Titlebook: Handbook of Geometry and Topology of Singularities V: Foliations; Felipe Cano,José Luis Cisneros-Molina,José Seade Book 2024 The Editor(s)

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Newton Polygon, with exponents in subgroups of . as coefficients. In booth cases we pointed up the possibility of the use valuations as solution of equations. The author wishes to thank to the referee for his (many) precise and detailed corrections that have improved this paper.

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conflate

Rolle Models in the Real and Complex World,solutions” of systems of equations, defined by algebraic equalities and differential equations with algebraic right hand sides (both ordinary and Pfaffian). In the purely algebraic context the paradigm is given by the Bézout theorem: the number of isolated solutions of a system of polynomial equatio

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Newton Polygon,equations. We first study the application of Newton’s polygon to algebraic equations with coefficients in a valued field, showing the limitations of its use for valuations of rank greater than one. The . is the key to have explicit solutions for the rank one case. For differential equations, the lac

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Closed Meromorphic 1-Forms,ry, like index theorems, existence of separatrices, and resolution of singularities under the lenses of the theory of closed meromorphic 1-forms and flat meromorphic connections. We apply the theory to investigate the algebraicity of separatrices in a semi-global setting (neighborhood of a compact c

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r describing them on the basis of a score. Individual therapy planning is possible. More treatment tends to produce better function scores and thus helps to lower the strain on the joint. Further study is required in order to determine whether this reduces the incidence of bleeding. Knee function is

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Bruno Scárduahilia treaters..Total joint replacement therapy in severe hemophilic arthropathy is possible without major bleeding complications and results in better quality of life due to pain reduction and reduction of bleeding frequency. In comparison to patients without hemophilia the results after total join