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Algorithms for coupled Burgers’ equations by sharing characteristic curves within BSLM
This paper introduces a new perspective of the traditional view on the velocity of each physical particle in the coupled Burgers’ equation in the...
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1900s–1930s: Branch Curves and the Italian School of Algebraic Geometry
In contrast to the separate beginnings during the nineteenth century presented in the previous chapter, the twentieth century saw the consolidation...
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Rational points on conic bundles over elliptic curves
We study rational points on conic bundles over elliptic curves with positive rank over a number field. We show that the étale Brauer–Manin...
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Singularity swap quadrature for nearly singular line integrals on closed curves in two dimensions
This paper presents a quadrature method for evaluating layer potentials in two dimensions close to periodic boundaries, discretized using the...
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On the Weyl–Ahlfors theory of derived curves
For derived curves intersecting a family of decomposable hyperplanes in subgeneral position , we obtain an analog of the Cartan–Nochka Second Main...
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Results on esca** set of an entire function and its composition
Given two permutable entire functions f and g , we establish vital relationship between esca** sets of entire functions f , g and their composition....
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Distinguished Curves and First Integrals on Poincaré–Einstein and Other Conformally Singular Geometries
We treat the problem of defining, and characterising in a practical way, an appropriate class of distinguished curves for Poincaré-Einstein...
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A landing theorem for entire functions with bounded post-singular sets
The Douady-Hubbard landing theorem for periodic external rays is one of the cornerstones of the study of polynomial dynamics. It states that, for a...
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Counting tropical rational space curves with cross-ratio constraints
This is a follow-up paper of Goldner (Math Z 297(1–2):133–174, 2021), where rational curves in surfaces that satisfy general positioned point and...
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Riemann Surfaces and Algebraic Curves
The following proof uses as the main tools the classical theorem of Liouville that characterizes polynomials among entire holomorphic functions by a...
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1930s–1950s: Chisini’s Branch Curves: The Decline of the Classical Approach
We saw in the last chapter the influence that Enriques and Castelnuovo (and as a consequence, Zariski and B. Segre) had on the research on branch...
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Two dimensional neighborhoods of elliptic curves: analytic classification in the torsion case
We investigate the analytic classification of two dimensional neighborhoods of an elliptic curve with torsion normal bundle. We provide the complete...
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On length measures of planar closed curves and the comparison of convex shapes
In this paper, we revisit the notion of length measures associated to planar closed curves. These are a special case of area measures of...
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Invariant Curves of Almost Periodic Twist Map**s
In this paper we are concerned with the existence of invariant curves of planar twist map**s which are almost periodic in a spatial variable. As an...
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On a Class of Generalized Curve Flows for Planar Convex Curves
In this paper, the authors consider a class of generalized curve flow for convex curves in the plane. They show that either the maximal existence...
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Chabauty–Coleman Computations on Rank 1 Picard Curves
We provably compute the full set of rational points on 1403 Picard curves defined over...
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