Short Gamma-Ray Bursts with Extended Emission Observed with Swift/BAT and Fermi/GBM

Some short GRBs are followed by longer extended emission, lasting anywhere from ~10 to ~100 s. These short GRBs with extended emission (EE) can possess observational characteristics of both short and long GRBs (as represented by GRB 060614), and the traditional classification based on the observed duration places some of them in the long GRB class. While GRBs with EE pose a challenge to the compact binary merger scenario, they may therefore provide an important link between short and long duration events. To identify the population of GRBs with EE regardless of their initial classifications, we performed a systematic search of short GRBs with EE using all available data (up to February 2013) of both Swift/BAT and Fermi/GBM. The search identified 16 BAT and 14 GBM detected GRBs with EE, several of which are common events observed with both detectors. We investigated their spectral and temporal properties for both the spikes and the EE, and examined correlations among these parameters. Here we present the results of the systematic search as well as the properties of the identified events. Finally, their properties are also compared with short GRBs with EE observed with BATSE, identified through our previous search effort. We found several strong correlations among parameters, especially when all of the samples were combined. Based on our results, a possible progenitor scenario of two-component jet is discussed.Comment: Published in MNRAS; matched to the published versio

Fixed Points of Generalized Contractive Multi-valued Mappings

In a recent paper N. Mizoguchi and W. Takahashi gave a positive answer to the conjecture of S. Reich concerning the existence of fixed points of multi-valued mappings that satisfy a certain contractive condition. In this paper, we provide an alternative and somewhat more straightforward proof for the theorem of Mizoguchi and Takahashi. Also the problems associated with fixed points of weakly contractive multi-valued mappings are studied. Finally, we make a few comments that improve other results from their paper (J. Math. Anal. Appl. 141 (1989), 177-188)

Trends in Competition and Profitability in the Banking Industry: A Basic Framework

This paper brings to the forefront the assumptions that we make when focusing on a particular type of explanation for bank profitability. We evaluate a broad field of research by introducing a general framework for a profit maximizing bank and demonstrate how different types of models can be fitted into this framework. Next, we present an overview of the current major trends in European banking and relate them to each model’s assumptions, thereby shedding light on the relevance, timeliness and shelf life of the different models. This way, we arrive at a set of recommendations for a future research agenda. We advocate a more prominent role for output prices, and suggest a modification of the intermediation approach. We also suggest ways to more clearly distinguish between market power and efficiency, and explain why we need time-dependent models. Finally, we propose the application of existing models to different size classes and sub-markets. Throughout we emphasize the benefits from applying several, complementary models to overcome the identification problems that we observe in individual models.

On a Conjecture of S. Reich

Simeon Reich (1974) proved that the fixed point theorem for single-valued mappings proved by Boyd and Wong can be generalized to multivalued mappings which map points into compact sets. He then asked (1983) whether his theorem can be extended to multivalued mappings whose range consists of bounded closed sets. In this note, we provide an affirmative answer for a certain subclass of Boyd-Wong contractive mappings

CP violation in neutrino oscillation and leptogenesis

We study the correlation between CP violation in neutrino oscillations and leptogenesis in the framework with two heavy Majorana neutrinos and three light neutrinos. Among three unremovable CP phases, a heavy Majorana phase contributes to leptogenesis. We show how the heavy Majorana phase contributes to Jarlskog determinant $J$ as well as neutrinoless double $\beta$ decay by identifying a low energy CP violating phase which signals the CP violating phase for leptogenesis. For some specific cases of the Dirac mass term of neutrinos, a direct relation between lepton number asymmetry and $J$ is obtained. For the most general case of the framework, we study the effect on $J$ coming from the phases which are not related to leptogenesis, and also show how the correlation can be lost in the presence of those phases.Comment: 4 pages and 3 figure

Symposium: The Future of Law and Development, Part III

I would like to take up Anna Gelpern’s invitation to define the study of Law and Development broadly and to reject the presumption that the inquiry will focus narrowly on the law-related projects of bilateral aid agencies and international organizations. I am interested in the relationship between law on the one hand and, on the other hand, development (however defined), and it is not clear to me that externally directed “Law and Development” projects are always central to understanding that relationship. (Isn’t that a reasonable inference to draw from all of the studies that question the impact of those projects?) Don’t get me wrong, I think it is often crucially important to take foreign actors into account when trying to understand where the “law” part of the equation comes from, as well as what factors besides law might be influencing development. But I am skeptical of the notion that foreign actors are always central to the story, especially in some of the larger developing countries; do we really understand the legal systems of Brazil, India, and China best by focusing on the components influenced by the World Bank and the IMF? As far as the future of Law and Development is concerned, I believe that it will and should involve becoming even more of a social science. I also believe, however, that the contributions to this Symposium have identified many of the pitfalls that lie in that direction. To begin with, there are obviously methodological questions about what empirical methods are best suited to uncovering the kinds of causal relationships between law and social outcomes we are looking for and theoretical questions about what legal and social variables ought to be measured. But I think that there are even more profound questions to be asked about the entire enterprise, especially if the purpose is to give policymakers insights into “what works.

Symposium: The Future of Law and Development, Part III

I would like to take up Anna Gelpern’s invitation to define the study of Law and Development broadly and to reject the presumption that the inquiry will focus narrowly on the law-related projects of bilateral aid agencies and international organizations. I am interested in the relationship between law on the one hand and, on the other hand, development (however defined), and it is not clear to me that externally directed “Law and Development” projects are always central to understanding that relationship. (Isn’t that a reasonable inference to draw from all of the studies that question the impact of those projects?) Don’t get me wrong, I think it is often crucially important to take foreign actors into account when trying to understand where the “law” part of the equation comes from, as well as what factors besides law might be influencing development. But I am skeptical of the notion that foreign actors are always central to the story, especially in some of the larger developing countries; do we really understand the legal systems of Brazil, India, and China best by focusing on the components influenced by the World Bank and the IMF? As far as the future of Law and Development is concerned, I believe that it will and should involve becoming even more of a social science. I also believe, however, that the contributions to this Symposium have identified many of the pitfalls that lie in that direction. To begin with, there are obviously methodological questions about what empirical methods are best suited to uncovering the kinds of causal relationships between law and social outcomes we are looking for and theoretical questions about what legal and social variables ought to be measured. But I think that there are even more profound questions to be asked about the entire enterprise, especially if the purpose is to give policymakers insights into “what works.