3,133 research outputs found

    Genuinely nonabelian partial difference sets

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    Strongly regular graphs (SRGs) provide a fertile area of exploration in algebraic combinatorics, integrating techniques in graph theory, linear algebra, group theory, finite fields, finite geometry, and number theory. Of particular interest are those SRGs with a large automorphism group. If an automorphism group acts regularly (sharply transitively) on the vertices of the graph, then we may identify the graph with a subset of the group, a partial difference set (PDS), which allows us to apply techniques from group theory to examine the graph. Much of the work over the past four decades has concentrated on abelian PDSs using the powerful techniques of character theory. However, little work has been done on nonabelian PDSs. In this paper we point out the existence of \textit{genuinely nonabelian} PDSs, i.e., PDSs for parameter sets where a nonabelian group is the only possible regular automorphism group. We include methods for demonstrating that abelian PDSs are not possible for a particular set of parameters or for a particular SRG. Four infinite families of genuinely nonabelian PDSs are described, two of which -- one arising from triangular graphs and one arising from Krein covers of complete graphs constructed by Godsil \cite{Godsil_1992} -- are new. We also include a new nonabelian PDS found by computer search and present some possible future directions of research.Comment: 24 page

    Nonabelian partial difference sets constructed using abelian techniques

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    A (v,k,λ,μ)(v,k,\lambda, \mu)-partial difference set (PDS) is a subset DD of a group GG such that ∣G∣=v|G| = v, ∣D∣=k|D| = k, and every nonidentity element xx of GG can be written in either λ\lambda or μ\mu different ways as a product gh−1gh^{-1}, depending on whether or not xx is in DD. Assuming the identity is not in DD and DD is inverse-closed, the corresponding Cayley graph Cay(G,D){\rm Cay}(G,D) will be strongly regular. Partial difference sets have been the subject of significant study, especially in abelian groups, but relatively little is known about PDSs in nonabelian groups. While many techniques useful for abelian groups fail to translate to a nonabelian setting, the purpose of this paper is to show that examples and constructions using abelian groups can be modified to generate several examples in nonabelian groups. In particular, in this paper we use such techniques to construct the first known examples of PDSs in nonabelian groups of order q2mq^{2m}, where qq is a power of an odd prime pp and m≥2m \ge 2. The groups constructed can have exponent as small as pp or as large as prp^r in a group of order p2rp^{2r}. Furthermore, we construct what we believe are the first known Paley-type PDSs in nonabelian groups and what we believe are the first examples of Paley-Hadamard difference sets in nonabelian groups, and, using analogues of product theorems for abelian groups, we obtain several examples of each. We conclude the paper with several possible future research directions.Comment: 26 page

    The Economic Impacts and Risks Associated with Electric Power Generation in Appalachia

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    This report provides a detailed examination of the economic impacts of changes in electric power generation in Appalachia between 2005 and 2015. It finds that while coal represented around 74 percent of total electric generation in Appalachia in 2005, that percentage dropped to 53 percent in 2015. However, despite this decline, Appalachia remains more dependent on coal for electricity generation when compared with the rest of the country. This report also offers a risk factor analysis for coal-fired generation retirements and repowerings, and notes that coal prices have little influence on coal-fired power plant retirement decisions

    Measuring Thermal Profiles in High Explosives using Neural Networks

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    We present a new method for calculating the temperature profile in high explosive (HE) material using a Convolutional Neural Network (CNN). To train/test the CNN, we have developed a hybrid experiment/simulation method for collecting acoustic and temperature data. We experimentally heat cylindrical containers of HE material until detonation/deflagration, where we continuously measure the acoustic bursts through the HE using multiple acoustic transducers lined around the exterior container circumference. However, measuring the temperature profile in the HE in experiment would require inserting a high number of thermal probes, which would disrupt the heating process. Thus, we use two thermal probes, one at the HE center and one at the wall. We then use finite element simulation of the heating process to calculate the temperature distribution, and correct the simulated temperatures based on the experimental center and wall temperatures. We calculate temperature errors on the order of 15{\deg}C, which is approximately 12% of the range of temperatures in the experiment. We also investigate how the algorithm accuracy is affected by the number of acoustic receivers used to collect each measurement and the resolution of the temperature prediction. This work provides a means of assessing the safety status of HE material, which cannot be achieved using existing temperature measurement methods. Additionally, it has implications for range of other applications where internal temperature profile measurements would provide critical information. These applications include detecting chemical reactions, observing thermodynamic processes like combustion, monitoring metal or plastic casting, determining the energy density in thermal storage capsules, and identifying abnormal battery operation

    Simulated Beam Extraction Performance Characterization of a 50-cm Ion Thruster Discharge

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    Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/97099/1/AIAA2012-3795.pd

    Prospectus, October 8, 1986

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    https://spark.parkland.edu/prospectus_1986/1024/thumbnail.jp

    Prospectus, September 3, 1986

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    https://spark.parkland.edu/prospectus_1986/1019/thumbnail.jp
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