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In the Λ-system, non-adiabatic holonomic quantum phases are used to construct holonomic quantum gates. An interesting approach would be to implement open path holonomies in the Λ-system. By dividing the loop into two curve segments with a unitary transformation between them, universality can be reached. In doing so the exibility of the scheme has been increased by the fact that one single full pulse is now enough for universality, and we have achieved a clearer proof of the geometric property of the Λ system. / I ett Λ-system så används icke-adiabatiska holonoma kvantfaser för att bygga holonoma kvantgrindar. I detta arbete undersöker vi om holonomier för öppna kurvor kan implementeras i Λsystemet. Genom att dela upp en loop i Λ-systemet i två sekvenser med en unitär transformation emellan så kan vi konstruera en universell holonom kvantgrind. Med detta så har vi ökat exibiliteten för systemet genom att vi nu bara behöver ta en loop för att nå universalitet, och vi har även erhållit en klarare bild över den geometriska egenskapen hos Λ-systemet.

In this thesis we present a general framework of geometric partial differential equations from the viewpoint of geometric energy functional. The proposed geometric functional involves the Gaussian curvature, the mean curvature and the squared norms of their gradients. The geometric partial differential equations are given as the Euler-Lagrangian Equations of the geometric energy functionals by using the calculus of variation method. As a special example, we focus on Gaussian curvature related geometric energy functionals and the corresponding partial differential equations. We present three numerical methods to solve the resulting geometric partial differential equations: the direct discretization method, the finite element method and the level set method. We test these numerical schemes with a large class of geometric models. Potential applications of our proposed geometric partial differential equations include mesh optimization, surface smoothing, surface blending, surface restoration and physical simulation. Finally, we point out some possible directions of future work including singular analysis of the derived geometric partial differential equations and numerical error estimates of our numerical schemes. / Yan, Yinhui. / "September 2008." / Adviser: Kwong Chung Piney. / Source: Dissertation Abstracts International, Volume: 73-01, Section: B, page: . / Thesis (Ph.D.)--Chinese University of Hong Kong, 2009. / Includes bibliographical references (leaves 121-134). / Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Electronic reproduction. [Ann Arbor, MI] : ProQuest Information and Learning, [201-] System requirements: Adobe Acrobat Reader. Available via World Wide Web.

Dentaries of the 6 species of Myotis that occur in the eastern United States were analyzed using landmark-based geometric morphometrics. The species could be distinguished with a high degree of accuracy. Evidence was found of a phylogenetic signal in the morphology of the Neotropical and Nearctic Myotis sub-clades. There is also evidence of convergence in the morphology of the dentary among Myotis species that feed primarily by gleaning. When analyzed together there was no evidence of sexual dimorphism among the 6 eastern U.S. Myotis, but when analyzed individually some dimorphism may be present. A sample of fossil Myotis of unknown species from Bat Cave, Kentucky, was analyzed in an attempt to identify the specimens to species. Results indicate that Myotis austroriparius and M. sodalis predominate the sample, possibly with smaller numbers of M. grisescens and M. leibii. This study demonstrates the ability to differentiate Myotis taxa from historic and prehistoric sites and provides a tool for researchers to better understand and potentially conserve these species.

Thesis (M. Phil.)--University of Hong Kong, 2007. / Title proper from title frame. Also available in printed format.

This paper presents algorithms for computing constraints on the position of an object due to the presence of obstacles. This problem arises in applications which require choosing how to arrange or move objects among other objects. The basis of the approach presented here is to characterize the position and orientation of the object of interest as a single point in a Configuration Space, in which each coordinate represents a degree of freedom in the position and/or orientation of the object. The configurations forbidden to this object, due to the presence of obstacles, can then be characterized as regions in the Configuration Space. The paper presents algorithms for computing these Configuration Space obstacles when the objects and obstacles are polygons or polyhedra. An approximation technique for high-dimensional Configuration Space obstacles, based on projections of obstacles slices, is described.

Two methods of obtaining approximate solutions to the classic General Job-shop Scheduling Program are investigated. The first method is iterative. A sampling of the solution space is used to decide which of a collection of space pruning constraints are consistent with "good" schedules. The selected space pruning constraints are then used to reduce the search space and the sampling is repeated. This approach can be used either to verify whether some set of space pruning constraints can prune with discrimination or to generate solutions directly. Schedules can be represented as trajectories through a Cartesian space. Under the objective criteria of Minimum maximum Lateness family of "good" schedules (trajectories) are geometric neighbors (reside with some "tube") in this space. This second method of generating solutions takes advantage of this adjacency by pruning the space from the outside in thus converging gradually upon this "tube." One the average this methods significantly outperforms an array of the Priority Dispatch rules when the object criteria is that of Minimum Maximum Lateness. It also compares favorably with a recent relaxation procedure.