The paper proposes a mathematical model for describing the dynamics of multicomponent emulsions, based on ideas and methods of the kinetic theory of gases. The methodological basis of the proposed theory is the ideas and methods of the theory of integral kinetic equations.
The article describes conceptual models of learning and teaching as a managed cybernetic system to achieve the knowledge and skills required by the standards. In the article, the learning process is examined as a system for building a knowledge system of a learner actively which is managed and directed by the tutor or teacher to achieve specified learning goal. The information received by the learner has a multimedia nature. The recipient receives the information through various channels (sensors), sight, hearing, smell, taste and touch. The received information arrives in the short-term memory where it is processed – confronted with the previous knowledge in long-term memory of the individual. New information and knowledge can reinforce and extend the recipient’s long-term knowledge system if they are consistent logically. If there is a conflict between new information and old knowledge and information – the conflict needs to be solved. The solution can be the clarification of the knowledge system, correction of misconceptions so they are in line with objective reality and relevant knowledge about the subject of learning. It means, learning is not a constant storage of isolated information and information units in memory, but their transformation into active knowledge which is connected to logical structures and forms the knowledge system of the learner. The actual knowledge system enables an individual to solve non-standard problems not only in everyday life but also in science and technology and in various research areas from which the necessary, suitable and useable knowledge (expert) system is built.
This paper shows that the constrained similarity transformation of surfaces under boundary constraints is a Laplacian preserving transformation. First, a general proof is presented and then the result is verified for mesh-functions through particular examples. The fact that the constrained similarity transformation, subject to boundary constraints, is a Laplacian preserving transformation is used to construct a method for solving boundary value problems for the Laplace’s and the Poisson’s equations. Given any solution to these equations we apply the constrained similarity transformation to get the particular solution that satisfies the given boundary conditions.
This paper deals with the process by which pure geometric problems, such as determining the position of the triangle or line whose points should lie on circles or straight lines, or that edges of the triangle tangle circles or similar. By moving from the field of geometry to the field of the theory of mechanisms, it is possible to relatively simply describe problem with the system of nonlinear equations to reduce on the problem of finding zeros of the polynomials of a certain degree. Problem of solving a system of nonlinear equations reduces to the problem of linear algebra, which, from the aspect of numerical analysis, is a significant advantage. The paper deals with the solution of a concrete problem.
Direct Metal Laser Sintering1 (DMLS) is a revolutionary technology that allows a production of fully functional metal parts directly from a 3D CAD data, eliminating the investment to production tools and technologies which brings considerable cost and time savings. Metal parts made by DMLS technology are fully comparable with casted or machined parts. A range of application of DMLS technologies is very wide – from prototypes, through short-run production to final products. Advantages of DMLS technology are arising along with complexity of parts – more complex geometry of parts (in terms of shape and occurrence of the detail) make DMLS technology even more economically effective.
This paper attempts to provide a transparent and, if possible, a formal hierarchy of the main types of mathematical models used in the description of dynamic processes inside, at first glance, different systems. It is emphasized that the mathematical modeling is a natural and universal environment for effective analysis of system processes of different nature. From our point of view, the term "system analysis" means the methodology for classification of real systems (physical, biological, economic, social, etc.), which is based on the classification of mathematical models that are used to describe these systems.