Vekua theory for the Helmholtz operator

Vekua operators map harmonic functions defined on domain in \mathbb R2R2 to solutions of elliptic partial differential equations on the same domain and vice versa. In this paper, following the original work of I. Vekua (Ilja Vekua (1907–1977), Soviet-Georgian mathematician), we define Vekua operators in the case of the Helmholtz equation in a completely explicit fashion, in any space dimension N ≥ 2. We prove (i) that they actually transform harmonic functions and Helmholtz solutions into each other; (ii) that they are inverse to each other; and (iii) that they are continuous in any Sobolev norm in star-shaped Lipschitz domains. Finally, we define and compute the generalized harmonic polynomials as the Vekua transforms of harmonic polynomials. These results are instrumental in proving approximation estimates for solutions of the Helmholtz equation in spaces of circular, spherical, and plane waves.

Cell walls of developing wheat starchy endosperm: comparison of composition and RNA-Seq transcriptome

The transcriptome of the developing starchy endosperm of hexaploid wheat (Triticum aestivum) was determined using RNA-Seq isolated at five stages during grain fill. This resource represents an excellent way to identify candidate genes responsible for the starchy endosperm cell wall, which is dominated by arabinoxylan (AX), accounting for 70% of the cell wall polysaccharides, with 20% (1,3; 1,4)-beta-D-glucan, 7% glucomannan, and 4% cellulose. A complete inventory of transcripts of 124 glycosyltransferase (GT) and 72 glycosylhydrolase (GH) genes associated with cell walls is presented. The most highly expressed GT transcript (excluding those known to be involved in starch synthesis) was a GT47 family transcript similar to Arabidopsis (Arabidopsis thaliana) IRX10 involved in xylan extension, and the second most abundant was a GT61. Profiles for GT43 IRX9 and IRX14 putative orthologs were consistent with roles in AX synthesis. Low abundances were found for transcripts from genes in the acyl-coA transferase BAHD family, for which a role in AX feruloylation has been postulated. The relative expression of these was much greater in whole grain compared with starchy endosperm, correlating with the levels of bound ferulate. Transcripts associated with callose (GSL), cellulose (CESA), pectin (GAUT), and glucomannan (CSLA) synthesis were also abundant in starchy endosperm, while the corresponding cell wall polysaccharides were confirmed as low abundance (glucomannan and callose) or undetectable (pectin) in these samples. Abundant transcripts from GH families associated with the hydrolysis of these polysaccharides were also present, suggesting that they may be rapidly turned over. Abundant transcripts in the GT31 family may be responsible for the addition of Gal residues to arabinogalactan peptide.

Operator space structure of JC*-triples and TROs, I

We embark upon a systematic investigation of operator space structure of JC*-triples via a study of the TROs (ternary rings of operators) they generate. Our approach is to introduce and develop a variety of universal objects, including universal TROs, by which means we are able to describe all possible operator space structures of a JC*-triple. Via the concept of reversibility we obtain characterisations of universal TROs over a wide range of examples. We apply our results to obtain explicit descriptions of operator space structures of Cartan factors regardless of dimension

On the operator space structure of Hilbert spaces

Operator spaces of Hilbertian JC∗ -triples E are considered in the light of the universal ternary ring of operators (TRO) introduced in recent work. For these operator spaces, it is shown that their triple envelope (in the sense of Hamana) is the TRO they generate, that a complete isometry between any two of them is always the restriction of a TRO isomorphism and that distinct operator space structures on a fixed E are never completely isometric. In the infinite-dimensional cases, operator space structure is shown to be characterized by severe and definite restrictions upon finite-dimensional subspaces. Injective envelopes are explicitly computed.

Salmon consumption during pregnancy alters fatty acid composition and secretory IgA concentration in human breast milk

Fish oil supplementation during pregnancy alters breast milk composition, but there is little information about the impact of oily fish consumption. We determined whether increased salmon consumption during pregnancy alters breast milk fatty acid composition and immune factors. Women (n = 123) who rarely ate oily fish were randomly assigned to consume their habitual diet or to consume 2 portions of farmed salmon per week from 20 wk of pregnancy until delivery. The salmon provided 3.45 g long-chain (LC) (n-3) PUFA/wk. Breast milk fatty acid composition and immune factors [soluble CD14, transforming growth factor-b (TGFb)1, TGFb2, and secretory IgA] were analyzed at 1, 5, 14, and 28 d postpartum (PP). Breast milk from the salmon group had higher proportions of EPA (80%), docosapentaenoic acid (30%), and DHA (90%) on d 5 PP compared with controls (P < 0.01). The LC (n-6) PUFA:LC (n-3) PUFA ratio was lower for the salmon group on all days of PP sampling (P < 0.004), although individual (n-6) PUFA proportions, including arachidonic acid, did not differ. All breast milk immune factors decreased between d 1 and 28 PP (P < 0.001). Breast milk secretory IgA (sIgA) was lower in the salmon group (d 1–28 PP; P = 0.006). Salmon consumption during pregnancy, at the current recommended intakes, increases the LC (n-3) PUFA concentration of breast milk in early lactation, thus improving the supply of these important fatty acids to the breast-fed neonate. The consequence of the lower breast milk concentration of sIgA in the salmon group is not clear.

