T
+34 946 567 842
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+34 946 567 842
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fponce@bcamath.org
Information of interest
 Orcid: 0000000210499752
I work on topics motivated by problems in aerospace engineering. I collaborate with researchers at the Aeronautics Advanced Manufacturing Center  CFAA, Basque Country Technology Park, Zamudio.
Currently, I am interested in modelling, monitoring and control of machining processes, like drilling or Electrical Discharge Machining.

SemiAnalytical Estimation for the Escape of Solutions of Linear Differential Equations with Slowly Varying Coefficients
(2024)Emerging vibrations are a major and often unpredictable limitation in engineering design. The engineering description of these vibrations is usually based on linear models with constant parameters. However, in reality, ...

On C0 and C1 continuity of envelopes of rotational solids and its application to 5axis CNC machining
(202310)We study the smoothness of envelopes generated by motions of rotational rigid bodies in the context of 5axis Computer Numerically Controlled (CNC) machining. A moving cutting tool, conceptualized as a rotational solid, ...

The Frisch–Parisi formalism for fluctuations of the Schrödinger equation
(2022)We consider the solution of the Schrödinger equation $u$ in $\mathbb{R}$ when the initial datum tends to the Dirac comb. Let $h_{\text{p}, \delta}(t)$ be the fluctuations in time of $\int\lvert x \rvert^{2\delta}\lvert ...

Counterexamples for the fractal Schrödinger convergence problem with an Intermediate Space Trick
(20211209)We construct counterexamples for the fractal Schrödinger convergence problem by combining a fractal extension of Bourgain's counterexample and the intermediate space trick of DuKimWangZhang. We confirm that the same ...

Pointwise Convergence over Fractals for Dispersive Equations with Homogeneous Symbol
(20210824)We study the problem of pointwise convergence for equations of the type $i\hbar\partial_tu + P(D)u = 0$, where the symbol $P$ is real, homogeneous and nonsingular. We prove that for initial data $f\in H^s(\mathbb{R}^n)$ ...

Static and Dynamical, Fractional Uncertainty Principles
(202103)We study the process of dispersion of lowregularity solutions to the Schrödinger equation using fractional weights (observables). We give another proof of the uncertainty principle for fractional weights and use it to get ...

Convergence over fractals for the Schrödinger equation
(202101)We consider a fractal refinement of the Carleson problem for the Schrödinger equation, that is to identify the minimal regularity needed by the solutions to converge pointwise to their initial data almost everywhere with ...

A Bilinear Strategy for Calderón’s Problem
(202005)Electrical Impedance Imaging would suffer a serious obstruction if two different conductivities yielded the same measurements of potential and current at the boundary. The Calderón’s problem is to decide whether the ...

A Bilinear Strategy for Calderón's Problem
(201908)Electrical Impedance Imaging would suffer a serious obstruction if for two different conductivities the potential and current measured at the boundary were the same. The Calder\'on's problem is to decide whether the ...

Reconstruction of the Derivative of the Conductivity at the Boundary
(201908)We describe a method to reconstruct the conductivity and its normal derivative at the boundary from the knowledge of the potential and current measured at the boundary. This boundary determination implies the uniqueness ...