1,721,105 research outputs found
Reconstruction of cracks and material losses by perimeter-like penalizations and phase-field methods: Numerical results
No full textWe numerically implement the variational approach for reconstruction in the inverse crack and cavity problems developed by one of the authors. The method is based on a suitably adapted freediscontinuity problem. Its main features are the use of phase-field functions to describe the defects to be reconstructed and the use of perimeter-like penalizations to regularize the ill-posed problem. The numerical implementation is based on the solution of the corresponding optimality system by a gradient method. Numerical simulations are presented to show the validity of the method. © European Mathematical Society 2011
Ownership and performance in the Italian stock exchange: the puzzle of family firms
Full text linkWe present new evidence on the relationship between ownership, control and performance in family firms, by using a sample of Italian publicly listed companies from 2000 to 2017. We account for the potential self-selection bias of family firms with an endogenous treatment selection model. We do not find consistent evidence of a performance premium of Italian family firms or family CEOs as family firms achieve superior profitability, but lower market to book ratios. Interestingly, however, firm value is negatively impacted when the high controlling shares are disjointed from family ownership and when the family CEO is also Chair of the board. We also find that the equity stake is significantly lower when the CEO is a member of the controlling family, suggesting a trade-off between ownership and control within family firms
Product Market Competition, Executive Compensation, and CEO Family Ties
Full text linkThis paper analyzes the interaction between product market competition and family ties on the structure of CEO pay, in a panel of publicly listed family firms. To account for the multi-dimensional nature of competition we use a variety of measures. We find that in industries where import penetration is high, products are differentiated or domestic concentration is high, family CEOs’ variable pay is lower than is professional CEOs’ variable pay; but the former is more closely related to firm performance. This result remains strong when we account for the equity component of compensation and for endogeneity concerns and when we test the hypothesis of family CEOs’ “pay for luck”. Our findings suggest that: (1) competition is likely to substitute incentive pay in homogeneous product markets and to complement them in differentiated industries and in markets that are open to international trade; and (2) product market characteristics are more important than are family ties in shaping managerial compensation
Mosco convergence of Sobolev spaces and Sobolev inequalities for nonsmooth domains
No full textWe find extremely general classes of nonsmooth open sets which guarantee Mosco convergence for corresponding Sobolev spaces and the validity of Sobolev inequalities with a uniform constant. An important feature of our results is that the conditions we impose on the open sets for Mosco convergence and for the Sobolev inequalities are of the same nature, therefore it is easy to check when both are satisfied. Our analysis is motivated, in particular, by the study of the stability of the direct acoustic scattering problem with respect to the scatterer, which we also discuss. Concerning Mosco convergence in dimension 3 or higher, our result extends all those previously known in the literature. Concerning Sobolev inequalities, our approach seems to be new and considerably simplifies the conditions previously required for the stability of acoustic direct scattering problems
Uniqueness for the determination of sound-soft defects in an inhomogeneous planar medium by acoustic boundary measurements
Full text linkWe consider the inverse problem of determining shape and location of sound-soft defects inside a known planar inhomogeneous and anisotropic medium through acoustic imaging at low frequency. In order to determine the defects, we perform acoustic boundary measurements, with prescribed boundary conditions of different types. We prove that at most two, suitably chosen, measurements allow us to uniquely determine multiple defects under minimal regularity assumptions on the defects and the medium containing them. Finally, we treat applications of these results to the case of inverse scattering
Stable determination of sound-soft polyhedral scatterers by a single measurement
Full text linkWe prove optimal stability estimates for the determination of a finite number of sound-soft polyhedral scatterers in R^3 by a single far-field measurement. The admissible multiple polyhedral scatterers satisfy minimal a priori assumptions of Lipschitz type and may include at the same time obstacles, screens and even more complicated scatterers. We characterize any multiple
polyhedral scatterer by a size parameter h which is related to the minimal size of the cells of its boundary. In a first step we show that, provided the error epsilon on the far-field measurement is small enough with respect to h, then the corresponding error, in the Hausdorff distance, on the multiple polyhedral scatterer can be controlled by an explicit function of epsilon which approaches zero,
as epsilon goes to 0, in an essentially optimal, although logarithmic, way. Then, we show how to improve this stability estimate, provided we restrict our attention to multiple polyhedral obstacles and epsilon is even smaller with respect to h. In this case we obtain an explicit estimate essentially of Hoelder type
Interior decay of solutions to elliptic equations with respect to frequencies at the boundary
Full text linkWe prove decay estimates in the interior for solutions to elliptic equations in divergence form with Lipschitz continuous coefficients. The estimates explicitly depend on the distance from the boundary and on suitable notions of frequency of the Dirichlet boundary datum. We show that, as the frequency at the boundary grows, the square of a suitable norm of the solution in a compact subset of the domain decays in an inversely proportional manner with respect to the corresponding frequency. Under Lipschitz regularity assumptions, these estimates are essentially optimal and have important consequences for the choice of optimal measurements for corresponding inverse boundary value problems
Reconstruction in the inverse crack problem by variational methods
No full textWe deal with a variational approach to the inverse crack problem, that is the detection and reconstruction of cracks, and other defects, inside a conducting body by performing boundary
measurements of current and voltage type. We formulate such an inverse problem in a free-discontinuity problems framework and propose a novel method for the numerical reconstruction
of the cracks by the available boundary data. The proposed method is amenable to numerical computations and it is justified by a convergence analysis, as the error on the measurements
goes to zero. We further notice that we use the Gamma-convergence approximation of the Mumford–Shah functional due to Ambrosio and Tortorelli as the required regularization term
Reconstruction of material losses by perimeter penalization and phase-field methods
Full text linkWe treat the inverse problem of determining material losses, such as cavities, in a conducting body, by performing electrostatic measurements at the boundary. We develop a numerical approach, based on variational methods, to reconstruct the unknown material loss by a single boundary measurement of current and voltage type.
The method is based on the use of phase-field functions to model the material losses and on a perimeter-like penalization to regularize the otherwise ill-posed problem. We justify the proposed approach by a convergence result, as the error on the measurement goes to zero
A variational approach to the reconstruction of cracks by boundary measurements
Full text linkWe consider a conducting body which presents some (unknown) perfectly insulating defects, such as cracks or cavities, for instance. We aim to reconstruct the defects by performing measurements of current and voltage type on a (known and accessible) part of the boundary of the conductor. A crucial step in this reconstruction is the determination of the electrostatic
potential inside the conductor, by the electrostatic boundary measurements performed. Since the defects are unknown,
we state such a determination problem as a free-discontinuity problem for the electrostatic potential in the framework of special functions of bounded variation. We provide a characterisation of the looked for electrostatic potential and we approximate it with the minimum points of a sequence of functionals, which take also in account the error in the measurements. These functionals are related to the so-called Mumford-Shah functional, which acts as a regularizing term and allows us to prove existence of minimizers and Gamma-convergence properties
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