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.     

Fast folding and comparison of RNA secondary structures

Summary Computer codes for computation and comparison of RNA secondary structures, the Vienna RNA package, are presented, that are based on dynamic programming algorithms and aim at predictions of structures with minimum free energies as well as at computations of the equilibrium partition functions and base pairing probabilities.An efficient heuristic for the inverse folding problem of RNA is introduced. In addition we present compact and efficient programs for the comparison of RNA secondary structures based on tree editing and alignment.All computer codes are written in ANSI C. They include implementations of modified algorithms on parallel computers with distributed memory. Performance analysis carried out on an Intel Hypercube shows that parallel computing becomes gradually more and more efficient the longer the sequences are.

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Schnelle Faltung und Vergleich von Sekundärstrukturen von RNA

Zusammenfassung Die im Vienna RNA package enthaltenen Computer Programme für die Berechnung und den Vergleich von RNA Sekundärstrukturen werden präsentiert. Ihren Kern bilden Algorithmen zur Vorhersage von Strukturen minimaler Energie sowie zur Berechnung von Zustandssumme und Basenpaarungswahrscheinlichkeiten mittels dynamischer Programmierung.Ein effizienter heuristischer Algorithmus für das inverse Faltungsproblem wird vorgestellt. Darüberhinaus präsentieren wir kompakte und effiziente Programme zum Vergleich von RNA Sekundärstrukturen durch Baum-Editierung und Alignierung.Alle Programme sind in ANSI C geschrieben, darunter auch eine Implementation des Faltungs-algorithmus für Parallelrechner mit verteiltem Speicher. Wie Tests auf einem Intel Hypercube zeigen, wird das Parallelrechnen umso effizienter je länger die Sequenzen sind.

     

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.     

Helicity‐Encoded Molecular Strands: Efficient Access by the Hydrazone Route and Structural Features

Control over the folding of molecular strands may be achieved by appropriate choice of the constituting subunits, in particular for chains of specific heterocycles such as sequences of directly connected pyridine (py) and pyrimidine (pym) rings, which are known to fold into extended helical structures. Since the hydrazone (hyz) group represents an isomorphic analogue of a py site, the condensation of hydrazine and carboxaldehyde derivatives of pym offers a very efficient approach to strands incorporating hyz instead of py units and constituted by sequences of alternating hyz and pym groups. A series of such strands of different lengths, up to ten hyz units, i.e., 1 – 7 , were synthesized. Their spectral properties indicate that they fold indeed into helical shapes. Extensive characterization was performed in solution by ¹HNMR spectroscopy and in the solid state by determination of the crystal structures of eight such strands. They all display the expected helical geometry with up to 3 ¹/₃ turns and direct stacking contacts. The efficiency and flexibility of the synthetic approach as well as its wide potential for generation of diversity through lateral decoration make the (hyz? pym) subunit a particularly attractive helicity codon.     

Analysis of RNA sequence structure maps by exhaustive enumeration I. Neutral networks

Summary Global relations between RNA sequences and secondary structures are understood as mappings from sequence space into shape space. These mappings are investigated by exhaustive folding of allGC andAU sequences with chain lengths up to 30. The computed structural data are evaluated through exhaustive enumeration and used as an exact reference for testing analytical results derived from mathematical models and sampling based on statistical methods. Several new concepts of RNA sequence to secondary structure mappings are investigated, among them that ofneutral networks (being sets of sequences folding into the same structure). Exhaustive enumeration allows to test several previously suggested relations: the number of (minimum free energy) secondary structures as a function of the chain length as well as the frequency distribution of structures at constant chain length (commonly resulting in generalized forms ofZipf's law).

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Analyse der Beziehungen zwischen RNA-Sequenzen und Sekundärstrukturen durch vollständige Faltung, 1. Mitt. Faltung, Neutrale Netzwerke

Zusammenfassung Die globalen Benziehungen zwischen RNA-Sequenzen und Sekundärstrukturen werden als Abbildungen aus einem Raum aller Sequenzen in einen Raum aller Strukturen aufgefaßt. Diese Abbildungen werden durch Falten aller binären Sequenzen desGC-undAU-Alphabets mit Kettenlängen bis zun=30 untersucht. Die berechneten Strukturdaten werden durch vollständiges Abzählen ausgewertet und als eine exakte Referenz zum Überprüfen analytischer Resultate aus mathematischen Modellen sowie zum Testen statistisch erhobener Proben verwendet. Einige neuartige Konzepte zur Beschreibung der Beziehungen zwischen Sequenzen und Strukturen werden eingehend untersucht, unter ihnen der Begriff derneutralen Netzwerke. Ein neutrales Netzwerk besteht aus allen Sequenzen, die eine bestimmte Struktur ausbilden. Vollständiges Abzählen ermöglicht beispielsweise die Bestimmung aller Strukturen minimaler freier Energie in Abhängigkeit von der Kettenlänge ebenso wie die Bestimmung der Häufigkeitsverteilungen der Strukturen bei konstanten Kettenlängen. Die letzteren folgen einer verallgemeinerten FormZipfschen Gesetzes.