Conjugacy invariants of Sl(2,H)

AbstractIn this paper, we use the quaternionic formalism of Möbius transformations on R4 to derive conjugacy invariants on Sl(2,H) (and hence on PSl(2,H)). We then use these invariants to distinguish between the various conjugacy classes of PSl(2,H)

What The Negro Parents Of The Mexia Independent School District Expect Of The School And Of The Teachers

Nature and Purpose of the Survey This survey was conducted for the purpose of determining whether or not the parents in Mexia Colored School District approved of the modem teacher and the school system as it was being practiced in this township in 1950. It was believed that certain questions could be answered by the parents which would lead to a better under** standing of the school problems of today concerning the teacher and parent. A secondary purpose of this survey was to obtain many suggestions from parents which would be helpful in making the school system a greater success than it had previously been. Reason for Selection of the Topic The writer was made to feel the importance of such a survey by facts and data presented in a magazine article entitled, Recent Education Survey Reflects New Attitude of Parents Toward School Program and the Teacher. The question which this article suggested was: Would a survey similar to this one reflect new attitudes of the parents of Mexia Colored School District toward the school and teacher? In this study, an attempt was made to determine whether or not the parents of the township were satisfied with the school system of 1950

THE EFFECT OF IMPACT CONDITION ON THE RELATIONSHIP BETWEEN LINEAR AND ANGULAR ACCELERATION LINEAR

Helmets are mandatory in many contact sports and are designed to prevent traumatic brain injuries. When assessing their performance, angular acceleration is not measured, as it is generally assumed to be highly correlated with linear acceleration (Pellman et al., 2003). Although being common, this assumption is not supported by strong data. The aim of this study was to establish the relationship between linear and angular acceleration

THE DETERMINATION OF NOVEL IMPACT CONDITIONS FOR THE ASSESMENT OF LINEAR AND ANGULAR HEADFORM ACCELERATIONS

Sports helmets, albeit very effective at preventing traumatic brain injury, have not mitigated the risk of mild traumatic brain injury in sport (Flik, Lyman, & Marx, 2005). Current protocols utilized in sports helmet testing incorporate only impact vectors through the center of mass, eliciting primarily linear accelerations. Angular acceleration has been suggested to be a better predictor of diffuse head injury than linear acceleration (Holbourn, 1943); therefore, the objective of this study was to develop a protocol capable of producing and measuring both forms of acceleration for future implementation into sports helmet standards

PERCEIVED DIFFERENCES IN SKATING CHARACTERISTICS RESULTING FROM THREE CROSS SECTIONAL SKATE BLADE PROFILES

The purpose of this study was to document differences in perceived skating characteristics resulting from three unique cross sectional skate blade profiles. Sixteen (n=16) University level hockey players were used in this double blind study looking at the perceived performance differences of four different skate blade profiles. No significant differences were found between skate blade profiles, preferred skate blade profile and time to complete given drills. Future research should look at different blade profiles and their interaction at ice level

Reflection of light and heavy holes from a linear potential barrier

In this paper we study reflection of holes in direct-band semiconductors from the linear potential barrier. It is shown that light-heavy hole transformation matrix is universal. It depends only on a dimensionless product of the light hole longitudinal momentum and the characteristic length determined by the slope of the potential and doesn't depend on the ratio of light and heavy hole masses, provided this ratio is small. It is shown that the transformation coefficient goes to zero both in the limit of small and large longitudinal momenta, however the phase of a reflected hole is different in these limits. An approximate analytical expression for the light-heavy hole transformation coefficient is found.Comment: 6 pages, 2 figure

FTIR spectroscopic imaging and mapping with correcting lenses for studies of biological cells and tissues

Histopathology of tissue samples is used to determine the progression of cancer usually by staining and visual analysis. It is recognised that disease progression from healthy tissue to cancerous is accompanied by spectral signature changes in the mid-infrared range. In this work, FTIR spectroscopic imaging in transmission mode using a focal plane array (96 × 96 pixels) has been applied to the characterisation of Barrett's oesophageal adenocarcinoma. To correct optical aberrations, infrared transparent lenses were used of the same material (CaF2) as the slide on which biopsies were fixed. The lenses acted as an immersion objective, reducing scattering and improving spatial resolution. A novel mapping approach using a sliding lens is presented where spectral images obtained with added lenses are stitched together such that the dataset contained a representative section of the oesophageal tissue. Images were also acquired in transmission mode using high-magnification optics for enhanced spatial resolution, as well as with a germanium micro-ATR objective. The reduction of scattering was assessed using k-means clustering. The same tissue section map, which contained a region of high grade dysplasia, was analysed using hierarchical clustering analysis. A reduction of the trough at 1077 cm−1 in the second derivative spectra was identified as an indicator of high grade dysplasia. In addition, the spatial resolution obtained with the lens using high-magnification optics was assessed by measurements of a sharp interface of polymer laminate, which was also compared with that achieved with micro ATR-FTIR imaging. In transmission mode using the lens, it was determined to be 8.5 μm and using micro-ATR imaging, the resolution was 3 μm for the band at a wavelength of ca. 3 μm. The spatial resolution was also assessed with and without the added lens, in normal and high-magnification modes using a USAF target. Spectroscopic images of cells in transmission mode using two lenses are also presented, which are necessary for correcting chromatic aberration and refraction in both the condenser and objective. The use of lenses is shown to be necessary for obtaining high-quality spectroscopic images of cells in transmission mode and proves the applicability of the pseudo hemisphere approach for this and other microfluidic systems

Long-distance remote comparison of ultrastable optical frequencies with 1e-15 instability in fractions of a second

We demonstrate a fully optical, long-distance remote comparison of independent ultrastable optical frequencies reaching a short term stability that is superior to any reported remote comparison of optical frequencies. We use two ultrastable lasers, which are separated by a geographical distance of more than 50 km, and compare them via a 73 km long phase-stabilized fiber in a commercial telecommunication network. The remote characterization spans more than one optical octave and reaches a fractional frequency instability between the independent ultrastable laser systems of 3e-15 in 0.1 s. The achieved performance at 100 ms represents an improvement by one order of magnitude to any previously reported remote comparison of optical frequencies and enables future remote dissemination of the stability of 100 mHz linewidth lasers within seconds.Comment: 7 pages, 4 figure