Because of the contamination of jets, using the size – continuum luminosity relation can overestimate the broad line region (BLR) size and black hole mass for radio-loud AGNs. We propose a new relation between the BLR size and Hβ emission line luminosity and present evidences for using it to get more accurate black hole masses of radio-loud AGNs. For extreme radio-loud AGNs such as blazars with...

In this paper we describe the geometry of the energy momentum mapping of the complexified spherical pendulum. For background on the classical spherical pendulum we refer the reader to [4, chpt. IV]. We show that this complex Hamiltonian system is Mumford-Jacobi completely integrable [9, p.3.51–3.53] and admits an analogue of the period lattice [5] and action angle coordinates [4, Apend. D]. Fol...

spherical polyhedron S = (V, F ;E): For a 2-connected planar graph GS = (V,ES), embedded on a sphere (or in the plane), we record the vertices as V and the regions as faces F , and rewrite the directed edges E as ordered 4-tuples e = 〈h, i; j, k〉, where the edge from vertex h to vertex i has face j on the right and face k on the left. (The reversed edge −e = 〈i, h; k, j〉 runs from i to h, with ...

spherical polyhedron S = (V, F ;E): For a 2-connected planar graph GS = (V,ES), drawn without self-intersection on a sphere (or in the plane), we record the vertices as V and the regions as faces F , and rewrite the directed edges E as ordered 4-tuples e = 〈h, i; j, k〉, where the edge from vertex h to vertex i has face j on the right and face k on the left. (The reversed edge −e = 〈i, h; k, j〉 ...

Microquasars (black hole X-ray binaries with relativistic jets) are first found by means of multiwavelengths observations with ground-based telescopes. Microquasars mimic, on a much smaller scale, many of their phenomena seen in quasars. The study about microquasars opens the door for better understanding of the relativistic jets elsewhere in the Universe, and may serve to determine the distanc...

menelaus’ sphaerica can be considered as the most important classical text in the tradition of spherics books, written with the aim of the solution of problems arising in spherical astonomy. euclid’s elements is the the most important book on plane geometry. this article aims at a comparative study of menelaus’s sphaerica and euclid’s elements, to show that book i of sphaerica is an attempt to ...

1.1. This article surveys some developments in pure mathematics which have, to varying degrees, grown out of the ideas of gauge theory in Mathematical Physics. The realisation that the gauge fields of particle physics and the connections of differential geometry are one and the same has had wide-ranging consequences, at different levels. Most directly, it has lead mathematicians to work on new ...

The kinetic spherical model with long-ranged interactions and an arbitrary initial order m0 quenched from a very high temperature to T (≤ Tc) is solved. In the short-time regime, the bulk order increases with a power law in both the critical and phase-ordering dynamics. To the latter dynamics, a power law for the relative order mr ∼ −t−k is found in the intermediate time-regime. The short-time ...

Nucleon-nucleon scattering at large momentum transfer is analyzed within the framework of quantum chromodynamic quark and gluon interactions. The spin dependence of the hadronic amplitude is found to be particularly sensitive to the underlying dynamical mechanisms. Detailed discussions of the quark interchange and Landshoff pinch singularity contributions are given for large angle pp, np and pi...