Structural studies on 9-hydrazono-6,7,8,9-tetrahydro-4-oxo-4H-pyrido[1,2-a]pyrimidines by 1H, 13C and 15N NMR spectroscopy

¹H, ¹³C and ¹⁵N NMR studies demonstrated that 9-hydrazono-6,7,8,9-tetrahydro-4-oxo-4H-pyrido-[1,2-a] pyrimidlnes exist as an equilibrium mixture of Z-E isomers in the hydrazono–imino tautomeric form having an exocyclic double bond. Proton-catalysed Z-E interconversion is fast. Substituent and solvent effects revealed that the decisive factors controlling the Z:E ratio are internal hydrogen bonding in the Z-isomer, stabilization by solvation and steric interaction.     

On the Chromatic Number of the Visibility Graph of a Set of Points in the Plane

The visibility graph V(P) of a point set P \subseteq R² has vertex set P, such that two points v,w ∈ P are adjacent whenever there is no other point in P on the line segment between v and w. We study the chromatic number of V(P). We characterise the 2- and 3-chromatic visibility graphs. It is an open problem whether the chromatic number of a visibility graph is bounded by its clique number. Our main result is a super-polynomial lower bound on the chromatic number (in terms of the clique number).     

High temperature determination of the rate coefficient for the reaction H2O + CN → HCN + OH

The rate coefficient, k, of the reaction has been determined in the temperature range 2460–2840 K using a shock tube technique. C₂N₂? H₂O? Ar mixtures were heated behind incident shock waves and the CN and OH concentration time histories were monitored simultaneously using broad-band absorption near 388 nm (CN) and narrow-line laser absorption at 306.67 nm (OH). The rate coefficient expression providing the best fit to the data was with uncertainty limits of about ±45% in the temperature range 2460–2840 K. The rate coefficient of the reverse reaction was calculated using detailed balancing, and its extrapolation to lower temperatures was compared with previously published results.     

Unexpected formation of higher polythionates in the oxidation of thiosulfate by hypochlorous acid in a slightly acidic medium

It has been clearly shown that not only tetrathionate but also pentathionate or even higher polythionates is formed in the oxidation of thiosulfate by hypochlorous acid in a slightly acidic medium. In thiosulfate excess, the absorbance-time curves registered at 250 nm may go through a maximum followed by a minimum, suggesting the presence of a short-lived absorbing intermediate proposed to be S(2)O(3)OCl(3-). Matrix rank analysis (MRA) studies have revealed that altogether five independent absorbing species are present in the wavelength range 240-400 nm. A kinetic model is suggested to take all of the experimental observations into account.     

Limits of random trees

Local convergence of bounded degree graphs was introduced by Benjamini and Schramm [2]. This result was extended further by Lyons [4] to bounded average degree graphs. In this paper, we study the convergence of a random tree sequence (T _n ), where the probability of a given tree T is proportional to $\prod_{v_{i}\in V(T)}d(v_{i})!$ . We show that this sequence is convergent and describe the limit object, which is a random infinite rooted tree.     

Exact integration of the von Mises elastoplasticity model with combined linear isotropic-kinematic hardening

The main purpose of this work is to present two semi-analytical solutions for the von Mises elastoplasticity model governed by combined linear isotropic-kinematic hardening. The first solution (SOLε) corresponds to strain-driven problems with constant strain rate assumption, whereas the second one (SOLσ) is proposed for stress-driven problems using constant stress rate assumption. The formulas are derived within the small strain theory Besides the new analytical solutions, a new discretized integration scheme (AMε) based on the time-continuous SOLε is also presented and the corresponding algorithmically consistent tangent tensor is provided. A main advantage of the discretized stress updating algorithm is its accuracy; it renders the exact solution if constant strain rate is assumed during the strain increment, which is a commonly adopted assumption in the standard finite element calculations. The improved accuracy of the new method (AMε) compared with the well-known radial return method (RRM) is demonstrated by evaluating two simple examples characterized by generic nonlinear strain paths.     

Influence of intermolecular interactions on the Mössbauer quadrupole splitting of organotin(IV) compounds as studied by DFT calculations

The influence of intermolecular interactions on the M?ssbauer quadrupole splitting (Delta) of 119Sn was investigated in detail by density functional theory (DFT) calculations. Six organotin(IV) complexes [Me2Sn(acac)2 (1), Ph3SnCl (2), Me3Sn-succinimide (3), Me3Sn-phthalimide (4), Me3SnCl (5), and cHex3SnCl (6)] of known solid-state structures and quadrupole splittings were selected. Theoretical Delta values were calculated for both fully optimized geometries and experimental solid-state structures of different size, and the results were compared to the experimental Delta values. Compared to a synthetic procedure described in the literature for compound 4, a more convenient synthesis is reported here. The experimental Delta of this compound has also been redetermined at 80 K. For compounds with negligible intermolecular interactions in the solid state, calculated Delta values obtained did not vary significantly. In contrast, the calculated Delta values turned out to be very sensitive to the size of the supramolecular moiety considered in the crystal lattice. The crystal structure of compound 2 shows no significant intermolecular interactions; however, the calculated and the experimental Delta values remained very different, even when the supramolecular moiety considered was extended. Distortion of the coordination sphere of tin in the molecule of 2 toward a trigonal bipyramidal geometry was considered, and a possible weak intermolecular Sn...Cl interaction was included in the model. Steps of the distortion followed the new structure correlation function, which was found for the R3SnCl (R=alkyl, aryl) compounds. The experimental Delta value could be approached by this method. These results suggest that compound 2 is involved in some unexpected intermolecular interaction at 80 K.