Experimental gas-phase basicity scale of superbasic phosphazenes

Seventeen superbasic phosphazenes and two Verkade's bases were used to supplement and extend the experimental gas-phase basicity scale in the superbasic region. For 19 strong bases the gas-phase basicity values (GB) were determined for the first time. Among them are such well-known bases as BEMP (1071.2 kJ/mol), Verkade's Me-substituted base (1083.8 kJ/mol), Et-N=P(NMe2)2-N=P(NMe2)3 (Et-P2 phosphazene, 1106.9 kJ/mol), and t-Bu-N=P(NMe2)3 (t-Bu-P1 phosphazene, 1058.0 kJ/mol). For the first time experimental GB values were determined for P2 phosphazenes. Together with our previous results self-consistent experimental gas-phase basicity scale between 1020 and 1107 kJ/mol is now established. This way an important region of the gas-phase basicity scale, which was earlier dominated by metal hydroxide bases, is now covered also with organic bases making it more accessible for further studies. The GB values for several superbases were calculated using density functional theory at the B3LYP/6-311+G** level. For the phosphazene family the standard deviation of the correlation between the experimental and theoretical values was 6.5 kJ/mol.     

Molecular theory of phase equilibria in model and real associated mixtures III. Binary solutions of inert gases and n-alkanes in ammonia and methanol

Using new molecular models of ammonia and methanol and thermodynamic perturbation theory, the global phase diagrams of model mixtures of these compounds with a van der Waals fluid, representing a simple nonpolar fluid, have been calculated. The global phase diagram of these mixtures is much richer than that of corresponding aqueous mixtures. More types of critical line behavior are found, including the presence of van Laar points and a small region where the mixtures exhibit a closed liquid-liquid immiscibility loop (Type VI phase behavior). The individual mixture components are characterized by two molecular parameters, which can be adjusted to their critical temperature and critical volume; the mixture model itself contains no adjustable parameters. It is shown that the theory gives qualitatively correct predietions of mixtures with n-alkanes. This includes the prediction of Type III critical line behavior for small and large values of the ratio of the critical temperatures of the components, and Type II over a large range of conditions, including the presence or absence of absolute or limited azeotropy, and temperature and pressure extrema of critical lines and their dependence on the number of carbon atoms.     

A product form solution to a system with multi-type jobs and multi-type servers

We consider a memoryless single station service system with servers \(\mathcal{S}=\{m_{1},\ldots,m_{K}\}\), and with job types \(\mathcal{C}=\{a,b,\ldots\}\). Service is skill-based, so that server m _i can serve a subset of job types \(\mathcal{C}(m_{i})\). Waiting jobs are served on a first-come-first-served basis, while arriving jobs that find several idle servers are assigned to a feasible server randomly. We show that there exist assignment probabilities under which the system has a product-form stationary distribution, and obtain explicit expressions for it. We also derive waiting time distributions in steady state.     

Minimal surfaces with prescribed topological type on a Schwarzian chain inMc3

Similar to the investigations of unstable polygonal minimal surfaces by Courant [1] we introduce here a variational principle for the free boundary problem with prescribed topological type which produces minimal surfaces in Riemannian manifolds with constant curvature. For special boundary configurations the surfaces have no branch points. The approach can be applied to numerical algorithms since it is constructive.     

Aggregation/Disaggregation Iterative Methods Applied to Leontev Systems and Markov Chains

The paper surveys some recent results on iterative aggregation/disaggregation methods (IAD) for computing stationary probability vectors of stochastic matrices and solutions of Leontev linear systems. A particular attention is paid to fast IAD methods.     

On Galois cohomology and realizability of 2-groups as Galois groups II

In [Michailov I.M., On Galois cohomology and realizability of 2-groups as Galois groups, Cent. Eur. J. Math., 2011, 9(2), 403–419] we calculated the obstructions to the realizability as Galois groups of 14 non-abelian groups of order 2 ⁿ , n ≥ 4, having a cyclic subgroup of order 2 ⁿ⁻², over fields containing a primitive 2 ⁿ⁻³th root of unity. In the present paper we obtain necessary and sufficient conditions for the realizability of the remaining 8 groups that are not direct products of smaller groups.     

Low-Temperature High-Resolution Solid-State (cryoMAS) NMR of Han Purple BaCuSi2O6

We present low-temperature (low-T, sub-liquid-N₂) high-speed high-resolution ²⁹Si solid-state (cryoMAS) nuclear magnetic resonance studies on a model 2D-BEC quantum magnet BaCuSi₂O₆, known also as Han Purple. We observe broadened ²⁹Si lines below the well-established 100 K structural phase transition confirming the existence of inhomogeneities at low temperatures. Interestingly, the low-T spectra of \({\mathrm{BaCuSi}}_{2}{\mathrm{O}}_{6}\) closely resemble those of the novel compound Ba₂CoSi₂O₆Cl₂ taken at room temperature. This suggests that the Co compound features structural modulations or inhomogeneities already at room temperature. The low-T crystal structure and magnetism of \({\mathrm{BaCuSi}}_{2}{\mathrm{O}}_{6}\) are more complex than previously believed, and deserve further investigation.