Non-scattering wavenumbers and far field invisibility for a finite set of incident/scattering directions

We investigate a time harmonic acoustic scattering problem by a penetrable inclusion with compact support embedded in the free space. We consider cases where an observer can produce incident plane waves and measure the far field pattern of the resulting scattered field only in a finite set of directions. In this context, we say that a wavenumber is a non-scattering wavenumber if the associated relative scattering matrix has a non trivial kernel. Under certain assumptions on the physical coefficients of the inclusion, we show that the non-scattering wavenumbers form a (possibly empty) discrete set. Then, in a second step, for a given real wavenumber and a given domain D, we present a constructive technique to prove that there exist inclusions supported in D for which the corresponding relative scattering matrix is null. These inclusions have the important property to be impossible to detect from far field measurements. The approach leads to a numerical algorithm which is described at the end of the paper and which allows to provide examples of (approximated) invisible inclusions.Comment: 20 pages, 7 figure

Научные подходы к диагностике социо-эколого-экономической устойчивости приморских регионов

На основе научных подходов предложена методика, позволяющая опреде-лить уровень социо-эколого-экономической устойчивости приморских ре-гионов. На основе использования системы показателей, характеризующих уровень социо-эколого-экономической устойчивости региона, сформули-рованы и предложены основные направления реализации методики опре-деления интегрального показателя уровня устойчивости приморской территории в социальном, экономическом и экологическом развитии.Based on the scientific approaches proposed technique allows to deter-mine the level of social, ecological and economic sustainability of coastal re-gions. On the basis of a system of indicators characterizing the level of social, ecological and economic sustainability of the region, formulate and propose guidelines implementation methodology for determining the integral indicator of the sustainability of the coastal territory in the social, economic and envi-ronmental development

Петрологічні дослідження в Україні: досягнення останніх десятиліть та нагальні проблеми

Викладено основні досягнення за останні 30–35 років українських геологів, в першу чергу — наукових працівників ІГМР ім. М. П. Семененка НАН України в області петрології. Висвітлені такі проблеми: 1 — метаморфізм, співвідношення грануліто-гнейсових і граніт-зеленокам’яних терейнів; 2 — чарнокіти; 3 — гранітоутворення та гранітоїдні формації; 4 — анортозит-рапаківігранітна формація; 5 — лужні породи; 6 — коматиїти; 7 — санукітоїди; 8 — метасоматоз; 9 — породоутворювальні та акцесорні мінерали; 10 — формаційний аналіз, петрологія та стратиграфія докембрію; 11 — фанерозойський магматизм; 12 — магматизм морського та океанічного дна; 13 — деякі нагальні проблеми.Изложены основные достижения за последние 30–35 лет украинских геологов, в первую очередь — научных сотрудников ИГМР им. Н. П. Семененко НАН Украины в области петрологии. Освещены такие проблемы: 1 — метаморфизм, соотношение гранулито-гнейсовых и гранит-зеленокаменных террейнов; 2 — чарнокиты; 3 — гранитообразование и гранитоидные формации; 4 — анортозит-рапакивигранитная формация; 5 — щелочные породы; 6 — коматииты; 7 — санукитоиды; 8 — метасоматоз; 9 — породообразующие и акцессорные минералы; 10 — формационный анализ, петрология и стратиграфия докембрия; 11 — фанерозойский магматизм; 12 — магматизм морского и океанического дна; 13 — некоторые насущные проблемы.Main achievements of Ukrainian geologists for the recent 30–35 years have been stated. In the first place the scientific results of petrologists of M. P. Semenenko Institute of Geochemistry, Mineralogy and Ore Formation of NAS of Ukraine. The following problems have been elucidated: 1 — metamorphism; interrelation of granulite-gneissic and granite-greenstone terrains; 2 — charnokites; 3 — granite formation and granitoid formations; 4 — anorthosite-rapakivi-granite formation; 5 — alkaline rocks; 6 — komatiites; 7 — sanukitoids; 8 — metasomatosis; 9 — rock-forming and accessory minerals; 10 — formation analysis, petrology and Precambrian stratigraphy; 11 — Phanerozoic magmatism; 12 — magmatism of the sea and ocean bottom; 13 — some current problems

On the use of Perfectly Matched Layers at corners for scattering problems with sign-changing coefficients

International audienceWe investigate in a 2D setting the scattering of time-harmonic electromagnetic waves by a plasmonic device, represented as a non dissipative bounded and penetrable obstacle with a negative permittivity. Using the $\texttt{T}$-coercivity approach, we first prove that the problem is well-posed in the classical framework $H^1_{loc}$ if the negative permittivity does not lie in some critical interval whose definition depends on the shape of the device. When the latter has corners, for values inside the critical interval, unusual strong singularities for the electromagnetic field can appear. In that case, well-posedness is obtained by imposing a radiation condition at the corners to select the outgoing black-hole plasmonic wave, that is the one which carries energy towards the corners. A simple and systematic criterion is given to define what is the outgoing solution. Finally, we propose an original numerical method based on the use of Perfectly Matched Layers at the corners. We emphasize that it is necessary to design an $\textit{ad hoc}$ technique because the field is too singular to be captured with standard finite element methods

Self-medication with over-the-counter analgesics : a survey of patient characteristics and concerns about pain medication

Pain is a common reason for self-medication with over-the-counter (OTC) analgesics. However, this self-treating population has remained largely uncharacterized. This cross-sectional observational study investigated individuals who self-medicate their pain with OTC analgesics to elucidate their pain characteristics and medication use. In addition, presence of and risk factors for concerns about pain medication were examined. The clinical profile of the participants (n = 1,889) was worse than expected with long-standing pain complaints (median pain duration of 9 years), pain located at multiple body sites (median of 4, and 13% with ≥10 painful body areas), about one-third suffering from daily pain and about 40% experiencing substantial pain-related disability. Head (58.6% of sample), low back (43.6%), and neck (30.7%) were the most common pain locations. About 73% had a physician diagnosis, mainly migraine and osteoarthritis. Paracetamol (used by 68.6% of patients) and nonsteroidal anti-inflammatory drugs (46.8%) were the most frequently used pain medications. About 40% of our sample showed substantial concern about the perceived need for pain medication and the perceived potential for harmful effects (eg, fear for addiction). These findings highlight the importance for health professionals to systematically probe pain patients about their self-medication practices and explore attitudes about pain medication. Perspective: This study found that the clinical picture of people who self-medicate their pain with OTC analgesics looked worse than expected. We also identified substantial concerns about pain medication. Therefore, we recommend that health professionals systematically probe pain patients about their self-medication practices and explore concerns about pain medication. © 2018 the American Pain Societ