Transmutations and spectral parameter power series in eigenvalue problems

We give an overview of recent developments in Sturm-Liouville theory concerning operators of transmutation (transformation) and spectral parameter power series (SPPS). The possibility to write down the dispersion (characteristic) equations corresponding to a variety of spectral problems related to Sturm-Liouville equations in an analytic form is an attractive feature of the SPPS method. It is based on a computation of certain systems of recursive integrals. Considered as families of functions these systems are complete in the $L_{2}$-space and result to be the images of the nonnegative integer powers of the independent variable under the action of a corresponding transmutation operator. This recently revealed property of the Delsarte transmutations opens the way to apply the transmutation operator even when its integral kernel is unknown and gives the possibility to obtain further interesting properties concerning the Darboux transformed Schr\"{o}dinger operators. We introduce the systems of recursive integrals and the SPPS approach, explain some of its applications to spectral problems with numerical illustrations, give the definition and basic properties of transmutation operators, introduce a parametrized family of transmutation operators, study their mapping properties and construct the transmutation operators for Darboux transformed Schr\"{o}dinger operators.Comment: 30 pages, 4 figures. arXiv admin note: text overlap with arXiv:1111.444

Localization of gravity on a de Sitter thick braneworld without scalar fields

In this work we present a simple thick braneworld model that is generated by an intriguing interplay between a 5D cosmological constant with a de Sitter metric induced in the 3-brane without the inclusion of scalar fields. We show that 4D gravity is localized on this brane, provide analytic expressions for the massive Kaluza-Klein (KK) fluctuation modes and also show that the spectrum of metric excitations displays a mass gap. We finally present the corrections to Newton's law due to these massive modes. This model has no naked singularities along the fifth dimension despite the existence of a mass gap in the graviton spectrum as it happens in thick branes with 4D Poincare symmetry, providing a simple model with very good features: the curvature is completely smooth along the fifth dimension, it localizes 4D gravity and the spectrum of gravity fluctuations presents a mass gap, a fact that rules out the existence of phenomenologically dangerous ultralight KK excitations in the model. We finally present our solution as a limit of scalar thick branes.Comment: 11 pages in latex, no figures, title and abstract changed, a new section and some references adde

Sexual Size Dimorphism and Body Condition in the Australasian Gannet

Funding: The research was financially supported by the Holsworth Wildlife Research Endowment. Acknowledgments We thank the Victorian Marine Science Consortium, Sea All Dolphin Swim, Parks Victoria, and the Point Danger Management Committee for logistical support. We are grateful for the assistance of the many field volunteers involved in the study.Peer reviewedPublisher PD

Cortisol secretion after adrenocorticotrophin (ACTH) and Dexamethasone tests in healthy female and male dogs

<p>Abstract</p> <p>Background</p> <p>For the conclusive diagnosis of Cushing's Syndrome, a stimulating ACTH test or a low suppressive Dexamethasone test is used. Reports in other species than the dog indicate that plasma cortisol concentration after ACTH administration is affected by gender. We investigated the effect of gender on the cortisol response to ACTH and Dexamethasone tests in dogs.</p> <p>Methods</p> <p>Seven healthy adult Cocker Spaniels (4 females and 3 males) were assigned to a two by two factorial design: 4 dogs (2 females and 2 males) received IV Dexamethasone 0.01 mg/kg, while the other 3 dogs received an IV saline solution (control group). Two weeks later the treatments were reversed. After one month, ACTH was given IV (250 μg/animal) to 4 dogs (2 female and 2 males) while the rest was treated with saline solution (control group). Cortisol concentrations were determined by a direct solid-phase radioimmunoassay and cholesterol and triglycerides by commercial kits.</p> <p>Results and Discussion</p> <p>No effect of treatment was observed in metabolite concentrations, but females presented higher cholesterol concentrations. ACTH-treated dogs showed an increase in cortisol levels in the first hour after sampling until 3 hours post injection. Cortisol concentrations in Dexamethasone-treated dogs decreased one hour post injection and remained low for 3 hours, thereafter cortisol concentrations increased. The increase in cortisol levels from one to two hours post ACTH injection was significantly higher in females than males. In Dexamethasone-treated males cortisol levels decreased one hour post injection up to 3 hours; in females the decrease was more pronounced and prolonged, up to 5 hours post injection.</p> <p>Conclusion</p> <p>We have demonstrated that cortisol response to ACTH and Dexamethasone treatment in dogs differs according to sex.</p

Phenylpropanoid Glycoside Analogues: Enzymatic Synthesis, Antioxidant Activity and Theoretical Study of Their Free Radical Scavenger Mechanism

Phenylpropanoid glycosides (PPGs) are natural compounds present in several medicinal plants that have high antioxidant power and diverse biological activities. Because of their low content in plants (less than 5% w/w), several chemical synthetic routes to produce PPGs have been developed, but their synthesis is a time consuming process and the achieved yields are often low. In this study, an alternative and efficient two-step biosynthetic route to obtain natural PPG analogues is reported for the first time. Two galactosides were initially synthesized from vanillyl alcohol and homovanillyl alcohol by a transgalactosylation reaction catalyzed by Kluyveromyces lactis β-galactosidase in saturated lactose solutions with a 30%–35% yield. To synthesize PPGs, the galactoconjugates were esterified with saturated and unsaturated hydroxycinnamic acid derivatives using Candida antarctica Lipase B (CaL-B) as a biocatalyst with 40%–60% yields. The scavenging ability of the phenolic raw materials, intermediates and PPGs was evaluated by the 2,2-diphenyl-1-picrylhydrazyl radical (DPPH•) method. It was found that the biosynthesized PPGs had higher scavenging abilities when compared to ascorbic acid, the reference compound, while their antioxidant activities were found similar to that of natural PPGs. Moreover, density functional theory (DFT) calculations were used to determine that the PPGs antioxidant mechanism proceeds through a sequential proton loss single electron transfer (SPLET). The enzymatic process reported in this study is an efficient and versatile route to obtain PPGs from different phenylpropanoid acids, sugars and phenolic alcohols

