Boundary relations and generalized resolvents of symmetric operators

The Kre\u{\i}n-Naimark formula provides a parametrization of all selfadjoint exit space extensions of a, not necessarily densely defined, symmetric operator, in terms of maximal dissipative (in \dC_+) holomorphic linear relations on the parameter space (the so-called Nevanlinna families). The new notion of a boundary relation makes it possible to interpret these parameter families as Weyl families of boundary relations and to establish a simple coupling method to construct the generalized resolvents from the given parameter family. The general version of the coupling method is introduced and the role of boundary relations and their Weyl families for the Kre\u{\i}n-Naimark formula is investigated and explained.Comment: 47 page

Generalized boundary triples, I. Some classes of isometric and unitary boundary pairs and realization problems for subclasses of Nevanlinna functions

© 2020 The Authors. Mathematische Nachrichten published by Wiley‐VCH Verlag GmbH & Co. KGaA. This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited.fi=vertaisarvioitu|en=peerReviewed

Formation of radiation-disturbed layer in Al/SiO2/n-Si structures irradiated with helium ions with energy 5 MeV

This paper presents the change in the volt-farad characteristics of the Al/SiO2/n-Si structure irradiated with helium ions with the energy of 5 MeV in the frequencies of 1, 10, 100, and 1000 kHz. The voltage dependence of the capacitance and the frequency dependence of the dissolution angle are measured on an LCR Agilent E4980A and Agilent 4285A meter. The hodograph of the irradiated structure shows that there is a formation of a quasi-continuous radiation-disturbed layer at a fluence of 1012 cm–2 with U < –7 V and 1013 cm–2 with U < –20 V, which enhances the speed of charged particles, thereby increasing the reverse current in the irradiated structure

On Biomedical Computations in Cluster and Cloud Environment

The experience of the use of applied containerized biomedical software tools in cloud environment is summarized. The reproducibility of scientific computing in relation to modern technologies of scientific calculations is discussed. The main approaches to biomedical data preprocessing and integration in the framework of the intelligent analytical system are described.Мета роботи. Опис сучасних технологій, що забезпечують відтворюваність чисельних експериментів у цій галузі, та інструментів, спрямованих на інтеграцію декількох джерел біомедичної інформації з метою поліпшення діагностики і прогнозу складних захворювань. Особлива увага приділяється методам обробки даних, отриманих з різних джерел біомедичної інформації і включеним до складу інтелектуальної аналітичної системи. Отримані результати. Узагальнено досвід використання прикладних контейнерних біомедичних програмних засобів у хмарному середовищі. Обговорюється відтворюваність наукових обчислень і можливості сучасних технологій наукових обчислень. Описано основні підходи до попередньої обробки та інтеграції біомедичних даних у рамках інтелектуальної аналітичної системи. Розроблена модель гібридної класифікації є основою інтелектуальної аналітичної системи і спрямована на інтеграцію декількох джерел біомедичної інформації.Цель работы. Описание современных технологий, обеспечивающих воспроизводимость численных экспериментов в этой области, и инструментов, направленных на интеграцию нескольких источников биомедицинской информации с целью улучшения диагностики и прогноза сложных заболеваний. Особое внимание уделяется методам обработки данных, полученных из разных источников биомедицинской информации и включенным в состав интеллектуальной аналитической системы. Полученные результаты. Обобщен опыт использования прикладных контейнерных биомедицинских программных средств в облачной среде. Обсуждается воспроизводимость научных вычислений и возможности современных технологий научных вычислений. Описаны основные подходы к предварительной обработке и интеграции биомедицинских данных в рамках интеллектуальной аналитической системы. Разработанная модель гибридной классификации представляет собой основу интеллектуальной аналитической системы и направлена на интеграцию нескольких источников биомедицинской информации

Linking Catastrophe Modeling and Stochastic Optimization Techniques for Integrated Catastrophe Risk Analysis and Management

