Contribution to the systematics of r0-derived molecular structure determinations from rotational parameters

This work investigates and enumerates the types of molecular structure that can, in principle, be obtained when moments of inertia, planar moments, or rotational constants or different forms of their isotopic differences are least-squares fitted to the respective experimental ground state values. Ther ₀-structure, ther ₀-derived pseudo-Kraitchman structuresr _I andr _B, and an inequality relation between them are discussed. A least-squares treatment that tries to determine not only the set of structural parameters but also constant, i.e., isotope-independent, rovibrational contributions to the moments of inertia or rotational constants is possible and merits preference. It is shown that the resulting structures are, however, identical with the formerr orr _B-structures, respectively.     

Synthesis, X-ray diffraction analysis and NMR studies of (Z)-2-methyl-3-triphenylstannyl-3-pentene-2-ol

The synthesis of (Z)-2-methyl-3-triphenylstannyl-3-pentene-2-ol and its characterization by an X-ray diffraction study and multinuclear NMR are reported. The tin atom exhibits a distorted tetrahedral SnC₄ geometry with the four Sn---C bond distances experimentally equivalent. The slight distortion from the ideal tetrahedral geometry is because of the presence of a weak intramolecular HO → Sn interaction of 3.012(3) Å which produces a loose four-membered ring. The title compound was characterized in solution by ¹H, ¹³C and ¹¹⁹Sn NMR, and the persistence of the weak intramolecular HO → Sn coordination in solution was revealed by ¹³C and ¹¹⁹Sn secondary isotope multiplet of partially labelled entities (SIMPLE-NMR) experiments.     

Neue Redoxserien auf der Basis von Übergangsmetallkomplexen heterocyclischer Arensulfonylhydrazone

New Redox Series Based on Transition Metal Complexes of Heterocyclic Arenesulfonylhydrazones Heterocyclic bidentate arenesulfonylhydrazones (2-acetylpyridine-p-toluenesulfonylhydrazone ? APSH? H, 2-acetylquinoline-p-toluenesulfonylhydrazone ? ACSH? H) with transition metal ions afford tetrahedral 1,2-complexes M^II(APSH)₂ and M^II(ACSH)₂. In most cases the E-isomers of APSH^? and ACSH^? are coordinated, five-membered chelate rings are formed with the pyridine and hydrazone nitrogen atoms as donor atoms. In the complexes Zn(APSH)₂ and Cu(APSH)₂ probably the Z-isomer of APSH^? is present with the pyridine and the sulfonylamide nitrogen atoms as a donor set, yielding a six-membered chelate ring. These proposals are based on the magnetic moments, the ligand field spectra, and the binding energies (ESCA). Normally the complexes M^II(APSH)₂ and M^II(ACSH)₂ are reduced in two reversible steps. For Fe(APSH)₂ and Fe(ACSH)₂ a third anodic wave, but for Cu(APSH)₂ only one wave is observed. Relations between redox properties and structure of the new complexes are discussed, and the redox series are compared with that of the M(dipy)₃ⁿ⁺-type complexes.     

Characterization of a putative sensory [FeFe]-hydrogenase provides new insight into the role of the active site architecture

[FeFe]-hydrogenases are known for their high rates of hydrogen turnover, and are intensively studied in the context of biotechnological applications. Evolution has generated a plethora of different subclasses with widely different characteristics. The M2e subclass is phylogenetically distinct from previously characterized members of this enzyme family and its biological role is unknown. It features significant differences in domain- and active site architecture, and is most closely related to the putative sensory [FeFe]-hydrogenases. Here we report the first comprehensive biochemical and spectroscopical characterization of an M2e enzyme, derived from Thermoanaerobacter mathranii. As compared to other [FeFe]-hydrogenases characterized to-date, this enzyme displays an increased H₂ affinity, higher activation enthalpies for H⁺/H₂ interconversion, and unusual reactivity towards known hydrogenase inhibitors. These properties are related to differences in active site architecture between the M2e [FeFe]-hydrogenase and “prototypical” [FeFe]-hydrogenases. Thus, this study provides new insight into the role of this subclass in hydrogen metabolism and the influence of the active site pocket on the chemistry of the H-cluster.

