An Introduction to Hyperbolic Barycentric Coordinates and their Applications

Barycentric coordinates are commonly used in Euclidean geometry. The adaptation of barycentric coordinates for use in hyperbolic geometry gives rise to hyperbolic barycentric coordinates, known as gyrobarycentric coordinates. The aim of this article is to present the road from Einstein's velocity addition law of relativistically admissible velocities to hyperbolic barycentric coordinates along with applications.Comment: 66 pages, 3 figure

Annona muricata (graviola): toxic or therapeutic

This paper examines annona muricata (graviola): toxic or therapeutic

Muon Capture on the Proton and Deuteron

By measuring the lifetime of the negative muon in pure protium (hydrogen-1), the MuCap experiment determines the rate of muon capture on the proton, from which the proton's pseudoscalar coupling g_p may be inferred. A precision of 15% for g_p has been published; this is a step along the way to a goal of 7%. This coupling can be calculated precisely from heavy baryon chiral perturbation theory and therefore permits a test of QCD's chiral symmetry. Meanwhile, the MuSun experiment is in its final design stage; it will measure the rate of muon capture on the deuteron using a similar technique. This process can be related through pionless effective field theory and chiral perturbation theory to other two-nucleon reactions of astrophysical interest, including proton-proton fusion and deuteron breakup.Comment: Submitted to the proceedings of the 2007 Advanced Studies Institute on Symmetries and Spin (SPIN-Praha-2007

Depth-Resolved Composition and Electronic Structure of Buried Layers and Interfaces in a LaNiO3_3/SrTiO3_3 Superlattice from Soft- and Hard- X-ray Standing-Wave Angle-Resolved Photoemission

LaNiO$_3$ (LNO) is an intriguing member of the rare-earth nickelates in exhibiting a metal-insulator transition for a critical film thickness of about 4 unit cells [Son et al., Appl. Phys. Lett. 96, 062114 (2010)]; however, such thin films also show a transition to a metallic state in superlattices with SrTiO$_3$ (STO) [Son et al., Appl. Phys. Lett. 97, 202109 (2010)]. In order to better understand this transition, we have studied a strained LNO/STO superlattice with 10 repeats of [4 unit-cell LNO/3 unit-cell STO] grown on an (LaAlO$_3$)$_{0.3}$(Sr$_2$AlTaO$_6$)$_{0.7}$ substrate using soft x-ray standing-wave-excited angle-resolved photoemission (SWARPES), together with soft- and hard- x-ray photoemission measurements of core levels and densities-of-states valence spectra. The experimental results are compared with state-of-the-art density functional theory (DFT) calculations of band structures and densities of states. Using core-level rocking curves and x-ray optical modeling to assess the position of the standing wave, SWARPES measurements are carried out for various incidence angles and used to determine interface-specific changes in momentum-resolved electronic structure. We further show that the momentum-resolved behavior of the Ni 3d eg and t2g states near the Fermi level, as well as those at the bottom of the valence bands, is very similar to recently published SWARPES results for a related La$_{0.7}$Sr$_{0.3}$MnO$_3$/SrTiO$_3$ superlattice that was studied using the same technique (Gray et al., Europhysics Letters 104, 17004 (2013)), which further validates this experimental approach and our conclusions. Our conclusions are also supported in several ways by comparison to DFT calculations for the parent materials and the superlattice, including layer-resolved density-of-states results

High thermal stress responses of Echinolittorina snails at their range edge predict population vulnerability to future warming

Populations at the edge of their species' distribution ranges are typically living at the physiological extreme of the environmental conditions they can tolerate. As a species' response to global change is likely to be largely determined by its physiological performance, subsequent changes in environmental conditions can profoundly influence populations at range edges, resulting in range extensions or retractions. To understand the differential physiological performance among populations at their distribution range edge and center, we measured levels of mRNA for heat shock protein 70 (hsp70) as an indicator of temperature sensitivity in two high-shore littorinid snails, Echinolittorina malaccana and E. radiata, between 1°N to 36°N along the NW Pacific coast. These Echinolittorina snails are extremely heat-tolerant and frequently experience environmental temperatures in excess of 55°C when emersed. It was assumed that animals exhibiting high temperature sensitivity will synthesize higher levels of mRNA, which will thus lead to higher energetic costs for thermal defense. Populations showed significant geographic variation in temperature sensitivity along their range. Snails at the northern range edge of E. malaccana and southern range edge of E. radiata exhibited higher levels of hsp70 expression than individuals collected from populations at the center of their respective ranges. The high levels of hsp70 mRNA in populations at the edge of a species' distribution range may serve as an adaptive response to locally stressful thermal environments, suggesting populations at the edge of their distribution range are potentially more sensitive to future global warming

Classical Cepheids: Yet another version of the Baade-Becker-Wesselink method

We propose a new version of the Baade--Becker--Wesselink technique, which allows one to independently determine the colour excess and the intrinsic colour of a radially pulsating star, in addition to its radius, luminosity, and distance. It is considered to be a generalization of the Balona approach. The method also allows the function F(CI) = BC + 10 log (Teff) for the class of pulsating stars considered to be calibrated. We apply this technique to a number of classical Cepheids with very accurate light and radial-velocity curves and with bona fide membership in open clusters (SZ Tau, CF Cas, U Sgr, DL Cas, GY Sge), and find the results to agree well with the reddening estimates of the host open clusters. The new technique can also be applied to other pulsating variables, e.g. RR Lyrae and RV Tauri.Comment: 6 pages, 2 figures, 1 table; Submitted to Astrophysical Bulletin, 201

