This paper presents the results of numerical modelling of the influence of various factors (geometrical layout of the structural layers of the railway track, climatic factors and ballast fouling) on the freezing of railway track structure with a built-in thermal insulation layer of extruded polystyrene (Styrodur). At the same time, the suitability and expediency of incorporating the thermal insulation layer at the sub-ballast upper surface level (i.e. below the rail ballast construction layer), or at the level of subgrade surface are discussed. Numerical modelling results in the main factors that should be taken into account in the dimensioning of the sub-ballast layers with a built-in thermal insulation layer. Based on the data on the depth of freezing of the railway track structure obtained from numerical modelling, a design nomogram for dimensioning was created and subsequently the influence of the changes of climatic characteristics on the freezing of the railway track structure was then mathematically expressed.

The article aims to present the modified structural composition of the sub-ballast layers of the railway substructure, in which a part of the natural materials for the establishment of sub-ballast or protective layers of crushed aggregate is replaced by thermal insulation and reinforcing material (layer of composite foamed concrete and extruded polystyrene board). In this purpose, the experimental field test was constructed and the bearing capacity of the modified sub-ballast layers’ structure and temperature parameters were analyzed. A significant increase in the original static modulus of deformation on the surface of composite foamed concrete was obtained (3.5 times and 18 times for weaker and strengthen subsoil, respectively). Based on real temperature measurement, it was determined the high consistency of the results of numerical analyses and experimental test (0.002 m for the maximum freezing depth of the railway line layers and maximum ±0.5 °C for temperature in the railway track substructure–subsoil system). Based on results of numerical analyses, modified railway substructure with built-in thermal insulating extruded materials (foamed concrete and extruded polystyrene) were considered. A nomogram for the implementation of the design of thicknesses of individual structural layers of a modified railway sub-ballast layers dependent on climate load, and a mathematical model suitable for the design of thicknesses of structural sub-ballast layers of railway line were created.

This paper treats the stability of two superposed gravitating streams rotating about the axis transverse to the horizontal magnetic field. The critical wave number for instability is found to be affected by rotation for propagation perpendicular to the axis about which the system rotates. The critical wave number for instability is not affected by rotation when waves propagate along the axis of rotation. The critical wave number is affected by both the magnetic field and the streaming velocity in both cases. Both the magnetic field and the rotation are stabilizing, while the streaming velocity is destabilizing.

Entasis, upward curvature, columnar inclination and several other manipulations or deviations from the strict geometrical rules were known in Ancient Greece and Rome and some of them - entasis could be taken as example - were used up to the beginning of the 20th century in eclectic and historicizing architecture. The article mentions historical texts about entasis from Vitruvius up to Renaissance works. Mainly Vignola’s description of proper and elegant way of how to construct columnar entasis curve of the Tuscan and Doric order columns is discussed in detail and expressed mathematically.

The late-Romanesque St. Martin´s Church in Dolní Újezd was probably built in the mid-13th century. The nave has a wooden joist ceiling whose beams serve as tie beams too. The Gothic vaults above the presbytery date from ´30s of the 15th century. The truss of the church is dendro-dated to 1420 - 1421. Some members of a truss structure are dendro-dated to 1823 - 1824, when the repair was undertaken. The examined truss is a rafter-collar tie structure with collar beams and pedestal struts. It has a characteristic shape and may be typologically classified as a structure of the earlier period. This type of a truss structure was typically built in this region and represents one of the features occurring in the particular social and culture circles at the time. Consequently, a numerical model of the roof structure was created in order to perform a static analysis of the roof structure in accordance with present standards. With regard to the structural analysis results, it can be said that the original design of the structure based on geometrical and proportional principles satisfy the reliability conditions defined by current European standards for structural design.