Application of “piercing the corporate veil” doctrine in the Ukrainian law

Purpose: In the article, authors develop a structure of applying the gaps of corporate law and the possibility of restricting all possible structures of the legal field in Ukraine. The functioning of corporate law is always exercised according to the principle of the company’s greatest possible involvement in the employee’s everyday life. There is always differentiation emerging, which determines to what extent the existence of corporate spirit and ethics are needed within the society. Design/Methodology/Approach: The method of comparative law was used as the subject of the study, which enabled us to compare the customary rules of law with specific corporate law rules. Additionally, it is appropriate to apply the historical method, which fully reflects that the article elaborates the historical aspect of the development of the studied phenomenon as well as the formation of the holistic component. Findings: The article implements the aspects of managing the legal regulation of corporate law on the basis of modernizing separate provisions of the legal area of a social environment. Practical Implications: The perspectives of applying the corporate law provisions in the state’s economic development can be defined as the conclusions of the study. Originality/Value: The authors clearly demonstrate the obligation to implement the provision that stipulates that the corporate law, in case its principles are violated, has still to be oriented at understanding the specificity of its application in commercial institutions.peer-reviewe

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

Boundary Conditions for Singular Perturbations of Self-Adjoint Operators

Let A:D(A)\subseteq\H\to\H be an injective self-adjoint operator and let \tau:D(A)\to\X, X a Banach space, be a surjective linear map such that \|\tau\phi\|_\X\le c \|A\phi\|_\H. Supposing that \text{\rm Range} (\tau')\cap\H' =\{0\}, we define a family $A^\tau_\Theta$ of self-adjoint operators which are extensions of the symmetric operator $A_{|\{\tau=0\}.}$. Any $\phi$ in the operator domain $D(A^\tau_\Theta)$ is characterized by a sort of boundary conditions on its univocally defined regular component \phireg, which belongs to the completion of D(A) w.r.t. the norm \|A\phi\|_\H. These boundary conditions are written in terms of the map $\tau$, playing the role of a trace (restriction) operator, as \tau\phireg=\Theta Q_\phi, the extension parameter $\Theta$ being a self-adjoint operator from X' to X. The self-adjoint extension is then simply defined by A^\tau_\Theta\phi:=A \phireg. The case in which $A\phi=T*\phi$ is a convolution operator on LD, T a distribution with compact support, is studied in detail.Comment: Revised version. To appear in Operator Theory: Advances and Applications, vol. 13

Using machine learning to speed up new and upgrade detector studies: a calorimeter case

In this paper, we discuss the way advanced machine learning techniques allow physicists to perform in-depth studies of the realistic operating modes of the detectors during the stage of their design. Proposed approach can be applied to both design concept (CDR) and technical design (TDR) phases of future detectors and existing detectors if upgraded. The machine learning approaches may speed up the verification of the possible detector configurations and will automate the entire detector R\&D, which is often accompanied by a large number of scattered studies. We present the approach of using machine learning for detector R\&D and its optimisation cycle with an emphasis on the project of the electromagnetic calorimeter upgrade for the LHCb detector\cite{lhcls3}. The spatial reconstruction and time of arrival properties for the electromagnetic calorimeter were demonstrated.Comment: Talk presented on CHEP 2019 conferenc

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

Bitangential interpolation in generalized Schur classes

Bitangential interpolation problems in the class of matrix valued functions in the generalized Schur class are considered in both the open unit disc and the open right half plane, including problems in which the solutions is not assumed to be holomorphic at the interpolation points. Linear fractional representations of the set of solutions to these problems are presented for invertible and singular Hermitian Pick matrices. These representations make use of a description of the ranges of linear fractional transformations with suitably chosen domains that was developed in a previous paper.Comment: Second version, corrected typos, changed subsection 5.6, 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

Spin-dependent recombination mechanisms for quintet bi-excitons generated through singlet fission

We investigate the physical mechanisms for spin-dependent recombination of a strongly bound pair of triplet excitons generated by singlet fission and forming a spin quintet (total spin of two) bi-exciton. For triplet excitons the spin-dependent recombination pathways can involve intersystem crossing or triplet-triplet annihilation back to the singlet ground state. However the modeling of spin-dependent recombination for quintets is still an open question. Here we introduce two theoretical models and compare their predictions with the broadband optically detected magnetic resonance spectrum of a long lived quintet bi-exciton with known molecular structure. This spectrum measures the change in the fluorescence signal induced by microwave excitation of each of the ten possible spin transitions within the quintet manifold as function of the magnetic field. While most of the experimental features can be reproduced for both models, the behavior of some of the transitions is only consistent with the quintet spin-recombination model inspired by triplet intersystem crossing which can reproduce accurately the experimental two-dimensional spectrum with a small number of kinetic parameters. Thus quantitative analysis of the broadband optically detected magnetic resonance signal enables quantitative understanding of the dominant spin-recombination processes and estimation of the out-of equilibrium spin populations.Comment: optimization code available at https://github.com/yneter/ampodm

ВПЛИВ АНТИБІОТИКІВ НА БІОПЛІВКОУТВОРЕННЯ MSSA ТА MRSA ШТАМАМИ СТАФІЛОКОКА

Experimental study the effect of antibiotics (amoksatsyllin/clavulanat, gentamicin and ciprofloxacin) to process formation of biofilms MSSA and MRSA strains of staphylococcus and their effect on the already established «mature» biofilm.Проведено експериментальне вивчення впливу антибіотиків (амоксациліну/клавуланату, гентаміцину та ципрофлоксацину) на процес біоплівкоутворення метициліночутливими (MSSA) та метицилінорезистентними (MRSA) штамами стафілокока та їх дії на вже сформовані «зрілі» біоплівки