Die kleinste Bedeckungszahl innerhalb einer Klasse von Flächenabbildungen

Ohne Zusammenfassung     

Über verallgemeinerte Momente additiver Funktionen

In this paper we give characterizations of additive functionsf, for which $$\mathop {\lim \sup }\limits_{x \to \infty } x^{ - 1} \sum\limits_{n \leqslant x} {\varphi (|f(n)|)}$$ is bounded, where φ: ?⁺ → ?⁺ is monotone and or $$\begin{array}{*{20}c} {\varphi (x) = c^x } & {(x \in \mathbb{R}).} \\ \end{array}$$ A typical example is φ (x)=x ^a (a>0) forx≥0.     

Use of solid-phase microextraction-capillary-gas chromatography (SPME-CGC) for the varietal characterization of wines by means of chemometrical methods

The extraction of wine aroma compounds was studied by direct-SPME (DI/SPME), headspace-SPME (HS/SPME) and multiple-headspace-extraction-SPME (MHE/SPME). The aromagrams obtained by HS/SPME-CGC were evaluated with chemometrical methods for the varietal classification of wines. Received: 25 July 1997 / Revised: 24 September 1997 / Accepted: 7 October 1997     

Ein biologischer Vergleich zwischen Benzol und Pyridin in kondensierten Ringsystemen

The synthesis of imidazo[4,5-b]pyridines and of [1,2,4]-triazolo[1,5-a]pyridines is described, and their biological activity in relation to the standard antiviral substance, 2-(α-hydroxybenzyl)benzimidazol, is discussed.     

GpdA-promoter-controlled production of glucose oxidase by recombinant aspergillus niger using nonglucose carbon sources

The gpdA-promoter-controlled exocellular production of glucose oxidase (GOD) by recombinant Aspergillus niger NRRL-3 (GOD3-18) during growth on glucose and nonglucose carbon sources was investigated. Screening of various carbon substrates in shake-flask cultures revealed that exocellular GOD activities were not only obtained on glucose but also during growth on mannose, fructose, and xylose. The performance of A. niger NRRL-3 (GOD3-18) using glucose, fructose, or xylose as carbon substrate was compared in more detail in bioreactor cultures. These studies revealed that gpdA-promoter-controlled GOD synthesis was strictly coupled to cell growth. The gpdA-promoter was most active during growth on glucose. However, the unfavorable rapid GOD-catalyzed transformation of glucose into gluconic acid, a carbon source not supporting further cell growth and GOD production, resulted in low biomass yields and, therefore, reduced the advantageous properties of glucose. The total (endo- and exocellular) specific GOD activities were lowest when growth occurred on fructose (only a third of the activity that was obtained on glucose), whereas utilization of xylose resulted in total specific GOD activities nearly as high as reached during growth on glucose. Also, the portion of GOD excreted into the culture fluid reached similar high levels (≅ 90%) by using either glucose or xylose as substrate, whereas growth on fructose resulted in a more pelleted morphology with more than half the total GOD activity retained in the fungal biomass. Finally, growth on xylose resulted in the highest biomass yield and, consequently, the highest total volumetric GOD activity. These results show that xylose is the most favorable carbon substrate for gpdA-promoter-controlled production of exocellular GOD.     

Über die bei hohen Ansäuerungsgraden auftretenden Polymolybdat-Typen,insbesondere zur Frage der „Dekamolybdate”︁ und „Phase C”︁-Polymolybdate

