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This paper is devoted to the study of unparameterized simple curves in the plane. We propose diverse canonical parameterizations of a 2D-curve. For instance, the arc-length parameterization is canonical, but we consider other natural…

We consider variational problems that model the bending behavior of curves that are constrained to belong to given hypersurfaces. Finite element discretizations of corresponding functionals are justified rigorously via Gamma-convergence.…

This paper shows how to build a formal analytical solution for a differential equation of arbitrary order and with variable coefficients. It proofs that the most known approximated solutions for such a problem can be derived from the…

The paper gives an overview of recent advances in structural equation modeling. A structural equation model is a multivariate statistical model that is determined by a mixed graph, also known as a path diagram. Our focus is on the…

This paper shows a finiteness property of a divisorial valuation in terms of arcs. First we show that every divisorial valuation over an algebraic variety corresponds to an irreducible closed subset of the arc space. Then we define the…

Real analytic generalized functions are investigated as well as the analytic singular support and analytic wave front of a generalized function in $\mathcal{G}(\Omega)$ are introduced and described.

Properties of the mappings \begin{align*} C&\mapsto\frac1{(2\pi i)^2}\int_{\Gamma_1}\int_{\Gamma_2}f(\lambda,\mu)\,R_{1,\,\lambda}\,C\, R_{2,\,\mu}\,d\mu\,d\lambda, C&\mapsto\frac1{2\pi i}\int_{\Gamma}g(\lambda)R_{1,\,\lambda}\,C\,…

We present a new notion of decomposition of semialgebraic sets by introducing a mode of irreducibility based on arc-analytic functions. The result is a refinement of the decomposition of such sets with respect to the Zariski topology as…

We prove local inequalities for analytic functions defined on a convex body in $\Re^{n}$ which generalize well-known classical inequalities for polynomials.

Topological transforms have been very useful in statistical analysis of shapes or surfaces without restrictions that the shapes are diffeomorphic and requiring the estimation of correspondence maps. In this paper we introduce two…

A classical result of variational analysis, known as Attouch theorem, establishes the equivalence between epigraphical convergence of a sequence of proper convex lower semicontinuous functions and graphical convergence of the corresponding…

We determine the convergence regions of certain local integrals on the moduli spaces of curves in neighborhoods of fixed stable curves in terms of the combinatorics of the corresponding graphs.

We give a characterization of the rational normal curve in terms of the rank function associated to a curve.

Parametric entities appear in many contexts, be it in optimisation, control, modelling of random quantities, or uncertainty quantification. These are all fields where reduced order models (ROMs) have a place to alleviate the computational…

This article shows a correspondence between abstract interpretation of imperative programs and the refinement calculus: in the refinement calculus, an abstract interpretation of a program is a specification which is a function. This…

We study a class of holomorphic matrix models. The integrals are taken over middle dimensional cycles in the space of complex square matrices. As the size of the matrices tends to infinity, the distribution of eigenvalues is given by a…

The action of ring automorphisms of the polynomial ring in two variables over the real numbers on real plane curves is considered. The orbits containing degree-three polynomials are computed, with one representative per orbit being…

We survey a few classes of analytic functions on the disk that have real boundary values almost everywhere on the unit circle. We explore some of their properties, various decompositions, and some connections these functions make to…

Given a finite number of samples of a continuous set-valued function F, mapping an interval to compact subsets of the real line, we develop good approximations of F, which can be computed efficiently.

For an elliptic curve E over an abelian extension k/K with CM by K of Shimura type, the L-functions of its [k:K] Galois representations are Mellin transforms of Hecke theta functions; a modular parametrization (surjective map) from a…