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While computational thinking arises as an essential skill worldwide, formal primary and secondary education in Latin America rarely incorporates mechanisms to develop it in their curricula. The extent to which students in the region acquire computational thinking skills remains largely unknown. To start addressing this void, this article presents findings from a cross-sectional study that characterizes the computational thinking abilities of incoming students at a Chilean university with a strong emphasis on STEM disciplines. Based on more than 500 responses, this study provides evidence of significant inequalities in computational thinking across gender, type of school (private or no), and prior programming knowledge. The discussion offers insights into how these disparities relate to contextual factors of the country, such as a highly socio-economically segregated educational system, public policies focused mainly on technology access, and heavy reliance on voluntary initiatives, to develop computational thinking. The findings can enlighten upcoming research endeavors and formulate strategies to create a more equitable field for students entering STEM degrees in nations facing similar circumstances., Comment: Pre-print. Final version published in: IEEE Transactions on Education

In this paper, we study the existence of solutions to the scalar additive Jump problem and the Riemann boundary value problems in the context of vectorial Clifford analysis on domains with fractal boundaries. A reduction procedure is applied with great effectiveness to find the solution of the problems.

We use a high-dimensional version of the Marcinkiewicz exponent, a metric characteristic for non-rectifiable plane curves, to present a direct application to the solution of some kind of Riemann boundary value problems on fractal domains of Euclidean space $\mathbb{R}^{n+1}, n\geq2$ for Clifford algebra-valued polymonogenic functions with boundary data in classes of higher order Lipschitz functions. Sufficient conditions to guarantee the existence and uniqueness of solution to the problems are proved. To illustrate the delicate nature of this theory we described a class of hypersurfaces where the results are more refined than those that exist in literature.

A well-known boundary observability inequality for the elasticity system establishes that the energy of the system can be estimated from the solution on a sufficiently large part of the boundary for a sufficiently large time. This inequality is relevant in different contexts as the exact boundary controllability, boundary stabilization, or some inverse source problems. Here we show that a corresponding boundary observability inequality for the spectral collocation approximation of the linear elasticity system in a d-dimensional cube also holds, uniformly with respect to the discretization parameter. This property is essential to prove that natural numerical approaches to the previous problems based on replacing the elasticity system by collocation discretization will give successful approximations of the continuous counterparts.

We propose a spectral collocation method to approximate the exact boundary control of the wave equation in a square domain. The idea is to introduce a suitable approximate control problem that we solve in the finite-dimensional space of polynomials of degree N in space. We prove that we can choose a sequence of discrete controls depending on the parameter N associated with the approximate control problem in such a way that they converge, as N goes to infinity, to a control of the continuous wave equation. Unlike other numerical approximations tried in the literature, this one does not require regularization techniques and can be easily adapted to other equations and systems where the controllability of the continuous model is known. The method is illustrated with several examples in 1-d and 2-d in a square domain. We also give numerical evidence of the highly accurate approximation inherent to spectral methods.

This paper aims to study the jump problem for monogenic functions in fractal hypersurfaces of Euclidean spaces. The notion of the Marcinkiewicz exponent has been taken into consideration. A new solvability condition is obtained, basing the work on specific properties of the Teodorescu transform in Clifford analysis. It is shown that this condition improves those involving the Minkowski dimension.

In this work we illustrate a number of properties of the Born approximation in the three-dimensional Calder\'on inverse conductivity problem by numerical experiments. The results are based on an explicit representation formula for the Born approximation recently introduced by the authors. We focus on the particular case of radial conductivities in the ball $B_R \subset \mathbb{R}^3 $ of radius $R$, in which the linearization of the Calder\'on problem is equivalent to a Hausdorff moment problem. We give numerical evidences that the Born approximation is well defined for $L^{\infty}$ conductivities, and we present a novel numerical algorithm to reconstruct a radial conductivity from the Born approximation under a suitable smallness assumption. We also show that the Born approximation has depth-dependent uniqueness and approximation capabilities depending on the distance (depth) to the boundary $\partial B_R$. We then investigate how increasing the radius $R$ affects the quality of the Born approximation, and the existence of a scattering limit as $R\to \infty$. Similar properties are also illustrated in the inverse boundary problem for the Schr\"odinger operator $-\Delta +q$, and strong recovery of singularity results are observed in this case., Comment: 31 pages, 15 figures

