Search results for "35"
showing 10 items of 2413 documents
A machine learning approach to determine airport asphalt concrete layer moduli using heavy weight deflectometer data
2021
An integrated approach based on machine learning and data augmentation techniques has been developed in order to predict the stiffness modulus of the asphalt concrete layer of an airport runway, from data acquired with a heavy weight deflectometer (HWD). The predictive model relies on a shallow neural network (SNN) trained with the results of a backcalculation, by means of a data augmentation method and can produce estimations of the stiffness modulus even at runway points not yet sampled. The Bayesian regularization algorithm was used for training of the feedforward backpropagation SNN, and a k-fold cross-validation procedure was implemented for a fair performance evaluation. The testing p…
A radiation condition for the 2-D Helmholtz equation in stratified media
2009
We study the 2-D Helmholtz equation in perturbed stratified media, allowing the existence of guided waves. Our assumptions on the perturbing and source terms are not too restrictive. We prove two results. Firstly, we introduce a Sommerfeld-Rellich radiation condition and prove the uniqueness of the solution for the studied equation. Then, by careful asymptotic estimates, we prove the existence of a bounded solution satisfying our radiation condition.
Monotonicity and local uniqueness for the Helmholtz equation
2017
This work extends monotonicity-based methods in inverse problems to the case of the Helmholtz (or stationary Schr\"odinger) equation $(\Delta + k^2 q) u = 0$ in a bounded domain for fixed non-resonance frequency $k>0$ and real-valued scattering coefficient function $q$. We show a monotonicity relation between the scattering coefficient $q$ and the local Neumann-Dirichlet operator that holds up to finitely many eigenvalues. Combining this with the method of localized potentials, or Runge approximation, adapted to the case where finitely many constraints are present, we derive a constructive monotonicity-based characterization of scatterers from partial boundary data. We also obtain the local…
Dimension bounds in monotonicity methods for the Helmholtz equation
2019
The article [B. Harrach, V. Pohjola, and M. Salo, Anal. PDE] established a monotonicity inequality for the Helmholtz equation and presented applications to shape detection and local uniqueness in inverse boundary problems. The monotonicity inequality states that if two scattering coefficients satisfy $q_1 \leq q_2$, then the corresponding Neumann-to-Dirichlet operators satisfy $\Lambda(q_1) \leq \Lambda(q_2)$ up to a finite-dimensional subspace. Here we improve the bounds for the dimension of this space. In particular, if $q_1$ and $q_2$ have the same number of positive Neumann eigenvalues, then the finite-dimensional space is trivial. peerReviewed
An optimal Poincaré-Wirtinger inequality in Gauss space
2013
International audience; Let $\Omega$ be a smooth, convex, unbounded domain of $\mathbb{R}^N$. Denote by $\mu_1(\Omega)$ the first nontrivial Neumann eigenvalue of the Hermite operator in $\Omega$; we prove that $\mu_1(\Omega) \ge 1$. The result is sharp since equality sign is achieved when $\Omega$ is a $N$-dimensional strip. Our estimate can be equivalently viewed as an optimal Poincaré-Wirtinger inequality for functions belonging to the weighted Sobolev space $H^1(\Omega,d\gamma_N)$, where $\gamma_N$ is the $N$% -dimensional Gaussian measure.
A sharp lower bound for some neumann eigenvalues of the hermite operator
2013
This paper deals with the Neumann eigenvalue problem for the Hermite operator defined in a convex, possibly unbounded, planar domain $\Omega$, having one axis of symmetry passing through the origin. We prove a sharp lower bound for the first eigenvalue $\mu_1^{odd}(\Omega)$ with an associated eigenfunction odd with respect to the axis of symmetry. Such an estimate involves the first eigenvalue of the corresponding one-dimensional problem. As an immediate consequence, in the class of domains for which $\mu_1(\Omega)=\mu_1^{odd}(\Omega)$, we get an explicit lower bound for the difference between $\mu(\Omega)$ and the first Neumann eigenvalue of any strip.
Deformation quantization of covariant fields
2002
After sketching recent advances and subtleties in classical relativistically covariant field theories, we give in this short Note some indications as to how the deformation quantization approach can be used to solve or at least give a better understanding of their quantization.
Assessing Master Students' Competencies Using Rubrics: Lessons Learned from Future Secondary Education Teachers
2020
The aim of this paper is to provide insights into the appropriateness of teaching-learning and evaluation processes using rubrics, for student self-assessments. We studied students enrolled on the Master&rsquo
Business Ethics as a Sustainability Challenge: Higher Education Implications
2018
Recent financial scandals worldwide have intensified concern for business (and especially accounting) ethics. Hence, under an overall economic and social sustainability approach, it is crucial to improve the effectiveness of business ethics and corporate social responsibility (CSR) education, in terms of its impact on business students&rsquo
Universities' Reporting on SDGs: Using THE Impact Rankings to Model and Measure Their Contribution to Sustainability
2021
Higher education institutions (HEIs) have voiced growing concerns about sustainability issues since Agenda 2030 was approved, but this is not enough for societal stakeholders seeking and delivering innovation and excellence. The 17 Sustainable Development Goals (SDGs) were adopted by all UN Member States in 2015 as a universal call to action, and pose a challenge for HEIs as for the efforts made to fulfill them and knowing how to assess their performance. However, the metric management system implemented by HEIs quickly led to rankings emerging, which compare HEIs to metrics not related to the sustainability dimensions of the 17 SDGs. The main aim of the paper is to assess the level of repo…