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

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.

Elaboration of equipotential surfaces of planets using biorthogonal expansions

Purpose. Using known and fixed Earth potential, presented asthe biorthogonal expansion, to culculate the geoid surface, which describes the actual shape of the planet. The external gravitational field is generally described by the series of spherical functions. Since the geoid is determined with the help of such functions,  a question arises converning the identity to define the shape, moreover its several points does not belong to the region of convergence. Methodology and results.

A circuit design of a cyclic voltage generator

The present paper describes a simple circuit for construction of a cyclic voltage generator, which can be used in electrochemical synthesis of conducting polymer films like polyaniline(PANI), polythiophene, polypyrrol etc. The circuit consists of a clock generator; its frequency is converted into digital voltage which is further converted to analog form using digital to analog converter (DAC). This analog voltage, after boosting, is used as a source of voltage in the synthesis of conducting polymer.