Lipschitz stability of an inverse boundary value problem for a Schr\"{o}dinger type equation

In this paper we study the inverse boundary value problem of determining the potential in the Schr\"{o}dinger equation from the knowledge of the Dirichlet-to-Neumann map, which is commonly accepted as an ill-posed problem in the sense that, under general settings, the optimal stability estimate is of logarithmic type. In this work, a Lipschitz type stability is established assuming a priori that the potential is piecewise constant with a bounded known number of unknown values

Inverse boundary value problem for the Helmholtz equation: quantitative conditional Lipschitz stability estimates

We study the inverse boundary value problem for the Helmholtz equation using the Dirichlet-to-Neumann map at selected frequencies as the data. A conditional Lipschitz stability estimate for the inverse problem holds in the case of wavespeeds that are a linear combination of piecewise constant functions (following a domain partition) and gives a framework in which the scheme converges. The stability constant grows exponentially as the number of subdomains in the domain partition increases. We establish an order optimal upper bound for the stability constant. We eventually realize computational experiments to demonstrate the stability constant evolution for three dimensional wavespeed reconstruction.Comment: 21 pages, 7 figures. arXiv admin note: text overlap with arXiv:1406.239

Stable determination of polyhedral interfaces from boundary data for the Helmholtz equation

We study an inverse boundary value problem for the Helmholtz equation using the Dirichlet-to-Neumann map as the data. We consider piecewise constant wavespeeds on an unknown tetrahedral partition and prove a Lipschitz stability estimate in terms of the Hausdorff distance between partitions

Paediatric endodontics. Part. 1: Portland Cements Apical Plug

Treatment of necrotic immature permanent anterior teeth with Portland cements apical plug. The long-term success of endodontic treatment depends on the quality of the apical and coronal seal. In necrotic immature teeth the treatment can be challenging for the clinician as the endodontic anatomy and the presence of bacterial infection need to be addressed with special techniques and materials in order to obtain an effective and biocompatible apical seal. Unfortunately, despite the best treatments, immature permanent teeth have a reduced resistance to fracture due to the arrest of root walls development

H2 from biofuels and carriers: A concerted homo-heterogeneous kinetic model of ethanol partial oxidation and steam reforming on Rh/Al2O3

Investigating bioethanol as a renewable energy source is crucial in the context of H2-based economy. Ethanol partial oxidation and steam reforming on Rh/Al2O3 represent promising processes that have already proved to be highly tangled reacting systems. In this work, a significant step forward has been done towards the development of an engineering tool that can capture all the relevant features of the process; a combined homo-heterogeneous kinetic scheme was developed and validated against experimental data, informative of the catalytic and thermal activation of the C2-alcohol. In particular, a 36-species reduced homogeneous scheme was developed, able to cap -ture observed trends with a limited computational load. On the other side, a macro-kinetic heterogeneous scheme with six molecular reactions (ethanol oxidative dehydrogenation, total oxidation, decomposition, dehydrogenation, steam reforming and acetaldehyde post -reforming) was tuned to accurately describe ethanol/O2 and ethanol/H2O reacting systems.& COPY; 2023 Hydrogen Energy Publications LLC. Published by Elsevier Ltd. All rights reserved

Efficient Hardware Design Of Iterative Stencil Loops

A large number of algorithms for multidimensional signals processing and scientific computation come in the form of iterative stencil loops (ISLs), whose data dependencies span across multiple iterations. Because of their complex inner structure, automatic hardware acceleration of such algorithms is traditionally considered as a difficult task. In this paper, we introduce an automatic design flow that identifies, in a wide family of bidimensional data processing algorithms, sub-portions that exhibit a kind of parallelism close to that of ISLs; these are mapped onto a space of highly optimized ad-hoc architectures, which is efficiently explored to identify the best implementations with respect to both area and throughput. Experimental results show that the proposed methodology generates circuits whose performance is comparable to that of manually-optimized solutions, and orders of magnitude higher than those generated by commercial HLS tools