Immune factors and fatty acid composition in human milk from river/lake, coastal and inland regions of China

Breast milk fatty acid composition may be affected by maternal diet during gestation and lactation. The influence of dietary and breast milk fatty acids on breast milk immune factors is poorly defined. We determined the fatty acid composition and immune factor concentrations of breast milk from women residing in river & lake, coastal, and inland regions of China, which differ in their consumption of lean fish and oily fish. Breast milk samples were collected on days 3 to 5 (colostrum), 14 and 28 post-partum and analysed for soluble CD14 (sCD14), transforming growth factor (TGF)-β1, TGF-β2, secretory immunoglobulin A (sIgA) and fatty acids. The fatty acid composition of breast milk differed between regions and with time post-partum. The concentrations of all four immune factors in breast milk decreased over time, with sCD14, sIgA and TGF-β1 being highest in colostrum in the river & lake region. Breast milk DHA and arachidonic acid (AA) were positively associated, and γ-linolenic acid and EPA negatively associated, with the concentrations of each of the four immune factors. In conclusion, breast milk fatty acids and immune factors differ between regions in China characterised by different patterns of fish consumption and change during the course of lactation. A higher breast milk DHA and AA concentration is associated with higher concentrations of immune factors in breast milk, suggesting a role for these fatty acids in promoting gastrointestinal and immune maturation of the infant.

Effect of TAG composition on performance of low saturate shortenings in puff pastry

Four blends formulated with low saturated fatty acid content, with the saturated component rich in stearic acid, were prepared from shea stearin, interesterified shea stearin, fully hardened soybean oil and high oleic sunflower oil in order to study their performance as shortenings in puff pastry products. The blends had a low saturated fatty acid content (30.1 ± 1.1%) compared to butter (65.9%). Saturates in the four blends examined came mainly from SSS, SOS, SSO and SOO. Puff pastry prepared from the blend that contained SOS as the main source of saturates had better properties than the other blends. It was similar to butter in compressibility of the baked product. The β-polymorphic form was present in all blends, although blends containing the highest levels of SSS also showed some β′ crystals.

Composition cyclique et programme d’illustrations. L’épisode de Grisandole dans le manuscrit enluminé de la Suite Vulgate du Merlin, B. L. Add. 10292

L'étude du texte et de l'illustration de l'épisode romain dans la Suite Vulgate du Merlin du manuscrit British Library Add. 10292 (XIVe s.) permet d'explorer la relation entre l'amplification cyclique à l'œuvre dans ce passage au statut textuel complexe et le développement spécifique d'une série voire d'un cycle d'illustrations.

Le livre de messire Lancelot du Lac" : présentation matérielle et composition des manuscrits arthuriens de Jacques d'Armagnac (BNF fr. 117-120 et 113-116)

L'organisation des manuscrits arthuriens du cycle du Graal de Jacques d'Armagnac (BNF fr. 117-120 qu'il a hérité de son arrière-grand-père le duc Jean de Berry et dont il a fait retoucher les peintures et BNF fr. 113-116 qu'il a fait exécuter entre 1470 et 1475), leur agencement, leur illustration et leurs subdivisions sont un indice précieux de la conception et de la réception de ces compilations. Ils soulignent l'effort de constitution d'un ensemble romanesque cohérent centré sur la figure de Lancelot.

Universally reversible JC*-triples and operator spaces

Abstract. We prove that the vast majority of JC∗-triples satisfy the condition of universal reversibility. Our characterisation is that a JC∗-triple is universally reversible if and only if it has no triple homomorphisms onto Hilbert spaces of dimension greater than two nor onto spin factors of dimension greater than four. We establish corresponding characterisations in the cases of JW∗-triples and of TROs (regarded as JC∗-triples). We show that the distinct natural operator space structures on a universally reversible JC∗-triple E are in bijective correspondence with a distinguished class of ideals in its universal TRO, identify the Shilov boundaries of these operator spaces and prove that E has a unique natural operator space structure precisely when E contains no ideal isometric to a nonabelian TRO. We deduce some decomposition and completely contractive properties of triple homomorphisms on TROs.

The influence of ozone precursor emissions from four world regions on tropospheric composition and radiative climate forcing

