Optimal Sobolev type inequalities in Lorentz spaces

It is well known that the classical Sobolev embeddings may be improved within the framework of Lorentz spaces L p,q : the space D 1,p (R n ) , 1\u2009<\u2009p\u2009<\u2009n, embeds into L p 17 ,q (R n ) , p\u2009 64\u2009q\u2009 64\u2009 1e. However, the value of the best possible embedding constants in the corresponding inequalities is known just in the case L p 17 ,p (R n ) . Here, we determine optimal constants for the embedding of the space D 1,p (R n ) , 1\u2009<\u2009p\u2009<\u2009n, into the whole Lorentz space scale L p 17 ,q (R n ) , p\u2009 64\u2009q\u2009 64\u2009 1e, including the limiting case q\u2009=\u2009p of which we give a new proof. We also exhibit extremal functions for these embedding inequalities by solving related elliptic problems

Lpa1-5525 : a new lpa1 mutant isolated in a mutagenized population by a novel non-disrupting screening method

Phytic acid, or myo-inositol 1,2,3,4,5,6-hexakisphosphate, is the main storage form of phosphorus in plants. It is localized in seeds, deposited as mixed salts of mineral cations in protein storage vacuoles; during germination, it is hydrolyzed by phytases to make available P together with all the other cations needed for seed germination. When seeds are used as food or feed, phytic acid and the bound cations are poorly bioavailable for human and monogastric livestock due to their lack of phytase activity. Therefore, reducing the amount of phytic acid is one strategy in breeding programs aimed to improve the nutritional properties of major crops. In this work, we present data on the isolation of a new maize (Zea mays L.) low phytic acid 1 (lpa1) mutant allele obtained by transposon tagging mutagenesis with the Ac element. We describe the generation of the mutagenized population and the screening to isolate new lpa1 mutants. In particular, we developed a fast, cheap and non-disrupting screening method based on the different density of lpa1 seed compared to the wild type. This assay allowed the isolation of the lpa1-5525 mutant characterized by a new mutation in the lpa1 locus associated with a lower amount of phytic phosphorus in the seeds in comparison with the wild type

Holographic renormalization and supersymmetry

Holographic renormalization is a systematic procedure for regulating divergences in observables in asymptotically locally AdS spacetimes. For dual boundary field theories which are supersymmetric it is natural to ask whether this defines a supersymmetric renormalization scheme. Recent results in localization have brought this question into sharp focus: rigid supersymmetry on a curved boundary requires specific geometric structures, and general arguments imply that BPS observables, such as the partition function, are invariant under certain deformations of these structures. One can then ask if the dual holographic observables are similarly invariant. We study this question in minimal N = 2 gauged supergravity in four and five dimensions. In four dimensions we show that holographic renormalization precisely reproduces the expected field theory results. In five dimensions we find that no choice of standard holographic counterterms is compatible with supersymmetry, which leads us to introduce novel finite boundary terms. For a class of solutions satisfying certain topological assumptions we provide some independent tests of these new boundary terms, in particular showing that they reproduce the expected VEVs of conserved charges.Comment: 70 pages; corrected typo

de Sitter Supersymmetry Revisited

We present the basic $\mathcal{N} =1$ superconformal field theories in four-dimensional de Sitter space-time, namely the non-abelian super Yang-Mills theory and the chiral multiplet theory with gauge interactions or cubic superpotential. These theories have eight supercharges and are invariant under the full $SO(4,2)$ group of conformal symmetries, which includes the de Sitter isometry group $SO(4,1)$ as a subgroup. The theories are ghost-free and the anti-commutator $\sum_\alpha\{Q_\alpha, Q^{\alpha\dagger}\}$ is positive. SUSY Ward identities uniquely select the Bunch-Davies vacuum state. This vacuum state is invariant under superconformal transformations, despite the fact that de Sitter space has non-zero Hawking temperature. The $\mathcal{N}=1$ theories are classically invariant under the $SU(2,2|1)$ superconformal group, but this symmetry is broken by radiative corrections. However, no such difficulty is expected in the $\mathcal{N}=4$ theory, which is presented in appendix B.Comment: 21 pages, 2 figure

