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

Unitary boundary pairs for isometric operators in Pontryagin spaces and generalized coresolvents

An isometric operator V in a Pontryagin space H is called standard, if its domain and the range are nondegenerate subspaces in H. A description of coresolvents for standard isometric operators is known and basic underlying concepts that appear in the literature are unitary colligations and characteristic functions. In the present paper generalized coresolvents of non-standard Pontryagin space isometric operators are described. The methods used in this paper rely on a new general notion of boundary pairs introduced for isometric operators in a Pontryagin space setting. Even in the Hilbert space case this notion generalizes the earlier concept of boundary triples for isometric operators and offers an alternative approach to study operator valued Schur functions without any additional invertibility requirements appearing in the ordinary boundary triple approach.Comment: 42 page

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

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

Деривація термінів мережі Інтернет в українській мові

У статті аналізується сучасний стан термінології мережі Інтернет у контексті сучасного розвитку науки і техніки. Розглядається система термінів мережі Інтернет у семантико-дериваційному та функціональному аспектах, визначені основні джерела та способи їх номінації, подана характеристика лексичних одиниць на позначення об’єктів та процесів у галузі мережі Інтернет. (This article is analyzed a current state of terminology of the Internet in the context of modern development of science and equipment. The system of terms is considered of the Internet semantiko-derivational and functional aspects, the main sources and ways of their nomination, the presented characteristic of lexical units are defined for designation of objects and processes in the field of the Internet. Modern stage of development of science and technology is characterized the rapid introduction of computers in our lives. This is a natural process – new technologies are in everyday use, while it is not common has the means necessary to refer to new concepts. New terminological units and linguistics – new the objects of study. The main directions of terminological work in Ukraine provide for coordination of the national and international terminology, develop methodological foundations for the unification of terminology, their enrichment at the expense of own linguistic units and necessary in the present lexical borrowing (theoretical aspect), the participation of the Ukrainian terminology in the work of international organizations on standardization (pragmatic aspect), enter into various terminological dictionaries in cooperation of specialists in the relevant fields of science and equipment and philologists (applied aspect). As you know, the first computer terminology was barely not entirely borrowed from the English language. However, many English terms today it does not require translation, as it has received General acceptance and apply as a result of transliteration (directory, file, program). There are cases of borrowing from this language, when saved Latin writing (Internet, CD-ROM, E-mail, on-line, offline, WEB, Windows, WORD, and others). Use a lot of borrowed words, some of them are useful because the Ukrainian version accurately reflects the content of the concept. The analysis gives reason to believe, the main body terminology the Internet has already formed, but requires a thorough streamlining and standardization. The main direction of work in this terminology remains practical aspect, namely the improvement, which manifests itself in a desire to avoid such unnecessary in terms of phenomena such as synonymy, pacema, the complexity nature of time, overload of foreign language units. Necessary is also the publication of dictionaries timing the Internet Ukrainian language for different categories users.

Boundary triplets for skew-symmetric operators and the generation of strongly continuous semigroups

We give a self-contained and streamlined exposition of a generation theorem for C0-semigroups based on the method of boundary triplets. We apply this theorem to port-Hamiltonian systems where we discuss recent results appearing in stability and control theory. We give detailed proofs and require only a basic knowledge of operator and semigroup theory.Comment: 19 page

Цивільно-правова відповідальність в доктрині цивільного права

Деркач А. В. Цивільно-правова відповідальність в доктрині цивільного права / А. В. Деркач // Римське право як підґрунтя сучасного права Європи : матеріали Міжнар. наук.-практ. конф. (м. Одеса, 27 травня 2016 р.) / за заг. ред. Є. О. Харитонова ; НУ "ОЮА". Півд. регіон. центр НАПрН України. - Одеса : Фенікс, 2016. - С. 174-176

The Low-Molecular-Weight Ligands of the Gonadotropin Receptors as the New Generation of the Regulators of the Reproductive Functions and Steroidogenesis

In clinic, the luteinizing (LH) and follicle-stimulating (FSH) hormones and human chorionic gonadotropin (hCG) are used to treat reproductive dysfunctions and in assisted reproductive technology. They are the αβ-heterodimeric complexes and specifically bind to ectodomain of G protein-coupled LH and FSH receptors. This leads to activation of many signaling cascades; some of which are responsible for steroidogenesis, folliculogenesis, and spermatogenesis, while the others, such as β-arrestin pathways, trigger the downregulation of gonadotropin receptors. A low selectivity of the intracellular signaling of gonadotropins and a large number of their isoforms are the main causes of undesirable effects of gonadotropins, limiting their clinical applications. Unlike gonadotropins, the low-molecular-weight (LMW) ligands interact with an allosteric site located in the transmembrane domain of the LH and FSH receptors and selectively activate the certain signaling pathway, preventing a number of side effects of gonadotropins. The LMW ligands are characterized by activity of the full and inverse agonists and neutral antagonists, as well as the positive and negative modulators, and they have the in vivo activity, including when administered orally. This review focuses on the advances in the development of LMW allosteric ligands of the LH and FSH receptors and the prospects for their use in reproductive medicine

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