2,209 research outputs found

    Constructing Carmichael numbers through improved subset-product algorithms

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    We have constructed a Carmichael number with 10,333,229,505 prime factors, and have also constructed Carmichael numbers with k prime factors for every k between 3 and 19,565,220. These computations are the product of implementations of two new algorithms for the subset product problem that exploit the non-uniform distribution of primes p with the property that p-1 divides a highly composite \Lambda.Comment: Table 1 fixed; previously the last 30 digits and number of digits were calculated incorrectl

    Letter, Addressed to Hughey P. Long, 1935

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    A letter written by W.D. Hayman addressed to Hughey P. Long on August 8, 1935

    Pre-thrust normal faults and post-tectonic micas in the Taconic Range of west-central Vermont

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    New geologic maps show that the Champlain Thrust System traces continuously between Shoreham and Benson, Vermont. The Champlain Thrust System consists of at least three internally imbricated thrust slices in continental shelf facies quartzites and carbonates. From north to south there is a structurally controlled thinning of the Champlain Thrust System, and a climbing in stratigraphic level by the thrusts. Within the Champlain Thrust System are a set of across-strike structures which create offsets in the thrusts and the surrounding lithic map unit boundaries. These structures function as lateral ramps in the thrust system geometry and bound thrust duplexes. Often there are changes in the stratigraphic level across these offsets which cannot be explained by the thrust geometry. These are interpreted to be to be pre-thrust normal faults, and a subsidiary (trench normal) set to the normal faults predicted by the model of Bradley and Kidd (1991), wherein normal faulting occurs in the continental crust in response to lithospheric flexure with the onset of collision. Trench parallel normal faults bounded grabens containing shales, and horsts of carbonate rocks. These horsts and grabens are now reflected in the thrust system\u27s geometry. The Mettawee River Fault, an east-side-down normal fault, juxtaposes an intermixed belt of Middle Ordovician shelf facies shale and Pre-Cambrian continental rise facies slates and arenites, and Middle Ordovician flysch and melange, against the Champlain Thrust System. This structure could be late Taconic (orogenic) to post-Taconic in age, and have amounts of throw of tens to hundreds of meters. East of the Mettawee River Fault is the westernmost Taconic allochthon, the Sunset Lake Slice. This is a roughly north-south trending belt of green slates interspersed with lenses of continental rise facies quartzites. The Sunset Lake Slice is bound to the east by the Taconic Frontal Thrust, a late, out of sequence thrust which transports an eastern belt of intermixed Ordovician and Taconic shales and melange, as well as an eastern thrust belt of shelf facies carbonates and shales. This belt of carbonates and shales is litholologically identical to the rocks found in the Champlain Thrust System but structurally dissimilar. The separation of these rocks from their facies equivalents in the Champlain Thrust System is suggested to be due to their topographically higher position on the paleo-continental shelf, the topography being largely (pre-thrust) normal fault controlled. Cross-micas are observed mica grains from the slates at the Cedar Point Quarry, W. Castleton, Vt.. The Cedar Point cross-micas cross-cut the boundaries of a late crenulation cleavage which has the morphology of micro-kinks at the microscopic scale. This cross-cutting relationship suggests that these grains grew later than the deformation which produced the micro-kinks, and therefore later than the deformation which produced the slaty cleavage. If this is the case, then perhaps many, or all of the mica grains in the slate grew at this later time. The investigation to gain insight into the timing of the development of the cross-micas included producing a structural map and cross-section of the Cedar Point Quarry which may be useful for related future studies. Field based observations provide insight into the deformation history recorded at Cedar Point. The cross-micas, and the surrounding micro-structure of the slate are documented with photomicrographs. The observation that some micro-kinks are enriched with opaque minerals (oxides and sulfides), whereas other, adjacent, micro-kinks are enriched with phyllosilicates, is evidence that there was some amount of mass transfer, presumably due to solution processes, after the formation of the micro-kinks. Electron microprobe data was attained from the slates in the hopes of confirming whether the cross-micas represent mica growth which was localized along the micro-kinks (and thus in the absence of a widespread metamorphic/mica growth event), or mica growth which was widespread throughout the slates. It was found that there are two groups of muscovite in the slate, a high K and a low K muscovite. There is also a group of interlayered muscovite and chlorite. There is no obvious relationship between structural setting, such as cross-micas, and the mineralogical variation, though with future work, such a relationship may be established

