4,129 research outputs found

    Invariable generation of the symmetric group

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    We say that permutations π1,,πrSn\pi_1,\dots, \pi_r \in \mathcal{S}_n invariably generate Sn\mathcal{S}_n if, no matter how one chooses conjugates π1,,πr\pi'_1,\dots,\pi'_r of these permutations, π1,,πr\pi'_1,\dots,\pi'_r generate Sn\mathcal{S}_n. We show that if π1,π2,π3\pi_1,\pi_2,\pi_3 are chosen randomly from Sn\mathcal{S}_n then, with probability tending to 1 as nn \rightarrow \infty, they do not invariably generate Sn\mathcal{S}_n. By contrast it was shown recently by Pemantle, Peres and Rivin that four random elements do invariably generate Sn\mathcal{S}_n with positive probability. We include a proof of this statement which, while sharing many features with their argument, is short and completely combinatorial.Comment: 15 pages. Corrections and clarifications suggested by the referees. Added a reference to a paper of Raouj and Stef which solves related problems about divisor

    The Sunken Vessels of Chauncey and Yeo in Lake Ontario

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    Naval power was central to controlling the Great Lakes and, by extension, the interior of North America during the War of 1812. On Lake Ontario, the naval conflict took the form of an arms race with virtually no actual engagements. As a result, few vessels were lost during the war. With the signing of the Rush-Bagot Agreement, however, both belligerents sold vessels and put others in storage, resulting in the wrecks of lost or abandoned war vessels all over the lake. Many of these vessels have been located and studied over the last century. This paper reviews the vessels that have been studied, discusses what has been and what can be learned from these vessels, and notes some of the shipwrecks that are still to be found

    Large gaps between consecutive prime numbers

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    Let G(X)G(X) denote the size of the largest gap between consecutive primes below XX. Answering a question of Erdos, we show that G(X)f(X)logXloglogXloglogloglogX(logloglogX)2,G(X) \geq f(X) \frac{\log X \log \log X \log \log \log \log X}{(\log \log \log X)^2}, where f(X)f(X) is a function tending to infinity with XX. Our proof combines existing arguments with a random construction covering a set of primes by arithmetic progressions. As such, we rely on recent work on the existence and distribution of long arithmetic progressions consisting entirely of primes.Comment: v2. very minor corrections. To appear in Ann. Mat

    Shipbuilding in Maryland, 1631-1850

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    E-Learning Barriers and Educational Applications of Broadband Technologies

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    The Psychology of Conflict and Combat

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    Geomorphic Traits and Water Chemistry as an Indicator of Fish Functional Diversity in Scott County, IA and Rock Island County, IL

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    Fish species diversity is a widely used indicator of stream health, however, the relationship between the functional diversity of fish communities and stream health is less documented. Although functional and species diversity are often related, it is also the case that functional diversity may reveal levels of community health or impairment that species based approaches may miss. Functional diversity has been previously defined as the diversity of functional traits, such as fin length. We will define functional diversity as the variance of fish trophic guilds according to the IA DNR reference. Fish were categorized as benthic invertivore, filter, generalist, herbivore, insectivore, omnivore, parasite, top carnivore, or N/A. Nineteen sampling sites were selected, making sure to select an even mix of urbanized, agricultural, and protected sites. Geographic Information Systems (GIS) was used to delineate the watersheds of the 19 sites across the area. An ETS Electrofishing Systems AbP-4-MR-HP Pulsed-DC backpack unit for collecting fish in the field. A 50 meter reach was sampled at each site, measured along the streambank following the water’s edge. Seine nets were placed across the entire width of the stream at the top and lower end of the sampling reach. Fish were identified to the species level. Predators were the least common guild identified and included: Micropterus salmoides, Micropterus dolomieu, and Esox americanus. We assessed each community for fish functional diversity through Shannon\u27s diversity calculation based on guild membership rather than species identity. A multiple regression model using entrenchment ratio, chloride, and stream width as predictors of Shannons index was significant (R2 = .744, F = 11.598, p \u3c .001). In this model, stream width was the variable most tightly linked with functional diversity (t=3.998), while entrenchment ratio and chloride concentrations were less influential (t = -2.803, -2.494 respectively). Our results suggest that geomorphology may be a stronger predictor of functional diversity in these assemblages than water quality, and geomorphic variables may limit the presence of top predators in these assemblages. Specifically, stream width could be used as an indicator to predict whether a top carnivore will be present in a stream

    Neotrusteeship or Mistrusteeship? The Authority Creep Dilemma in United Nations Transitional Administration

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    State failure poses one of the greatest threats to international peace and security. The collapse of governing institutions breeds civil wars, generates refugee flows, causes enormous civilian suffering, foments instability in neighboring countries, and provides safe havens for transnational criminal and terrorist organizations. As a result, commentators and policymakers have increasingly called for a remedy to the problem of state failure. One of the most compelling arguments is to draw on an old legal institution: international trusteeship by the United Nations (U.N.). This Article argues that while trusteeship may prove effective in managing state failure, it also carries risks. International interventions typically take limited control of the domestic environment of weak countries without absorbing their sovereignty. Trusteeship, in contrast, vests enormous authority and discretion in temporary international administrators, who in turn tend to centralize their power and decision-making in order to meet challenging mission mandates under difficult conditions. This authority creep absorbs sovereignty and in the process risks eroding incentives for leaders of failing states to cooperate with the U.N. Worse, unmitigated authority creep may weaken the political basis for successive international administration and reconstruction efforts. This Article concludes by outlining an alternative system of oversight for U.N. transitional administrators as a means of preserving partial sovereign authority and control for domestic political actors

    Towards a conceptual framework for the prevention of gambling-related harms: Findings from a scoping review

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    The global gambling sector has grown significantly over recent years due to liberal deregulation and digital transformation. Likewise, concerns around gambling-related harms—experienced by individuals, their families, their local communities or societies—have also developed, with growing calls that they should be addressed by a public health approach. A public health approach towards gambling-related harms requires a multifaceted strategy, comprising initiatives promoting health protection, harm minimization and health surveillance across different strata of society. However, there is little research exploring how a public health approach to gambling-related harms can learn from similar approaches to other potentially harmful but legal sectors such as the alcohol sector, the tobacco sector, and the high in fat, salt and sugar product sector. Therefore, this paper presents a conceptual framework that was developed following a scoping review of public health approaches towards the above sectors. Specifically, we synthesize strategies from each sector to develop an overarching set of public health goals and strategies which—when interlinked and incorporated with a socio-ecological model—can be deployed by a range of stakeholders, including academics and treatment providers, to minimise gambling-related harms. We demonstrate the significance of the conceptual framework by highlighting its use in mapping initiatives as well as unifying stakeholders towards the minimization of gambling-related harms, and the protection of communities and societies alike
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