Painlev\'{e}-Gullstrand-type coordinates for the five-dimensional Myers-Perry black hole

The Painleve-Gullstrand coordinates provide a convenient framework for presenting the Schwarzschild geometry because of their flat constant-time hypersurfaces, and the fact that they are free of coordinate singularities outside r=0. Generalizations of Painleve-Gullstrand coordinates suitable for the Kerr geometry have been presented by Doran and Natario. These coordinate systems feature a time coordinate identical to the proper time of zero-angular-momentum observers that are dropped from infinity. Here, the methods of Doran and Natario are extended to the five-dimensional rotating black hole found by Myers and Perry. The result is a new formulation of the Myers-Perry metric. The properties and physical significance of these new coordinates are discussed.Comment: 15 page

Coordinate families for the Schwarzschild geometry based on radial timelike geodesics

We explore the connections between various coordinate systems associated with observers moving inwardly along radial geodesics in the Schwarzschild geometry. Painlev\'e-Gullstrand (PG) time is adapted to freely falling observers dropped from rest from infinity; Lake-Martel-Poisson (LMP) time coordinates are adapted to observers who start at infinity with non-zero initial inward velocity; Gautreau-Hoffmann (GH) time coordinates are adapted to observers dropped from rest from a finite distance from the black hole horizon. We construct from these an LMP family and a proper-time family of time coordinates, the intersection of which is PG time. We demonstrate that these coordinate families are distinct, but related, one-parameter generalizations of PG time, and show linkage to Lema\^itre coordinates as well.Comment: 13 pages and 10 figures. New title and abstract; expanded discussion on Gautreau-Hoffmann coordinates, and coordinate classifications; figures added; references added. Submitted for publicatio

Solutions of the Yang-Baxter equation: descendants of the six-vertex model from the Drinfeld doubles of dihedral group algebras

The representation theory of the Drinfeld doubles of dihedral groups is used to solve the Yang-Baxter equation. Use of the 2-dimensional representations recovers the six-vertex model solution. Solutions in arbitrary dimensions, which are viewed as descendants of the six-vertex model case, are then obtained using tensor product graph methods which were originally formulated for quantum algebras. Connections with the Fateev-Zamolodchikov model are discussed.Comment: 34 pages, 2 figure

Computing the Mertens and Meissel-Mertens constants for sums over arithmetic progressions

We give explicit numerical values with 100 decimal digits for the Mertens constant involved in the asymptotic formula for $\sum\limits_{\substack{p\leq x p\equiv a \bmod{q}}}1/p$ and, as a by-product, for the Meissel-Mertens constant defined as $\sum_{p\equiv a \bmod{q}} (\log(1-1/p)+1/p)$, for $q \in \{3$, ..., $100\}$ and $(q, a) = 1$.Comment: 12 pages, 6 table

Integrable boundary conditions for a non-abelian anyon chain with D(D3)D(D_3) symmetry

A general formulation of the Boundary Quantum Inverse Scattering Method is given which is applicable in cases where $R$-matrix solutions of the Yang--Baxter equation do not have the property of crossing unitarity. Suitably modified forms of the reflection equations are presented which permit the construction of a family of commuting transfer matrices. As an example, we apply the formalism to determine the most general solutions of the reflection equations for a solution of the Yang-Baxter equation with underlying symmetry given by the Drinfeld double $D(D_3)$ of the dihedral group $D_3$. This $R$-matrix does not have the crossing unitarity property. In this manner we derive integrable boundary conditions for an open chain model of interacting non-abelian anyons

Reference Standards for Body Fat Measure Using GE Dual Energy X-Ray Absorptiometry in Caucasian Adults

Background Dual energy x-ray absorptiometry (DXA) is an established technique for the measurement of body composition. Reference values for these variables, particularly those related to fat mass, are necessary for interpretation and accurate classification of those at risk for obesityrelated health complications and in need of lifestyle modifications (diet, physical activity, etc.). Currently, there are no reference values available for GE-Healthcare DXA systems and it is known that whole-body and regional fat mass measures differ by DXA manufacturer. Objective To develop reference values by age and sex for DXA-derived fat mass measurements with GE-Healthcare systems. Methods A de-identified sample of 3,327 participants (2,076 women, 1,251 men) was obtained from Ball State University\u27s Clinical Exercise Physiology Laboratory and University of Wisconsin- Milwaukee\u27s Physical Activity & Health Research Laboratory. All scans were completed using a GE Lunar Prodigy or iDXA and data reported included percent body fat (%BF), fat mass index (FMI), and ratios of android-to-gynoid (A/G), trunk/limb, and trunk/leg fat measurements. Percentiles were calculated and a factorial ANOVA was used to determine differences in the mean values for each variable between age and sex. Results Normative reference values for fat mass variables from DXA measurements obtained from GE-Healthcare DXA systems are presented as percentiles for both women and men in 10- year age groups. Women had higher (p\u3c0.01) mean %BF and FMI than men, whereas men had higher (p\u3c0.01) mean ratios of A/G, trunk/limb, and trunk/leg fat measurements than women

Universal Baxterization for Z\mathbb{Z}-graded Hopf algebras

We present a method for Baxterizing solutions of the constant Yang-Baxter equation associated with $\mathbb{Z}$-graded Hopf algebras. To demonstrate the approach, we provide examples for the Taft algebras and the quantum group $U_q[sl(2)]$.Comment: 8 page

Indication of electron neutrino appearance from an accelerator-produced off-axis muon neutrino beam

The T2K experiment observes indications of nu(mu) -> nu(mu) e appearance in data accumulated with 1.43 x 10(20) protons on target. Six events pass all selection criteria at the far detector. In a three-flavor neutrino oscillation scenario with |Delta m(23)(2)| = 2.4 x 10(-3) eV(2), sin(2)2 theta(23) = 1 and sin(2)2 theta(13) = 0, the expected number of such events is 1.5 +/- 0.3(syst). Under this hypothesis, the probability to observe six or more candidate events is 7 x 10(-3), equivalent to 2.5 sigma significance. At 90% C.L., the data are consistent with 0.03(0.04) < sin(2)2 theta(13) < 0.28(0.34) for delta(CP) = 0 and a normal (inverted) hierarchy