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Karl-Heinz Indlekofer 《Monatshefte für Mathematik》1987,103(2):121-132
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. 相似文献
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4.
Demetrio De Calle García M. Reichenbächer Klaus Danzer Christian Hurlbeck Christine Bartzsch Karl-Heinz Feller 《Analytical and bioanalytical chemistry》1998,360(7-8):784-787
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 相似文献
5.
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+/MoO42?) 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. 相似文献
6.
Balakumar A Lysenko AB Carcel C Malinovskii VL Gryko DT Schweikart KH Loewe RS Yasseri AA Liu Z Bocian DF Lindsey JS 《The Journal of organic chemistry》2004,69(5):1435-1443
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. 相似文献
7.
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. 相似文献
8.
Jean‐Louis Schmitt Adrian‐Mihail Stadler Nathalie Kyritsakas Jean‐Marie Lehn 《Helvetica chimica acta》2003,86(5):1598-1624
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. 相似文献
9.
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. 相似文献
10.