Vereinfachte Approximationsmodelle für das Temperatur-Zeit-Verhalten homogener,unendlich langer Zylinder

Zusammenfassung Die analytischen Lösungsfunktionen der Fourierschen Differentialgleichung für homogene, unendlich lange Zylinder bei Randbedingung 3. Art werden in verschiedenen Kennwertermittlungs-und -umrechnungsverfahren für das dynamische Verhalten industrieller Temperaturfühler in Flüssigkeiten und Gasen als Modellfunktionen benutzt. Werden dabei nur die ersten Glieder der unendlichen Reihe verwendet (Abbruchapproximation), treten für kleine Zeiten z. T. erhebliche Approximationsfehler auf. Ausgehend von der Zeitkonstantensumme eines homogenen Zylinders werden vereinfachte Approximationsmodelle niederer Ordnung angegeben, die auch für den Anfangsbereich der Übergangsfunktion nur geringe Abweichungen besitzen.

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Simplified model for the approximation of the temperature behaviour and the time response of homogeneous cylinders

The analytical solutions of Fourier differential equations for homogeneous cylinders of infinite length at convection boundary conditions of the 3th type are used to define the characteristic values and the transformation methods for the dynamic behaviour of industrial probes for temperature measurement in fluids. By using only the first terms of the series at smallt the errors of the approximation are becoming significant. Considering the sum of the time constant for homogeneous cylinders, simplified low order models for approximation are given. These models are exact even for the small time range.

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Herrn Prof. Dr.-Ing. U. Grigull zm 80. Geburtstag gewidmet     

Cyclic Heptapeptides Axinastatin 2, 3, and 4: Conformational analysis and evaluation of the biological potential

The conformational analysis of naturally occurring cytostatic cyclic heptapeptides axinastatin 2, 3, and 4 was carried out by two-dimensional NMR spectroscopy in combination with distance-geometry (DG) and molecular-dynamics (MD) calculations in explicit solvents. The synthesized secondary metabolites were examined in (D₆)DMSO. Axinastatin 2 was also investigated in CD₃OH. In all structures, Pro² is in the i + 1 position of a βI turn and Pro⁶ occupies the i + 2 position of a βVIa turn about the cis amide bond between residue 5 and Pro^6. In all peptides, a bifurcated H-bond occurs between residue 4 CO and the amide protons of residue 1 and 7. For axinastatin 2 and 3, an Asn I_g turn was found about Asn¹ and Pro^2. We compared these structures with conformations of cyclic heptapeptides obtained by X-ray and NMR studies. A β-bulge motif with two β turns and one bifurcated H-bond is found as the dominating backbone conformation of cyclic all-L-heptapeptides. Axinastatin 2, 3, and 4 can be characterized by six trans and one cis amide bond resulting in a β/βVI(a)-turn motif, a conformation found for many cyclic heptapeptides. Detailed biological tests of the synthetic compounds in different human cancer cell lines indicates these axinastatins to be inactive or of low activity.     

Insight into the drastically different triplet lifetimes of BODIPY obtained by optical/magnetic spectroscopy and theoretical computations

The triplet state lifetimes of organic chromophores are crucial for fundamental photochemistry studies as well as applications as photosensitizers in photocatalysis, photovoltaics, photodynamic therapy and photon upconversion. It is noteworthy that the triplet state lifetime of a chromophore can vary significantly for its analogues, while the exact reason was rarely studied. Herein with a few exemplars of typical BODIPY derivatives, which show triplet lifetimes varying up to 110-fold (1.4–160 μs), we found that for these derivatives with short triplet state lifetimes (ca. 1–3 μs), the electron spin polarization (ESP) pattern of the time-resolved electron paramagnetic resonance (TREPR) spectra of the triplet state is inverted at a longer delay time after laser pulse excitation, as a consequence of a strong anisotropy in the decay rates of the zero-field state sublevel of the triplet state. For the derivatives showing longer triplet state lifetimes (>50 μs), no such ESP inversion was observed. The observed fast decay of one sublevel is responsible for the short triplet state lifetime; theoretical computations indicate that it is due to a strong coupling between the T_z sublevel and the ground state mediated by the spin–orbit interaction. Another finding is that the heavy atom effect on the shortening of the triplet state lifetime is more significant for the T₁ states with lower energy. To the best of our knowledge, this is the first systematic study to rationalize the short triplet state lifetime of visible-light-harvesting organic chromophores. Our results are useful for fundamental photochemistry and the design of photosensitizers showing long-lived triplet states.

