Special functions associated to a certain fourth order differential equation

We develop a theory of "special functions" associated to a certain fourth order differential operator $\mathcal{D}_{\mu,\nu}$ on $\mathbb{R}$ depending on two parameters $\mu,\nu$. For integers $\mu,\nu\geq-1$ with $\mu+\nu\in2\mathbb{N}_0$ this operator extends to a self-adjoint operator on $L^2(\mathbb{R}_+,x^{\mu+\nu+1}dx)$ with discrete spectrum. We find a closed formula for the generating functions of the eigenfunctions, from which we derive basic properties of the eigenfunctions such as orthogonality, completeness, $L^2$-norms, integral representations and various recurrence relations. This fourth order differential operator $\mathcal{D}_{\mu,\nu}$ arises as the radial part of the Casimir action in the Schr\"odinger model of the minimal representation of the group $O(p,q)$, and our "special functions" give $K$-finite vectors

QTL for phytosterol and sinapate ester content in Brassica napus L. collocate with the two erucic acid genes

Improving oil and protein quality for food and feed purposes is an important goal in rapeseed (Brassica napus L.) breeding programs. Rapeseed contains phytosterols, used to enrich food products, and sinapate esters, which are limiting the utilization of rapeseed proteins in the feed industry. Increasing the phytosterol content of oil and lowering sinapate ester content of meal could increase the value of the oilseed rape crop. The objective of the present study was to identify quantitative trait loci (QTL) for phytosterol and sinapate ester content in a winter rapeseed population of 148 doubled haploid lines, previously found to have a large variation for these two traits. This population also segregated for the two erucic acid genes. A close negative correlation was found between erucic acid and phytosterol content (Spearman’s rank correlation, rs = −0.80**). For total phytosterol content, three QTL were detected, explaining 60% of the genetic variance. The two QTL with the strongest additive effects were mapped on linkage groups N8 and N13 within the confidence intervals of the two erucic acid genes. For sinapate ester content four QTL were detected, explaining 53% of the genetic variance. Again, a close negative correlation was found between erucic acid and sinapate ester content (rs = −0.66**) and the QTL with the strongest additive effects mapped on linkage groups N8 and N13 within the confidence intervals of the two erucic acid genes. The results suggests, that there is a pleiotropic effect of the two erucic acid genes on phytosterol and sinapate ester content; the effect of the alleles for low erucic acid content is to increase phytosterol and sinapate ester content. Possible reasons for this are discussed based on known biosynthetic pathways

Spectroscopic studies of electrochemical reactions of adsorbed dye layers

Dye reactions at transparent electrodes were studied by spectroscopic investigations using the attenuated total reflection technique. All experiments were performed by modulating the concentration and consequently the absorption itself (potential modulation). The applicability of this method has been demonstrated by studying the distribution of monomers and dimers in adsorbed dye layers (viologene) or in the vicinity of the electrode. Measurements at higher modulation frequencies have shown that unstable semiquinones in adsorbed dye layers (methylene blue, thionine) involved in the oxidation-reduction cycle could be detected

Horseradish (Armoracia rusticana), a neglected medical and condiment species with a relevant glucosinolate profile: a review

Armoracia rusticana (horseradish), a member of the Brassicaceae family, has been known since ancient times as a folk medicinal herb and as a plant of nutritional value and culinary interest. Currently horseradish is cultivated for its thick, fleshy and white roots which have a delicious intense pungency and for its tender leaves which are frequently used for salad mixed to other vegetables. The traditions to use horseradish plant for medicinal purpose are still applied in many countries. Horseradish is a rich source of a number of bioactive compounds such as glucosinolates (GLSs) and their breakdown products. Sinigrin is the dominant glucosinolate in both leaves and roots. Recent studies have shown that crude plant extracts have a complex profile of naturally occurring GLSs, with particular regard to sprouts. The increasing interest in these secondary metabolites, associated to the long and diffuse tradition of using horseradish in food preservation and as condiment in many parts of the world, is generating new applications of this plant in several agro-industrial and pharmaceutical sectors and is encouraging the use of its roots and leaves in functional food and medicine for human health. A bibliography review is discussed on ethnobotanical aspects and uses of this plant, as well as knowledge about its flavour compounds and GLS content and composition. This study summarizes also the updated information concerning the influence of the genotype and environment on GLS profile in horseradish

The involvement of demethylation in the myeloid-specific function of the mouse M lysozyme gene downstream enhancer.

Lysozyme gene expression is a specific marker for the macrophage/granulocyte lineage of hematopoietic differentiation in mammals, its expression being gradually increased during maturation. Analysis of the mechanisms regulating mouse M lysozyme gene expression during myeloid differentiation revealed a complicated pattern of DNase I hypersensitive sites (HS sites) within the flanking regions of the gene. The HS-3 site, located in the 3'-flanking region of the gene, overlapped with an enhancer element, which is the only strong enhancer identified in the vicinity of the gene. We demonstrate a positive correlation between undermethylation of the entire 3'-flanking region, the appearance of the HS-3 site, and M lysozyme gene expression during in vitro differentiation of hematopoietic stem cells. We furthermore show that methylation of a single CpG site within the enhancer core element, only observed in immature macrophage cells in vivo, is sufficient to inhibit nuclear factor binding to this element in vitro and to inhibit its transactivation potential in DNA transfection experiments