On the Quantum Invariant for the Brieskorn Homology Spheres

We study an exact asymptotic behavior of the Witten-Reshetikhin-Turaev invariant for the Brieskorn homology spheres $\Sigma(p_1,p_2,p_3)$ by use of properties of the modular form following a method proposed by Lawrence and Zagier. Key observation is that the invariant coincides with a limiting value of the Eichler integral of the modular form with weight 3/2. We show that the Casson invariant is related to the number of the Eichler integrals which do not vanish in a limit $\tau\to N \in \mathbb{Z}$. Correspondingly there is a one-to-one correspondence between the non-vanishing Eichler integrals and the irreducible representation of the fundamental group, and the Chern-Simons invariant is given from the Eichler integral in this limit. It is also shown that the Ohtsuki invariant follows from a nearly modular property of the Eichler integral, and we give an explicit form in terms of the L-function.Comment: 26 pages, 2 figure

The Lyapunov exponent in the Sinai billiard in the small scatterer limit

We show that Lyapunov exponent for the Sinai billiard is $\lambda = -2\log(R)+C+O(R\log^2 R)$ with $C=1-4\log 2+27/(2\pi^2)\cdot \zeta(3)$ where $R$ is the radius of the circular scatterer. We consider the disk-to-disk-map of the standard configuration where the disks is centered inside a unit square.Comment: 15 pages LaTeX, 3 (useful) figures available from the autho

Quantum Invariants, Modular Forms, and Lattice Points II

We study the SU(2) Witten--Reshetikhin--Turaev invariant for the Seifert fibered homology spheres with M-exceptional fibers. We show that the WRT invariant can be written in terms of (differential of) the Eichler integrals of modular forms with weight 1/2 and 3/2. By use of nearly modular property of the Eichler integrals we shall obtain asymptotic expansions of the WRT invariant in the large-N limit. We further reveal that the number of the gauge equivalent classes of flat connections, which dominate the asymptotics of the WRT invariant in N ->\infinity, is related to the number of integral lattice points inside the M-dimensional tetrahedron

Morphometric properties of nivation hollows on Hart Mountain, Lake County, Oregon

Hart Mountain is a basaltic fault block mountain in the semi-desert region of the northern Basin and Range province in south-central Oregon. Geomorphic processes associated with lingering snowpatches have formed nivation hollows, which are small scale depressions in the hillsides. The lingering snow in the hollows prohibits shrub growth. Bedrock scarps, present in some of the hollows, show indications of chemical alteration. Bills are present below most of the hollows, indicating that surface runoff from these sites occurs. Average hillslope, which controls the shear stress placed on soil particles, is statistically related to morphometric attributes defining the size and angles of the hollows. Simple linear regressions and the nonparametric Kendall's rank correlation coefficient (p-) and Theil's C test for the regression line slope suggest that average hillslope is directly related to the morphometric attributes of the hollows. Heat transfer controls the areal distribution and duration of snowpatcnes. A relative insolation factor and elevation are taken as surrogates for heat transfer. These surrogates are likewise correlated with the morphometric attributes of the hollows. Both the elevation and the relative insolation factor suggest an inverse relationship between heat transfer and the size of nivation hollows. The hollows on Hart Mountain appear to have been formed by accelerated nivation processes during the Pleistocene and are currently being modified by less intense nivation

The Digital Death Conundrum: How Federal and State Laws Prevent Fiduciaries from Managing Digital Property

This article discusses four types of fiduciaries, each of which is affected by the vast growth in and the need to manage digital property. The article begins by defining digital property and discussing why it must be managed. The article then discusses how digital property affects powers of attorney, conservatorships, probate administration, and trusts. After illustrating the problems that digital property creates for each fiduciary, the article shifts to resolving these problems. It begins by debunking purported solutions by both private and governmental entities. It concludes by offering a holistic approach to resolving the conflicts facing account holders, fiduciaries, and service providers and providing the level of security sought in fiduciary property management, as well as a best-practices approach in the interim to a complete solution

The Relation between Packing Effects and Solid State Fluorescence of Dyes

The solid state fluorescence of diketopyrrolopyrrole dyes and perylene-3,4:9,10- tetracarboxylic bisimides with alkyl substituents are investigated and compared with noncovalent interactions. The latter are estimated by crystal structure analysis, heats and entropies of fusion and solubilities in organic solvents. Applications of the dyes are discussed

A Polynomial Number of Random Points does not Determine the Volume of a Convex Body

We show that there is no algorithm which, provided a polynomial number of random points uniformly distributed over a convex body in R^n, can approximate the volume of the body up to a constant factor with high probability

Global properties of tight Reeb flows with applications to Finsler geodesic flows on S2S^2

We show that if a Finsler metric on $S^2$ with reversibility $r$ has flag curvatures $K$ satisfying $(\frac{r}{r+1})^2 <K \leq 1$, then closed geodesics with specific contact-topological properties cannot exist, in particular there are no closed geodesics with precisely one transverse self-intersection point. This is a special case of a more general phenomenon, and other closed geodesics with many self-intersections are also excluded. We provide examples of Randers type, obtained by suitably modifying the metrics constructed by Katok \cite{katok}, proving that this pinching condition is sharp. Our methods are borrowed from the theory of pseudo-holomorphic curves in symplectizations. Finally, we study global dynamical aspects of 3-dimensional energy levels $C^2$-close to $S^3$.Comment: 27 page

How Competent Are Emergency Medicine Interns for Level 1 Milestones: Who Is Responsible?

