The fractional Bessel equation in H\"older spaces

Motivated by the Poisson equation for the fractional Laplacian on the whole space with radial right hand side, we study global H\"older and Schauder estimates for a fractional Bessel equation. Our methods stand on the so-called semigroup language. Indeed, by using the solution to the Bessel heat equation we derive pointwise formulas for the fractional operators. Appropriate H\"older spaces, which can be seen as Campanato-type spaces, are characterized through Bessel harmonic extensions and fractional Carleson measures. From here the regularity estimates for the fractional Bessel equations follow. In particular, we obtain regularity estimates for radial solutions to the fractional Laplacian.Comment: 36 pages. To appear in Journal of Approximation Theor

Variable exponent Sobolev spaces associated with Jacobi expansions

In this paper we define variable exponent Sobolev spaces associated with Jacobi expansions. We prove that our generalized Sobolev spaces can be characterized as variable exponent potential spaces and as variable exponent Triebel-Lizorkin type spaces.Comment: 30 pages, small typos corrected in the introductio

Discovery of 15-second oscillations in Hubble Space Telescope observations of WZ Sagittae following the 2001 outburst

We report the discovery of 15-s oscillations in ultraviolet observations of WZ Sge obtained with the Hubble Space Telescope approximately one month after the peak of the 2001 outburst. This is the earliest detection of oscillations in WZ Sge following an outburst and the first time that a signal near 15 s has been seen to be dominant. The oscillations are quite strong (amplitude about 5%), but not particularly coherent. In one instance, the oscillation period changed by 0.7 s between successive observations separated by less than 1 hour. We have also found evidence for weaker signals with periods near 6.5 s in some of our data. We discuss the implications of our results for the models that have been proposed to account for the 28-s oscillations seen in quiescence. If the periods of the 15-s oscillations can be identified with the periods of revolution of material rotating about the white dwarf, the mass of the white dwarf must satisfy M_WD > 0.71 M_sun. The corresponding limit for the 6.5-s signals is M_WD > 1.03 M_sun.Comment: accepted for publication in ApJ Letters; 13 pages, 4 postscript figures; new version corrects a few typos and matches version that will appear in ApJ

Microbial and genetically engineered oils as replacements for fish oil in aquaculture feeds

As the global population grows more of our fish and seafood are being farmed. Fish are the main dietary source of the omega-3 (n-3) long-chain polyunsaturated fatty acids (LC-PUFA), eicosapentaenoic (EPA) and docosahexaenoic (DHA) acids, but these cannot be produced in sufficient quantities as are now required for human health. Farmed fish have traditionally been fed a diet consisting of fishmeal and fish oil, rich in n-3 LC-PUFA. However, the increase in global aquaculture production has resulted in these finite and limited marine ingredients being replaced with sustainable alternatives of terrestrial origin that are devoid of n-3 LC-PUFA. Consequently, the nutritional value of the final product has been partially compromised with EPA and DHA levels both falling. Recent calls from the salmon industry for new sources of n-3 LC-PUFA have received significant commercial interest. Thus, this review explores the technologies being applied to producede novon-3 LC-PUFA sources, namely microalgae and genetically engineered oilseed crops, and how they may be used in aquafeeds to ensure that farmed fish remain a healthy component of the human diet

The compositional and metabolic responses of gilthead seabream (Sparus aurata) to a gradient of dietary fish oil and associated n-3 long-chain PUFA content

The authors express their gratitude to the technical team at the BioMar Feed Trial Unit, Hirtshals, in particular, Svend Jørgen Steenfeldt for expert care of the experimental subjects, for training and supervision provided by laboratory staff at Nutrition Analytical Services and Molecular Biology at the Institute of Aquaculture, University of Stirling, UK. S. J. S. H’s. PhD was co-funded by BioMar and the Marine Alliance for Science and Technology Scotland. BioMar provided the experimental feeds, trial facilities and fish, and covered travel expenses. V. K. and J. T. designed and executed the nutritional trial and all authors contributed to planning the analyses. V. K., J. T. and S. J. S. H. carried out the sampling. O. M., D. R. T and S. A. M. M. supervised the lead author. M. B. B. provided training in molecular biology to S. J. S. H. who carried out all analytical procedures. S. J. S. H. analysed all of the data and prepared the manuscript. Subsequently the manuscript was shared between all authors who made amendments, contributions and recommendations. The authors declare that there are no conflicts of interestPeer reviewedPublisher PD

HS 0139+0559, HS 0229+8016, HS 0506+7725, and HS 0642+5049 : four new long-period cataclysmic variables

