Intrinsic Brightness Temperature of Compact Radio Sources at 86 GHz

We present results on the intrinsic brightness temperature of a sample of compact radio sources observed at 86 GHz using the Global Millimeter VLBI Array. We use the observed brightness temperatures at 86 GHz and the observed superluminal motions at 15 GHz for the sample in order to constrain the characteristic intrinsic brightness temperature of the sample. With a statistical method for studying the intrinsic brightness temperatures of innermost jet cores of compact radio sources, assuming that all sources have the same intrinsic brightness temperature and the viewing angles of their jets are around the critical value for the maximal apparent speed, we find that sources in the sample have a characteristic intrinsic brightness temperature, $T_{\rm 0} = 4.8^{+2.6}_{-1.5}\times 10^{9}$ K, which is lower than the equipartition temperature for the condition that the particle energy equals to the magnetic field energy. Our results suggest that the VLBI cores seen at 86 GHz may be representing a jet region where the magnetic field energy dominates the total energy in the jet.Comment: 9 pages, 4 figures, one table, to appear in JKAS. Corrections made for typos and Journal's further request

Market liberalization and ownership status of incumbent telecom enterprises: global evidence from the telecom sector

Coupled with the early wave of privatization in the 80s of state-owned telecom enterprises, the reform trend in the telecom market has shifted toward the market liberalization since the 90s, resulting in extended multilateral negotiations on the introduction of competition into basic telecommunications. Building on the empirical model of Greene (1998), this study employs a recursive simultaneous bivariate probit model and examines how the ownership status of incumbent telecom operators affects the market liberalization in basic telecom services. The results show that the implementation of market liberalization programs is clustered where private ownership is more present while opportune stock market conditions and the government's capital constraints are positively associated with the privatization. This study provides the concerned governments with policy choices that can facilitate or retard the implementation of a market liberalization program in their respective countries.

The infimum, supremum and geodesic length of a braid conjugacy class

Algorithmic solutions to the conjugacy problem in the braid groups B_n were given by Elrifai-Morton in 1994 and by the authors in 1998. Both solutions yield two conjugacy class invariants which are known as `inf' and `sup'. A problem which was left unsolved in both papers was the number m of times one must `cycle' (resp. `decycle') in order to increase inf (resp. decrease sup) or to be sure that it is already maximal (resp. minimal) for the given conjugacy class. Our main result is to prove that m is bounded above by n-2 in the situation of the second algorithm and by ((n^2-n)/2)-1 in the situation of the first. As a corollary, we show that the computation of inf and sup is polynomial in both word length and braid index, in both algorithms. The integers inf and sup determine (but are not determined by) the shortest geodesic length for elements in a conjugacy class, as defined by Charney, and so we also obtain a polynomial-time algorithm for computing this geodesic length.Comment: 15 pages. Journa

Periodic elements in Garside groups

Let $G$ be a Garside group with Garside element $\Delta$, and let $\Delta^m$ be the minimal positive central power of $\Delta$. An element $g\in G$ is said to be 'periodic' if some power of it is a power of $\Delta$. In this paper, we study periodic elements in Garside groups and their conjugacy classes. We show that the periodicity of an element does not depend on the choice of a particular Garside structure if and only if the center of $G$ is cyclic; if $g^k=\Delta^{ka}$ for some nonzero integer $k$, then $g$ is conjugate to $\Delta^a$; every finite subgroup of the quotient group $G/$ is cyclic. By a classical theorem of Brouwer, Ker\'ekj\'art\'o and Eilenberg, an $n$-braid is periodic if and only if it is conjugate to a power of one of two specific roots of $\Delta^2$. We generalize this to Garside groups by showing that every periodic element is conjugate to a power of a root of $\Delta^m$. We introduce the notions of slimness and precentrality for periodic elements, and show that the super summit set of a slim, precentral periodic element is closed under any partial cycling. For the conjugacy problem, we may assume the slimness without loss of generality. For the Artin groups of type $A_n$, $B_n$, $D_n$, $I_2(e)$ and the braid group of the complex reflection group of type $(e,e,n)$, endowed with the dual Garside structure, we may further assume the precentrality.Comment: The contents of the 8-page paper "Notes on periodic elements of Garside groups" (arXiv:0808.0308) have been subsumed into this version. 27 page