392 research outputs found

    The Full Automorphism Group of a Cyclic pp-gonal Surface

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    If pp is prime, a compact Riemann surface XX of genus g2g\geq 2 is called cyclic pp-gonal if it admits a cyclic group of automorphisms CpC_{p} of order pp such that the quotient space X/CpX/C_{p} has genus 0. If in addition CpC_{p} is not normal in the full automorphism GG, then we call GG a non-normal cyclic pp-gonal group. In the following we classify all non-normal pp-gonal groups.Comment: 18 pages, 5 figure

    Mary in Three Movements

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    Mary in Three Movements is an imagined account of how Mary might have felt and observed her experiences through the three most important events of both Christian and human existence, the conception, the birth, and finally the death of her son. I have attempted to remain true to the biblical Marian references which primarily speak to Mary as a young woman in a first century patriarchal Roman Jewish society. Therefore, I have taken these three events and put them to verse for mezzo-soprano with piano accompaniment. The accompanying paper outlines both the historical and musical context in which this project was framed as well as a brief analysis of the harmonic and textual structure

    The minimal degree of plane models of double covers of smooth curves

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    If XX is a smooth curve such that the minimal degree of its plane models is not too small compared with its genus, then XX has been known to be a double cover of another smooth curve YY under some mild condition on the genera. However there are no results yet for the minimal degrees of plane models of double covers except some special cases. In this paper, we give upper and lower bounds for the minimal degree of plane models of the double cover XX in terms of the gonality of the base curve YY and the genera of XX and YY. In particular, the upper bound equals to the lower bound in case YY is hyperelliptic. We give an example of a double cover which has plane models of degree equal to the lower bound.Comment: 13 pages; Sharpened the main result (Theorem 3.8); Corrected some errors (Theorem 4.1); Final version to appear in JPA

    Measuring the effectiveness of Seattle’s seawall enhancements on juvenile salmon-an acoustic perspective

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    Seattle’s waterfront is a key migration route for juvenile Pacific salmon including: Chinook (Oncorhynchus tshawytscha), pink (Oncorhynchus gorbuscha), and chum (Oncorhynchus keta). The hardwired tendency of these salmon to inhabit nearshore waters results in close association with coastline urbanization, including piers and seawalls. Part of Seattle’s seawall was replaced in 2018 with enhancements intended to aid the movement and distribution of juvenile salmon. These enhancements include: light-penetrating glass blocks in the overhanging sidewalk to decrease shade in the water below, a bench along the seawall to restore shallow water depths, and textured seawall and shelves for invertebrate colonization. The objective of our research is to study the effectiveness of the seawall enhancements on improving juvenile salmon habitat. We used a high-frequency acoustic camera mounted to the hull of a kayak to quantify salmon and other fish population densities along enhanced and original seawall habitats. Acoustic surveys during April-August 2019 compared salmon distributions and densities 1) between enhanced and original seawall habitat and a reference beach, 2) during day and night, 3) by overhead structures with varying ambient light, and 4) compared to fish densities from snorkel surveys. Preliminary results suggest higher salmon densities occur in 1) enhanced seawall sites compared to old seawall sites and the reference beach, 2) new pier enhanced corridor compared to old piers, and 3) nighttime enhanced corridor compared to daytime. Two main implications are that the seawall enhancements are important to juvenile salmon both during the day and night, and that juvenile salmon may still navigate more around pier ends along the old seawall that is not enhanced. Results from this study can be used to evaluate the cost-benefit of fish-friendly coastal armoring for the next phase of Seattle’s seawall and at similar sites throughout the world

    Value-sharing of meromorphic functions on a Riemann surface

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    We present some results on two meromorphic functions from S to the Riemann sphere sharing a number of values where S is a Riemann surface of one of the following types: compact, compact minus finitely many points, the unit disk, a torus, the complex plane.Comment: 15 page

    Small linearly equivalent GG-sets and a construction of Beaulieu

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    Two GG-sets (GG a finite group) are called linearly equivalent over a commutative ring kk if the permutation representations k[X]k[X] and k[Y]k[Y] are isomorphic as modules over the group algebra kGkG. Pairs of linearly equivalent non-isomorphic GG-sets have applications in number theory and geometry. We characterize the groups GG for which such pairs exist for any field, and give a simple construction of these pairs. If kk is \Q, these are precisely the non-cyclic groups. For any non-cyclic group, we prove that there exist GG-sets which are non-isomorphic and \lineq over \Q, of cardinality \leq 3(#G)/2. Also, we investigate a construction of P. Beaulieu which allows us to construct pairs of transitive linearly equivalent SnS_n-sets from arbitrary GG-sets for an arbitrary group GG. We show that this construction works over all fields and use it construct, for each finite set \mc P of primes, SnS_n-sets linearly equivalent over a field kk if and only if the characteristic of kk lies in \mc P.Comment: v2: fixed proof of Lemma 2.

    Infinite-genus surfaces and the universal Grassmannian

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    Correlation functions can be calculated on Riemann surfaces using the operator formalism. The state in the Hilbert space of the free field theory on the punctured disc, corresponding to the Riemann surface, is constructed at infinite genus, verifying the inclusion of these surfaces in the Grassmannian. In particular, a subset of the class of OHDO_{HD} surfaces can be identified with a subset of the Grassmannian. The concept of flux through the ideal boundary is used to study the connection between infinite-genus surface and the domain of string perturbation theory. The different roles of effectively closed surfaces with Dirichlet boundaries in a more complete formulation of string theory are identified.Comment: 14 pages, TeX, 3 figures. The July, 1995 version contains an expanded introductio

    Abelian Functions for Cyclic Trigonal Curves of Genus Four

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    We discuss the theory of generalized Weierstrass σ\sigma and \wp functions defined on a trigonal curve of genus four, following earlier work on the genus three case. The specific example of the "purely trigonal" (or "cyclic trigonal") curve y3=x5+λ4x4+λ3x3+λ2x2+λ1x+λ0y^3=x^5+\lambda_4 x^4 +\lambda_3 x^3+\lambda_2 x^2 +\lambda_1 x+\lambda_0 is discussed in detail, including a list of some of the associated partial differential equations satisfied by the \wp functions, and the derivation of an addition formulae.Comment: 23 page

    Naturally occurring genotype 2b/1a hepatitis C virus in the United States

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    <p>Abstract</p> <p>Background</p> <p>Hepatitis C Virus (HCV) infected patients are frequently repeatedly exposed to the virus, but very few recombinants between two genotypes have been reported.</p> <p>Findings</p> <p>We describe the discovery of an HCV recombinant using a method developed in a United States clinical lab for HCV genotyping that employs sequencing of both 5' and 3' portions of the HCV genome. Over twelve months, 133 consecutive isolates were analyzed, and a virus from one patient was found with discordant 5' and 3' sequences suggesting it was a genotype 2b/1a recombinant. We ruled out a mixed infection and mapped a recombination point near the NS2/3 cleavage site.</p> <p>Conclusions</p> <p>This unique HCV recombinant virus described shares some features with other recombinant viruses although it is the only reported recombinant of a genotype 2 with a subtype 1a. This recombinant represents a conundrum for current clinical treatment guidelines, including treatment with protease inhibitors. This recombinant is also challenging to detect by the most commonly employed methods of genotyping that are directed primarily at the 5' structural portion of the HCV genome.</p
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