We present time-resolved optical spectroscopy and photometry of four relatively bright (V ∼ 14.0−15.5) long-period cataclysmic variables(CVs) discovered in the Hamburg Quasar Survey: HS 0139+0559, HS 0229+8016, HS 0506+7725, and HS 0642+5049. Their respective orbital periods, 243.69 ± 0.49 min, 232.550 ± 0.049 min, 212.7 ± 0.2 min, and 225.90 ± 0.23 min are determined from radial velocity and photometric variability studies. HS 0506+7725 is characterised by strong Balmer and He emission lines, short-period (∼10−20 min) flickering, and weak X-ray emission in the ROSAT All Sky Survey. The detection of a deep low state (B 18.5) identifies HS 0506+7725 as a member of the VY Scl stars. HS 0139+0559, HS 0229+8016, and HS 0642+5049 display thick-disc like spectra and no or only weak flickering activity. HS 0139+0559 and HS 0229+8016 exhibit clean quasi-sinusoidal radial velocity variations of their emission lines but no or very little orbital photometricvariability. In contrast, we detect no radial velocity variation in HS 0642+5049 but a noticeable orbital brightness variation. We identify all three systems either as UX UMa-type novalike variables or as Z Cam-type dwarf novae. Our identification of these four new systems underlines that the currently known sample of CVs is rather incomplete even for bright objects. The four new systems add to the clustering of orbital periods in the 3−4 h range found in the sample of HQS selected CVs, and we discuss the large incidence of magnetic CVs and VY Scl/SW Sex stars found in this period range among the known population of CVs

Profiling Phospholipids within Atlantic Salmon Salmo salar with Regards to a Novel Terrestrial Omega-3 Oil Source

The development and inclusion of novel oils derived from genetically modified (GM) oilseeds into aquafeeds, to supplement and supplant current terrestrial oilseeds, as well as fish oils, warrants a more thorough investigation into lipid biochemical alterations within finfish species, such as Atlantic salmon. Five tissues were examined across two harvesting timepoints to establish whether lipid isomeric alterations could be detected between a standard commercial diet versus a diet that incorporated the long-chain polyunsaturated fatty acids (LC-PUFA), EPA (eicosapentaenoic acid), and DHA (docosahexaenoic acid), derived from the GM oilseed Camelina sativa. Tissue-dependent trends were detected, indicating that certain organs, such as the brain, have a basal limit to LC-PUFA incorporation, though enrichment of these fatty acids is possible. Lipid acyl alterations, as well as putative stereospecific numbering (sn) isomer alterations, were also detected, providing evidence that GM oils may modify lipid structure, with lipids of interest providing a set of targeted markers by which lipid alterations can be monitored across various novel diets

Effects of dietary fatty acids on mitochondrial phospholipid compositions, oxidative status and mitochondrial gene expression of zebrafish at different ages

Mitochondrial decay is generally associated with impairment in the organelle bioenergetics function and increased oxidative stress, and it appears that deterioration of mitochondrial inner membrane phospholipids (PL) and accumulation of mitochondrial DNA (mtDNA) mutations are among the main mechanisms involved in this process. In the present study, mitochondrial membrane PL compositions, oxidative status (TBARS content and SOD activity) and mtDNA gene expression of muscle and liver were analyzed in zebrafish fed two diets with lipid supplied either by rapeseed oil (RO) or a blend 60:40 of RO and DHA500 TG oil (DHA). Two feeding trials were performed using zebrafish from the same population of two ages (8 and 21 months). Dietary FA composition affected fish growth in 8-month-old animals, which could be related to an increase in stress promoted by diet composition. Lipid peroxidation was considerably higher in mitochondria of 8-month-old zebrafish fed the DHA diet than in animals fed the RO diet. This could indicate higher oxidative damage to mitochondrial lipids, very likely due to increased incorporation of DHA in PL of mitochondrial membranes. Lipids would be among the first molecules affected by mitochondrial reactive oxygen species, and lipid peroxidation could propagate oxidative reactions that would damage other molecules, including mtDNA. Mitochondrial lipid peroxidation and gene expression of 21-month-old fish showed lower responsiveness to diet composition than those of younger fish. Differences found in the effect of diet composition on mitochondrial lipids between the two age groups could be indicating age-related changes in the ability to maintain structural homeostasis of mitochondrial membranes

Encapsulated fish oil products available in the UK meet regulatory guidelines with respect to EPA + DHA contents and oxidative status

Encapsulated fish oil products continue to be of high interest, particularly concerning labelling claims and oxidative status. Thus, the present study analysed twenty‐three encapsulated fish oil products from the UK for their lipid and fatty acid composition as well as oxidation parameters. Oil contents ranged from 91.4‐118.9% of the manufacturers stated level. Lipid class analyses revealed three different types of oil products consisting of either triacylglycerol (TAG), ethyl ester (EE) or in combination (EE/TAG). Fatty acid profiles varied according to oil form with long‐chain omega‐3 fatty acids, eicosapentaenoic acid (EPA) and docosahexaenoic acid (DHA), more concentrated in EE compared to TAG‐based oils with TAG/EE oils containing intermediary levels. Twelve products had EPA + DHA contents lower than advertised, although this was reduced to 11 when the actual measured capsule oil content was taken into consideration. All products had peroxide (PV) and anisidine values below those set by pharmacopeias, although four products had a PV above the industry set limit of 5 meq.kg−1. No relationships were found between oxidative parameters and missing EPA + DHA contents, although a significant relationship was observed between PV and days to expiry. In summary, encapsulated fish oil products on the UK market are not oxidized and meet regulatory guidelines with respect to EPA + DHA contents and oxidative status. Practical Applications: The study highlights the importance of quantifying the actual capsule oil content when determining EPA + DHA levels with respect to label claims. Furthermore, it also places results into context regarding regulatory guidelines demonstrating to regulatory bodies and consumers alike that UK fish oil products do meet specification and are not oxidised