2,294 research outputs found

    Singular Points of Real Quartic and Quintic Curves

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    There are thirteen types of singular points for irreducible real quartic curves and seventeen types of singular points for reducible real quartic curves. This classification is originally due to D. A. Gudkov. There are nine types of singular points for irreducible complex quartic curves and ten types of singular points for reducible complex quartic curves. There are 42 types of real singular points for irreducible real quintic curves and 49 types of real singular points for irreducible real quintic curves. The classification of real singular points for irreducible real quintic curves is originally due to Golubina and Tai. There are 28 types of singular points for irreducible complex quintic curves and 33 types of singular points for reducible complex quintic curves. We derive the complete classification with proof by using the computer algebra system Maple. We clarify that the classification is based on computing just enough of the Puiseux expansion to separate the branches. Thus, the proof consists of a sequence of large symbolic computations that cam be done nicely using Maple

    Singular Points of Reducible Sextic Curves

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    There are 106 individual types of singular points for reducible complex sextic curves.</jats:p

    Singular Points of Real Sextic Curves I

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    A complete classiļ¬cation of the individual types of singular points is given for irreducible real sextic curves. This classiļ¬cation is derived by using the computer algebra system Maple. There are 191 types of singular points for real irreducible sextic curves. We clarify that the classiļ¬cation is based on computing just enough of the Puiseux expansion to separate the branches. A signiļ¬cant portion of the proof consists of a sequence of large symbolic computations that can be done nicely using Maple

    Singular Points of Reducible Sextic Curves

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    There are 106 individual types of singular points for reducible complex sextic curves.Comment: 11 page

    Improving the normalization of complex interventions: measure development based on normalization process theory (NoMAD): study protocol

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    &lt;b&gt;Background&lt;/b&gt; Understanding implementation processes is key to ensuring that complex interventions in healthcare are taken up in practice and thus maximize intended benefits for service provision and (ultimately) care to patients. Normalization Process Theory (NPT) provides a framework for understanding how a new intervention becomes part of normal practice. This study aims to develop and validate simple generic tools derived from NPT, to be used to improve the implementation of complex healthcare interventions.&lt;p&gt;&lt;/p&gt; &lt;b&gt;Objectives&lt;/b&gt; The objectives of this study are to: develop a set of NPT-based measures and formatively evaluate their use for identifying implementation problems and monitoring progress; conduct preliminary evaluation of these measures across a range of interventions and contexts, and identify factors that affect this process; explore the utility of these measures for predicting outcomes; and develop an online usersā€™ manual for the measures.&lt;p&gt;&lt;/p&gt; &lt;b&gt;Methods&lt;/b&gt; A combination of qualitative (workshops, item development, user feedback, cognitive interviews) and quantitative (survey) methods will be used to develop NPT measures, and test the utility of the measures in six healthcare intervention settings.&lt;p&gt;&lt;/p&gt; &lt;b&gt;Discussion&lt;/b&gt; The measures developed in the study will be available for use by those involved in planning, implementing, and evaluating complex interventions in healthcare and have the potential to enhance the chances of their implementation, leading to sustained changes in working practices

    A protective role for BRCA2 at stalled replication forks

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    The hereditary breast and ovarian cancer predisposition genes BRCA1 and BRCA2 account for the lion's share of heritable breast cancer risk in the human population. Loss of function of either gene results in defective homologous recombination (HR) and triggers genomic instability, accelerating breast tumorigenesis. A long-standing hypothesis proposes that BRCA1 and BRCA2 mediate HR following attempted replication across damaged DNA, ensuring error-free processing of the stalled replication fork. A recent paper describes a new replication fork protective function of BRCA2, which appears to collaborate with its HR function to suppress genomic instability
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