Unruh response functions for scalar fields in de Sitter space

We calculate the response functions of a freely falling Unruh detector in de Sitter space coupled to scalar fields of different coupling to the curvature, including the minimally coupled massless case. Although the responses differ strongly in the infrared as a consequence of the amplification of superhorizon modes, the energy levels of the detector are thermally populated.Comment: 16 pages, 1 figure, accepted for publication by Classical and Quantum Gravit

Predictability and trapping under conditions of globalization and agricultural trade : an application of the CDS approach

The purpose of the paper is to demonstrate how timely investments in the ecosphere promote high level stable agricultural income. It is shown that the recovery capability of the ecosphere together with strong agricultural productivity relative to the rest of the economy may be considered as control parameters of the system. They play a crucial role for agriculture to escape from a low level trap. The scenario leading to the escape is based on an economic strategy leading to a sequence of local and global bifurcations, changing the dynamical structure of the system. The effects of globalization on the system’s dynamics and stable sets are considered. Globalization is taken into account by means of nonautonomous impulses making selected system parameters oscillate. Necessary conditions for sustainable agriculture development are established

Imapcts of Recovery Rates and Terms of Trade on Strange Attractors and Predictability in Sustainable Agriculture

Sustaining agricultural systems requires the ability to predict approaching extinction. Thus a suitable model needs to generate predictability as an intrinsic attribute. Such a model should provide several featuers for managerse. It should incorporate learning about the minimum sustainable ecospheric threshold. The model requires a capability to cope with uneven system coevolution. Solutions should reveal how to maneuver parameters to achieve'favourable' system dynamics. Models based on assumptions of lienarity and randomness are not able to explain sharp changes in system behaviour and do not result in predictability. Fortunately, theories for complex nonlinear dynamical systems are emerging from mathematics and physics in applications such as ecology, economics and immunology. This paper addresses the relationships between the structural parameters of a complex three-dimensional system and the predictability of wealth and sustainability. The subsystems are agriculture, the ecosphere and industry. Their interaction is modelled by a dynamical system based on the rpedator prey paradigm. The ecosphere is considered as a living interactive system that can regenerate, reproduce and become extinct. The model explores the dynamics of the whole system as the strucutral properties of its parts coevolve over time. We demonstrate that the structural parameters may pass through bifurcation values, which not only result in new equilibria and periodic trajectories, but account for the presence of strange attractors. Most of our attention is place on exploring the conditions under which strange attractors appear and dissappear in coevolution. The presence of strange attractors connotes great uncertainty and severely limits predictability. The policy problem for sustainable agriculture is to prevent strange attractors from appearing. The results are that agricultural terms of trade and ecospheric recovery rates are partially substitutable in sustaining agriculture. Strange attractors may be avoided and replaced by predictable periodic trajectories or stable node type equilibria by equilibria by changing the rate of ecospheric recovery, or terms of trade or the productivity of the ecosphere in agricultural uses. Portraits of the trasjectories are provided to make it easier to understand the dynamics. The results suggest that sustainability is sensitive to learning processes which address these tradeoffs, the approach to minimum thresholds of persistence for the ecosphere and the mutualism in economic predation. It may be ntoed that farmers historically learned about these things through artisan apprenticeship. Just as this learning method has been replaced by social, biological and physical sciences to achieve remarkable productivity gains, so resources need to be shifted to address the co-requisite ecospheric recovery processes

Table of integrals, series, and products

The eighth edition of the classic Gradshteyn and Ryzhik is an updated completely revised edition of what is acknowledged universally by mathematical and applied science users as the key reference work concerning the integrals and special functions. The book is valued by users of previous editions of the work both for its comprehensive coverage of integrals and special functions, and also for its accuracy and valuable updates. Since the first edition, published in 1965, the mathematical content of this book has significantly increased due to the addition of new material, though the size of the book has remained almost unchanged. The new 8th edition contains entirely new results and amendments to the auxiliary conditions that accompany integrals and wherever possible most entries contain valuable references to their source.The Table of Integrals, Series, and Products is the essential reference for integrals in the English language. Mathematicians, scientists, and engineers, rely on it when identifying and subsequently solving extremely complex problems. Since publication of the first English-language edition in 1965, it has been thoroughly revised and enlarged on a regular basis, with substantial additions and, where necessary, existing entries corrected or revised. The seventh edition includes a fully searchable CD-Rom.- Fully searchable CD that puts information at your fingertips included with text- Most