generalize the notion of the simplicial density function in the extended hyperbolic space $\overline{\mathbf{H}}^{n}$ (n≧2), and prove that, in this sense, the well known B?r?czky–Florian density upper bound for “congruent horoball” packings of ? $\overline{\mathbf{H}}^{3}$ does not remain valid to the fully asymptotic tetrahedra. The density of this locally densest packing is ≈0.874994, may be surprisingly larger than the B?r?czky–Florian density upper bound ≈0.853276 but our local ball arrangement seems not to have extension to the whole hyperbolic space.     

Classification of Sol lattices

Sol geometry is one of the eight homogeneous Thurston 3-geometries $${\bf E}^{3}, {\bf S}^{3}, {\bf H}^{3}, {\bf S}^{2}\times{\bf R}, {\bf H}^{2}\times{\bf R}, \widetilde{{\bf SL}_{2}{\bf R}}, {\bf Nil}, {\bf Sol}.$$ In [13] the densest lattice-like translation ball packings to a type (type I/1 in this paper) of Sol lattices has been determined. Some basic concept of Sol were defined by Scott in [10], in general. In our present work we shall classify Sol lattices in an algorithmic way into 17 (seventeen) types, in analogy of the 14 Bravais types of the Euclidean 3-lattices, but infinitely many Sol affine equivalence classes, in each type. Then the discrete isometry groups of compact fundamental domain (crystallographic groups) can also be classified into infinitely many classes but finitely many types, left to other publication. To this we shall study relations between Sol lattices and lattices of the pseudoeuclidean (or here rather called Minkowskian) plane [1]. Moreover, we introduce the notion of Sol parallelepiped to every lattice type. From our new results we emphasize Theorems 3?C6. In this paper we shall use the affine model of Sol space through affine-projective homogeneous coordinates [6] which gives a unified way of investigating and visualizing homogeneous spaces, in general.     

In situ polyphenyl derivatisation and the effect of thermal decomposition of adsorbed and chemisorbed polyphenyls on the structure of multi-wall carbon nanotubes

This study presents the exploitation of an alternative reaction route of deamination of arylamines to perform in situ derivatisation of multi-walled carbon nanotubes (MWCNTs) with polyphenyl (PPh) species of various masses. As a result of consecutive derivatisation, high conversion of PPh grafting of the MWCNTs was realised with the collateral outgrowth of physical modification with adsorbed additional PPhs. Applied derivatisation process exceeds the monolayer coverage related superficial saturation limitations in the overall grafting yield of the nanotubes. Thus, a linear relationship was recognized between the overall quantities of chemisorbed PPhs composed of D₅-phenylene oligomers and the applied excess of diazonium activated reagents, corresponding to ²H MAS NMR spectroscopy results. According to mass spectrometry (MS) investigations, uniform thermal decomposition of the chemisorbed PPhs modified MWCNTs was found besides the more intense and altered decomposition characteristic-featured adsorbate-chemisorbate PPhs contained MWCNTs during sequential pyrolysis under inert atmosphere. This is attributed to the pyrolysis provoked isomerisation, decomposition and the formation of adsorbed and chemisorbed PPh moieties. As a result, a mediated and an even more pronounced degradation in the order of graphitic lattice of the MWCNTs were evidenced in the adsorbate-chemisorbate and the chemisorbate PPhs contained samples by FT-Raman spectroscopy and transmission electron microscopy (TEM), respectively. ²H MAS NMR supplied results of relevant amount of deuterium in the chemisorbate PPh contained sample without traces of aromatic related MS detected volatile products, these allow us to conclude about a thermally stable derivatisation that is interpreted as an endohedral modification of the nanotubes.     

On finite pseudorandom sequences of k symbols

In earlier papers C. Mauduit and A. Sárközy have introduced and studied the measures of pseudorandomness for finite binary sequences. In [8] they extend this theory to sequences of k symbols: they give the definitions and also construct a “good” pseudorandom sequence of k symbols. In this paper these measures are studied for a “truely random” sequence.     

Use of capillary electrophoresis to monitor wheat maturation

Summary The maturation of wheat varieties with different harvest times has been examined by high-performance capillary electrophoresis. The unique proteins of the albumin, gliadin and glutenin fractions of Hungarian winter wheat cultivars Bánkúti 1201 (early harvest time), Martonvásári 23 (medium harvest time), and Martonvásári 15 (semi-late harvest time) were analysed. An acidic phosphate buffer containing a polymeric additive and organic modifiers was used in capillary zone electrophoresis mode. Formation of albumin followed the same time scale, and the patterns were quite similar, for all three cultivars. For gliadins and glutenins the time scale and patterns were different and some correlation was observed between harvest time and gliadin formation. Presented at Balaton Symposium '01 on High-Performance Separation Methods, Siófok, Hungary, September 2–4, 2001     

Beiträge zur Chemie der Pyrrolpigmente, 3. Mitt.1: Die NH-Tautomerie von substituierten Pyrromethenen: Protonenresonanzspektrometrische Untersuchungen

NMR-spectra of several pyrromethenes were measured at different temperatures, concentrations and in different solvents. The chemical shifts of all protons were assigned and long range coupling constants determined. This variation of temperature, concentration and solvent provided evidence forintra- andinter-molecular proton transfer. In all pyrromethenes investigated the tautomeric NH exchanges are too fast—even at –100°C—to be measured by NMR.

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Mit 2 Abbildungen     

CD spectrometric methods for the simultaneous determination of ethisterone and its delta5-isomer

Quick and accurate direct and indirect circular dichroism (CD) spectrometric methods were developed for the simultaneous determination of ethisterone (17alpha-ethinyl-17-hydroxy-4-androstene-3-one) and its delta(5)-isomer (delta(5)-ethisterone). The direct method is based on the selective negative Cotton effect of the delta(4)-3-oxo group in ethisterone (negative maximum at 348 nm in dioxan) and measurement of the ellipticity at 296 nm (positive maximum of delta(5)-ethisterone), where the measured ellipticity is the sum of those of the two isomers. In the indirect procedure delta(5)-ethisterone is transformed to ethisterone by base-catalysed isomerization and the ellipticities are measured at 339 nm in ethanol before and after isomerization. Preliminary experiments show the usefulness of CD detector in the HPLC determination of the mixture of the isomers. A major advantage of the direct CD spectrometric and the HPLC/CD methods is that the delta(5)-isomer with extremely low UV activity can also be directly measured with high sensitivity.     

Kondo effect and spin filtering in triangular artificial atoms

We studied, strongly correlated states in triangular artificial atoms. Symmetry-driven orbital degeneracy of the single particle states can give rise to an SU(4) Kondo state with entangled orbital and spin degrees of freedom, and a characteristic phase shift δ=π/4. Upon application of a Zeeman field, a purely orbital Kondo state is formed with somewhat smaller Kondo temperature and a fully polarized current through the device. The Kondo temperatures are in the measurable range. The triangular atom also provides a tool to systematically study the singlet-triplet transitions observed in recent experiments [Phys. Rev. Lett., 88 (2002) 126803, cond-mat/0208268 (2002)].