Accurate relative pKa calculations for carboxylic acids using complete basis set and Gaussian-n models combined with continuum solvation methods

The complete basis set methods CBS-4, CBS-QB3, and CBS-APNO, and the Gaussian methods G2 and G3 were used to calculate the gas phase energy differences between six different carboxylic acids and their respective anions. Two different continuum methods, SM5.42R and CPCM, were used to calculate the free energy differences of solvation for the acids and their anions. Relative pKa values were calculated for each acid using one of the acids as a reference point. The CBS-QB3 and CBS-APNO gas phase calculations, combined with the CPCM/HF/6-31+G(d)//HF/6-31G(d) or CPCM/HF/6-31+G(d)//HF/6-31+G(d) continuum solvation calculations on the lowest energy gas phase conformer, and with the conformationally averaged values, give results accurate to ½ pKa unit. © 2001 American Institute of Physics.

Pervasive Algebras and Maximal Subalgebras.

A uniform algebra A on its Shilov boundary X is maximal if A is not C(X) and no uniform algebra is strictly contained between A and C(X) . It is essentially pervasive if A is dense in C(F) whenever F is a proper closed subset of the essential set of A. If A is maximal, then it is essentially pervasive and proper. We explore the gap between these two concepts. We show: (1) If A is pervasive and proper, and has a nonconstant unimodular element, then A contains an infinite descending chain of pervasive subalgebras on X . (2) It is possible to find a compact Hausdorff space X such that there is an isomorphic copy of the lattice of all subsets of N in the family of pervasive subalgebras of C(X). (3) In the other direction, if A is strongly logmodular, proper and pervasive, then it is maximal. (4) This fails if the word “strongly” is removed. We discuss examples involving Dirichlet algebras, A(U) algebras, Douglas algebras, and subalgebras of H∞(D), and develop new results that relate pervasiveness, maximality, and relative maximality to support sets of representing measures.

Suitability of real-time quantitative PCR to estimate the relative telomere length in European Hake (Merluccius merluccius Linnaeus, 1758)

Telomere length measurement has been proposed as a promising tool to estimate the age of individuals in natural populations. We used real-time quantitative PCR (qPCR) to measure relative telomere length in four tissues (brain, kidney, liver and muscle) of European hake (Merluccius merluccius) in different groups based upon body length an otolith age estimate. We observed a high level of inter-individual differences in the measurements of relative telomere length in hakes of similar age and body length groups. The results of qPCR analysis showed a great variability in all measures and a lack of repeatability and reproducibility with significant statistical differences in the results of the different assays. The paper discusses the technical reasons for the variability in qPCR obtained in this work and by other authors.