The electron spin polarization inversion and anisotropic decay of triplet substates explain the short triplet state lifetime of BODIPY derivatives.     

Analysis of bonding properties in molecular ground and excited states by a Cohen-type bond order

We propose a Cohen-type bond order analysis in terms of orthogonalized atomic basis functions which can be used to analyze NDO wave functions of large organic and metal–organic molecules. It is shown that for small molecules the results gained with this method are in excellent agreement with the same analysis based on ab initio STO -3G wavefunctions. For large planar aromatic systems these all-valence electron bond orders are found to be a consistent generalization of the π-bond order. A simple relation between these bond orders and the corresponding covalent bond energies is established. The method can be easily extended to study excited state multiconfiguration wave functions. We present calculations for C₂H₂, C₂H₄, C₂H₆, and Mn₂(CO)₁₀. The results indicate that the method can be used to discuss the photochemistry of organic and metal–organic compounds.     

Efforts to expand the genetic alphabet: identification of a replicable unnatural DNA self-pair

Six unnatural nucleotides featuring fluorine-substituted phenyl nucleobase analogues have been synthesized, incorporated into DNA, and characterized in terms of the structure and replication properties of the self-pairs they form. Each unnatural self-pair is accommodated in B-form DNA without detectable structural perturbation, and all are thermally stable and selective to roughly the same degree. Furthermore, the efficiency of polymerase-mediated mispair synthesis is similar for each unnatural nucleotide in the template. In contrast, the efficiency of polymerase-mediated self-pair extension is highly dependent on the specific fluorine substitution pattern. The most promising unnatural base pair candidate of this series is the 3-fluorobenzene self-pair, which is replicated with reasonable efficiency and selectivity.     

Hydrogen-induced metal-oxide interaction studied on noble metal model catalysts

Summary The effect of hydrogen reduction on the structure and catalytic properties of “thin film”and “inverse”model systems for supported metal catalysts is discussed. Thin film model catalysts were obtained by epitaxial growth of Pt and Rh nanoparticles on NaCl(001), which were coated with amorphous or crystalline supports of alumina, silica, titania, ceria and vanadia. Structural and morphological changes upon hydrogen reduction between 473 and 973 K were examined by high resolution electron microscopy. Metal-oxide interaction sets in at a specific reduction temperature and is characterized by an initial “wetting”stage, followed by alloy formation at increasing temperature, in the order VO_x< TiO_x< SiO₂< CeO_x< Al₂O₃. “Inverse”model systems were prepared by deposition of oxides on a metal substrate, e.g. VO_x/Rh and VO_x/Pd. Reduction of inverse systems at elevated temperature induces subsurface alloy formation. In contrast to common bimetallic surfaces, the stable subsurface alloys of V/Rh and V/Pd have a purely noble metal-terminated surface, with V positioned in near-surface layers. The uniform composition of the metallic surface layer excludes catalytic ensemble effects in favor of ligand effects. Activity and selectivity, e.g. for CO and CO₂methanation and for partial oxidation of ethene, are mainly controlled by the temperature of annealing or reduction. Reduction above 573 K turned out to be beneficial for the catalytic activity of the subsurface alloys, but not for the corresponding thin film systems which tend to deactivate viaparticle encapsulation.</o:p>     

Direct structure determination using residual dipolar couplings: reaction-site conformation of methionine sulfoxide reductase in solution

