The paper shows an example of performed optimization of sizes in terms of welding costs in a characteristic loaded welded joint. Hence, in the first stage, the variables and constant parameters are defined, and mathematical shape of the optimization function is determined. The following stage of the procedure defines and places the most important constraint functions that limit the design of structures, that the technologist and the designer should take into account. Subsequently, a mathematical optimization model of the problem is derived, that is efficiently solved by a proposed method of geometric programming. Further, a mathematically based thorough optimization algorithm is developed of the proposed method, with a main set of equations defining the problem that are valid under certain conditions. Thus, the primary task of optimization is reduced to the dual task through a corresponding function, which is easier to solve than the primary task of the optimized objective function. The main reason for this is a derived set of linear equations. Apparently, a correlation is used between the optimal primary vector that minimizes the objective function and the dual vector that maximizes the dual function. The method is illustrated on a computational practical example with a different number of constraint functions. It is shown that for the case of a lower level of complexity, a solution is reached through an appropriate maximization of the dual function by mathematical analysis and differential calculus.

In this paper, for characteristic polytropic change of state of ideal gas is given graphical planimetric graphical representation of the most important energy values in workplace and thermal diagram, trough the appropriate area. In this paper, we used differential forms of First and Second law of thermodynamics and basic equation which define the observed change of state, written in a suitable form. The results for the polytropic change of state, are applied to the isobaric and isochoric change of state. It is shown that any of the energy values ( q12, w12, wt12, Δh12, Δu12) can be present in both workplace (p, v) as well as thermal (T-s) diagram. Graphical solutions, compared to the analytical, provide efficient theoretical explain and presentation of various thermo-dynamical processes of ideal gas with different aspects and greatly assist a clearer view of the problem and enhance each other living arrangement. Graphical representation of external influences or energy values shown in the diagrams, make it possible to more clearly we see connection between these effects, change of state, as well as their each other relations. This is particularly evident in the case when there are (p, v) and (T-s) diagram for a particular ideal gas, which is common in technical practices (e. g., air as an ideal gas).

Mesoporous silica particles were prepared from highly basic sodium silicate solutions, having different silica modulus and SiO 2 concentrations, by adding sulphuric acid at different temperatures. Pore structure of prepared silica particles (aggregates) is strongly influenced by processing conditions and easy controllable in broad range of the specific surface area, pore size, pore volume and size distribution. It is shown that there is a clear correlation between volume of absorbed oil and processing parameters used in preparation of silica aggregates. Thus, oil absorption is higher in the samples prepared from sodium silicate solution with higher SiO 2 concentration and at higher synthesis temperature.