Projective Geometry and PT\cal PT-Symmetric Dirac Hamiltonian

The $(3 + 1)$-dimensional (generalized) Dirac equation is shown to have the same form as the equation expressing the condition that a given point lies on a given line in 3-dimensional projective space. The resulting Hamiltonian with a $\gamma_5$ mass term is not Hermitian, but is invariant under the combined transformation of parity reflection $\cal P$ and time reversal $\cal T$. When the $\cal PT$ symmetry is unbroken, the energy spectrum of the free spin-$\frac {1}{2}$ theory is real, with an appropriately shifted mass.Comment: 7 pages, LaTeX; version accepted for publication in Phys. Lett. B; revised version incorporates useful suggestions from an anonymous refere

Monitoring of livestock grazing effects on Bureau of Land Management land

Public land management agencies, such as the Bureau of Land Management (BLM), are charged with managing rangelands throughout the Western United States for multiple uses such as livestock grazing and conservation of sensitive species and their habitats. Monitoring of condition and trends of these rangelands, particularly with respect to effects of livestock grazing, provide critical information for effective management of these multi-use landscapes. We therefore investigated the availability of livestock grazing-related quantitative monitoring data and qualitative region-specific Land Health Standards (LHS) data across BLM grazing allotments in the Western United States. We then queried university and federal rangeland science experts about how best to prioritize rangeland monitoring activities. We found that the most commonly available monitoring data were permittee-reported livestock numbers and season-of-use data (71% of allotments) followed by repeat photo points (58%), estimates of forage utilization (52%), and finally, quantitative vegetation measurements (37%). Of the 57% of allotments in which LHS had been evaluated as of 2007, BLM indicated 15% had failed to meet LHS due to livestock grazing. A full complement of all types of monitoring data, however, existed for only 27% of those 15%. Our data inspections, as well as conversations with rangeland experts, indicated a need for greater emphasis on collection of grazing-related monitoring data, particularly ground cover. Prioritization of where monitoring activities should be focused, along with creation of regional monitoring teams may help improve monitoring. Overall, increased emphasis on monitoring of BLM rangelands will require commitment at multiple institutional levels

Presidential Address - The Relation of Physics to the Other Material Sciences

The last year or two of the nineteenth century and this first year of the twentieth have been prolific in literature dealing in one way or another with science topics. There have been addresses before learned and educational gatherings, articles in science journals, and in periodicals of well-nigh all kinds, much of all this writing having been produced by the masters and leaders of science; and the object of these productions has been, generally, to give a view of the present condition and importance of scientific work and knowledge, or to review recent progress either of science in general or of special departments. The condition of science at the beginning has been contrasted with that at the end of the century just past, or the greatest discoveries and most important researches have been passed in review, and the consequences that have followed have been appraised and estimated

Season- and herbivore-dependent competition and facilitation in a semi-aridsavanna

Empirical and theoretical evidence suggests that facilitation between plants, when it occurs, is more likely during periods of abiotic stress, while competition predominates under more moderate conditions. Therefore, one might expect the relative importance of competition vs. facilitation to vary seasonally in ecosystems characterized by pronounced dry (abiotically stressful) and wet (benign) seasons. Herbivory also varies seasonally and can affect the net outcome of plant-plant interactions, but the interactive effects of seasonality and herbivory on the competition-facilitation balance are not known. I experimentally manipulated neighboring plants and herbivory during wet and dry periods for two species of grass: Cynodon plectostachyus and Pennisetum stramineum, in the semiarid Laikipia District of Kenya. These experiments indicate that Pennisetum was competitively dominant during the wet season and that it responded negatively to grazing, especially during the dry season. Cynodon showed more complex season- and herbivore-dependent responses. Cynodon experienced facilitation that was simultaneously dependent on presence of herbivores and on dry season. During the wet season Cynodon experienced net competition. These results illustrate how herbivory and seasonality can interact in complex ways to shift species-species competition-facilitation balance. Additionally, because Cynodon and Pennisetum are key players in a local successional process, these results indicate that herbivory can affect the direction and pace of succession

Some Improved Laboratory Devices and Apparatus

The base of the model is a plain board 26 by 9 inches. At the rear edge of this is another board 5 inches wide, set on edge, A, Fig. 1. To the upper edge of the latter are hinged 27 metal rods A D, 8 inches long. The front ends of the rods are free to move up and down in vertical slots C, and each carries a white disc D half an inch in diameter, which is soldered at its center to the end of the rod, and at right angles with it. Approximately simple harmonic motion is imparted to these discs, so that they represent the vibrations of the particles of an elastic medium transmitting a simple transverse wave motion

A Study in the Hereditary Transmission of Finger Patterns

By finger patterns is meant figures formed by the minute papillary ridges upon the inside surface of the last joint of the thumb and fingers. They are most conveniently studied by inking the fingers with printer\u27s ink and making impressions on paper or any smooth light surface to which the ink will adhere. Sir Francis Galton in his work Finger Prints and other publications, treats the subject of these patterns exhaustively and scientifically. The patterns are of practically infinite variety. They are also persistent and unchanging through the life of the individual, and are destroyed or obliterated only by violent and deep injuries to the fingers. Finger prints therefore constitute a certain and convenient means of personal identification