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

Update of the Unitarity Triangle Analysis

We present the status of the Unitarity Triangle Analysis (UTA), within the Standard Model (SM) and beyond, with experimental and theoretical inputs updated for the ICHEP 2010 conference. Within the SM, we find that the general consistency among all the constraints leaves space only to some tension (between the UTA prediction and the experimental measurement) in BR(B -> tau nu), sin(2 beta) and epsilon_K. In the UTA beyond the SM, we allow for New Physics (NP) effects in (Delta F)=2 processes. The hint of NP at the 2.9 sigma level in the B_s-\bar B_s mixing turns out to be confirmed by the present update, which includes the new D0 result on the dimuon charge asymmetry but not the new CDF measurement of phi_s, being the likelihood not yet released.Comment: 4 pages, 2 figures, Proceedings of the 35th International Conference of High Energy Physics - ICHEP2010 (July 22-28, 2010, Paris

Deep learning for inferring cause of data anomalies

Daily operation of a large-scale experiment is a resource consuming task, particularly from perspectives of routine data quality monitoring. Typically, data comes from different sub-detectors and the global quality of data depends on the combinatorial performance of each of them. In this paper, the problem of identifying channels in which anomalies occurred is considered. We introduce a generic deep learning model and prove that, under reasonable assumptions, the model learns to identify 'channels' which are affected by an anomaly. Such model could be used for data quality manager cross-check and assistance and identifying good channels in anomalous data samples. The main novelty of the method is that the model does not require ground truth labels for each channel, only global flag is used. This effectively distinguishes the model from classical classification methods. Being applied to CMS data collected in the year 2010, this approach proves its ability to decompose anomaly by separate channels.Comment: Presented at ACAT 2017 conference, Seattle, US

Синтез і дослідження антимікробних властивостей 5-R,R’-амінометиленпохідних тіазолідин- 2,4-діону та 4-тіоксотіазолідин-2-ону

The study is devoted to the rational search of modern potential antimicrobial agents among of 4-thiazolidine(thi)ones. 5-R,R’-Enamin(thi)ones of thiazolidinone series have been tested for design and the initial screening of the antibacterial properties. The use of 5-ethoxymetylene derivatives of thiazolidine-2,4-dione and 4-thioxothiazolidin-2-one as effective “building blocks” for the synthesis of small libraries of bioactive compounds has been proposed. Nucleophilic substitution reactions between 5-ethoxymetylene derivatives and amino alcohols, the primary and secondary functionalized aromatic and heteroaromatic amines, heterocyclic amines (piperidine and substituted pyrazolines) have been studied. The pharmacological screening of the antimicrobial activity for the enamin(thi)ones synthesized on clinical isolates of staphylococci with different resistance mechanisms to protected β-lactams and multiresistance strains of E. coli and Ps. Aeruginosa has been performed. Compounds with a distinct antimicrobial effect have been identified. They can also increase the sensitivity of S. aureus and S. haemolyticus clinical strains to oxacillin, and can be used to create new combined antimicrobial chemotherapeutic agents. The “structure – antimicrobial activity” relationships for design and search for new antimicrobial agents have been analysed.Исследование посвящено рациональному поиску современных потенциальных противомикробных агентов среди производных 4-тиазолидин(ти)онов. Для дизайна и первичного скрининга антибактериальных свойств апробированы 5-R,R’-енамин(ти)оны тиазолидинового ряда. Предложено использование 5-этоксиметилентиазолидин-2,4-диона и 4-тиоксотиазолидин-2-она как эффективных «структурных блоков» для синтеза малых библиотек биологически активных соединений. Изучены реакции нуклеофильного замещения 5-этоксиметилентиазолидинов с аминоспиртами, функционализированными первичными и вторичными ароматическими и гетероароматическими аминами, гетероциклическими аминами (пиперидин и замещенные пиразолины). Проведен фармакологический скрининг противомикробной активности синтезированных енаминов на клинических изолятах стафилококков с различными механизмами резистентности к защищенным β-лактамам и полиантибиотикорезистентных штаммах E. coli и Ps. Aeruginosa. Идентифицированы соединения с выразительным противомикробным эффектом, способные повышать чувствительность клинических штаммов S. Aureus и S. haemolyticus к оксациллину, что может быть использовано при создании новых комбинированных противомикробных химиотерапевтических средств. Проанализирована зависимость связей «структура – противомикробное действие» для направленного дизайна и поиска новых противомикробных агентов.Дослідження присвячене раціональному пошуку сучасних потенційних антимікробних агентів серед похідних 4-тіазолідин(ті)онів. Здійснено спробу дизайну та первинного скринінгу антибактеріальних препаратів на основі 5-R,R’-єнамін(ті)онів тіазолідинового ряду. Запропоновано використання 5-етоксиметилентіазолідин-2,4-діону та 4-тіоксотіазолідин-2-ону як ефективних «структурних блоків» для синтезу малих бібліотек біологічно активних сполук. Вивчені реакції нуклеофільного заміщення 5-етоксиметилентіазолідинонів з аміноспиртами, функціоналізованими первинними і вторинними ароматичними та гетероароматичними амінами, гетероциклічними амінами (піперидин та заміщені піразоліни). Проведено фармакологічний скринінг антимікробної активності синтезованих єнамінів щодо клінічних ізолятів стафілококів з різними механізмами резистентності до захищених β-лактамів та поліантибіотикорезистентних штамів E. coli і Ps. Aeruginosa. Ідентифіковані сполуки з виразним антимікробним ефектом, здатні підвищувати чутливість клінічних штамів S. aureus і S. Haemolyticus до оксациліну, що може бути використано при створенні нових комбінованих антимікробних хіміотерапевтичних засобів. Проаналізовано залежність зв’язків «структура – антимікробна активність» для спрямованого дизайну та пошуку нових антибактеріальних і протигрибкових агентів