Gold nanoparticles supported on functionalized silica as catalysts for alkyne hydroamination: A chemico-physical insight

Highly stable gold nanoparticles anchored on propynylcarbamate-functionalized silica (Au/SiO2@Yne) have been efficiently utilized for the heterogeneous hydroamination of phenylacetylene with aniline under different reaction conditions. In order to ascertain the eventual influence of surface silanol groups on the system activity and selectivity tailored modifications of Au/SiO2@Yne catalysts were pursued according to two different strategies, involving respectively functionalization with trimethylethoxysilane (Au/SiO2@Yne-TMS) or post-treatment with triethylamine (Au/SiO2@Yne-NEt3). The prepared materials were analysed by several complementary techniques such as Solid State NMR (SS NMR), Transmission Electron Microscopy (TEM), X-ray Photoelectron Spectroscopy (XPS), X-ray Diffraction (XRD). A comparison of the resulting catalytic activities with that of the pristine Au/SiO2@Yne revealed a significant improvement for Au/SiO2@Yne-NEt3 in terms of both conversion and selectivity. Recycling and stability studies showed a catalytic activity decrease after the first run, due to the formation of polyphenylacetylene (PPhA) oligomers shielding the active sites. PPhA removal by sonication in acetone fully restored the catalytic activity and empowered the system with a good operational stability, a very crucial issue in view of eventual practical applications

On N = 2 Truncations of IIB on T^{1,1}

We study the N=4 gauged supergravity theory which arises from the consistent truncation of IIB supergravity on the coset T^{1,1}. We analyze three N=2 subsectors and in particular we clarify the relationship between true superpotentials for gauged supergravity and certain fake superpotentials which have been widely used in the literature. We derive a superpotential for the general reduction of type I supergravity on T^{1,1} and this together with a certain solution generating symmetry is tantamount to a superpotential for the baryonic branch of the Klebanov-Strassler solution.Comment: 32 pages, v2:references adde

Defective dystrophic thymus determines degenerative changes in skeletal muscle.

In Duchenne muscular dystrophy (DMD), sarcolemma fragility and myofiber necrosis produce cellular debris that attract inflammatory cells. Macrophages and T-lymphocytes infiltrate muscles in response to damage-associated molecular pattern signalling and the release of TNF-α, TGF-β and interleukins prevent skeletal muscle improvement from the inflammation. This immunological scenario was extended by the discovery of a specific response to muscle antigens and a role for regulatory T cells (Tregs) in muscle regeneration. Normally, autoimmunity is avoided by autoreactive T-lymphocyte deletion within thymus, while in the periphery Tregs monitor effector T-cells escaping from central regulatory control. Here, we report impairment of thymus architecture of mdx mice together with decreased expression of ghrelin, autophagy dysfunction and AIRE down-regulation. Transplantation of dystrophic thymus in recipient nude mice determine the up-regulation of inflammatory/fibrotic markers, marked metabolic breakdown that leads to muscle atrophy and loss of force. These results indicate that involution of dystrophic thymus exacerbates muscular dystrophy by altering central immune tolerance

Consistent reduction of charged D3-D7 systems

We provide a consistent reduction to five dimensions of the system of D3-branes at Calabi-Yau singularities coupled to D7-branes with world-volume gauge flux. The D3-branes source the dual to would-be conformal quiver theories. The D7-branes, which are homogeneously distributed in their transverse directions, are dual to massless matter in the fundamental representation at finite (baryon) density. We provide the five-dimensional action and equations of motion, and discuss a few sub-truncations. The reduction can be used in the study of transport properties and stability of D3-D7 charged systems.Comment: 23 pages. v2: references added and minor change

Heterotic Flux Attractors

We find attractor equations describing moduli stabilization for heterotic compactifications with generic SU(3)-structure. Complex structure and K\"ahler moduli are treated on equal footing by using SU(3)xSU(3)-structure at intermediate steps. All independent vacuum data, including VEVs of the stabilized moduli, is encoded in a pair of generating functions that depend on fluxes alone. We work out an explicit example that illustrates our methods.Comment: 37 pages, references and clarifications adde