On the covariance of the level sizes in random recursive trees

In this paper we study the covariance structure of the number of nodes k and l steps away from the root in random recursive trees. We give an analytic expression valid for all k, l and tree sizes N. The fraction of nodes k steps away from the root is a random probability distribution in k. The expression for the covariances allows us to show that the total variation distance between this (random) probability distribution and its mean converges in probability to zero. © 2002 Wiley Periodicals, Inc. Random Struct. Alg., 20: 519–539, 2002     

LC Determination of Propylene Glycol in Human Plasma After Pre-Column Derivatization with Benzoyl Chloride

A simple high-performance liquid chromatographic method, using photodiode array detection was developed for the determination of propylene glycol in human plasma and in the fluid retreived after continuous veno-venous hemofiltration. The method entailed alkaline derivatization with benzoyl chloride and ethylene glycol as internal standard. The separation of the compounds, after extraction with pentane, was carried out on a Pursuit C8 column with UV-detection at 230 nm. Validation samples were analyzed with an accuracy between 95 and 105%, and intra- and inter-day coefficients of variation of less than 8%. The calibration curve was linear over a concentration range of 5–100 mg L⁻¹ with a detection limit of 1 mg L⁻¹. Blood plasma samples of several patients were analysed by using the prescribed method with propylene glycol concentrations varying from 5 to 98 mg L⁻¹. Compared to previously described LC methods, this method is ten times more sensitive and thus suitable for use in pharmacokinetic studies of propylene glycol.     

Study of Hg22+ and complexes of NpO2+ and UO22+ in solution. examples of cation-cation interactions

Density functional theory (BPW91/TZ2P) is used to explore the nature of cation-cation interactions (CCIs) that exist between two actinyl cations in solution. Solvation, which is modeled using COSMO, favors the complexes (ONpO-ONpO)2+ and (ONpO-OUO)3+ over separated NpO2+(aq) and UO2(2+)(aq) cations because of the quadratic dependence of solvation on charge. For (OUO-OUO)4+, solvation effects, even though very large, are unable to overcome intrinsic electrostatic repulsion between the units. The actinyl-actinyl complexes are T-shaped, with the oxygen of one unit coordinated to the actinide metal of the other unit. The association free energies of (ONpO-ONpO)2+ and (ONpO-OUO)3+ are calculated as -42.1 and -29.2 kcal/mol. Explicit consideration of the first solvation shell at the B3LYP/LANL2DZ level suggests that the free energies of binding may be overestimated. The Hg2(2+) dication, though not considered a "traditional" CCI, is very similar to the actinyl-actinyl interaction. The binding free energy of Hg2(2+) in solution is calculated as -16.0 kcal/mol.     

Hydrogen bonds of RNA are stronger than those of DNA, but NMR monitors only presence of methyl substituent in uracil/thymine

Recently, Vakonakis and LiWang (J. Am. Chem. Soc. 2004, 126, 5688) reported experimental evidence for stronger hydrogen bonds in RNA A:U than in DNA A:T base pairs, which was based on differences in NMR shielding for adenine C2. We have analyzed the proposed correlation between NMR shielding and hydrogen-bond strength using density functional theory. Although we agree with the conclusion that A:U is more strongly bound, we find no correlation between the hydrogen-bond strength and the NMR shielding of C2. Our study shows that NMR merely probes the presence/absence of the methyl group in thymine/uracil, without any relation to the strength of the hydrogen bonds involved. In other words, one cannot infer the Watson-Crick hydrogen-bond strength from the NMR shielding constant of adenine C2.     

On the escape process during phase inversion of an emulsion

This paper deals with a phenomenon which plays an important role in the phase inversion process of emulsions. This process is governed by the interplay of coalescence of droplets, often leading to double emulsions, and the escape of those internal droplets. The latter process retards the inversion process. Coalescence has been the subject of many studies, contrary to the escape event. This paper addresses the escape process both theoretically and experimentally. The model developed analyses the rate of the escape of internal droplets from the mother droplet via a coalescence process, where the internal flow, as generated by the external flow, generates the viscous force for coalescence. Incomplete mixing in the droplet has been assumed. Experimental data on the escape rate of oil droplets from O/W/O emulsions have been analysed using a Computational Fluid Dynamics approach, where the model as indicated above has been incorporated. Experimental data and simulations compare very well. Data have been compared on varying the size of the inner droplets and the rotational speed of the vessel where the double emulsion has been formed and where the escape took place.     

A unified orbital model of delocalised and localised currents in monocycles, from annulenes to azabora-heterocycles

Why are some (4n+2)π systems aromatic, and some not? The ipsocentric approach to the calculation of the current density induced in a molecule by an external magnetic field predicts a four‐electron diatropic (aromatic) ring current for (4n+2)π carbocycles and a two‐electron paratropic (antiaromatic) current for (4n)π carbocycles. With the inclusion of an electronegativity parameter, an ipsocentric frontier‐orbital model also predicts the transition from delocalised currents in carbocycles to nitrogen‐localised currents in alternating azabora‐heterocycles, which rationalises the differences in (magnetic) aromaticity between these isoelectronic π‐conjugated systems. Ab initio valence‐bond calculations confirm the localisation predicted by the naïve model, and coupled‐Hartree–Fock calculations give current‐density maps that exhibit the predicted delocalised‐to‐localised/carbocycle–heterocycle transition.