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Michele Cook 《Compositio Mathematica》1998,111(2):221-244
In this paper we will give necessary conditions for a Borel-fixed monomial ideal to be the generic initial ideal of a reduced, irreducible, non-degenerate curve in P3. 相似文献
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Peter Stadler 《Journal of Difference Equations and Applications》2018,24(5):812-824
AbstractOn complete Riemannian manifolds, a geodesic linking two different points could be approximated by applying short ruler methods to shorten a given path iteratively. In this paper we take a closer look at a short ruler method on a cone. To handle the problems caused by the fact that the cone is not smooth at its apex, we unwind the cone isometrically into the plane, and show that the sequence of shortened curves converges to a geodesic. 相似文献
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The aim of this paper is to present a new graphical approach to the shape design of the active magnetic bearing (AMB) stator. The AMB is a tool to levitate the rotor without contact. The standard design method uses a computer-aided design (CAD) software in the modeling process. Therefore the designed AMB shape consists of graphical primitives like lines and arcs with fixed properties. For the advanced interdisciplinary analysis of the AMB construction the shape generation and modifications ought to be done automatically. The proposed method is based on mathematical analysis and representation of the AMB stator by curves. Second and third order Bézier curves given in polynomial and rational form are compared to the circle and arc based arcs. The fitting quality is considered for the selection of the appropriate arc representation. The obtained shapes are ready to be used in the magnetic field analysis and optimization procedures to find an optimal form of the AMB construction. The author’s experience in modeling and vector graphics was a motivation to look at the AMB construction from mathematical and programming point of view. The AMB components are modeled with parametric curves under constraints defined by the AMB static and dynamic properties. Such a described 2D or 3D model can be generated automatically in a programming way for a wide range of AMB configurations in further research. Selected configurations are presented to show features of the proposed method and realized algorithm. The selected features of the proposed solution as well as feedback from industry are discussed. 相似文献
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Julian J. Faraway 《Journal of computational and graphical statistics》2013,22(1):60-68
Abstract In a longitudinal study, individuals are observed over some period of time. The investigator wishes to model the responses over this time as a function of various covariates measured on these individuals. The times of measurement may be sparse and not coincident across individuals. When the covariate values are not extensively replicated, it is very difficult to propose a parametric model linking the response to the covariates because plots of the raw data are of little help. Although the response curve may only be observed at a few points, we consider the underlying curve y(t). We fit a regression model y(t) = x Tβ(t) + ε(t) and use the coefficient functions β(t) to suggest a suitable parametric form. Estimates of y(t) are constructed by simple interpolation, and appropriate weighting is used in the regression. We demonstrate the method on simulated data to show its ability to recover the true structure and illustrate its application to some longitudinal data from the Panel Study of Income Dynamics. 相似文献
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Yerko Torres-Nova 《Journal of Pure and Applied Algebra》2021,225(1):106465
Let be integers. A generalized Fermat curve of type is a compact Riemann surface S that admits a subgroup of conformal automorphisms isomorphic to , such that the quotient surface is biholomorphic to the Riemann sphere and has branch points, each one of order k. There exists a good algebraic model for these objects, which makes them easier to study. Using tools from algebraic topology and integration theory on Riemann surfaces, we find a set of generators for the first homology group of a generalized Fermat curve. Finally, with this information, we find a set of generators for the period lattice of the associated Jacobian variety. 相似文献