The Microcanonical Functional Integral. I. The Gravitational Field

The gravitational field in a spatially finite region is described as a microcanonical system. The density of states $\nu$ is expressed formally as a functional integral over Lorentzian metrics and is a functional of the geometrical boundary data that are fixed in the corresponding action. These boundary data are the thermodynamical extensive variables, including the energy and angular momentum of the system. When the boundary data are chosen such that the system is described semiclassically by {\it any} real stationary axisymmetric black hole, then in this same approximation $\ln\nu$ is shown to equal 1/4 the area of the black hole event horizon. The canonical and grand canonical partition functions are obtained by integral transforms of $\nu$ that lead to "imaginary time" functional integrals. A general form of the first law of thermodynamics for stationary black holes is derived. For the simpler case of nonrelativistic mechanics, the density of states is expressed as a real-time functional integral and then used to deduce Feynman's imaginary-time functional integral for the canonical partition function.Comment: 29 pages, plain Te

Integers represented as a sum of primes and powers of two

It is shown that every sufficiently large even integer is a sum of two primes and exactly 13 powers of 2. Under the Generalized Rieman Hypothesis one can replace 13 by 7. Unlike previous work on this problem, the proof avoids numerical calculations with explicit zero-free regions of Dirichlet L-functions. The argument uses a new technique to bound the measure of the set on which the exponential sum formed from powers of 2 is large.Comment: 32 Pages; typos correcte

NaCl transport stimulates prostaglandin release in cultured renal epithelial (MDCK) cells

Prostaglandins (PGs) can modulate a variety of renal functions, including Na+ and Cl- reabsorption. However, it is not known if a direct interdependence exists between PG synthesis and transport activity. The present study was done to find out whether or not the rate of NaCl transport has an influence on PG synthesis in renal tubular cells. For our studies we used cultures of so-called high-resistance MDCK cells, which were originally derived from canine kidney. This cell type has a loop diuretic- and ouabain-sensitive NaCl transport that can be enhanced by activation of the adenylate cyclase (AC). In MDCK cell cultures we found that each state of increased NaCl transport during stimulation of AC by either epinephrine (10(-6) M), isoprenaline (10(-5) M), or forskolin (10(-5) M) was accompanied by a twofold increase in PG release. During inhibition of NaCl transport by furosemide (10(-4) M) or ouabain (2 X 10(-4) M), stimulation of AC failed to increase PGE2 release, whereas basal PG production was not inhibited by either furosemide or ouabain. Furthermore, PG formation during activation of AC was dependent on the concentration of extracellular Na+, whereas PG formation in the absence of activators of AC was independent of extracellular Na+. These results suggest that increased NaCl transport stimulates PG formation in cultures of high-resistance MDCK cells

Boundary States and Black Hole Entropy

Black hole entropy is derived from a sum over boundary states. The boundary states are labeled by energy and momentum surface densities, and parametrized by the boundary metric. The sum over state labels is expressed as a functional integral with measure determined by the density of states. The sum over metrics is expressed as a functional integral with measure determined by the universal expression for the inverse temperature gradient at the horizon. The analysis applies to any stationary, nonextreme black hole in any theory of gravitational and matter fields.Comment: 4 pages, Revte

The great outdoors: how a green exercise environment can benefit all

The studies of human and environment interactions usually consider the extremes of environment on individuals or how humans affect the environment. It is well known that physical activity improves both physiological and psychological well-being, but further evidence is required to ascertain how different environments influence and shape health. This review considers the declining levels of physical activity, particularly in the Western world, and how the environment may help motivate and facilitate physical activity. It also addresses the additional physiological and mental health benefits that appear to occur when exercise is performed in an outdoor environment. However, people's connectedness to nature appears to be changing and this has important implications as to how humans are now interacting with nature. Barriers exist, and it is important that these are considered when discussing how to make exercise in the outdoors accessible and beneficial for all. The synergistic combination of exercise and exposure to nature and thus the 'great outdoors' could be used as a powerful tool to help fight the growing incidence of both physical inactivity and non-communicable disease. © 2013 Gladwell et al.; licensee BioMed Central Ltd

Energy Conversion Alternatives Study (ECAS), General Electric Phase 1. Volume 2: Advanced energy conversion systems. Part 1: Open-cycle gas turbines

Ten energy conversion systems are defined and analyzed in terms of efficiency. These include: open-cycle gas turbine recuperative; open-cycle gas turbine; closed-cycle gas turbine; supercritical CO2 cycle; advanced steam cycle; liquid metal topping cycle; open-cycle MHD; closed-cycle inert gas MHD; closed-cycle liquid metal MHD; and fuel cells. Results are presented

Comparative health and safety assessment of the SPS and alternative electrical generation systems

A comparative analysis of health and safety risks is presented for the Satellite Power System and five alternative baseload electrical generation systems: a low-Btu coal gasification system with an open-cycle gas turbine combined with a steam topping cycle; a light water fission reactor system without fuel reprocessing; a liquid metal fast breeder fission reactor system; a central station terrestrial photovoltaic system; and a first generation fusion system with magnetic confinement. For comparison, risk from a decentralized roof-top photovoltaic system with battery storage is also evaluated. Quantified estimates of public and occupational risks within ranges of uncertainty were developed for each phase of the energy system. The potential significance of related major health and safety issues that remain unquantitied are also discussed

Achieving coexistence - Comment on "Modelling rain forest diversity:The role of competition by Bampfylde et al. (2005)

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An instinct for detection: psychological perspectives on CCTV surveillance

The aim of this article is to inform and stimulate a proactive, multidisciplinary approach to research and development in surveillance-based detective work. In this article we review some of the key psychological issues and phenomena that practitioners should be aware of. We look at how human performance can be explained with reference to our biological and evolutionary legacy. We show how critical viewing conditions can be in determining whether observers detect or overlook criminal activity in video material. We examine situations where performance can be surprisingly poor, and cover situations where, even once confronted with evidence of these detection deficits, observers still underestimate their susceptibility to them. Finally we explain why the emergence of these relatively recent research themes presents an opportunity for police and law enforcement agencies to set a new, multidisciplinary research agenda focused on relevant and pressing issues of national and international importance