    The effects of racially-motivated emotional arousal on the eating behaviors of african american women

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    Disparities between African Americans and Caucasians remain vast across a wide variety of health indicators. Chronic stress has been identified as a risk factor for a variety of chronic illnesses and poor health outcomes. One type of chronic stress that has been linked to health disparities is the stress associated with experiences of racial discrimination. The stress African Americans encounter as a result of their racist experiences contributes to a chronic elevation of their physiological stress response. In addition to stress, a major risk factor for coronary heart disease and diabetes is obesity, which has been established as a major health problem in the United States. Obesity in African American women tends to be the result of psychosocial, behavioral, cultural, and environmental factors, among others. The purpose of this dissertation was to investigate possible psychosocial contributions of racism-related stress and the eating behaviors of African American women to their high rates of obesity. Thus, this study was designed to link survey research demonstrating racial discrimination as a stressor with negative effects on health behaviors and outcomes in African Americans with laboratory studies demonstrating how stress produces binge eating among individuals who typically try to restrain their eating. A number of hypotheses guided this two-part study, which followed a 2 (Eating Style: Restrained vs. Unrestrained Eating) x 2 (Ostracism: Inclusion vs. Exclusion) x 2 (Reference Group: Outgroup vs. Ingroup) design. Three hundred nineteen women participated in Study 1 where they completed questionnaires on their eating behaviors and racist experiences, and 124 of those women participated in the lab portion, Study 2, where they ate snacks as they engaged in an online social interaction with 3 other participants. Results indicate that although the in-lab manipulated experience of discrimination had numerous detrimental effects on psychological well-being, it did not influence the amount of food participants ate in the laboratory. Although many of the hypotheses were not supported, this study may provide procedural precedence for future restrained or emotional eating, racial microaggressions, or social ostracism studies. Results from this study also suggest several useful implications for obesity treatment and prevention programs

    Letter, W.D. Hayman to His Granddaughter, 1935

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    A letter written by W.D. Hayman to his grandaughter on August 9, 1935. This letter mentions another is being sent for Hughey P. Long

    On the nature of clear-air turbulence (CAT)

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    CER62ERR11.February 1962.Includes bibliographical references.Scientific interim report.Prepared for Navy Weather Research Facility N189(188)538-28A

    Computer managed learning system: annual report no. 1

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    April 1, 1970.CER69-70RWH-WL-WZS36.AN CMLS - 1 - 70

    Entire functions with Julia sets of positive measure

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    Let f be a transcendental entire function for which the set of critical and asymptotic values is bounded. The Denjoy-Carleman-Ahlfors theorem implies that if the set of all z for which |f(z)|>R has N components for some R>0, then the order of f is at least N/2. More precisely, we have log log M(r,f) > (N/2) log r - O(1), where M(r,f) denotes the maximum modulus of f. We show that if f does not grow much faster than this, then the escaping set and the Julia set of f have positive Lebesgue measure. However, as soon as the order of f exceeds N/2, this need not be true. The proof requires a sharpened form of an estimate of Tsuji related to the Denjoy-Carleman-Ahlfors theorem.Comment: 17 page

    The Schwarzian derivative and the Wiman-Valiron property

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    Consider a transcendental meromorphic function in the plane with finitely many critical values, such that the multiple points have bounded multiplicities and the inverse function has finitely many transcendental singularities. Using the Wiman-Valiron method it is shown that if the Schwarzian derivative is transcendental then the function has infinitely many multiple points, the inverse function does not have a direct transcendental singularity over infinity, and infinity is not a Borel exceptional value. The first of these conclusions was proved by Nevanlinna and Elfving via a fundamentally different method
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