Related papers: On the EIT problem for nonorientable surfaces

We present a novel approach for the inverse problem in electrical impedance tomography based on regularized quadratic regression. Our contribution introduces a new formulation for the forward model in the form of a nonlinear integral…

We numerically construct the spectrum of the Laplacian on Page's inhomogeneous Einstein metric on $\mathbb{CP}^2 \# \overline{\mathbb{CP}}^2$ by reducing the problem to a (singular) Sturm-Liouville problem in one dimension. We perform a…

In this paper, we present a discussion on the algorithms design of Electrical Impedance Tomography (EIT) for biomedical applications. Based on the Maxwell differential equations and the derived the finite element(FE) linear equations, we…

The tilted-wave interferometer is a promising technique for the development of a reference measurement system for the highly accurate form measurement of aspheres and freeform surfaces. The technique combines interferometric measurements,…

Let $(M,g)$ be a compact $n$-dimensional Riemannian manifold without boundary and $e_\lambda$ be an $L^2$-normalized eigenfunction of the Laplace-Beltrami operator with respect to the metric $g$, i.e \[ -\Delta_g e_\lambda = \lambda^2…

We characterize the observability property (and, by duality, the controllability and the stabilization) of the wave equation on a Riemannian manifold $\Omega,$ with or without boundary, where the observation (or control) domain is…

Let $G=(V,E)$ be a locally finite graph, $\Omega\subset V$ be a bounded domain, $\Delta$ be the usual graph Laplacian, and $\lambda_1(\Omega)$ be the first eigenvalue of $-\Delta$ with respect to Dirichlet boundary condition. Using the…

We study closed orientable surfaces satisfying the spectral condition $\lambda_1(-\Delta+\beta K)\geq\lambda\geq0$, where $\beta$ is a positive constant and $K$ is the Gauss curvature. This condition naturally arises for stable minimal…

Hybrid inverse problems such as Acousto-Electric Tomography, Current Density Imaging or Magnetic Resonance Electric Impedance Tomography are concerned with reconstructing the electrical conductivity from interior measurements. For a…

Let $\Omega$ be an open set in Euclidean space $\R^m,\, m=2,3,...$, and let $v_{\Omega}$ denote the torsion function for $\Omega$. It is known that $v_{\Omega}$ is bounded if and only if the bottom of the spectrum of the Dirichlet Laplacian…

This thesis is concerned with the application of operadic methods, particularly modular operads, to questions arising in the study of moduli spaces of surfaces as well as applications to the study of homotopy algebras and new constructions…

Let $(E,\|.\|)$ be a Banach space and let $(\Omega,\mu)$ be a Lebesgue measure space. We characterize, for all $p>0$, measurable functions $u:\Omega\rightarrow \mathbb{R}$ for which \begin{equation*} \left\| \int_{\Omega} f\,d\mu…

In this paper we develop theoretical analysis and numerical reconstruction techniques for the solution of an inverse boundary value problem dealing with the nonlinear, time-dependent monodomain equation, which models the evolution of the…

The incompressible Euler equations on a compact Riemannian manifold $(M,g)$ take the form \begin{align*} \partial_t u + \nabla_u u &= - \mathrm{grad}_g p \mathrm{div}_g u &= 0. \end{align*} We show that any quadratic ODE $\partial_t y =…

We show uniqueness for overdetermined elliptic problems defined on topological disks $\Omega$ with $C^2$ boundary, i.e., positive solutions $u$ to $\Delta u + f(u)=0$ in $\Omega \subset (M^2,g)$ so that $u = 0$ and $\frac{\partial…

Let $\Omega $ be a bounded domain in $\mathbb{R} ^N $, and let $u\in C^1 (\overline{\Omega }) $ be a weak solution of the following overdetermined BVP: $-\nabla (g(|\nabla u|)|\nabla u|^{-1} \nabla u )=f(|x|,u)$, $ u>0 $ in $\Omega $ and…

Let $(M,g)$ be a closed, connected and orientable Riemannian manifold with nonnegative Ricci curvature. Consider a Lagrangian $L(x,v):TM\to\R$ defined by $L(x,v):=\frac 12g_x(v,v)-\omega(v)+c$, where $c\in\R$ and $\omega$ is a closed…

Structural identifiability analysis of fractional-order equivalent circuit models (FO-ECMs), obtained through electrochemical impedance spectroscopy (EIS) is still a challenging problem. No peer-reviewed analytical or numerical proof does…

Let $\Omega \subseteq \mathbb{R}^d$ be open, $A$ a complex uniformly strictly accretive $d\times d$ matrix-valued function on $\Omega$ with $L^\infty$ coefficients, and $V$ a locally integrable function on $\Omega$ whose negative part is…

For a given smooth compact manifold $M$, we introduce an open class $\mathcal G(M)$ of Riemannian metrics, which we call \emph{metrics of the gradient type}. For such metrics $g$, the geodesic flow $v^g$ on the spherical tangent bundle $SM…