Female Inheritance and Forged Documents: John Hardyng’s Use of Scottish Materials in his Chronicle

In his Chronicle of John Hardyng (1st version, 1457; 2nd version, 1465), Hardyng shows that Scottish kings did homage to English kings, adding a map and an itinerary of Scotland. In support, Hardyng forged several documents, to prove Scotland\u27s vassal status, which he submitted to the English government with his Chronicle. Hardyng\u27s motive for the forgeries, their function or how they relate to the Chronicle text, or his intent in incorporating Scottish materials. This paper argues that Hardyng\u27s description of Scotland, combined with his forged documents, was his response to finding Scottish historical materials contradicting his claim for English sovereignty over Scotland. Hargyng\u27s forged documents rebutted a discourse tracing through holy women a hereditary for Scottish kings to the English crown

General Relativistic Ray-Tracing Method for Estimating the Energy and Momentum Deposition by Neutrino Pair Annihilation in Collapsars

Bearing in mind the application to the collapsar models of gamma-ray bursts (GRBs), we develop a numerical scheme and code for estimating the deposition of energy and momentum due to the neutrino pair annihilation ($\nu + {\bar \nu} \rightarrow e^{-} + e^{+}$) in the vicinity of accretion tori around a Kerr black hole. Our code is designed to solve the general relativistic neutrino transfer by a ray-tracing method. To solve the collisional Boltzmann equation in curved spacetime, we numerically integrate the so-called rendering equation along the null geodesics. For the neutrino opacity, the charged-current $\beta$-processes are taken into account, which are dominant in the vicinity of the accretion tori. The numerical accuracy of the developed code is certificated by several tests, in which we show comparisons with the corresponding analytic solutions. Based on the hydrodynamical data in our collapsar simulation, we estimate the annihilation rates in a post-processing manner. Increasing the Kerr parameter from 0 to 1, it is found that the general relativistic effect can increase the local energy deposition rate by about one order of magnitude, and the net energy deposition rate by several tens of percents. After the accretion disk settles into a stationary state (typically later than $\sim 9$ s from the onset of gravitational collapse), we point out that the neutrino-heating timescale in the vicinity of the polar funnel region can be shorter than the dynamical timescale. Our results suggest the neutrino pair annihilation has a potential importance equal to the conventional magnetohydrodynamic mechanism for igniting the GRB fireballs.Comment: 33 pages, 15 figures, accepted to the Ap

Gravitational Wave Signatures of Hyperaccreting Collapsar Disks

By performing two-dimensional special relativistic (SR) magnetohydrodynamic simulations, we study possible signatures of gravitational waves (GWs) in the context of the collapsar model for long-duration gamma-ray bursts. In our SR simulations, the central black hole is treated as an absorbing boundary. By doing so, we focus on the GWs generated by asphericities in neutrino emission and matter motions in the vicinity of the hyperaccreting disks. We compute nine models by adding initial angular momenta and magnetic fields parametrically to a precollapse core of a $35 M_{\odot}$ progenitor star. As for the microphysics, a realistic equation of state is employed and the neutrino cooling is taken into account via a multiflavor neutrino leakage scheme. To accurately estimate GWs produced by anisotropic neutrino emission, we perform a ray-tracing analysis in general relativity by a post-processing procedure. By employing a stress formula that includes contributions both from magnetic fields and special relativistic corrections, we study also the effects of magnetic fields on the gravitational waveforms. We find that the GW amplitudes from anisotropic neutrino emission show a monotonic increase with time, whose amplitudes are much larger than those from matter motions of the accreting material. We show that the increasing trend of the neutrino GWs stems from the excess of neutrino emission in the direction near parallel to the spin axis illuminated from the hyperaccreting disks. We point out that a recently proposed future space-based interferometer like Fabry-Perot type DECIGO would permit the detection of these GW signals within $\approx$ 100 Mpc.Comment: 38 pages, 14 figures, ApJ in pres