Orthogonal polynomials of discrete variable and Lie algebras of complex size matrices

We give a uniform interpretation of the classical continuous Chebyshev's and Hahn's orthogonal polynomials of discrete variable in terms of Feigin's Lie algebra gl(N), where N is any complex number. One can similarly interpret Chebyshev's and Hahn's q-polynomials and introduce orthogonal polynomials corresponding to Lie superlagebras. We also describe the real forms of gl(N), quasi-finite modules over gl(N), and conditions for unitarity of the quasi-finite modules. Analogs of tensors over gl(N) are also introduced.Comment: 25 pages, LaTe

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

Schrödinger operators with δ and δ′-potentials supported on hypersurfaces

Self-adjoint Schrödinger operators with δ and δ′-potentials supported on a smooth compact hypersurface are defined explicitly via boundary conditions. The spectral properties of these operators are investigated, regularity results on the functions in their domains are obtained, and analogues of the Birman–Schwinger principle and a variant of Krein’s formula are shown. Furthermore, Schatten–von Neumann type estimates for the differences of the powers of the resolvents of the Schrödinger operators with δ and δ′-potentials, and the Schrödinger operator without a singular interaction are proved. An immediate consequence of these estimates is the existence and completeness of the wave operators of the corresponding scattering systems, as well as the unitary equivalence of the absolutely continuous parts of the singularly perturbed and unperturbed Schrödinger operators. In the proofs of our main theorems we make use of abstract methods from extension theory of symmetric operators, some algebraic considerations and results on elliptic regularity

Standard Model updates and new physics analysis with the Unitarity Triangle fit

International audienceWe present the update of the Unitarity Triangle (UT) analysis performed by the UTfit Collaboration within the Standard Model (SM) and beyond. Within the SM, combining the direct measurements on sides and angles, the UT turns out to be over-constrained in a consistent way, with some tension due to recently included contributions to the theoretical prediction of εK and the updated lattice average for BK. Generalising the UT analysis to investigate NP effects, constraints on b→s transitions are also included and both CKM and NP parameters are fitted simultaneously. The most interesting results on the b→s transitions come from the Bs−¯ Bs mixing and the di-muon charge asymmetry with updated results recently available from the Tevatron experiments. We observe a departure from the SM in the Bs sector

The Unitarity Triangle Analysis within and beyond the Standard Model

International audienceWe present the status of the Unitarity Triangle Analysis (UTA) performed by the UTfit Collaboration, with experimental and theoretical inputs updated for the last summer conferences. Several analyses are presented, corresponding to different assumptions for the theoretical model, that is either the Standard Model, or Minimal Flavour Violation orc ompletely generic NewPhysics