ABSTRACT
We show novel types of uniqueness and rigidity results for Schrödinger equations in either the nonlinear case or in the presence of a complex-valued potential. As our main result we obtain that the trivial solution u = 0 is the only solution for which the assumptions u ( t = 0 ) | D = 0 , u ( t = T ) | D = 0 hold, where D â R d are certain subsets of codimension one. In particular, D is discrete for dimension d = 1 . Our main theorem can be seen as a nonlinear analogue of discrete Fourier uniqueness pairs such as the celebrated Radchenko-Viazovska formula in [21], and the uniqueness result of the second author and M. Sousa for powers of integers [22]. As an additional application, we deduce rigidity results for solutions to some semilinear elliptic equations from their zeros.
ABSTRACT
CERN-MEDICIS is an off-line isotope separator facility for the extraction of radioisotopes from irradiated targets of interest to medical applications. The beamline, between the ion source and the collection chamber, consists of ion extraction and focusing elements, and a dipole magnet mass spectrometer recovered from the LISOL facility in Louvain-la-Neuve. The latter has been modified for compatibility with MEDICIS, including the installation of a window for injecting laser light into the ion source for resonance photo-ionization. Ion beam optics and magnetic field modeling using SIMION and OPERA respectively were performed for the design and characterization of the beamline. The individual components and their optimal configuration in terms of ion beam extraction, mass separation, and ion transport efficiency is described, along with details of the commissioning and initial performance assessment with stable ion beams.
ABSTRACT
The CERN-MEDICIS (MEDical Isotopes Collected from ISolde) facility has delivered its first radioactive ion beam at CERN (Switzerland) in December 2017 to support the research and development in nuclear medicine using non-conventional radionuclides. Since then, fourteen institutes, including CERN, have joined the collaboration to drive the scientific program of this unique installation and evaluate the needs of the community to improve the research in imaging, diagnostics, radiation therapy and personalized medicine. The facility has been built as an extension of the ISOLDE (Isotope Separator On Line DEvice) facility at CERN. Handling of open radioisotope sources is made possible thanks to its Radiological Controlled Area and laboratory. Targets are being irradiated by the 1.4 GeV proton beam delivered by the CERN Proton Synchrotron Booster (PSB) on a station placed between the High Resolution Separator (HRS) ISOLDE target station and its beam dump. Irradiated target materials are also received from external institutes to undergo mass separation at CERN-MEDICIS. All targets are handled via a remote handling system and exploited on a dedicated isotope separator beamline. To allow for the release and collection of a specific radionuclide of medical interest, each target is heated to temperatures of up to 2,300°C. The created ions are extracted and accelerated to an energy up to 60 kV, and the beam steered through an off-line sector field magnet mass separator. This is followed by the extraction of the radionuclide of interest through mass separation and its subsequent implantation into a collection foil. In addition, the MELISSA (MEDICIS Laser Ion Source Setup At CERN) laser laboratory, in service since April 2019, helps to increase the separation efficiency and the selectivity. After collection, the implanted radionuclides are dispatched to the biomedical research centers, participating in the CERN-MEDICIS collaboration, for Research & Development in imaging or treatment. Since its commissioning, the CERN-MEDICIS facility has provided its partner institutes with non-conventional medical radionuclides such as Tb-149, Tb-152, Tb-155, Sm-153, Tm-165, Tm-167, Er-169, Yb-175, and Ac-225 with a high specific activity. This article provides a review of the achievements and milestones of CERN-MEDICIS since it has produced its first radioactive isotope in December 2017, with a special focus on its most recent operation in 2020.
ABSTRACT
The ß--particle-emitting erbium-169 is a potential radionuclide toward therapy of metastasized cancer diseases. It can be produced in nuclear research reactors, irradiating isotopically-enriched 168Er2O3. This path, however, is not suitable for receptor-targeted radionuclide therapy, where high specific molar activities are required. In this study, an electromagnetic isotope separation technique was applied after neutron irradiation to boost the specific activity by separating 169Er from 168Er targets. The separation efficiency increased up to 0.5% using resonant laser ionization. A subsequent chemical purification process was developed as well as activity standardization of the radionuclidically pure 169Er. The quality of the 169Er product permitted radiolabeling and pre-clinical studies. A preliminary in vitro experiment was accomplished, using a 169Er-PSMA-617, to show the potential of 169Er to reduce tumor cell viability.
ABSTRACT
Delimitation and classification of each heart sound is a rather difficult task. Elevated heart rates, as found in pediatrics and in some adults as well, influence some of the most reliable features used by existing methods. Furthermore, in real life scenarios, cardiologists will not have the time to acquire the signal's length required by some of the existing algorithms, which make us think that different approaches ought to be pursued. This paper presents the work on heart sound segmentation using structural and energy based features. It is an attempt to not rely on features considered crucial to most existing approaches. Yet, it achieves a high sensitivity and specificity comparable to some literature.
