3 resultados para Primitive and Irreducible Polynomials

em Duke University


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This is a dissertation about identity and governance, and how they are mutually constituted. Between 1838 and 1917, the British brought approximately half a million East Indian laborers to the Atlantic to work on sugar plantations. The dissertation argues that contrary to previous historiographical assumptions, indentured East Indians were an amorphous mass of people drawn from various regions of British India. They were brought together not by their innate "Indian-ness" upon their arrival in the Caribbean, but by the common experience of indenture recruitment, transportation and plantation life. Ideas of innate "Indian-ness" were products of an imperial discourse that emerged from and shaped official approaches to governing East Indians in the Atlantic. Government officials and planters promoted visions of East Indians as "primitive" subjects who engaged in child marriage and wife murder. Officials mobilized ideas about gender to sustain racialized stereotypes of East Indian subjects. East Indian women were thought to be promiscuous, and East Indian men were violent and depraved (especially in response to East Indian women's promiscuity). By pointing to these stereotypes about East Indians, government officials and planters could highlight the promise of indenture as a civilizing mechanism. This dissertation links the study of governance and subject formation to complicate ideas of colonial rule as static. It uncovers how colonial processes evolved to handle the challenges posed by migrant populations.

The primary architects of indenture, Caribbean governments, the British Colonial Office, and planters hoped that East Indian indentured laborers would form a stable and easily-governed labor force. They anticipated that the presence of these laborers would undermine the demands of Afro-Creole workers for higher wages and shorter working hours. Indenture, however, was controversial among British liberals who saw it as potentially hindering the creation of a free labor market, and abolitionists who also feared that indenture was a new form of slavery. Using court records, newspapers, legislative documents, bureaucratic correspondence, memoirs, novels, and travel accounts from archives and libraries in Britain, Guyana, and Trinidad and Tobago, this dissertation explores how indenture was envisioned and constantly re-envisioned in response to its critics. It chronicles how the struggles between the planter class and the colonial state for authority over indentured laborers affected the way that indenture functioned in the British Atlantic. In addition to focusing on indenture's official origins, this dissertation examines the actions of East Indian indentured subjects as they are recorded in the imperial archive to explore how these people experienced indenture.

Indenture contracts were central to the justification of indenture and to the creation of a pliable labor force in the Atlantic. According to English common law, only free parties could enter into contracts. Indenture contracts limited the period of indenture and affirmed that laborers would be remunerated for their labor. While the architects of indenture pointed to contracts as evidence that indenture was not slavery, contracts in reality prevented laborers from participating in the free labor market and kept the wages of indentured laborers low. Further, in late nineteenth-century Britain, contracts were civil matters. In the British Atlantic, indentured laborers who violated the terms of their contracts faced criminal trials and their associated punishments such as imprisonment and hard labor. Officials used indenture contracts to exploit the labor and limit the mobility of indentured laborers in a manner that was reminiscent of slavery but that instead established indentured laborers as subjects with limited rights. The dissertation chronicles how indenture contracts spawned a complex inter-imperial bureaucracy in British India, Britain, and the Caribbean that was responsible for the transportation and governance of East Indian indentured laborers overseas.

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We present a theory of hypoellipticity and unique ergodicity for semilinear parabolic stochastic PDEs with "polynomial" nonlinearities and additive noise, considered as abstract evolution equations in some Hilbert space. It is shown that if Hörmander's bracket condition holds at every point of this Hilbert space, then a lower bound on the Malliavin covariance operatorμt can be obtained. Informally, this bound can be read as "Fix any finite-dimensional projection on a subspace of sufficiently regular functions. Then the eigenfunctions of μt with small eigenvalues have only a very small component in the image of Π." We also show how to use a priori bounds on the solutions to the equation to obtain good control on the dependency of the bounds on the Malliavin matrix on the initial condition. These bounds are sufficient in many cases to obtain the asymptotic strong Feller property introduced in [HM06]. One of the main novel technical tools is an almost sure bound from below on the size of "Wiener polynomials," where the coefficients are possibly non-adapted stochastic processes satisfying a Lips chitz condition. By exploiting the polynomial structure of the equations, this result can be used to replace Norris' lemma, which is unavailable in the present context. We conclude by showing that the two-dimensional stochastic Navier-Stokes equations and a large class of reaction-diffusion equations fit the framework of our theory.

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As complex radiotherapy techniques become more readily-practiced, comprehensive 3D dosimetry is a growing necessity for advanced quality assurance. However, clinical implementation has been impeded by a wide variety of factors, including the expense of dedicated optical dosimeter readout tools, high operational costs, and the overall difficulty of use. To address these issues, a novel dry-tank optical CT scanner was designed for PRESAGE 3D dosimeter readout, relying on 3D printed components and omitting costly parts from preceding optical scanners. This work details the design, prototyping, and basic commissioning of the Duke Integrated-lens Optical Scanner (DIOS).

The convex scanning geometry was designed in ScanSim, an in-house Monte Carlo optical ray-tracing simulation. ScanSim parameters were used to build a 3D rendering of a convex ‘solid tank’ for optical-CT, which is capable of collimating a point light source into telecentric geometry without significant quantities of refractive-index matched fluid. The model was 3D printed, processed, and converted into a negative mold via rubber casting to produce a transparent polyurethane scanning tank. The DIOS was assembled with the solid tank, a 3W red LED light source, a computer-controlled rotation stage, and a 12-bit CCD camera. Initial optical phantom studies show negligible spatial inaccuracies in 2D projection images and 3D tomographic reconstructions. A PRESAGE 3D dose measurement for a 4-field box treatment plan from Eclipse shows 95% of voxels passing gamma analysis at 3%/3mm criteria. Gamma analysis between tomographic images of the same dosimeter in the DIOS and DLOS systems show 93.1% agreement at 5%/1mm criteria. From this initial study, the DIOS has demonstrated promise as an economically-viable optical-CT scanner. However, further improvements will be necessary to fully develop this system into an accurate and reliable tool for advanced QA.

Pre-clinical animal studies are used as a conventional means of translational research, as a midpoint between in-vitro cell studies and clinical implementation. However, modern small animal radiotherapy platforms are primitive in comparison with conventional linear accelerators. This work also investigates a series of 3D printed tools to expand the treatment capabilities of the X-RAD 225Cx orthovoltage irradiator, and applies them to a feasibility study of hippocampal avoidance in rodent whole-brain radiotherapy.

As an alternative material to lead, a novel 3D-printable tungsten-composite ABS plastic, GMASS, was tested to create precisely-shaped blocks. Film studies show virtually all primary radiation at 225 kVp can be attenuated by GMASS blocks of 0.5cm thickness. A state-of-the-art software, BlockGen, was used to create custom hippocampus-shaped blocks from medical image data, for any possible axial treatment field arrangement. A custom 3D printed bite block was developed to immobilize and position a supine rat for optimal hippocampal conformity. An immobilized rat CT with digitally-inserted blocks was imported into the SmART-Plan Monte-Carlo simulation software to determine the optimal beam arrangement. Protocols with 4 and 7 equally-spaced fields were considered as viable treatment options, featuring improved hippocampal conformity and whole-brain coverage when compared to prior lateral-opposed protocols. Custom rodent-morphic PRESAGE dosimeters were developed to accurately reflect these treatment scenarios, and a 3D dosimetry study was performed to confirm the SmART-Plan simulations. Measured doses indicate significant hippocampal sparing and moderate whole-brain coverage.