Moderate Deviations for Longest Increasing Subsequences: The Lower Tail

We derive a moderate deviation principle for the lower tail probabilities of the length of a longest increasing subsequence in a random permutation. It refers to the regime between the lower tail large deviation regime and the central limit regime. The present article together with the upper tail moderate deviation principle in Ref. 12 yields a complete picture for the whole moderate deviation regime. Other than in Ref. 12, we can directly apply estimates by Baik, Deift, and Johansson, who obtained a (non-standard) Central Limit Theorem for the same quantity.     

Monte Carlo simulation of cluster kinetics in three-dimensional Ising model

Simulations in lattices of size 100³ at the critical point of the three-dimensional Glauber kinetic Ising model indicate that the 1935 Becker-Doring equation no longer works there: The growth rates decay in time. These conclusions confirm those in two dimensions.     

Diastereomer-differentiating hydrolysis of 1,3-diol-acetonides: a simplified procedure for the separation of syn- and anti-1,3-diols

[reaction: see text] A new method to facilitate the separation of diastereomeric syn- and anti-1,3-diols is described. The method relies on the different hydrolysis rates of the corresponding diastereomeric acetonides. Treatment of a dichloromethane solution of syn- and anti-1,3-diol-acetonide with a catalytic amount of diluted aqueous hydrochloric acid leads to the selective cleavage of the anti diastereomer. The resulting anti-1,3-diol can be easily separated from the unchanged syn-1,3-diol-acetonide.     

A note on the thermodynamics of dimanganese and dirhenium decacarbonyls

The results of low temperature heat capacity studies on Mn₂(CO)₁₀(s) and Re₂(CO)₁₀(s) are compared with literature reports. It is shown that the values of vaporization enthalpies and entropies correspond with those of the low temperature stable phase.