The relativistic Scott correction for atoms and molecules

We prove the first correction to the leading Thomas-Fermi energy for the ground state energy of atoms and molecules in a model where the kinetic energy of the electrons is treated relativistically. The leading Thomas-Fermi energy, established in [Sorensen], as well as the correction given here are of semi-classical nature. Our result on atoms and molecules is proved from a general semi-classical estimate for relativistic operators with potentials with Coulomb-like singularities. This semi-classical estimate is obtained using the coherent state calculus introduced in [Solovej-Spitzer]. The paper contains a unified treatment of the relativistic as well as the non-relativistic case.Comment: 59 page

Bacteremia causes hippocampal apoptosis in experimental pneumococcal meningitis

Bacteremia and systemic complications both play important roles in brain pathophysiological alterations and the outcome of pneumococcal meningitis. Their individual contributions to the development of brain damage, however, still remain to be defined

The Ground State Energy of Heavy Atoms According to Brown and Ravenhall: Absence of Relativistic Effects in Leading Order

It is shown that the ground state energy of heavy atoms is, to leading order, given by the non-relativistic Thomas-Fermi energy. The proof is based on the relativistic Hamiltonian of Brown and Ravenhall which is derived from quantum electrodynamics yielding energy levels correctly up to order $\alpha^2$Ry

Analytic structure of solutions to multiconfiguration equations

We study the regularity at the positions of the (fixed) nuclei of solutions to (non-relativistic) multiconfiguration equations (including Hartree--Fock) of Coulomb systems. We prove the following: Let {phi_1,...,phi_M} be any solution to the rank--M multiconfiguration equations for a molecule with L fixed nuclei at R_1,...,R_L in R^3. Then, for any j in {1,...,M} and k in {1,...,L}, there exists a neighbourhood U_{j,k} in R^3 of R_k, and functions phi^{(1)}_{j,k}, phi^{(2)}_{j,k}, real analytic in U_{j,k}, such that phi_j(x) = phi^{(1)}_{j,k}(x) + |x - R_k| phi^{(2)}_{j,k}(x), x in U_{j,k} A similar result holds for the corresponding electron density. The proof uses the Kustaanheimo--Stiefel transformation, as applied earlier by the authors to the study of the eigenfunctions of the Schr"odinger operator of atoms and molecules near two-particle coalescence points.Comment: 15 page

Determination of fatty acid composition in seed oil of rapeseed (Brassica napus L.) by mutated alleles of the FAD3 desaturase genes

One of the goals in oilseed rape programs is to develop genotypes producing oil with low linolenic acid content (C18:3, ≤3%). Low linolenic mutant lines of canola rapeseed were obtained via chemical mutagenesis at the Plant Breeding and Acclimatization Institute – NRI, in Poznan, Poland, and allele-specific SNP markers were designed for monitoring of two statistically important single nucleotide polymorphisms detected by SNaPshot analysis in two FAD3 desaturase genes, BnaA.FAD3 and BnaC.FAD3, respectively. Strong negative correlation between the presence of mutant alleles of the genes and linolenic acid content was revealed by analysis of variance. In this paper we present detailed characteristics of the markers by estimation of the additive and dominance effects of the FAD3 genes with respect to particular fatty acid content in seed oil, as well as by calculation of the phenotypic variation of seed oil fatty acid composition accounted by particular allele-specific marker. The obtained percentage of variation in fatty acid composition was considerable only for linolenic acid content and equaled 35.6% for BnaA.FAD3 and 39.3% for BnaC.FAD3, whereas the total percentage of variation in linolenic acid content was 53.2% when accounted for mutations in both genes simultaneously. Our results revealed high specificity of the markers for effective monitoring of the wild-type and mutated alleles of the Brassica napus FAD3 desaturase genes in the low linolenic mutant recombinants in breeding programs