There are well-known numerical methods for solving the initial‐boundary value problems for partial differential equations. We mention only some of them: finite difference method (FDM), finite element method (FEM), boundary element method (BEM), Galerkin type methods and others. In the given work FDM and BEM are considered for determination a distribution of heat in the multilayer media. These methods were used for the reduction of the 1D heat transfer problem described by a partial differential equation to an initial‐value problem for a system of ordinary differential equations (ODEs). Such a procedure allows us to obtain a simple engineering algorithm for solving heat transfer equation in multilayered domain. In a stationary case the exact finite difference scheme is obtained. An inverse problem is also solved. The heat transfer coefficients are found and temperatures in the interior layers depending on the given temperatures inside and outside of a domain are obtained.

The approximations of some heat transport problem in a thin plate are based on the finite volume and conservative averaging methods [1,2]. These procedures allow one to reduce the two dimensional heat transport problem described by a partial differential equation to an initial‐value problem for a system of two ordinary differential equations (ODEs) of the first order or to an initial‐value problem for one ordinary differential equations of the first order with one algebraic equation. Solution of the corresponding problems is obtained by using MAPLE routines “gear”, “mgear” and “lsode”.

3D printing capabilities are also used in the fashion and textile industries. 3D printed textiles are a new opportunity to create an individual design. Traditional textile structures can be interpreted using 3D printing technologies and materials. One of the most important factors associated with the use of 3D printing technology is to reduce the impact of processing on the physical properties of textile fabrics. Availability of 3D printers at Rezekne Academy of Technologies (RTA) provides experimental work with fabrics of different thickness and fibres as well as different filaments. This study is based on the analysis of synthetic fibre cloth processing and the effect of 3D printing parameters on textile materials. By applying successive layers of materials, the interaction between 3D printing and textiles is studied. In terms of adhesion and stability, the best adhesion parameters for a particular type of fabric are determined by analysing the type of the fabric. The variance analysis method is used to process the research results.

In this paper we study the problem of the diffusion of one substance through the pores of a porous material which may absorb and immobilize some of the diffusing substances with the evolution or absorption of heat. The transfer of moisture and the heat are described by the model. The system of two partial differential equations (PDEs) is derived, one equation expresses the rate of change of concentration of water vapour in the air spaces and the other the rate of change of temperature. The obtained initial‐boundary value problem is approximated by using the finite volume method. This procedure allows us to reduce the 2D transfer problem described by a system of PDEs to initial value problem for a system of ordinary differential equations (ODEs) of the first order.

<p><em>The aim of the research is to investigate the essence of the notion ”competence” and the differences in the usage of the </em><em>career's terminology in semantic, methodological and pragmatic areas in academic theories of the second part of the 20 century; to work out evaluation criteria by comparing the succession of the </em><em>notions capacity. The research is based on the Latvian and international sources of scientific literature – books, magazines, sources in digital form, and etc. A </em><em>personality was </em><em>investigated holistically </em><em>( Džarviss (Jarvis, 2010); Devis (Dove, 1976); Kross (Cross, 1981) )</em><em>:</em></p><p><em>Body (genetic, physical, biological; reflection, self-capacity);</em></p><p><em>Mind (know-how – t</em><em>he cognitive skills </em><em>being based on knowledge and competence; readiness for life activities; an attitude as a means of creativity; a system of evolution; imagination, confidence, sense).</em></p><p> </p>