Ozone (O3) precursor emissions influence regional and global climate and air quality through changes in tropospheric O3 and oxidants, which also influence methane (CH4) and sulfate aerosols (SO42−). We examine changes in the tropospheric composition of O3, CH4, SO42− and global net radiative forcing (RF) for 20% reductions in global CH4 burden and in anthropogenic O3 precursor emissions (NOx, NMVOC, and CO) from four regions (East Asia, Europe and Northern Africa, North America, and South Asia) using the Task Force on Hemispheric Transport of Air Pollution Source-Receptor global chemical transport model (CTM) simulations, assessing uncertainty (mean ± 1 standard deviation) across multiple CTMs. We evaluate steady state O3 responses, including long-term feedbacks via CH4. With a radiative transfer model that includes greenhouse gases and the aerosol direct effect, we find that regional NOx reductions produce global, annually averaged positive net RFs (0.2 ± 0.6 to 1.7 ± 2 mWm−2/Tg N yr−1), with some variation among models. Negative net RFs result from reductions in global CH4 (−162.6 ± 2 mWm−2 for a change from 1760 to 1408 ppbv CH4) and regional NMVOC (−0.4 ± 0.2 to −0.7 ± 0.2 mWm−2/Tg C yr−1) and CO emissions (−0.13 ± 0.02 to −0.15 ± 0.02 mWm−2/Tg CO yr−1). Including the effect of O3 on CO2 uptake by vegetation likely makes these net RFs more negative by −1.9 to −5.2 mWm−2/Tg N yr−1, −0.2 to −0.7 mWm−2/Tg C yr−1, and −0.02 to −0.05 mWm−2/Tg CO yr−1. Net RF impacts reflect the distribution of concentration changes, where RF is affected locally by changes in SO42−, regionally to hemispherically by O3, and globally by CH4. Global annual average SO42− responses to oxidant changes range from 0.4 ± 2.6 to −1.9 ± 1.3 Gg for NOx reductions, 0.1 ± 1.2 to −0.9 ± 0.8 Gg for NMVOC reductions, and −0.09 ± 0.5 to −0.9 ± 0.8 Gg for CO reductions, suggesting additional research is needed. The 100-year global warming potentials (GWP100) are calculated for the global CH4 reduction (20.9 ± 3.7 without stratospheric O3 or water vapor, 24.2 ± 4.2 including those components), and for the regional NOx, NMVOC, and CO reductions (−18.7 ± 25.9 to −1.9 ± 8.7 for NOx, 4.8 ± 1.7 to 8.3 ± 1.9 for NMVOC, and 1.5 ± 0.4 to 1.7 ± 0.5 for CO). Variation in GWP100 for NOx, NMVOC, and CO suggests that regionally specific GWPs may be necessary and could support the inclusion of O3 precursors in future policies that address air quality and climate change simultaneously. Both global net RF and GWP100 are more sensitive to NOx and NMVOC reductions from South Asia than the other three regions.

Fatty acid composition of cooked chicken meat and chicken meat products as influenced by price range at retail

The primary objective was to determine fatty acid composition of skinless chicken breast and leg meat portions and chicken burgers and nuggets from the economy price range, standard price range (both conventional intensive rearing) and the organic range from four leading supermarkets. Few significant differences in the SFA, MUFA and PUFA composition of breast and leg meat portions were found among price ranges, and supermarket had no effect. No significant differences in fatty acid concentrations of economy and standard chicken burgers were found, whereas economy chicken nuggets had higher C16:1, C18:1 cis, C18:1 trans and C18:3 n-3 concentrations than had standard ones. Overall, processed chicken products had much higher fat contents and SFA than had whole meat. Long chain n-3 fatty acids had considerably lower concentrations in processed products than in whole meat. Overall there was no evidence that organic chicken breast or leg meat had a more favourable fatty acid composition than had meat from conventionally reared birds.

Differential effects of two fermentable carbohydrates on central appetite regulation and body composition

BACKGROUND: Obesity is rising at an alarming rate globally. Different fermentable carbohydrates have been shown to reduce obesity. The aim of the present study was to investigate if two different fermentable carbohydrates (inulin and b-glucan) exert similar effects on body composition and central appetite regulation in high fat fed mice. METHODOLOGY/PRINCIPAL FINDINGS: Thirty six C57BL/6 male mice were randomized and maintained for 8 weeks on a high fat diet containing 0% (w/w) fermentable carbohydrate, 10% (w/w) inulin or 10% (w/w) b-glucan individually. Fecal and cecal microbial changes were measured using fluorescent in situ hybridization, fecal metabolic profiling was obtained by proton nuclear magnetic resonance (1H NMR), colonic short chain fatty acids were measured by gas chromatography, body composition and hypothalamic neuronal activation were measured using magnetic resonance imaging (MRI) and manganese enhanced MRI (MEMRI), respectively, PYY (peptide YY) concentration was determined by radioimmunoassay, adipocyte cell size and number were also measured. Both inulin and b-glucan fed groups revealed significantly lower cumulative body weight gain compared with high fat controls. Energy intake was significantly lower in b-glucan than inulin fed mice, with the latter having the greatest effect on total adipose tissue content. Both groups also showed an increase in the numbers of Bifidobacterium and Lactobacillus-Enterococcus in cecal contents as well as feces. b- glucan appeared to have marked effects on suppressing MEMRI associated neuronal signals in the arcuate nucleus, ventromedial hypothalamus, paraventricular nucleus, periventricular nucleus and the nucleus of the tractus solitarius, suggesting a satiated state. CONCLUSIONS/SIGNIFICANCE: Although both fermentable carbohydrates are protective against increased body weight gain, the lower body fat content induced by inulin may be metabolically advantageous. b-glucan appears to suppress neuronal activity in the hypothalamic appetite centers. Differential effects of fermentable carbohydrates open new possibilities for nutritionally targeting appetite regulation and body composition.