Faces, Edges, Vertices of Some Polyhedra

A proof that: for any given polyhedron so shaped that every closed non-self intersecting broken line composed of edges of the polyhedron divides the surface of the polyhedron into precisely two disjoint regions each of which is bounded by the closed broken line, v - e + f = 2, where v is the number of vertices of the polyhedron, e the number of edges and f the number of faces

The Smallest Particles in Saturn's A and C Rings

Radio occultations of Saturn's main rings by spacecraft suggest a power law particle size-distribution down to sizes of the order of 1 cm (Marouf et al., 1983), (Zebker et al., 1985). The lack of optical depth variations between ultraviolet and near-IR wavelengths indicate a lack of micron-sized particles. Between these two regimes, the particle-size distribution is largely unknown. A cutoff where the particle-size distribution turns over must exist, but the position and shape of it is not clear from existing studies. Using a series of solar occultations performed by the VIMS instrument on-board Cassini in the near-infrared, we are able to measure light forward scattered by particles in the A and C rings. With a model of diffraction by ring particles, and the previous radio work as a constraint on the slope of the particle size distribution, we estimate the minimum particle size using a truncated power-law size distribution. The C Ring shows a minimum particle size of $4.1^{+3.8}_{-1.3}$ mm, with an assumed power law index of q=3.1 and a maximum particle size of 10 m. The A Ring signal shows a similar level of scattered flux, but modeling is complicated by the presence of self-gravity wakes and higher optical depths. If q<3, our A Ring model requires a minimum particle size below one millimeter (< 0.34 mm for an assumed q=2.75, or $0.56^{+0.35}_{-0.16}$ mm for a steeper q=2.9) to be consistent with VIMS observations. These results might seem to contradict previous optical(Dones et al., 1993) and infrared (French and Nicholson, 2000) work, which implied that there were few particles in the A Ring smaller than 1 cm. But, because of the shallow power law, relatively little optical depth (between 0.03 and 0.16 in extinction, or 0.015 - 0.08 in absorption) is provided by these particles.Comment: 47 pages, 16 figures, 3 Table

Episodic Disorders of Vision

Of all our senses, vision is most commonly associated with patient distress, if not overt alarm, when abruptly compromised. Despite patient concern, a rare, or rarely recognizable, clinical entity is perhaps of less significance to the physician than to the patient. When the broad spectrum of episodic disturbance of vision is closely examined, it becomes apparent that these visual symptoms are indeed of common occurrence in the population at large. Surprisingly, despite their ultimate effect on the eye, a majority of the clinical entities that produce episodic disturbance of vision are neurologic. Episodic is defined as being ...made up of separate, loosely connected episodes. In turn, an episode is ...a usually brief unit of action...an occurrence or connected series of occurrences and developments which may be viewed as distinctive and apart, although part of a larger or more comprehensive series

Using MRI of the Optic Nerve Sheath to Detect Elevated Intracranial Pressure

The current gold standard for the diagnosis of elevated intracranial pressure (ICP) remains invasive monitoring. Given that invasive monitoring is not always available or clinically feasible, there is growing interest in non-invasive methods of assessing ICP using diagnostic modalities such as ultrasound or magnetic resonance imaging (MRI). Increased ICP is transmitted through the cerebrospinal fluid surrounding the optic nerve, causing distention of the optic nerve sheath diameter (ONSD). In this issue of Critical Care, Geeraerts and colleagues describe a non-invasive method of diagnosing elevated ICP using MRI to measure the ONSD. They report a positive correlation between measurements of the ONSD on MRI and invasive ICP measurements. If the findings of this study can be replicated in larger populations, this technique may be a useful non-invasive screening test for elevated ICP in select populations

Investigating mathematics teacher efficacy beliefs in primary initial teacher education

This paper will discuss the mathematics teacher efficacy beliefs (MTEB) of primary initial teacher education (ITE) students. We are interested in studying how ITE students’ MTEBs are influenced (or not) by mathematics education modules undertaken as part of an undergraduate Bachelor of Education (BEd) programme. We will detail how approximations of practice (Grossman, Compton, Igra, Ronfeldt, Shahan, & Williamson, 2009) have been incorporated into mathematics education modules to create opportunities for the development of MTEBs and will report on focus group interviews which explored MTEBs of ITE student

