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We give a simple analytic criterion which characterizes linearizable 1-codimensional webs. Then we give an invariant geometrical interpretation of it, in term of projective connection. We explain then how our approach allows to study…

This paper presents a spline-based parameterisation framework for plane graphs. The plane graph is characterised by a collection of curves forming closed loops that fence-off planar faces which have to be parameterised individually. Hereby,…

When finding an original proof to a known result describing expansive mappings on compact metric spaces as surjective isometries, we reveal that relaxing the condition of compactness to total boundedness preserves the isometry property and…

We investigate the properties of a fairly large class of boundary conditions for the linearised Einstein equations in the Riemannian setting, ones which generalise the linearised counterpart of boundary conditions proposed by Anderson.…

In this work, we study the geodesics of the space of certain geometrically and physically motivated subspaces of the space of immersed curves endowed with a first order Sobolev metric. This includes elastic curves and also an extension of…

Any generalized distance-squared mapping of equidimensional case has singularities, and their singularity types are wrapped into mystery in higher dimensional cases. Any generalized distance-squared mapping of equidimensional case is not…

We present a novel way to apply the singularity confinement property as a discrete integrability criterion. We shall use what we call a full deautonomisation approach, which consists in treating the free parameters in the mapping as…

Establishing bounds on the accuracy achievable by localization techniques represents a fundamental technical issue. Bounds on localization accuracy have been derived for cases in which the position of an agent is estimated on the basis of a…

Current practice in parameter space exploration in euclidean space is dominated by randomized sampling or design of experiment methods. The biggest issue with these methods is not keeping track of what part of parameter space has been…

Following recent work by van der Hoeven and Lecerf (ISSAC 2017), we discuss the complexity of linear mappings, called untangling and tangling by those authors, that arise in the context of computations with univariate polynomials. We give a…

We study the complex Dulac map for a holomorphic foliation of the complex plane, near a non-degenerate singularity (both eigenvalues of the linearization are nonzero) with two separatrices. Following the well-known results of Y. Il'yashenko…

We derive two sets of explicit algebraic constraint preserving boundary conditions for the linearized BSSN system. The approach can be generalized to inhomogeneous differential and evolution conditions, the examples of which are given. The…

This paper considers generalizations of open mappings, closed mappings, pseudo-open mappings, and quotient mappings from topological spaces to generalized topological spaces. Characterizations of these classes of mappings are obtained and…

We study linearizability of actions of finite groups on cubic threefolds with non-isolated singularities.

The linear programming (LP) approach is, together with value iteration and policy iteration, one of the three fundamental methods to solve optimal control problems in a dynamic programming setting. Despite its simple formulation,…

An algorithmic method using conservation law multipliers is introduced that yields necessary and sufficient conditions to find invertible mappings of a given nonlinear PDE to some linear PDE and to construct such a mapping when it exists.…

We study hyperbolic systems of one-dimensional partial differential equations under general, possibly non-local boundary conditions. A large class of evolution equations, either on individual 1-dimensional intervals or on general networks,…

We study the statistical properties of piecewise expanding maps in the general setting of metric measure spaces. We provide sufficient conditions for exponential mixing of such systems with explicit estimates on the constants. We also…

In this note we study some properties of topological entropy for noncompact non-metrizable spaces.

We study the relationship between singularities of finite-dimensional integrable systems and singularities of the corresponding spectral curves. For the large class of integrable systems on matrix polynomials, which is a general framework…