Inherent Stability Limits of Intramolecular Boron Nitrogen Lewis Acid–Base Pairs

The reaction of (C₆F₅)₂BH ( 1 ) with N,N‐dimethylallylamine ( 2 ), N,N‐diethylallylamine ( 3 ) and 1‐allylpiperidine ( 4 ) afforded the five‐membered ring systems (C₆F₅)₂B(CH₂)₃NR₂ (R=Me ( 5 ), Et ( 6 )) and (C₆F₅)₂B(CH₂)₃N(CH₂)₅ ( 7 ) with an intramolecular dative B? N bond. A different product was obtained from the reaction of (C₆F₅)₂BH ( 1 ) with N,N‐diisopropylallylamine ( 8 ), which afforded the seven‐membered ring system (C₆F₅)₂B(CH₂)₃N(iPr)CH(Me)CH₂ ( 9 ) under extrusion of dihydrogen. All compounds were characterised by elemental analysis, NMR spectroscopy and single‐crystal X‐ray diffraction experiments. Density functional theory (DFT) studies were performed to rationalise the different reaction mechanism for the formation of products 6 and 9 . The bonding situation of compound 9 was analysed in terms of its electron density topology to describe the delocalised nature of a borane– enamine adduct.     

Colorful monochromatic connectivity

An edge-coloring of a connected graph is monochromatically-connecting if there is a monochromatic path joining any two vertices. How “colorful” can a monochromatically-connecting coloring be? Let mc(G) denote the maximum number of colors used in a monochromatically-connecting coloring of a graph G. We prove some nontrivial upper and lower bounds for mc(G) and relate it to other graph parameters such as the chromatic number, the connectivity, the maximum degree, and the diameter.     

A relaxation-based approach to damage modeling

Common material models that take into account softening effects due to damage have the problem of ill-posed boundary value problems if no regularization is applied. This condition leads to a non-unique solution for the resulting algebraic system and a strong mesh dependence of the numerical results. A possible solution approach to prevent this problem is to apply regularization techniques that take into account the non-local behavior of the damage [1]. For this purpose a field function is often used to couple the local damage parameter to a non-local level, in which differences between the local and non-local parameter as well as the gradient of the non-local parameter can be penalized. In contrast, we present a novel approach [2] to regularization that no longer needs a non-local level but directly provides mesh-independent results. Due to the new variational approach we are also able to improve the calculation times and convergence behavior. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Zum Auftreten von Marangoni-Instabilität

Zusammenfassung Es wird nachgewiesen, daß in einem fluiden Zweiphasensystem unter den Bedingungene ² > 1 >r ², d/dc>0 Marangoni-Instabilität in Form von Rollzellen bei Stoffübergang aus der Phase mit der kleineren kinematischen Zähigkeit und Stabilität bei Übergang aus der Phase mit der größeren kinematischen Zähigkeit auftritt. Führt der Stoffübergang zu einer instationären Dichtekonvektion, kann zusätzlich freie Grenzflächenkonvektion in Form von Spreitungen auftreten.

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On the occurrence of Marangoni instability

It is proved, that in a fluid two-phase system under the conditionse ²>1>r ², d/dc> 0 Marangoni instability occured in form of roll cells during mass transfer out of the phase with the lower kinematic viscosity and stability during mass transfer out of the phase with the higher kinematic viscosity. If a unsteady-state density convection results from mass transfer interfacial turbulence can occur in form of eruptions.

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Bezeichungen e ² _a/_b - r ² D _a/D _b - kinematische Zähigkeit - D Diffusionskoeffizient - Grenzflächenspannung - c Konzentration Indices a kennzeichnet Phase mit der größeren kinematischen Zähigkeit - b kennzeichnet Phase mit der kleineren kinematischen Zähigkeit     

Towards an AD based diagnosis of singularities of DAEs

The detection of singular points of DAEs is a challenging task, which has not been sufficiently considered so far. Combining automatic differentiation (AD) with the projector based analysis of DAEs, it becomes possible to monitor singularities while integrating the DAE. In this brief outline we restrict our considerations to linear DAEs. The corresponding treatment of nonlinear DAEs is based on linearization and can be found in the cited literature. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

On the three diagonals of a cyclic quadrilateral

If the side lengths of a non-degenerate cyclic quadrilateral are given, but not necessarily in cyclic order, then three diagonal lengths arise in the resulting three cyclic quadrilaterals, just as three possible pairs of supplementary angles arise as opposite vertices, and where the diagonals intersect, in each of the three configurations. We obtain a formula for the sum of the lengths of the three diagonals minus the sum of the four sides which enables us to deduce the geometric inequality that the sum of the side lengths is less than the sum of the lengths of the three diagonals. We obtain another formula when these lengths are replaced by their squares, and this yields a similar inequality. A proof of both formulas is given which uses algebraic geometry, but which proceeds by analysis of degenerate situations. Two alternative proofs of the linear version of the inequality (which implies the quadratic version) are supplied which use trigonometry and Lagrange multipliers respectively. An unusual feature of these results is that they refer not to one configuration, but rather concern three possible configurations.     

Corrigendum: On the Floer Homology of Cotangent Bundles

We fix an orientation issue that appears in our previous paper about the isomorphism between Floer homology of cotangent bundles and loop space homology. When the second Stiefel‐Whitney class of the underlying manifold does not vanish on 2‐tori, this isomorphism requires the use of a twisted version of the Floer complex. © 2014 Wiley Periodicals, Inc.     

Poly(thioester)s

Syntheses and properties of aliphatic and aromatic polythioesters (PTEs) were reviewed including polythiocarbonates and polythiourethanes. The content is subdivided into the following sections: PTEs of aliphatic α‐mercapto carboxylic acid, PTEs of ω‐mercapto carboxylic acids, PTEs derived from α,ω‐dimercapto alkanes, aromatic poly(thioester)s, aliphatic poly(thiocarbonate)s, aliphatic poly(thiourethane)s and aromatic polythiocarbonates. The synthetic strategies reviewed in this article include anionic and cationic ring‐opening polymerizations, polycondensations in bulk, polycondensations in solutions, interfacial polycondensations and in vitro enzymatic polycondensations.     

On Two Different Objectives of the Concepts of Ionic Radii

Experimentally and theoretically derived interatomic distances (D) and ionic radii (R) of more than a hundred monomeric (AX), dimeric (A₂X₂, ABXY), and crystalline ([AX]) alkali halide species (A=Li, Na, K, Rb, Cs, Fr; X=H, F, Cl, Br, I, At) have been analyzed. Chemists use the word “atomic radius” for two antithetic concepts. Let D_CiEE′jj′ be the “billion” of distances i between two adjacent atoms in the millions of known compounds C from a hundred different elements E in bonding states j. The common chemical aim is partitioning D approximately into increments R_Ej+R_E′j′. This can be achieved with a few (say <thousand) predictive constants R_Ej. An antipodal aim is specifying in hindsight an electron density feature in the “billion” of different bonds i, by partitioning them into “two billions” of exact bonded radii ${R{{{\rm C}i\hfill \atop {\rm E}\hfill}}}$ +${R{{{\rm C}i\hfill \atop {\rm E}{^\prime}\hfill}}}$ . The constant incremental and the variable bonded radii concepts with the same generic name are useful in different fields of research. Different concepts should be well distinguished, since they have different meaning, different numerical values, and different purposes.