Investigation of the asymmetry of the Earth's gravitational field using the representation of potentials of disks

The paper considers representations of the Earth external gravitational field, supplementing its traditional approximation by series in spherical functions. The necessity for additional means of describing the external potential is dictated by the need to study and use it at points in space close to the Earth's surface. It is in such areas that the need arises to investigate the convergence of series with respect to spherical functions and to adequately determine the value of the potential.


Purpose – The purpose of this study is to develop a strategy for improving the innovation of domestic industrial enterprises in modern conditions. The basis for solving this problem is a deep retrospective analysis of innovation in Ukraine in terms of investment sources and areas of expenditure on innovation of industrial enterprises.

Modernization of the food industry in the context of sustainable development of Ukraine: public-management aspect


Problem setting. The food industry of Ukraine holds a unique position among other industries, as it is one of the backbone elements of the national economy, is in the top five industries in terms of filling the state budget, ranks second in terms of production in the structure of industrial production in Ukraine, providing one of the highest growth rates of production volumes among other sectors of the economy.

The methodology of approximate construction of the three-dimensional mass distribution function and its gradient for the ellipsoidal planet subsidies

Purpose. To create an algorithm for constructing a three-dimensional masses distribution function of the planet and its derivatives taking into account the Stokes constants of arbitrary orders. Being based on this method, the task is to perform the research on the internal structure of the Earth. Methodology. The derivatives of the inhomogeneous mass distribution are presented by linear combinations of biorthogonal polynomials which coefficients are obtained from the system of equations.

Method for approximate construction of three-dimensional mass distribution function and gradient of an elipsoidal planet based on external gravitational field parameters

Purpose. To investigate the technique for constructing a three-dimensional distribution function for the masses of the interior of the Earth and its derivatives, coordinated with the parameters of the planet's gravitational field to fourth order inclusive. By using the mass distribution function constructed, to make an interpretation of the features of the internal structure of an ellipsoidal planet. Methodology. Based on the created initial approximation of the function, which includes a reference density model, further refinements are built.

Finite element approximations in projection methods for solution of some Fredholm integral equation of the first kind

Approximation properties of B-splines and Lagrangian finite elements in Hilbert spaces of functions defined on surfaces in three-dimensional space are investigated.  The conditions for the convergence of Galerkin and collocation methods for solution of the Fredholm integral equation of the first kind for the simple layer potential that is equivalent to the Dirichlet problem for Laplace equation in $\mathbb{R}^3$ are established.  The estimation of the error of approximate solution of this problem, obtained by means of the potential theory methods, is determined.

The Essence and Methodical Approaches to the Evaluation of the Tourist Potential of the Territory

The contemporary content is disclosed and the possibility of using the term “tourist potential of the territory” is explained. My position on the content of the concept “tourist potential of the territory” is formulated. The complex approach to estimation of tourist potential of a locality with consideration of its components and indicators is offered

The problems of improving the planning and accounting of innovative development of enterprise

The problems of planning and accounting the innovation activity of company during its 
development are considered. The prospects for the development of any company today are 
increasingly dependent on its business reputation and the possibility of introducing innovations. 
Innovative activity is not represented directly in financial accounting. The existing accounting 
system doesn’t encourage activities on strategic development and ensure the growth of its value. 

Legendre polynomials use one-dimensional approximation for distribution density mass planet and investigation of their convergence

This paper presents investigation of the image's possibility of distribution of lumply-continuous functions with are presented by Legendre polynomials and practical realization of this technique and methods for its improving were investigated.


Decomposition of the gravitational field of the triaxial ellipsoidal planet using a class of nonorthogonal harmonic functions

In this work is presented a potential of triaxial ellipsoid this help of converging rows. The koeficients which are determined integral descriptions of distributing function density of planet. This approach gives a possibility in a complex to study distributing of the masses of planet, its figure and its external gravity field.