Neuro-Ophthalmology in Severe Head Injury

If asked what the significance of neuro-ophthalmology is in the evaluation of severe head injury, many medical and surgical practitioners of neurology would promptly reply that it consists of monitoring pupillary reactivity in anticipation of the uncal herniation syndrome. A discussion of two broad premises of a factual nature, however, should easily convince these same practitioners that the neuro-ophthalmic evaluation of patients with severe head injuries offers far more than the Hutchinson pupil

Nutation versus angular dependent NQR spectroscopy and the impact of underdoping on charge inhomogeneities in YBa2_2Cu3_3Oy_y

We describe two different nuclear quadrupole resonance (NQR) based techniques, designed to measure the local asymmetry of the internal electric field gradient, and the tilt angle of the main NQR principal axis z from the crystallographic axis c. These techniques use the dependence of the NQR signal on the duration of the radio frequency (rf) pulse and on the direction of the rf field H1 with respect to the crystal axis. The techniques are applied to oriented powder of YBa$_{2}$Cu$$O$_{y}$ fully enriched with 63Cu. Measurements were performed at different frequencies, corresponding to different in-plane copper sites with respect to the dopant. Combining the results from both techniques, we conclude that oxygen deficiency in the chain layer lead to a rotation of the NQR main principal axis at the nearby Cu on the CuO2 planes by 20+-degrees. This occurs with no change to the asymmetry. The axis rotation associated with oxygen deficiency means that there must be electric field inhomogeneities in the CuO2 planes only in the vicinity of the missing oxygen.Comment: 9 pages, 10 figure

Formation of Low Threshold Voltage Microlasers

Vertical cavity surface emitting lasers (VCSELs) with threshold voltages of 1.7V have been fabricated. The resistance-area product in these new vertical cavity lasers is comparable to that of edge-emitting lasers, and threshold currents as low as 3 mA have been measured. Molecular beam epitaxy was used to grow n-type mirrors, a quantum well active region, and a heavily Be-doped p-contact. After contact definition and alloying, passive high-reflectivity mirrors were deposited by reactive sputter deposition of SiO2/Si3N4 to complete the laser cavity

The Footsteps Die Out For Ever (2016) for narrator, drum set, and orchestra

Title from PDF of title page, viewed on June 3, 2016Thesis advisor: James MobberleyVitaThesis (M.M.)--Conservatory of Music and Dance. University of Missouri--Kansas City, 2016A Tale of Two Cities, serialized in weekly and monthly installments and finally published as a single volume in November 1859, is one of Charles Dickens’s best-loved and most-analyzed novels. In The Footsteps Die Out For Ever, I have sought to pay homage to Dickens’s work, heightening and extending the drama of the story by writing music for drum set and orchestra to accompany the narrator, who recites text drawn from the novel. The Footsteps Die Out For Ever begins with a brief flourish on the tubular bells, introducing the piece’s scalar material, and the narrator reciting the opening paragraph of A Tale of Two Cities: “It was the best of times, it was the worst of times....” This text sets the stage for the action and commentary to follow in the narrative, as well as reminding the listener of his or her own place in time. Dickens compares the period of the French Revolution to “the present period,” a conceit which makes the work relevant not only to his time, but just as much to our own. The rest of the composition’s text is an edited version of the novel’s final chapter, titled “The Footsteps Die Out For Ever.” The music uses recurring motives to represent characters, themes, and ideas, and serves as background illustrating much of the action, including the tumbrils that carry the prisoners of the Revolution, the guillotine’s grim work, an intimate conversation between Sydney Carton and a seamstress, Carton’s recollection of Christ’s declaration “I am the resurrection and the life...”, Carton’s execution, and his prophetic last thoughts foreseeing the end of the Revolution and its evils. In those final words, Carton’s thoughts turn to the lives for which he is laying down his life, and end with the famous concluding words of the novel: “It is a far, far better thing that I do, than I have ever done; it is a far, far better rest that I go to than I have ever known.”
Abstract -- Instrumentation -- Program notes -- Performance notes and duration -- Motives -- Text -- The footsteps die out for ever -- Vit