Measurements of the radius and limb brightening of the Sun provide important information about the solar atmosphere structure and temperature. The solar radius increases as the observation at radio frequency decreases, indicating that each emission originates higher in the atmosphere. Thus, different layers of the solar atmosphere can be probed by observing at multiple wavelengths. In this work, we determined the average radius and limb brightening at 100, 212, 230, and 405 GHz, using data from the Solar Submillimeter Telescope and ALMA's single-dish observations. For the first time, limb brightening values for frequencies of 212 and 405 GHz were estimated. At sub-THz frequencies, the observed limb brightening may affect the solar radius measurements. We use two different and well known approaches to determine the radius: the half-power method and the inflection-point method. We investigate how the antenna beam size and the limb brightening level, LB, can affect the radius measurements using both methods. Our results showed that the inflection-point method is the least affected by these parameters, and should thus be used for solar radius estimates at radio wavelengths. The measured average radii are 968"~$\pm$~3" (100 GHz), 963"~$\pm$~3" (212 GHz), 963"~$\pm$~2" (230 GHz), and 963"~$\pm$~5" (405 GHz). Finally, we used forward modeling to estimate the ranges of LB of the solar disk resulting in 5%-19% (100 GHz), 2%-12% (212 GHz), 6%-18% (230 GHz), and 3%-17% (405 GHz). Both radius and limb brightening estimates agree with previous measurements reported in the literature.

Uniqueness and reconstruction in the three-dimensional Calder\'on inverse conductivity problem can be reduced to the study of the inverse boundary problem for Schr\"odinger operators $-\Delta +q $. We study the Born approximation of $q$ in the ball, which amounts to studying the linearization of the inverse problem. We first analyze this approximation for real and radial potentials in any dimension $d\ge 3$. We show that this approximation satisfies a closed formula that only involves the spectrum of the Dirichlet-to-Neumann map associated to $-\Delta + q$, which is closely related to a particular moment problem. We then turn to general real and essentially bounded potentials in three dimensions and introduce the notion of averaged Born approximation, which captures the exact invariance properties of the inverse problem. We obtain explicit formulas for the averaged Born approximation in terms of the matrix elements of the Dirichlet to Neumann map in the basis spherical harmonics. To show that the averaged Born approximation does not destroy information on the potential, we also study the high-energy behavior of the matrix elements of the Dirichlet to Neumann map., Comment: 36 pages. Changes from v1: updated references, simplified notation for more precision in the statement of theorems 1 and 3 and other minor modifications

In this work, we study the Schr\"odinger equation $i\partial_t\psi=-\Delta\psi+\eta(t)\sum_{j=1}^J\delta_{x=a_j(t)}\psi$ on $L^2((0,1),C)$ where $\eta:[0,T]\longrightarrow R^+$ and $a_j:[0,T]\longrightarrow (0,1)$, $j=1,...,J$. We show how to permute the energy associated to different eigenmodes of the Schr\"odinger equation via suitable choice of the functions $\eta$ and $a_j$. To the purpose, we mime the control processes introduced in [17] for a very similar equation where the Dirac potential is replaced by a smooth approximation supported in a neighborhood of $x=a(t)$. We also propose a Galerkin approximation that we prove to be convergent and illustrate the control process with some numerical simulations.

We propose a numerical method to approximate the scattering amplitudes for the elasticity system with a non-constant matrix potential in dimensions $d=2$ and $3$. This requires to approximate first the scattering field, for some incident waves, which can be written as the solution of a suitable Lippmann-Schwinger equation. In this work we adapt the method introduced by G. Vainikko in \cite{V} to solve such equations when considering the Lam\'e operator. Convergence is proved for sufficiently smooth potentials. Implementation details and numerical examples are also given.