Unbounded Wiener–Hopf Operators and Isomorphic Singular Integral Operators

Some basics of a theory of unbounded Wiener–Hopf operators (WH) are developed. The alternative is shown that the domain of a WH is either zero or dense. The symbols for non-trivial WH are determined explicitly by an integrability property. WH are characterized by shift invariance. We study in detail WH with rational symbols showing that they are densely defined, closed and have finite dimensional kernels and deficiency spaces. The latter spaces as well as the domains, ranges, spectral and Fredholm points are explicitly determined. Another topic concerns semibounded WH. There is a canonical representation of a semibounded WH using a product of a closable operator and its adjoint. The Friedrichs extension is obtained replacing the operator by its closure. The polar decomposition gives rise to a Hilbert space isomorphism relating a semibounded WH to a singular integral operator of Hilbert transformation type. This remarkable relationship, which allows to transfer results and methods reciprocally, is new also in the thoroughly studied case of bounded WH.

STATE REGULATION OF THE DEVELOPMENT OF CORPORATE SOCIAL RESPONSIBILITY IN THE TRANSFORMATION TYPE COUNTRIES IN EASTERN EUROPE

The purpose of this research is to investigate the processes of formation of corporate social responsibility in countries of transformation type in Eastern Europe and to study the perspectives of development of socially responsible investing based on studying the world experience in the field of corporate responsibility and the practices of its realization by economic entities in the world. The theoretical and methodological basis of the research is the dialectical method of cognition of the processes of formation of corporate social responsibility in transformation societies, using the experience of the foreign community in similar processes and the possibility of applying individual practices in domestic business. The following scientific methods were used in the research: abstract-logical, in particular, its methods of generalization, analogy, analysis and synthesis, induction and deduction for the formulation of theoretical generalizations of research results, formulation of conclusions and suggestions. Main objects of the study are: theoretical bases of formation and realization of mechanisms of state regulation of corporate social responsibility and socially responsible investing in the world and opportunities to apply their experience in the countries of Eastern Europe; determining the current level of corporate social responsibility at enterprises and organizations and assessing the prospects for their development and influence on socio-economic processes. Practical implications. The stakeholder theory is considered, which reveals the essence of corporate social responsibility in the process of satisfying interests and requirements of various counterparties that may affect the ultimate financial results of the enterprise. It is determined that the main causes of state regulation of corporate social responsibility are a moral obligation, sustainability, and reputation. Corporate social responsibility is an effective tool for enterprise development, as well as for the development of the process of state regulation and constructive dialogue with different social categories that enhances the investment attractiveness of the enterprise and strengthens its reputation, promotes effective labour relations and enhances productivity, supports the marketing policy and trust of the target audience by forming a positive opinion about products, works or services of the enterprise. Modern strategies on the basis of which companies perform the formation of their investment portfolios are considered (sustainable investment strategy, norms-based screening and exclusion of holding from investment universe, integration of ESG factors in financial analysis, impact investments, engagement and voting on sustainability matters). The issue of the undeveloped practice of submitting social reports and difficult public access to them by stakeholders is considered. A model for analysing the prospects of corporate social responsibility development at enterprises is proposed; corporate social responsibility strategy provides for the fulfilment of economic, social, and environmental goals for the successful implementation of corporate social responsibility and socially responsible investment initiatives.

Application of Least Squares Estimation Techniques in 2D Conformal Coordinates Transformation from Local to National

A two-dimensional conformal coordinate transformation is a similarity transformation which is also known as the four parameter transformation since it maintains scale relationships between the two coordinates system. This transformation type uses a mathematical model that establish a geometrical relationship between coordinates of points in different reference frames. It gained wider acceptance because of its capability to retain the shape of an area represented. This paper utilizes three control points; PT02, PT03 and PT04 to compute the transformation parameters and later all validated the derived coordinates of point PT04 known in the local system to national system using manual computation check. The second approach was to derive the transformation parameters using four control points. The result obtained was validated and found to agree with the derived national coordinates system for point PT07. Subsequently, all other points within the areas covered in the scope of work were transformed by writing script and running it in MATLAB software environment. The total area covered was 457.457hectares.

Kinematic Theory of Spatial Rack Drives

On the basis of performed vector analysis of spatial motion transformation of type rotation into translation is created a kinematic theory of this transformation type. Using the kinematic theory the basic kinematic-geometric characteristics of spatial rack mechanisms, applicable to their analysis and synthesis are initiated. These characteristics: kinematic cylinder of level, kinematic relative helicoids, and kinematic pitch surfaces are elements of kinematic geometry of the spatial rack drives

A gold-catalyzed 1,2-acyloxy migration/intramolecular cyclopropanation/ring enlargement cascade: syntheses of medium-sized heterocycles

A gold catalyzed 1,2-acyloxy migration/intramolecular cyclopropanation/ring enlargement cascade of furan substrates provides a new highly efficient procedure for the formation of ten and eleven-membered ring compounds. A new transformation type of intermolecular furan compound catalyzed by a gold catalyst was reported.