Strongly magnetized pulsars: explosive events and evolution

Well before the radio discovery of pulsars offered the first observational confirmation for their existence (Hewish et al., 1968), it had been suggested that neutron stars might be endowed with very strong magnetic fields of $10^{10}$-$10^{14}$G (Hoyle et al., 1964; Pacini, 1967). It is because of their magnetic fields that these otherwise small ed inert, cooling dead stars emit radio pulses and shine in various part of the electromagnetic spectrum. But the presence of a strong magnetic field has more subtle and sometimes dramatic consequences: In the last decades of observations indeed, evidence mounted that it is likely the magnetic field that makes of an isolated neutron star what it is among the different observational manifestations in which they come. The contribution of the magnetic field to the energy budget of the neutron star can be comparable or even exceed the available kinetic energy. The most magnetised neutron stars in particular, the magnetars, exhibit an amazing assortment of explosive events, underlining the importance of their magnetic field in their lives. In this chapter we review the recent observational and theoretical achievements, which not only confirmed the importance of the magnetic field in the evolution of neutron stars, but also provide a promising unification scheme for the different observational manifestations in which they appear. We focus on the role of their magnetic field as an energy source behind their persistent emission, but also its critical role in explosive events.Comment: Review commissioned for publication in the White Book of "NewCompStar" European COST Action MP1304, 43 pages, 8 figure

Determining the neurotransmitter concentration profile at active synapses

Establishing the temporal and concentration profiles of neurotransmitters during synaptic release is an essential step towards understanding the basic properties of inter-neuronal communication in the central nervous system. A variety of ingenious attempts has been made to gain insights into this process, but the general inaccessibility of central synapses, intrinsic limitations of the techniques used, and natural variety of different synaptic environments have hindered a comprehensive description of this fundamental phenomenon. Here, we describe a number of experimental and theoretical findings that has been instrumental for advancing our knowledge of various features of neurotransmitter release, as well as newly developed tools that could overcome some limits of traditional pharmacological approaches and bring new impetus to the description of the complex mechanisms of synaptic transmission

Azimuthal anisotropy and correlations at large transverse momenta in p+pp+p and Au+Au collisions at sNN\sqrt{s_{_{NN}}}= 200 GeV

Results on high transverse momentum charged particle emission with respect to the reaction plane are presented for Au+Au collisions at $\sqrt{s_{_{NN}}}$= 200 GeV. Two- and four-particle correlations results are presented as well as a comparison of azimuthal correlations in Au+Au collisions to those in $p+p$ at the same energy. Elliptic anisotropy, $v_2$, is found to reach its maximum at $p_t \sim 3$ GeV/c, then decrease slowly and remain significant up to $p_t\approx 7$ -- 10 GeV/c. Stronger suppression is found in the back-to-back high-$p_t$ particle correlations for particles emitted out-of-plane compared to those emitted in-plane. The centrality dependence of $v_2$ at intermediate $p_t$ is compared to simple models based on jet quenching.Comment: 4 figures. Published version as PRL 93, 252301 (2004

Azimuthal anisotropy in Au+Au collisions at sqrtsNN = 200 GeV

The results from the STAR Collaboration on directed flow (v_1), elliptic flow (v_2), and the fourth harmonic (v_4) in the anisotropic azimuthal distribution of particles from Au+Au collisions at sqrtsNN = 200 GeV are summarized and compared with results from other experiments and theoretical models. Results for identified particles are presented and fit with a Blast Wave model. Different anisotropic flow analysis methods are compared and nonflow effects are extracted from the data. For v_2, scaling with the number of constituent quarks and parton coalescence is discussed. For v_4, scaling with v_2^2 and quark coalescence is discussed.Comment: 26 pages. As accepted by Phys. Rev. C. Text rearranged, figures modified, but data the same. However, in Fig. 35 the hydro calculations are corrected in this version. The data tables are available at http://www.star.bnl.gov/central/publications/ by searching for "flow" and then this pape

Rapidity and Centrality Dependence of Proton and Anti-proton Production from Au+Au Collisions at sqrt(sNN) = 130GeV

We report on the rapidity and centrality dependence of proton and anti-proton transverse mass distributions from Au+Au collisions at sqrt(sNN) = 130GeV as measured by the STAR experiment at RHIC. Our results are from the rapidity and transverse momentum range of |y|<0.5 and 0.35 <p_t<1.00GeV/c. For both protons and anti-protons, transverse mass distributions become more convex from peripheral to central collisions demonstrating characteristics of collective expansion. The measured rapidity distributions and the mean transverse momenta versus rapidity are flat within |y|<0.5. Comparisons of our data with results from model calculations indicate that in order to obtain a consistent picture of the proton(anti-proton) yields and transverse mass distributions the possibility of pre-hadronic collective expansion may have to be taken into account.Comment: 4 pages, 3 figures, 1 table, submitted to PR