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The paper brings forward the results of the study with respect to the synthesis of complex mechanism of guiding roof supports for the coal mining. The mechanism of guiding roof supports for the coal must fulfill the following functions: leading the beam shield on a course roughly rectilinear, parallel to the coal face, to gauge how much lower the front-operated space, packaging as well as the support that it can be transported in assembled condition, not to obstruct the free spaces of the roof support it belongs to. The geometric parameters of the complex mechanism shall be determined using the method of vector contours with vectors expressed in their complex form. [ABSTRACT FROM AUTHOR]

When conceiving, designing and realising main pipe petroleum products transport systems, in order to find the optimum choice concerning their architecture and structure, the most modern and efficient research method is represented by the modelling and simulation of the considered system. The research focused on conceiving mathematical models which describe the construction and operation of main pipes, pumping groups and the entire network. [ABSTRACT FROM AUTHOR]