67 research outputs found

    Subject Index Volumes 1–200

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    Generation of Graph Classes with Efficient Isomorph Rejection

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    In this thesis, efficient isomorph-free generation of graph classes with the method of generation by canonical construction path(GCCP) is discussed. The method GCCP has been invented by McKay in the 1980s. It is a general method to recursively generate combinatorial objects avoiding isomorphic copies. In the introduction chapter, the method of GCCP is discussed and is compared to other well-known methods of generation. The generation of the class of quartic graphs is used as an example to explain this method. Quartic graphs are simple regular graphs of degree four. The programs, we developed based on GCCP, generate quartic graphs with 18 vertices more than two times as efficiently as the well-known software GENREG does. This thesis also demonstrates how the class of principal graph pairs can be generated exhaustively in an efficient way using the method of GCCP. The definition and importance of principal graph pairs come from the theory of subfactors where each subfactor can be modelled as a principal graph pair. The theory of subfactors has applications in the theory of von Neumann algebras, operator algebras, quantum algebras and Knot theory as well as in design of quantum computers. While it was initially expected that the classification at index 3 + √5 would be very complicated, using GCCP to exhaustively generate principal graph pairs was critical in completing the classification of small index subfactors to index 5¼. The other set of classes of graphs considered in this thesis contains graphs without a given set of cycles. For a given set of graphs, H, the Turán Number of H, ex(n,H), is defined to be the maximum number of edges in a graph on n vertices without a subgraph isomorphic to any graph in H. Denote by EX(n,H), the set of all extremal graphs with respect to n and H, i.e., graphs with n vertices, ex(n,H) edges and no subgraph isomorphic to any graph in H. We consider this problem when H is a set of cycles. New results for ex(n, C) and EX(n, C) are introduced using a set of algorithms based on the method of GCCP. Let K be an arbitrary subset of {C3, C4, C5, . . . , C32}. For given n and a set of cycles, C, these algorithms can be used to calculate ex(n, C) and extremal graphs in Ex(n, C) by recursively extending smaller graphs without any cycle in C where C = K or C = {C3, C5, C7, . . .} ᴜ K and n≤64. These results are considerably in excess of the previous results of the many researchers who worked on similar problems. In the last chapter, a new class of canonical relabellings for graphs, hierarchical canonical labelling, is introduced in which if the vertices of a graph, G, is canonically labelled by {1, . . . , n}, then G\{n} is also canonically labelled. An efficient hierarchical canonical labelling is presented and the application of this labelling in generation of combinatorial objects is discussed

    Cosserat Analysis of Microscale Structures

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    In this thesis, the application of Cosserat mechanics to micro-scale structures is explored. Different structures considered include micro-scale gyroscopes, micro-cantilevers, and clamped-clamped micro-structures. Two-dimensional formulations with nonlinearities up to third order are derived and presented. Different parameterization schemes are used and the equivalence between the obtained results is discussed. Comparisons with prior results available in the literature are made in terms of inertia properties, stiffness properties, and natural frequencies. The present work points to the importance of considering Cosserat mechanics for examining the motions of micro-scale structures that undergo large as well as coupled deformations

    Aeronautical engineering: A continuing bibliography with indexes (supplement 225)

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    This bibliography lists 429 reports, articles, and other documents introduced into the NASA scientific and technical information system in March, 1988

    NAS Technical Summaries, March 1993 - February 1994

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    NASA created the Numerical Aerodynamic Simulation (NAS) Program in 1987 to focus resources on solving critical problems in aeroscience and related disciplines by utilizing the power of the most advanced supercomputers available. The NAS Program provides scientists with the necessary computing power to solve today's most demanding computational fluid dynamics problems and serves as a pathfinder in integrating leading-edge supercomputing technologies, thus benefitting other supercomputer centers in government and industry. The 1993-94 operational year concluded with 448 high-speed processor projects and 95 parallel projects representing NASA, the Department of Defense, other government agencies, private industry, and universities. This document provides a glimpse at some of the significant scientific results for the year

    Cal Poly Rose Float Overheight Mechanism

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    The Cal Poly Universities jointly build and enter a floral entry, commonly known as a float, into the Pasadena Tournament of Roses Rose Parade. At the end of this parade route, there is a 16’6” bridge all floats must drive under. The scope of our project is to design and build a mechanism roughly described as an “overheight” mechanism, as its function is to raise and lower large heavy structures so the float is able to pass under the bridge. This hydraulic mechanism is powered via the float animation system

    Aeronautical Engineering: A continuing bibliography with indexes

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    This bibliography lists 499 reports, articles and other documents introduced into the NASA scientific and technical information system in August 1985

    LIPIcs, Volume 274, ESA 2023, Complete Volume

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    LIPIcs, Volume 274, ESA 2023, Complete Volum
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