On the Polymolybdate Types Occurring at High Degrees of Acidification, with Particular Reference to the “Decamolybdates” and “Phase C” Polymolybdates It is shown that in the range of high acidification (> 1.6H⁺/MoO₄^2?) of aqueous molybdate solutions only two types of solid polymolybdates occur, namely the 36-molybdate and the “decamolybdate” types. These types can be most conveniently identified by their Raman spectra and also by some other characteristics. All the other polymolybdate types proposed in the literature for this range of acidification (“hexamolybdates”, “octamolybdates”, “dodecamolybdates”, “16-molybdates”, a 19-molybdate, the large group of polymolybdates characterized by a wide range of b in the general formula M₂O · bMoO₃ · cH₂O, “phase C” polymolybdates, a “hexagonal hydrate of molybdenum trioxide”, a “reactive molybdic acid”, “NH₃(MoO₃)₃”, and others) can be assigned to one of these two types. The most important reason for the erroneous assignments in the literature is the isomorphous exchange of varying quantities of the alkali or alkaline earth metal cations by H₃O⁺ in the crystal structure, occurring in the highly acidic solutions, particularly with the small cations. This cannot be recognized by the presently available methods of investigation and, hence, leads to the creation of new polymolybdate types. Another reason causing some of the confusion is the assignment of virtually identical X-ray diffraction data to two different types of lattices, a hexagonal and cubic lattice.     

Diverse redox-active molecules bearing O-, S-, or Se-terminated tethers for attachment to silicon in studies of molecular information storage

A molecular approach to information storage employs redox-active molecules tethered to an electroactive surface. Attachment of the molecules to electroactive surfaces requires control over the nature of the tether (linker and surface attachment group). We have synthesized a collection of redox-active molecules bearing different linkers and surface anchor groups in free or protected form (hydroxy, mercapto, S-acetylthio, and Se-acetylseleno) for attachment to surfaces such as silicon, germanium, and gold. The molecules exhibit a number of cationic oxidation states, including one (ferrocene), two [zinc(II)porphyrin], three [cobalt(II)porphyrin], or four (lanthanide triple-decker sandwich compound). Electrochemical studies of monolayers of a variety of the redox-active molecules attached to Si(100) electrodes indicate that molecules exhibit a regular mode of attachment (via a Si-X bond, X = O, S, or Se), relatively homogeneous surface organization, and robust reversible electrochemical behavior. The acetyl protecting group undergoes cleavage during the surface deposition process, enabling attachment to silicon via thio or seleno groups without handling free thiols or selenols.     

Photophysical aspects of single-molecule detection by two-photon excitation with consideration of sequential pulsed illumination.

An important goal in single molecule fluorescence correlation spectroscopy is the theoretical simulation of the fluorescence signal stemming from individual molecules and its autocorrelation function. The simulation approaches developed up to now are based exclusively on continuous-wave (cw) illumination and consequently on cw-excitation. However, this approximation is no longer valid in the case of two-photon excitation, for which pulsed illumination is usually employed. We present a novel theoretical model for the simulation of the fluorescence signal of single molecules and its autocorrelation function with consideration of the time dependence of the excitation flux and thus of all illumination-dependent photoprocesses: two-photon excitation, induced emission and photobleaching. Further important characteristics of our approach are the consideration of the dependence of the photobleaching rate on illumination and the low intersystem-crossing rates of the studied coumarins. Moreover, using our approach, we can predict quantitatively the effect of the laser pulse width on the fluorescence signal of a molecule, that is, the contributions of the photobleaching and saturation effects, and thus we can calculate the optimal laser pulse width. The theoretical autocorrelation functions were fitted to the experimental data, and we could ascertain a good agreement between the resulting and the expected parameters. The most important parameter is the photobleaching constant sigma, the cross section of the transition Sn<--S1, which characterises the photostability of the molecules independent of the experimental conditions. Its value is 1.7 x 10(-23) cm2 for coumarin 153 and 5 x 10(-23) cm2 for coumarin 314.     

Neue Wege zu 1H- und 2H-Pyrrolen

New Routes to 1H- and 2H-Pyrroles A synthesis of 1H-pyrroles is described starting with pyridine analogues of chalcones and involving the reaction of acetic anhydride with 1-pyrroline-1-oxides. Another route leads from 1-pyrrolines to 2 H-pyrroles via bromination with N-bromosuccinimide and subsequent dehydrobromination in dimethylformamide.