Planning regional economic developments and social welfare without addressing issues related to mitigation and adaptation to low probability-high consequences catastrophe risks may lead to dangerous clustering of people, production facilities, and infrastructure in hazard-prone areas thereby critically increasing regional vulnerability. The endogeneity of the risks on production allocation and land use decisions represents new challenges for regional sustainable development planning. This chapter argues that catastrophe risk analysis and management have to be addressed with an Integrated Assessment and Management Model (IAMM) linking catastrophe risk modeling (CRM) with stochastic optimization (STO) techniques for the design of optimal and robust mitigation and adaptation strategies for dealing with catastrophe risks of all kinds. IAMM enables us to address the challenging characteristics on policies, mutually dependent losses, the lack of information, the need for long-term perspectives and geographically explicit models, the involvement of various agents (such as individuals, farmers, producers, consumers, governments, insurers, investors), safety and security standards, and the need for robust decisions. Safety and security criteria relate to Value-at-Risk and Conditional Value at Risk measures generalizing the well-known risk criteria and indicators used for regulating engineering, critical infrastructure, energy, water, agricultural safety and security requirements. These are key indicators for dealing with low probability-high consequences risks. The linkage between CRM and STO is established through an iterative stochastic quasigradient procedure (SQG) defining a sequential “searching” process, which resembles an adaptive learning environment and improvement of decisions from data and simulations, i.e., the so-called Adaptive Monte Carlo optimization. The SQG methods are applicable in cases when traditional stochastic approximation, gradient or stochastic gradient methods do not work, in particular, to general two-stage problems with implicitly defined goals and constraints functions, nonsmooth and possibly discontinuous performance indicators, risk and uncertainties shaped by decision of various agents

Effects of Fluences of Irradiation with 107 MeV Krypton Ions on the Recovery Charge of Silicon p+np^{+}n-Diodes

The diodes manufactured on the wafers of single-crystalline silicon uniformly doped with phosphorus are studied. The wafer resistivity was 90 Ω cm. Krypton ions are implanted to the side of the $p^{+}$-region of diodes (energy 107 MeV, fluence Φp from 5 × $10^7$ to 4 × $10^9 cm^{-2}$). It is shown that recovery charge $Q_{rr}$ is inversely proportional to the square root of the irradiation fluence value Φp. When the fluence increases, the part of the recovery charge Q_{rrA}, due to the high reverse conductance phase, decreases faster than the value $Q_{rr}$

Influence of Defects Introduced by Irradiation with 4-9 MeV Helium Ions on Impedance of Silicon Diodes

Silicon diodes irradiated with helium ions with energies of 4.1, 6.8 and 8.9 MeV are studied. It is shown that the mechanism determining the behaviour of frequency dependence of complex electric module and correspondingly the behavior of impedance of diodes irradiated with helium ions in the frequency region 3-200 kHz is a recharging of vacancy complexes localized in the space charge region

Current-Voltage Characteristic Features of Diodes Irradiated with 170~MeV Xenon Ions

Diodes manufactured on the wafers of single-crystalline silicon uniformly doped with phosphorus are studied. The wafer resistivity was 90 Ω cm. Xenon ions were implanted into the diodes from the side of the $p^{+}$-region (implantation energy 170 MeV, fluence Φp from $5 \times 10^7$ to $10^9 cm^{-2}$). It is shown that the formation of a continuous irradiation damaged layer with the thickness of the order of magnitude of the average projective range creates prerequisites for the negative differential resistance in the current-voltage characteristics of the irradiated diodes

Advanced pulse EPR study of natural Mongolian coals

EPR spectra of the studied coals were registered as the first derivative of the microwave absorption versus applied magnetic field. The parameters of the EPR spectra: g-factor, linewidth and integral intensity were evaluated. As mentioned above lower group coals and high rank coals from upper group are declined to the asymmetry and the appearance of dip in the field swept. Consequently, the phenomenon could be assigned to the coal different maceral types that have different spin-spin relaxation times. The relaxation times for the coals have been measured in a few cases. It is well known that relaxation times determine both saturation and linewidth. Coal spin-lattice time, T1, relates with the coal spin concentration and molecular motion and the coal spin-spin relaxation time, T2, relates to the linewidth. The results of T1 and T2 relaxation times of some coals are shown as dependences of linewidth and the elements contents. For the characterization of the paramagnetic species in coal, we have also applied hyperfine sublevel correlation spectroscopy (HYSCORE) method. This method enhances the frequency resolution of the spectrum that makes possible to observe hyperfine structure under the symmetrical, singlet, broad EPR signals.Белорусский Республиканский Фонд Фундаментальных Исследовани