Lutian Zhao UID: 661622198 The Duistermaat-Heckman theorems concern the measure associated to moment map of a torus action of symplectic manifold. Typically, this name refers to two theorems, one is called the ”Duistermaat-Heckman measure", which says that ”the Radon-Nikodym derivative is piecewise polynomial", the definition of each terms will be introduced later. The second one is called ”Dui...

— The nature of point defects in nematic liquid crystals has been studied by placing droplets on a water substrate and viewing these between crossed polarizers. Three configurations are observed. These configurations are accounted for by minimizing the Frank elastic energies with suitable boundary conditions. The second order nonlinear simultaneous partial differential equations that describe s...

In this article we define a new family of subgroups of Fuchsian groups H( √ m), for a squarefree positive integer m, and calculate their index in H( √ m) and their parabolic class number. Moreover, we will show that the index of these subgroups is closely related to the solvability of a quadratic congruence x2 ≡ m(mod n) and the number of inequivalent solutions of a quadratic congruence x2 ≡ 1(...

The authors have reported to the ACCP that no significant conflicts of interest exist with any companies/organizations whose products or services may be discussed in this article. © 2009 American College of Chest Physicians. Reproduction of this article is prohibited without written permission from the American College of Chest Physicians (www.chestjournal.org/site/ misc/reprints.xhtml). Corres...

To determine if individuals with extensive exposure to rodent habitats were infected with Sin Nombre hantavirus (SNV), we evaluated forest and park service personnel from the region of endemicity in the southwestern United States. Information about work and recreational activities, including exposure to rodents and a history of recent illnesses, was obtained via a standardized questionnaire. Se...

The Schizosaccharomyces pombe septation initiation network (SIN) is an Spg1-GTPase-mediated protein kinase cascade that triggers actomyosin ring constriction, septation, and cell division. The SIN is assembled at the spindle pole body (SPB) on the scaffold proteins Cdc11 and Sid4, with Cdc11 binding directly to SIN signaling components. Proficient SIN activity requires the asymmetric distributi...

Problem P01: Compute the first N decimal digits after the decimal point of sin(sin(sin 1)), rounded toward zero. We have sin(sin(sin 1)) ≈ 0.678: the first N decimal digits after the decimal point match the first N mantissa digits. We use a target decimal precision N1 > N , and a binary precision p. We compute x = ◦(sin 1), y = ◦(sinx), z = ◦(sin y), with all roundings to nearest. It is easy to...