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Confocal conics and 4-webs of maximal rank
Confocal conics form an orthogonal net. Supplementing this net with one of the following: (1) the net of Cartesian coordinate lines aligned along the...
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On the formal principle for curves on projective surfaces
We prove that the formal completion of a complex projective surface along a rigid smooth curve with trivial normal bundle determines the birational...
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Point and Contact Transformations
In an introductory course in PDEs we found that by introducing new variables (4.1)...
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Exceptional Webs
This last chapter is devoted to planar webs of maximal rank. More specifically, it surveys the current state of the art concerning exceptional planar...
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Convergence Rate for a Gauss Collocation Method Applied to Unconstrained Optimal Control
A local convergence rate is established for an orthogonal collocation method based on Gauss quadrature applied to an unconstrained optimal control...
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The Converse to Abel’s Theorem
The main result of this chapter is a converse to Abel’s addition Theorem stated in Sect. 4.1. It ensures the algebraicity of local datum satisfying...
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Algebraization of Maximal Rank Webs
This chapter is devoted to the following result.
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On Rank Problems for Planar Webs and Projective Structures
We present some old and recent results on rank problems and linearizability of geodesic planar webs.
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Abelian equations and rank problems for planar webs
We find an invariant characterization of planar webs of maximum rank. For 4-webs, we prove that a planar 4-web is of maximum rank three if and only...
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SCIP: solving constraint integer programs
Constraint integer programming (CIP) is a novel paradigm which integrates constraint programming (CP), mixed integer programming (MIP), and satisfiability...
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On the Blaschke conjecture for 3-webs
We find relative differential invariants of orders eight and nine for a planar nonparallelizable 3-web such that their vanishing is necessary and...
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Abelian functional equations, planar web geometry and polylogarithms
We study some abelian functional equations
(Afe) . They are equations in the F i ’s of the form F 1 ( U 1 ) + ... + F N ( U N ) = 0 where the U ... -
Linearizability of d-webs, d ≥ 4, on two-dimensional manifolds
We find d − 2 relative differential invariants for a d -web, d ≥ 4, on a two-dimensional manifold and prove that their vanishing is necessary and...
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Information-equivalence: On Filtrations Created by Independent Increments
This article investigates filtrations created by the increments-processes of processes with independent increments: Suppose two processes create the...
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4-Webs in the Plane and Their Linearizability
We investigate the linearizability problem for different classes of 4-webs in the plane. In particular, we apply the linearizability conditions,...