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     

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.     

Composition and properties of freeze-dried products of nicotinic acid withβ-cyclodextrin and heptakis (2,6-0-dimethyl)-β-cyclodextrin

The purpose of the study was to examine the formation of inclusion compounds in the freeze-dried products obtained from aqueous solutions of nicotinic acid and -cyclodextrin (-CD), or heptakis (2,6-0-dimethyl)--cyclodextrin (DIMEB). The molar ratios used were 1:1 and 2:1. In addition two freezing temperatures (–40 and –196°C) and different secondary drying temperatures (+50 and +80°C) were used. Freeze-dried products with -CD obtained after low temperature freezing are of the same crystallographic structure as seen in a pure inclusion compound prepared by coprecipitation. Amorphous products were formed after fast freezing. The molar ratios of included nicotinic acid in the freeze-dried products vary — dependent on the preparation conditions — between 0.75:1 and 1:1. A factorial design proves that the included drug amount can be increased by enhancement of the amount of nicotinic acid used, by faster freezing, and by the combination of these two factors. The proof of inclusion formation was given by a combination of X-ray diffractography, differential scanning calorimetry, thermogravimetry and thermofractography.The freeze-dried preparations obtained with DIMEB were amorphous mixtures of the two components. No proof for inclusion of the nicotinic acid in the cyclodextrin cavity could be given. Higher (–40°C) or lower (–196°C) freezing temperatures and the running of the secondary drying process could not influence these results. The very low stability constant of the complex and steric reasons are responsible for this behavior.     

Was ist „Molybdänsäure”︁ oder „Polymolybdänsäure”︁?

What is “Molybdic Acid” or “Polymolybdic Acid”? According to a comparative study of the literature, supplemented by well-aimed experimental investigations and equilibrium calculations, the terms “molybdic acid” or “polymolybdic acid”, used for many substances, species, or solutions in the literature, are applicable to a species, a solution, and two solids:

• a) The monomeric molybdic acid, most probably having the formula MoO₂(OH)₂(H₂O)₂(? H₂MoO₄, aq), exists in (aqueous) solution only and never exceeds a concentration of ≈ 10^?3 M since at higher concentrations it reacts with other monomemeric molybdenum (VI) species to give anionic or cationic polymers.
• b) A concentrated (>0.1 M Mo^VI) aqueous molybdate solution of degree of acidification P = 2 (realized, e. g., by a solution of one of the Mo^VI oxides; by any molybdate solutions whose cations have been exchanged by H₃O⁺ on a cation exchanger; by suitable acidification of a molybdate solution) contains 8 H₃O⁺ and the well-known polyanion Mo₃₆O₁₁₂(H₂O)₁₆^8? exactly in the stoichiometric proportions.
• c) A glassy substance, obtained from an alkali metal salt-free solution prepared according to (b), refers to the compound (H₃O)₈[Mo₃₆O₁₁₂(H₂O)₁₆]·xH₂O, x = 25—29.
• d) A solid having the ideal composition [(H₃O)Mo₅O₁₅(OH)H₂O·H₂O]∞ consists of a polymolybdate skeleton (the well-known ?decamolybdate”? structure), in the tunnels of which H₃O⁺ and H₂O are intercalate. The structure is very unstable if only H₃O⁺ cations are present, but it is enormously stabilized by a partial exchange of H₃O⁺ by certain alkali or alkaline earth metal cations.

For the compounds MoO₃, MoO₃·H₂O, and MoO₃·2H₂O the term ?molybdic acid”? is unjustified. The commercial product ?molybdic acid, ≈85% MoO₃”? is the well-known polymolybdate (NH₄)₂O·4 MoO₃ with a layer structure of the polyanion.     

Coupled liquid chromatography-gas chromatography for the rapid analysis of gamma-oryzanol in rice lipids

An approach based on on-line coupled liquid chromatography-gas chromatography (LC-GC) was developed for the rapid analysis of gamma-oryzanol in rice. Total lipids were extracted from rice and subjected to LC-GC without any prior purification. gamma-Oryzanol was pre-separated by HPLC from rice lipids and transferred on-line to GC analysis in order to separate its major constituents. 24-methylenecycloartanyl ferulate, cycloartenyl ferulate, campesteryl ferulate, beta-sitosteryl ferulate and campestanyl ferulate. The identities of the compounds were confirmed by off-line GC-MS analysis. Total gamma-oryzanol content could be quantified by HPLC-UV detection and the distribution of gamma-oryzanol constituents could be determined by on-line coupled GC analysis. The proposed methodology paves the way for high-throughput investigations providing information on natural variations in gamma-oryzanol content and its composition in different rice varieties.