Projective Group Representations in Quaternionic Hilbert Space

We extend the discussion of projective group representations in quaternionic Hilbert space which was given in our recent book. The associativity condition for quaternionic projective representations is formulated in terms of unitary operators and then analyzed in terms of their generator structure. The multi--centrality and centrality assumptions are also analyzed in generator terms, and implications of this analysis are discussed.Comment: 16 pages, no figures, plain Te

On the realization of Symmetries in Quantum Mechanics

The aim of this paper is to give a simple, geometric proof of Wigner's theorem on the realization of symmetries in quantum mechanics that clarifies its relation to projective geometry. Although several proofs exist already, it seems that the relevance of Wigner's theorem is not fully appreciated in general. It is Wigner's theorem which allows the use of linear realizations of symmetries and therefore guarantees that, in the end, quantum theory stays a linear theory. In the present paper, we take a strictly geometrical point of view in order to prove this theorem. It becomes apparent that Wigner's theorem is nothing else but a corollary of the fundamental theorem of projective geometry. In this sense, the proof presented here is simple, transparent and therefore accessible even to elementary treatments in quantum mechanics.Comment: 8 page

Observations of C-Band Brightness Temperatures and Ocean Surface Wind Speed and Rain Rate from the Hurricane Imaging Radiometer (HIRAD) during GRIP and HS3

HIRAD flew on high-altitude aircraft over Earl and Karl during NASA s GRIP (Genesis and Rapid Intensification Processes) campaign in August - September of 2010, and at the time of this writing plans to fly over Atlantic tropical cyclones in September of 2012 as part of the Hurricane and Severe Storm Sentinel (HS3) mission. HIRAD is a new C-band radiometer using a synthetic thinned array radiometer (STAR) technology to obtain cross-track resolution of approximately 3 degrees, out to approximately 60 degrees to each side of nadir. By obtaining measurements of emissions at 4, 5, 6, and 6.6 GHz, observations of ocean surface wind speed and rain rate can be retrieved. This technique has been used for many years by precursor instruments, including the Stepped Frequency Microwave Radiometer (SFMR), which has been flying on the NOAA and USAF hurricane reconnaissance aircraft for several years to obtain observations within a single footprint at nadir angle. Results from the flights during the GRIP and HS3 campaigns will be shown, including images of brightness temperatures, wind speed, and rain rate. Comparisons will be made with observations from other instruments on the campaigns, for which HIRAD observations are either directly comparable or are complementary. Features such as storm eye and eye-wall, location of storm wind and rain maxima, and indications of dynamical features such as the merging of a weaker outer wind/rain maximum with the main vortex may be seen in the data. Potential impacts on operational ocean surface wind analyses and on numerical weather forecasts will also be discussed

The Hurricane Imaging Radiometer: Present and Future

The Hurricane Imaging Radiometer (HIRAD) is an airborne passive microwave radiometer designed to provide high resolution, wide swath imagery of surface wind speed in tropical cyclones from a low profile planar antenna with no mechanical scanning. Wind speed and rain rate images from HIRAD's first field campaign (GRIP, 2010) are presented here followed, by a discussion on the performance of the newly installed thermal control system during the 2012 HS3 campaign. The paper ends with a discussion on the next generation dual polarization HIRAD antenna (already designed) for a future system capable of measuring wind direction as well as wind speed

Noncommutative geometry and physics: a review of selected recent results

This review is based on two lectures given at the 2000 TMR school in Torino. We discuss two main themes: i) Moyal-type deformations of gauge theories, as emerging from M-theory and open string theories, and ii) the noncommutative geometry of finite groups, with the explicit example of Z_2, and its application to Kaluza-Klein gauge theories on discrete internal spaces.Comment: Based on lectures given at the TMR School on contemporary string theory and brane physics, Jan 26- Feb 2, 2000, Torino, Italy. To be published in Class. Quant. Grav. 17 (2000). 3 ref.s added, typos corrected, formula on exterior product of n left-invariant one-forms corrected, small changes in the Sect. on integratio

Observations During GRIP from HIRAD: Images of C-Band Brightness Temperatures and Ocean Surface Wind Speed and Rain Rate

No abstract availabl

Observations of C-band Brightness Temperature from the Hurricane Imaging Radiometer (HIRAD) During GRIP