Formation of black hole and accretion disk in a massive high-entropy stellar core collapse

We present the first numerical result of fully general relativistic axisymmetric simulations for the collapse of a rotating high-entropy stellar core to a black hole and an accretion disk. The simulations are performed taking into account the relevant microphysics. We adopt as initial condition a spherical core with constant electron fraction ($Y_e = 0.5$) and entropy per baryon $s$ = 8 $k_B$, and angular velocity is superimposed. In the early phase, the core collapses in a homologous manner. Then, it experiences a weak bounce due to the gas pressure of free nucleons. Because the bounce is weak, the core collapses eventually to a black hole. Subsequent evolution depends on initial angular velocity. When the rotation is not fast, a geometrically thin (but optically thick) accretion disk is formed, and shock waves are formed in the inner part of the disk. For the moderately rotating case, the thin accretion disk expands eventually to be a geometrically thick torus after sufficient accumulation of the thermal energy generated at the shocks. Furthermore, convection occurs inside the torus. Neutrino luminosities vary violently with time because of the convective motion. For the rapidly rotating case, by contrast, a geometrically thick torus is formed soon after the black hole formation, and convective activity is weak due to the presence of epicyclic mode.Comment: 30 pages, 33 figures with low resolution, accepted for publication in Ap

Translation and Annotation of “Continuation of Ancient Mathematics （緝古算経）” Vol. 5

“Continuation of Ancient Mathematics （ 緝古算経）” was written by early Tang dynasty calendarist and mathematician Wang Xiaotong some time after the year 626,and was listed as one of the Ten Computational Canons （ 算経十書） compiled during Tang dynasty. The aim of our studies is to provide a complete translation and annotation of the book based on a series of our researches on ancient Chinese mathematical books. 　This is the fifth article, in which we treat with the problems 13 to 20.『緝古算経』は初唐の暦学者であり数学者である王孝通によって626年の少し後に書かれたもので、唐代に編纂された算経十書中の一書である。我々の研究が目的とするのは、我々の一連の中国古算書研究を踏まえ、同書に完全な訳と注を与えることにある。 　本論文はその第５ 号であり、算題［一三］～［二〇］について扱う。departmental bulletin pape

『算数書』と『九章算術』の数値比較(1)

The "Suanshu-shu" (算数書) is the oldest book of mathematics in China. Before the book was discovered, "Jiuzhang-suanshu" (九章算術) was thought to be the oldest. We compare these books from an arithmetical point of view

Establishment of testis-specific SOX9 activation requires high-glucose metabolism in mouse sex differentiation

AbstractIn mouse sex differentiation, SRY promotes Sertoli cell differentiation via SOX9 action, resulting in testis formation. SRY/SOX9 also initiates various testis-specific morphogenic events including glycogenesis in pre-Sertoli cells, suggesting the importance of glucose storage for certain SRY/SOX9-downstream events in gonadal sex determination. However, it remains unclear which cell types and what molecular/cellular events require sex-dimorphic high-energy metabolic rate. Here we show that the establishment of SOX9 activation itself is a metabolically active process with sex-dimorphic high-energy requirements in gonadal sex differentiation. The glucose-deprivation and metabolic rescue experiments using genital ridge cultures of the XY/XX-wildtype and XX/Sry transgenic embryos demonstrated that, among the various somatic cell types, pre-Sertoli cells are the most sensitive to glucose starvation despite the differences between XX/Sry and XY genotypes. Moreover, our data showed that, in developing pre-Sertoli cells, the high-glucose metabolic state is required for the establishment of SOX9 expression through an ECM (extracellular matrix)-mediated feed-forward pathway. In contrast, the expression of SRY, SF1/Ad4Bp, GATA4 and WT1, as well as initiation of early SOX9 expression, is properly maintained in the glucose-deprived condition. Therefore, our results imply the metabolic importance of the high-glucose condition for the establishment of SOX9 activation in testis differentiation