Quantales of open groupoids

It is well known that inverse semigroups are closely related to \'etale groupoids. In particular, it has recently been shown that there is a (non-functorial) equivalence between localic \'etale groupoids, on one hand, and complete and infinitely distributive inverse semigroups (abstract complete pseudogroups), on the other. This correspondence is mediated by a class of quantales, known as inverse quantal frames, that are obtained from the inverse semigroups by a simple join completion that yields an equivalence of categories. Hence, we can regard abstract complete pseudogroups as being essentially ``the same'' as inverse quantal frames, and in this paper we exploit this fact in order to find a suitable replacement for inverse semigroups in the context of open groupoids that are not necessarily \'etale. The interest of such a generalization lies in the importance and ubiquity of open groupoids in areas such as operator algebras, differential geometry and topos theory, and we achieve it by means of a class of quantales, called open quantal frames, which generalize inverse quantal frames and whose properties we study in detail. The resulting correspondence between quantales and open groupoids is not a straightforward generalization of the previous results concerning \'etale groupoids, and it depends heavily on the existence of inverse semigroups of local bisections of the quantales involved.Comment: 55 page

Parity oscillations of Kondo temperature in a single molecule break junction

We study the Kondo temperature ($T_K$) of a single molecule break junction. By employing a numerical renormalization group calculations we have found that $T_K$ depends dramatically upon the position of the molecule in the wire formed between the contacts. We show that $T_K$ exhibits strong \emph{oscillations} when the parity of the left {and/or} right number of atomic sites ($N_L,N_R$) is changed. For a given set of parameters, the maximum value of $T_K$ occurs for ($odd,odd$) combination, while its minimum values is observed for ($even,even$). These oscillations are fully understood in terms of the effective hybridization function.Comment: 4 pages, 5 figure

Tacit Collusion under Imperfect Monitoring in the Canadian Manufacturing Industry: An Empirical Study

The paper undertakes a cross-sectoral analysis of a salient empirical implication of the model of tacit collusion advanced by Abreu et al (1986). Specifically, the prevalence of a first order Markovian process for alternating between price wars and collusive periods is assessed by means of non-parametric tests. The analysis focuses on 30 different industries in Canada. The evidence provides weak support for optimal collusion in one industry, which is consistent with the idea that such collusive arrangements are unusual.tacit collusion, game theory, Canada, price war

Accounting and Economic Rates of Return: a Dynamic Econometric Investigation

Many studies have questioned empirical utilization of accounting data as internal rates of return would be more consistent with the relevant economic concept. The paper investigates the dynamic relationships between different measures of accounting rates of return (ARRs) and different approximations for the internal rates of returns (IRRs). In contrast with the prevailing case-study investigations, one considers a panel for quoted Brazilian firms in the manufacturing industry along the 1988-3/2003-2 period. Granger causality tests are considered and even though the results are not completely clear cut, some discernible uni-directional patterns emerge. In particular, there seems to be informational content between economic and accounting rates of return, between ROA (Net Profits/Total Assets) and PM (Gross Profits/ Operational Income), and internal rates of return. This seems to indicate that there is some validity in using accounting rates of return in certain economic studies.

Measuring Market Conduct in the Brazilian Cement Industry: a Dynamic Econometric Investigation

Indirect assessments of market conduct have become widespread in the New Empirical Industrial Organization-NEIO literature. Recently, Steen and Salvanes (1999) provided a flexible dynamic econometric formulation of the approach advanced by Bresnahan (1982) and Lau (1982). The present paper considers a similar approach as applied to regional cement markets in Brazil under more favorable data availability and it also attempts to address part of the critiques that usually emerge with respect to the NEIO literature. In particular, issues pertaining to structural stability and yet the control for the number of competing firms are addressed. The evidence clearly indicates non-negligible and distinct market power in the different regions and yet distinct conduct patterns in the short and long-run.