Residual dipolar couplings (RDC) from partially aligned molecules provide long-range structural data and are thus particularly well adapted to rapid structure validation or protein fold recognition. Extensive measurements in two alignment media can also provide precise de novo structure from RDC alone. We have applied a novel combination of these approaches to the study of methionine sulfoxide reductase (MsrA) from Erwinia chrysanthemi, a 27 kDa enzyme essential for repairing oxidative stress damage. The tertiary fold was initially validated by comparing backbone RDC to expected values from the crystal structure of the homologous MsrA from Escherichia coli. Good agreement was found throughout the chain, verifying the overall topology of the molecule, with the exception of the catalytically important peptide P196-L202, where strong and systematic RDC violation was observed. No evidence for local differential mobility in this region was detected, implying that the structure of the strand differs in the two molecules. We have therefore applied the de novo approach meccano to determine the conformation of this peptide using only RDC. A single conformation is found that is in agreement with all measured data. The aligned peptide can be docked onto the expected covalence of the rest of the template molecule while respecting its strictly defined relative orientation. In contrast to the structure of MsrA from E. coli, the reactive side chain of Cys200 is oriented toward the interior of the molecule and therefore closer to the catalytic Cys53, obviating the need for previously proposed conformational reorganization prior to formation of this disulfide intermediate. This analysis requires only backbone assignment and uses unambiguously assigned and readily measurable structural data, thereby greatly economizing investigation time compared to established nuclear Overhauser effect- (nOe-) based structure calculation methods.     

Self-assembly of tetrahedral and trigonal antiprismatic clusters [Fe4(L4)4] and [Fe6(L5)6] on the basis of trigonal tris-bidentate chelators

In a one-pot reaction, the tetranuclear iron chelate complex [Fe4(L4)4] 6 was generated from benzene-1,3,5-tricarboxylic acid trichloride (4), bis-tert-butyl malonate (5a), methyllithium, and iron(II) dichloride under aerobic conditions. Alternatively, hexanuclear iron chelate complex [Fe(L5)6] 7 was formed starting from bis-para-tolyl malonate (5b) by employing identical reaction conditions to those applied for the synthesis of 6. The clusters 6 and 7 are present as racemic mixtures of homoconfigurational (delta,delta,delta,delta)/(lambda,lambda,lambda,lambda)-fac or (delta,delta,delta,delta,delta,delta)/(lambda,lambda,lambda,lambda,lambda,lambda)-fac stereoisomers. The structures of 6 and 7 were unequivocally resolved by single-crystal X-ray analyses. The all-iron(III) character of 6 and 7 was determined by M?ssbauer spectroscopy.     

Die metrisierbaren linearen Teilräume des Raumes\mathfrak{O}_M von L. Schwartz

In Schwartz' terminology, a real or complex valued functionf, defined and infinitely differentiable on ? _n , belongs to \(\mathfrak{O}_M \) iff, as well as any of its derivatives, is at most of polynomial growth. The topology of \(\mathfrak{O}_M \) is defined by the seminorms sup{∣?(x)D ^p f(x)∣;x∈? ⁿ }, where ? belongs to \(\mathfrak{S}\) andD ^p is any derivative. It is well-known that \(\mathfrak{O}_M \) is non-metrisable. For any μ: ? ⁿ →?, let \(\mathfrak{B}_\mu \) be the space of all infinitely differentiable functionsf satisfying, for eachp, sup{∣(1+∣x∣²)^?μ(p) D ^p f(x)∣;x∈? ⁿ }<∞, with the obvious topology. These spaces, which are of very little use elsewhere in the theory of distributions, can be conveniently applied to characterise the metrisable linear subspaces of \(\mathfrak{O}_M \) : A linear subspace of \(\mathfrak{O}_M \) is metrisable if and only if it is, algebraically and topologically, a subspace of some \(\mathfrak{B}_\mu \) .