We study the exact and approximate controllabilities of the Langevin equation describing the Brownian motion of particles with a white noise. The Langevin equation is shown to describe also the bacterial run-and-tumble motion. Applying the Green’s function approach to the Green’s function representation of the Langevin equation, we obtain necessary and sufficient conditions for exact controllability in the form of a finite-dimensional problem of moments. For the approximate controllability, we obtain only sufficient conditions. The sets of resolving controls are characterized in both cases. The theoretical derivations are supported by a numerical analysis.

The sensor-shifted stereo camera provides the mechanism for obtaining 3D information in a wide field of view. This novel kind of stereo requires a simpler matching process in comparison to convergence stereo. In addition to this, the uncertainty of depth estimation of a target point in 3D space is defined by the spatial quantization caused by the digital images. The dithering approach is a way to reduce the depth reconstruction uncertainty through a controlled adjustment of the stereo parameters that shift the spatial quantization levels. In this paper, a mathematical model that relates the stereo setup parameters to the iso-disparities is developed and used for depth estimation. The enhancement of the depth measurement accuracy for this kind of stereo through applying the dithering method is verified by simulation and physical experiment. For the verification, the uncertainty of the depth measurement using dithering is compared with the uncertainty produced by the direct triangulation method. A 49% improvement of the uncertainly in the depth reconstruction is proved.

The presence of the Bible in the movies is a complex reality: besides direct interpretations of the stories from the Holy Scriptures, a number of films has been inspired by other cultural sources (passion-plays, arts, literature, music, other films). By reason of its subject and its non-religious origin, a biblical film is important for theologians: numerous audiovisual adaptations of the Gospel have raised the issues of the faithfulness of this particular kind of translation (transmediatization) of the Bible. A particular attention should be paid to Jesus-movies because of their impact on the audiences and very different ways of portraying of Jesus (from a relatively simple „historical" Jesus till elaborated Christ-figures).

The energy saving tendencies, in reference to residential buildings, can be recently seen in Europe and in the world. Therefore, there are a lot of studies being conducted aiming to find technical solutions in order to improve the energy efficiency of existing, modernized, and also new buildings. However, there are obligatory solutions and requirements, which must be implemented during designing stage of the building envelope and its heating/cooling system. They are gathered in the national regulations.

The paper describes the process of raising the energy standard of buildings between 1974–2021 in Poland. Therefore, the objective of this study is to show energy savings, which can be generated by modernization of thermal insulation of partitions of existing buildings and by the use of different ways of heat supply. The calculations are made on the selected multi-family buildings located in Poland, with the assumption of a 15 years payback time.

It is shown that it is not possible to cover the costs of the modernization works by the projected savings with the compliance to the assumption of 15 years payback time.