Poincare Analyticity and the Complete Variational Equations

According to a theorem of Poincare, the solutions to differential equations are analytic functions of (and therefore have Taylor expansions in) the initial conditions and various parameters providing the right sides of the differential equations are analytic in the variables, the time, and the parameters. We describe how these Taylor expansions may be obtained, to any desired order, by integration of what we call the complete variational equations. As illustrated in a Duffing equation stroboscopic map example, these Taylor expansions, truncated at an appropriate order thereby providing polynomial approximations, can well reproduce the behavior (including infinite period doubling cascades and strange attractors) of the solutions of the underlying differential equations.Comment: 86 pages including 22 figure

Quantum Effects for the Dirac Field in Reissner-Nordstrom-AdS Black Hole Background

The behavior of a charged massive Dirac field on a Reissner-Nordstrom-AdS black hole background is investigated. The essential self-adjointness of the Dirac Hamiltonian is studied. Then, an analysis of the discharge problem is carried out in analogy with the standard Reissner-Nordstrom black hole case.Comment: 18 pages, 5 figures, Iop styl

PACE Technical Report Series, Volume 4: Cloud Retrievals in the PACE Mission: PACE Science Team Consensus Document

Earth is a complex dynamical system exhibiting continuous change in its atmosphere, ocean,and surface elements. Nearly all (99.97%) of the energy driving these systems is linked to the Sun. Measurements of reflected sunlight contain a unique signature of wavelength-specific scattering and absorption interactions occurring between incoming solar energy and atmospheric (molecules, aerosols,clouds) and surface features Clouds can affect significantly both shortwave and long wave radiation, depending on altitude/vertical structure, thermodynamic phase, and optical properties. Low, warm, and optically thick clouds predominantly have a cooling effect, while high, cold, optically thin clouds can cause warming by absorbing warmer radiation emitted from the surface and lower atmosphere.When the net difference between outgoing and incoming solar radiation is matched by the net infrared radiation emitted to space, the Earth's climate is in radiative balance. While radiative forcing components (GHGs, aerosols - direct and indirect) contribute to a net radiative imbalance, climate sensitivity is ultimately determined by the contribution of various system feed backs. The role of cloud feedback in a warming climate is currently the largest inter-model uncertainty in climate sensitivity and therefore in climate prediction [Bony and Dufresne 2005]. A comprehensive understanding of current cloud propertiesand dynamic/microphysical processes requires a global perspective from satellites

Sexual dimorphism in the Arachnid orders.

Sexual differences in size and shape are common across the animal kingdom. The study of sexual dimorphism (SD) can provide insight into the sexual- and natural-selection pressures experienced by males and females in different species. Arachnids are diverse, comprising over 100,000 species, and exhibit some of the more extreme forms of SD in the animal kingdom, with the males and females of some species differing dramatically in body shape and/or size. Despite this, research on arachnid SD has primarily focused on specific clades as opposed to observing traits across arachnid orders, the smallest of which have received comparatively little attention. This review provides an overview of the research to date on the trends and potential evolutionary drivers for SD and sexual size dimorphism (SSD) in individual arachnid orders, and across arachnids as a whole. The most common trends across Arachnida are female-biased SSD in total body size, male-biased SSD in relative leg length and SD in pedipalp length and shape. However, the evolution of sexually dimorphic traits within the group is difficult to elucidate due to uncertainty in arachnid phylogenetic relationships. Based on the dataset we have gathered here, we highlight gaps in our current understanding and suggest areas for future research

Environmental marketing : positive strategies for reaching the green consumer

Bibliografi hlm. 243-246Indeksxi, 242 hlm. : il. ; 22 cm