M-theory on eight-manifolds revisited: N=1 supersymmetry and generalized Spin(7) structures

The requirement of ${\cal N}=1$ supersymmetry for M-theory backgrounds of the form of a warped product ${\cal M}\times_{w}X$, where $X$ is an eight-manifold and ${\cal M}$ is three-dimensional Minkowski or AdS space, implies the existence of a nowhere-vanishing Majorana spinor $\xi$ on $X$. $\xi$ lifts to a nowhere-vanishing spinor on the auxiliary nine-manifold $Y:=X\times S^1$, where $S^1$ is a circle of constant radius, implying the reduction of the structure group of $Y$ to $Spin(7)$. In general, however, there is no reduction of the structure group of $X$ itself. This situation can be described in the language of generalized $Spin(7)$ structures, defined in terms of certain spinors of $Spin(TY\oplus T^*Y)$. We express the condition for ${\cal N}=1$ supersymmetry in terms of differential equations for these spinors. In an equivalent formulation, working locally in the vicinity of any point in $X$ in terms of a `preferred' $Spin(7)$ structure, we show that the requirement of ${\cal N}=1$ supersymmetry amounts to solving for the intrinsic torsion and all irreducible flux components, except for the one lying in the $\bf{27}$ of $Spin(7)$, in terms of the warp factor and a one-form $L$ on $X$ (not necessarily nowhere-vanishing) constructed as a $\xi$ bilinear; in addition, $L$ is constrained to satisfy a pair of differential equations. The formalism based on the group $Spin(7)$ is the most suitable language in which to describe supersymmetric compactifications on eight-manifolds of $Spin(7)$ structure, and/or small-flux perturbations around supersymmetric compactifications on manifolds of $Spin(7)$ holonomy.Comment: 24 pages. V2: introduction slightly extended, typos corrected in the text, references added. V3: the role of Spin(7) clarified, erroneous statements thereof corrected. New material on generalized Spin(7) structures in nine dimensions. To appear in JHE

Calculations of binding energies and masses of heavy quarkonia using renormalon cancellation

We use various methods of Borel integration to calculate the binding ground energies and masses of b-bbar and t-tbar quarkonia. The methods take into account the leading infrared renormalon structure of the hard+soft part of the binding energies E(s), and of the corresponding quark pole masses m_q, where the contributions of these singularities in M(s) = 2 m_q + E(s) cancel. Beforehand, we carry out the separation of the binding energy into its hard+soft and ultrasoft parts. The resummation formalisms are applied to expansions of m_q and E(s) in terms of quantities which do not involve renormalon ambiguity, such as MSbar quark mass, and alpha_s. The renormalization scales are different in calculations of m_q, E(s) and E(us). The MSbar mass of b quark is extracted, and the binding energies of t-tbar and the peak (resonance) energies for (t+tbar) production are obtained.Comment: 23 pages, 8 double figures, revtex4; the version to appear in Phys.Rev.D; extended discussion between Eqs.(25) and (26); the paragraph between Eqs.(32) and (33) is new and explains the numerical dependence of the residue parameter on the factorization scale; several new references were added; acknowledgments were modified; the numerical results are unchange

Quarkonium spectroscopy and perturbative QCD: massive quark-loop effects

We study the spectra of the bottomonium and B_c states within perturbative QCD up to order alpha_s^4. The O(Lambda_QCD) renormalon cancellation between the static potential and the pole mass is performed in the epsilon-expansion scheme. We extend our previous analysis by including the (dominant) effects of non-zero charm-quark mass in loops up to the next-to-leading non-vanishing order epsilon^3. We fix the b-quark MSbar mass $\bar{m}_b \equiv m_b^{\bar{\rm MS}}(m_b^{\bar{\rm MS}})$ on Upsilon(1S) and compute the higher levels. The effect of the charm mass decreases $\bar{m}_b$ by about 11 MeV and increases the n=2 and n=3 levels by about 70--100 MeV and 240--280 MeV, respectively. We provide an extensive quantitative analysis. The size of non-perturbative and higher order contributions is discussed by comparing the obtained predictions with the experimental data. An agreement of the perturbative predictions and the experimental data depends crucially on the precise value (inside the present error) of alpha_s(M_Z). We obtain $m_b^{\bar{\rm MS}}(m_b^{\bar{\rm MS}}) = 4190 \pm 20 \pm 25 \pm 3 ~ {\rm MeV}$.Comment: 33 pages, 21 figures; v2: Abstract modified; Table7 (summary of errors) added; Version to appear in Phys.Rev.

Heavy quark mass determination from the quarkonium ground state energy: a pole mass approach

The heavy quark pole mass in perturbation theory suffers from a renormalon caused, inherent uncertainty of $O(\Lambda_{\rm QCD})$. This fundamental difficulty of determining the pole mass to an accuracy better than the inherent uncertainty can be overcome by direct resummation of the first infrared renormalon. We show how a properly defined pole mass as well as the $\bar {\rm MS}$ mass for the top and bottom quarks can be determined accurately from the $O(m\alpha_s^5)$ quarkonium ground state energy.Comment: 16 pages; published versio