14,870 research outputs found

    Abel Summation of Ramanujan-Fourier Series

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    Using Abel summation the paper proves a weak form of the Wiener-Khinchin formula for arithmetic functions with point-wise convergent Ramanujan-Fourier expansions. The main result is that the convolution of most arithmetic functions possessing an R-F expansion are Abel-summable to a result involving only the Ramanujan-Fourier coefficients of the R-F expansion(s).Comment: 13 pages. No Figures. Updated the definitions and made the theorem on uniform convergence more explici

    Circular 19

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    The turnip maggot, seed-corn maggot and onion maggot are the root maggots of economic importance in Alaska. They feed on crucifers, crucifers and other crops, and onions, respectively. The damage they cause can be materially lessened by properly timed applications of insecticide and certain cultural practices.Cooperating with the United States Department of Agriculture, Agricultural Research Administratio

    The Historical Context of American Indian Legal Problems

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    Federal Law, State Policy, and Indian Gaming

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    This Article will set forth the legal authorization and the economic success of Indian gaming by asking and answering two rhetorical questions: What makes Indian gaming lawful? and What makes Indian gaming successful? This Article will conclude with the observation that Indian gaming exists almost entirely at the mercy of state governments. It will argue that, while Indian gaming began as a cross-border issue, it no longer has those features. Indeed, it has been transformed into the very antithesis of a cross-border issue, a political issue that is addressed almost entirely in the sphere of state political processes. The issue no longer spans borders, but is an internal state political issue. This Article will then explain the ramifications of this transformation both for federal Indian law and policy and for those who wish to study the development and resolution of cross-border problems

    Oath of Office vs. the Pledge

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    All members of Congress take an oath of office to support the Constitution. Some of them make a pledge to Americans for Tax Reform (Grover Norquist, president) to oppose tax increases. For reasons stated in the article, we contend that the pledge has no force and effect and is not binding on members of Congress. The article identifies and numbers 8 topics. This outline-type format helps a) to organize the subject matter, b) to highlight issues, and c) to reduce the word count as we don’t have to worry about smooth transitions

    Improved Lignin Polyurethane Properties with Lewis Acid Treatment

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    Chemical modification strategies to improve the mechanical properties of lignin-based polyurethanes are presented. We hypothesized that treatment of lignin with Lewis acids would increase the concentration of hydroxyl groups available to react with diisocyanate monomers. Under the conditions used, hydrogen bromide-catalyzed modification resulted in a 28% increase in hydroxyl group content. Associated increases in hydrophilicity of solvent-cast thin films were also recorded as evidenced by decreases in water contact angle. Polyurethanes were then prepared by first preparing a prepolymer based on mixtures of toluene-2,4-diisocyanate (TDI) and unmodified or modified lignin, then polymerization was completed through addition of polyethylene glycol (PEG), resulting in mass ratios of TDI:lignin:PEG of 43:17:40 in the compositions investigated here. The mixture of TDI and unmodified lignin resulted in a lignin powder at the bottom of the liquid, suggesting it did not react directly with TDI. However, a homogeneous solution resulted when TDI and the hydrogen bromide-treated lignin were mixed, suggesting demethylation indeed increased reactivity and resulted in better integration of lignin into the urethane network. Significant improvements in mechanical properties of modified lignin polyurethanes were observed, with a 6.5-fold increase in modulus, which were attributed to better integration of the modified lignin into the covalent polymer network due to the higher concentration of hydroxyl groups. This research indicates that chemical modification strategies can lead to significant improvements in the properties of lignin-based polymeric materials using a higher fraction of an inexpensive lignin monomer from renewable resources and a lower fraction an expensive, petroleum-derived isocyanate monomer to achieve the required material properties

    Effect of Local Magnetic Moments on the Metallic Behavior in Two Dimensions

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    The temperature dependence of conductivity σ(T)\sigma (T) in the metallic phase of a two-dimensional electron system in silicon has been studied for different concentrations of local magnetic moments. The local moments have been induced by disorder, and their number was varied using substrate bias. The data suggest that in the limit of T→0T\to 0 the metallic behavior, as characterized by dσ/dT<0d\sigma/dT < 0, is suppressed by an arbitrarily small amount of scattering by local magnetic moments.Comment: 4 pages, revtex, plus four encapsulated postscript figure
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