Objectives The Next Accreditation System ( NAS ) of the Accreditation Council for Graduate Medical Education ( ACGME ) includes the implementation of developmental milestones for each specialty. The milestones include five progressively advancing skill levels, with Level 1 defining the skill level of a medical student graduate, and Level 5, that of an attending physician. The goal of this study was to query interns on how well they thought their medical school had prepared them to meet the proposed emergency medicine ( EM ) Level 1 milestones. Methods In July 2012, an electronic survey was distributed to the interns of 13 EM residency programs, asking interns whether they were taught and assessed on the proposed Level 1 milestones. Results Of possible participants, 113 of 161 interns responded (70% response rate). The interns represented all four regions of the country. The interns responded that the rates of Level 1 milestones they had been taught ranged from 61% for ultrasound to 98% for performance of focused history and physical examination. A substantial number of interns (up to 39%) reported no instruction on milestones such as patient disposition, pain management, and vascular access. Graduating medical students were less commonly assessed than taught the milestones. Skills with technology, including “explain the role of the electronic health record and computerized physician order entry,” were assessed for only 39% of interns, and knowledge ( USMLE ) and history and physical were assessed in nearly all interns. Disposition, ultrasound, multitasking, and wound management were assessed less than half of the time. Conclusions Many entering EM interns may not have had either teaching or assessment on the knowledge, skills, and behaviors making up the Level 1 milestones expected for graduating medical students. Thus, there is a potential gap in the teaching and assessment of EM interns. Based on these findings, it is unclear who will be responsible (medical schools, EM clerkships, or residency programs) for ensuring that medical students entering residency have achieved Level 1 milestones. Resumen Competencia de los Residentes de Medicina de Urgencias y Emergencias para el Nivel 1: ¿Quién es el Responsable? El próximo sistema de acreditación ( NAS , Next Accreditation System ) del Accreditation Council for Graduate Medical Education ( ACGME ) incluye la implementación de objetivos por área de desarrollo para cada especialidad. Los objetivos por área incluyen cinco niveles de habilidades progresivamente avanzadas, con un nivel 1 definido por el nivel de habilidad de un estudiante licenciado de medicina, y un nivel definido por el nivel, de un médico adjunto. El objetivo de este estudio fue preguntar a los residentes cómo pensaban que sus universidades les habían preparado para alcanzar los objetivos por área de nivel 1 propuestos en medicina de urgencias y emergencias ( MUE ). Metodología En julio de 2012, se distribuyó una encuesta electrónica a los residentes de 13 programas de residencia de MUE , preguntándoles si estaban formados y evaluados en los objetivos por área de nivel 1 propuestos. Resultados De los posibles participantes, 113 de 161 residentes (70%) respondieron. Los residentes representaban las cuatro regiones del país. Los residentes respondieron que los porcentajes de objetivos por área de nivel 1 en los que se habían formado variaron del 61% para la ecografía al 98% para la realización de la historia clínica y la exploración física. Un número importante de residentes (hasta un 39%) respondieron no formarse en objetivos por áreas tales como la ubicación del paciente, el manejo del dolor y el acceso vascular. Los estudiantes licenciados de medicina fueron menos frecuentemente evaluados que formados en los objetivos por área. Las habilidades con la tecnología, incluyendo la explicación del rol de la historia clínica electrónica y la solicitud de órdenes médicas computarizadas, se evaluaron sólo en el 39% de los residentes y el conocimiento ( USMLE , United States Medical Licensing Examination ) y la historia clínica y exploración física se evaluaron en casi todos los residentes. Es más, la ubicación, la ecografía, la multitarea y el manejo de heridas se evaluaron en menos de la mitad de las ocasiones. Conclusiones Muchos de los residentes que se inician en MUE pueden no haber tenido formación o evaluación en el conocimiento, las habilidades y los comportamientos preparatorios para los objetivos por área de nivel 1 esperados para los estudiantes licenciados de medicina. Además, hay una brecha potencial en la formación y la evaluación de los residentes de MUE . En base a estos hallazgos, no está claro quién será el responsable, las facultades de medicina, la administración de la MUE o los programas de residencia, para asegurar que los estudiantes de medicina que entren en la residencia hayan alcanzado los objetivos por área de nivel 1.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/99036/1/acem12162.pd