The bulk Lorentz factors of Fermi-LAT GRBs

The Lorentz factor (LF) of gamma-ray burst (GRB) ejecta may be constrained by observations of high-energy (HE) spectral attenuation. The recent Fermi-LAT observations of prompt GeV emission from several bright GRBs have leaded to conclusions of unexpectedly large LFs, $\Gamma>10^3$. Here we revisit this problem with two main concerns. (1) With one-zone assumption where all photons are assumed to be generated in the same region (radius) and time, we {\em self-consistently} calculate the $\gamma\gamma$ optical depth by adopting a target photon spectrum with HE cutoff. We find that this might be important when the GRB LF is below a few hundreds. (2) Recent Fermi-LAT observations suggest that the bulk MeV-range and HE (\ga100 MeV) emission may arise from different regions. We then consider a two-zone case where HE emission is generated in much larger radii than that of the MeV-range emission. We find that the HE emission may be mainly attenuated by MeV-range emission and that the attenuated HE spectrum does not show an exponential spectral cutoff but a slight steepening. This suggests that there may be no abrupt cutoff due to $\gamma\gamma$ attenuation if relaxing the one-zone assumption. By studying the spectra of three bright Fermi-LAT GRBs 080916C, 090510 and 090902B, we show that a bulk LF of\textbf{ $\Gamma\sim600$ }can be consistent with observations in the two-zone case. Even lower LFs can be obtained in the multi-zone case.Comment: 8 pages, a schematic figure added, the other 5 figures updated, ApJ, in pres

Nonexistence of solutions for singular nonlinear ordinary inequalities

In this paper we prove nonexistence theorems of nonnegative nontrivial solutions for a singular nonlinear ordinary inequality in bounded domains with singular points on the boundary. The proofs are based on the test function method developed by Mitidieri and Pohozaev. We also give the examples demonstrating that the conditions obtained are sharp in the case of the problem under consideratio

A five-year profile of employee satisfaction for UK local government buildings

A substantial five-year database, totalling over 20,000 responses across more than four hundred UK local government office buildings, is used to analyse employee satisfaction towards their work environment. Within this database, twenty-seven employee satisfaction attributes have been collected, for different sets of individuals and buildings, by an annual online survey for five years. The collective views of these responses in each of those years have been compared. The results have been strikingly consistent. The problematic areas are persistently the same. They appear to be the control of heating and ventilation and the need for, and ability to use, quiet areas for concentration, followed by document storage facilities, provision of meeting rooms, car parking facilities, and other personal needs related facilities, such as toilets and kitchen facilities. These areas are important concerns which need to be brought to the attention of local authorities and should not be neglected by decision makers. The findings by the comparison should also stimulate the proposals of improvement initiatives. This five-year profile provides a baseline against which the future investigations can be compared in the same sector. This study also provides an analytic method for performing other satisfaction related investigations. Keywords: employee satisfaction, work environment, local governmen

Relating practice to performance : a study of investment and technology in UK manufacturing industry

A thesis submitted for the degree of Doctor of Philosophy of the University of LutonThis study has quantitatively explored the relationships between investment, the use oftechnology and manufacturing perfonnance in UK manufacturing industry from 1979 to 1995. The exploration ofthe relationships is based on the review and the meta-analysis ofmanufacturing practice and performance relationships in the past along with the related theories and economic factors. The review of the operational management theory and the economic factors, which may influence manufacturing performance and practice relationship, helps to establish the wide context for this research and also contributes to the identified gaps. The meta-analysis ofthe relationships between practice and performance in the published studies has also contributed to the identified gaps in this research area. After the consideration ofthe discovered gaps and the availability of the database, the relationship between investment, the use oftechnology and manufacturing performance has been explored in this research. In order to quantitatively evaluate the relationships between investment, the use of technology, their interaction and manufacturing perfonnance, econometric modelling techniques have been used as methodological approaches. Two types ofmethods have been developed based on the review ofthe econometric techniques used in the past and the exploration of relevant econometric literature. The first method uses multiplicative interaction regression models combined with the centralisation method and ordinary least square estimation technique to investigate the relationship between investment, technology usage and their interaction and one dimensional perfonnance. The second method employs multiple-output models using the maximum correlation estimation technique to investigate the relationships between investment, technology usage and their interaction and two dimensional performance measures. A UK manufacturing database including two time periods, the 1980s and the early 1990s, covering seventeen years has been used to test the hypothesised relationships between investment in several forms, technology usage, their interaction and financial performance. The research discovers that it was difficult for investment to bring benefits for performance improvement at the year ofinvestment. The results support the hypotheses that a long-term planned investment brought benefits for manufacturing companies in the 1980s, however was not the case in the early 1990s. Technology usage was very important for performance improvement in the 1980s but the benefits brought by technology were diminishing as the mature stage ofsome key technologies was reached in the early 1990s. The analysis of the data suggests that the economic recession in the early 1990s was an important factor in explaining the phenomena and other economic factors might playa role as well. Investment and technology did interact with each other to contribute to performance improvement but it was not always the case. The results of the multiple-outputs model support the hypothesis that profitability and growth were two joint products of investment, the use oftechnology and their interaction in the immediate year or two after investment. This research also demonstrates the values of mUltiplicative interaction regression modelling and multiple-outputs modelling for manufacturing relationship studies