2,594 research outputs found
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
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 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 of self-adjoint
operators which are extensions of the symmetric operator .
Any in the operator domain 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 , playing the role of
a trace (restriction) operator, as \tau\phireg=\Theta Q_\phi, the extension
parameter 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 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
МІКРОБІОЛОГІЧНІ АСПЕКТИ ЛІКУВАННЯ ГНІЙНО- ЗАПАЛЬНИХ ЗАХВОРЮВАНЬ
SUMMARY. Results of diverse studies (antibiotic- and phagoresistance, the ability to biofilm formation) MRSA and MSSA strains of community-acquired pathogens inflammatory processes. Directions of improving diagnosis and treatment of purulent-inflammatory diseases are determined.Key words: purulent-inflammatory diseases, antibiotic resistance, phagosensitivity, MRSA and MSSA strains, biofilm.Проаналізовані результати різнопланових досліджень (антибіотико- та фагорезистентності, здатності до плівкоутворення) MRSA та MSSA позалікарняних штамів-збудників гнійно-запальних процесів. Визначені напрямки удосконалення діагностики та лікування гнійно-запальних захворювань.Ключові слова: гнійно-запальні захворювання, антибіотикорезистентність, фагочутливість, MRSA та MSSA штами, біоплівки
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
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
Experimental Appropriateness Verification of K. Gorodetsky`s Mathematical Model for Losses Determinination in Hydrostatic Transmissions for Modern Hydrolic Machines
There were experimentally obtained dependences of efficiency coefficients for two hydrostatic transmissions of various sizes and performance on the basis of axial-piston hydraulic machines under various loading conditions. The experimental data is compared with the calculated one obtained using the mathematical model of K. Gorodetsky. The object of study was the hydrostatic monoblock transmission manufactured in 1999 and the hydrostatic transmission made in 2012 with a spaced hydraulic pump and hydraulic motor
Spectra of self-adjoint extensions and applications to solvable Schroedinger operators
We give a self-contained presentation of the theory of self-adjoint
extensions using the technique of boundary triples. A description of the
spectra of self-adjoint extensions in terms of the corresponding Krein maps
(Weyl functions) is given. Applications include quantum graphs, point
interactions, hybrid spaces, singular perturbations.Comment: 81 pages, new references added, subsection 1.3 extended, typos
correcte
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