Characterization of a group D putative sensory [FeFe]-hydrogenase reveals how the active site can be tuned to decrease CO inhibition and increase stability of a reduced H-cluster while retaining the ability to catalyze H⁺/H₂ interconversion.     

A Levi–Civita functional equation on semigroups

Aequationes mathematicae - Let S be a semigroup. We describe the solutions $$f,g:S \rightarrow \mathbb {C}$$ of the functional equation $$\begin{aligned} f(xy) = f(x)g(y) + g(x)f(y) - g(x)g(y), \...     

Wilson's functional equations on groups

We study properties of solutionsf, g, h C(G) of the functional equation

Almost block independence and bernoullicity of ℤ d -actions by automorphisms of compact abelian groups

Summary We prove that a ^d -action by automorphisms of a compact, abelian group is Bernoulli if and only if it has completely positive entropy. The key ingredients of the proof are the extension of certain notions of asymptotic block independence from -actions to ^d -action and their equivalence with Bernoullicity, and a surprisingly close link between one of these asymptotic block independence properties for ^d -actions by automorphisms of compact, abelian groups and the product formula for valuations on global fields.Oblatum 20-X-1994     

Wiener-Wintner return-times ergodic theorem

We state a new ergodic theorem, combining the Wiener-Wintner theorem and Bourgain’s theorem concerning the convergence of ergodic averages along return-times sequences. We consider ergodic averages of the form $$\frac{1}{N}\sum\limits_{n = 0}^{N - 1} {e^{in\theta } \cdot f'(S^n y) \cdot f(T^n x)} $$ and we show that the behaviour of these averages characterizes an algebraC of functions, which contains the Kronecker algebra and has interesting properties, linked with multiple recurrence ergodic theorems.     

(Z)-1-[2-(Triarylstannyl)vinyl]-1-cycloheptanols: Synthesis, characterization, halodemetallation and crystal structures

The synthesis and characterization by ¹H, ¹³C, ¹¹⁹Sn NMR and ¹¹⁹Sn Mössbauer spectroscopy of (Z)-1-[2-(triphenylstannyl)vinyl]-1-cycloheptanol,

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(1), and (Z)-1-[2-tri-p-tolylstannyl)vinyl-1-cycloheptanol,

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(2), are described, together with their halodemetallation by I₂, Br₂ and ICIl to yield derivatives of the types

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(Ar = phenyl or p-tolyl, N = 1, 2; X = I, Br, Cl, respectively). The solid-state structures of four compounds have been determined by X-ray diffraction analysis. In the crystals of

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(1) and

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(2) the Sn atom has a tetrahedral geometry distorted towards trigonal bipyramid as a consequence of a close intramolecular contact with the hydroxyl O(1) atom of 2.742(3) Å and 2.768(3) Å, respectively. A trigonal bipyramidal geometry is found in

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(12) and

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(4), in which significant Sn---O(1) interactions are noted [2.437(8) Å and 2.407(8) Å, respectively].     

Measuring the similarity between trajectories using clustering techniques

A clustering method has been developed to group signals that display similar dynamic behavior. The procedure involves using the method of time delay embedding to construct a trajectory in state space from a time series. Certain features that characterize the geometry of the trajectory have been defined. These features were subjected to a series of statistical tests to determine their usefulness in a hierarchical clustering analysis. The latter is aimed at finding groups of similar trajectories. The trajectory-based clustering algorithm has been applied to simulated data, which included both stochastic data generated by a linear AR model, and nonlinear data generated by a Duffing oscillator. The results show that the algorithm works reliably in both cases.