HIRAD is a new technology developed by NASA/MSFC, in partnership with NOAA and the Universities of Central Florida, Michigan, and Alabama-Huntsville. HIRAD is designed to measure wind speed and rain rate over a wide swath in heavy-rain, strong-wind conditions. HIRAD is expected to eventually fly routinely on unmanned aerial vehicles (UAVs) such as Global Hawk over hurricanes threatening the U.S. coast and other Atlantic basin areas, and possibly in the Western Pacific as well. HIRAD first flew on GRIP in 2010 and is planned to fly 2012-14 on the NASA Hurricane and Severe Storm Sentinel (HS3) missions on the Global Hawk, a high-altitude UAV. HIRAD technology will eventually be used on a satellite platform to extend the dynamical range of Ocean Surface Wind (OSV) observations from space

Hybrid materials for molecular sieves

Hybrid microporous organosilica membranes for molecular separations made by acid-catalyzed solgel synthesis from bridged silsesquioxane precursors have demonstrated good performance in terms of flux and selectivity and remarkable hydrothermal stability in various pervaporation and gas separation processes. The availability of wide range of α,ω-bis(trialkoxysilyl)alkane and 1,4-bis (triethoxysilyl)benzene precursors allows tuning of membrane properties such as pore size and chemistry. This chapter presents an overview of the synthesis and application of hybrid organosilica microporous membranes in liquid and gas separation processes. After a concise discussion of the history of solgel-derived microporous ceramic membranes for molecular separations, the solgel chemistry of bridged silsesquioxanes and all relevant processing steps needed to obtain a supported microporous films suitable for molecular separations are discussed. The performance of these membranes is correlated with the membrane compositional properties, such as nature, stiffness and length of the bridging group, and details of the solgel process

Radiographic closure time of appendicular growth plates in the Icelandic horse

<p>Abstract</p> <p>Background</p> <p>The Icelandic horse is a pristine breed of horse which has a pure gene pool established more than a thousand years ago, and is approximately the same size as living and extinct wild breeds of horses. This study was performed to compare the length of the skeletal growth period of the "primitive" Icelandic horse relative to that reported for large horse breeds developed over the recent centuries. This information would provide practical guidance to owners and veterinarians as to when the skeleton is mature enough to commence training, and would be potentially interesting to those scientists investigating the pathogenesis of osteochondrosis. Interestingly, osteochondrosis has not been documented in the Icelandic horse.</p> <p>Methods</p> <p>The radiographic closure time of the appendicular growth plates was studied in 64 young Icelandic horses. The results were compared with previously published closure times reported for other, larger horse breeds. The radiographs were also examined for any signs of developmental orthopaedic diseases. In order to describe further the growth pattern of the Icelandic horse, the total serum alkaline phosphatase (ALP) activity was determined and the height at the withers was measured.</p> <p>Results</p> <p>Most of the examined growth plates were fully closed at the age of approximately three years. The horses reached adult height at this age; however ALP activity was still mildly increased over baseline values. The growth plates in the digits were the first to close at 8.1 to 8.5 months of age, and those in the regions of the distal radius (27.4 to 32.0 months), tuber olecrani (31.5 to 32.2 months), and the stifle (27.0 to 40.1 months) were the last to close. No horse was found to have osteochondrosis type lesions in the neighbouring joints of the evaluated growth plates.</p> <p>Conclusion</p> <p>The Icelandic horse appears to have similar radiographic closure times for most of the growth plates of its limbs as reported for large new breeds of horses developed during the past few centuries. It thus appears that different breeding goals and the intensity of breeding have not altered the length of the growth period in horses. Instead, it can be assumed that the pristine and relatively small Icelandic horse has a slower rate of growth. The appendicular skeleton of Icelandic horses has completed its bone growth in length at approximately 3 years of age, and therefore may be able to enter training at this time.</p

Observations During GRIP from HIRAD: Ocean Surface Wind Speed and Rain Rate

HIRAD (Hurricane Imaging Radiometer) flew on the WB-57 during NASA's GRIP (Genesis and Rapid Intensification Processes) campaign in August - September of 2010. HIRAD is a new C-band radiometer using a synthetic thinned array radiometer (STAR) technology to obtain cross-track resolution of approximately 3 degrees, out to approximately 60 degrees to each side of nadir. By obtaining measurements of emissions at 4, 5, 6, and 6.6 GHz, observations of ocean surface wind speed and rain rate can be inferred. This technique has been used for many years by precursor instruments, including the Stepped Frequency Microwave Radiometer (SFMR), which has been flying on the NOAA and USAF hurricane reconnaissance aircraft for several years. The advantage of HIRAD over SFMR is that HIRAD can observe a +/- 60-degree swath, rather than a single footprint at nadir angle. Results from the flights during the GRIP campaign will be shown, including images of brightness temperatures, wind speed, and rain rate. To the extent possible, comparisons will be made with observations from other instruments on the GRIP campaign, for which HIRAD observations are either directly comparable or are complementary. Potential impacts on operational ocean surface wind analyses and on numerical weather forecasts will also be discussed