This paper presents the results of modelling the heat transfer process in heterogeneous media with the assumption that part of the heat flux is dispersed in the air around the beam. The heat transfer process in a solid material (beam) can be described by an integer order partial differential equation. However, in heterogeneous media, it can be described by a sub-or hyperdiffusion equation which results in a fractional order partial differential equation. Taking into consideration that part of the heat flux is dispersed into the neighbouring environment we additionally modify the main relation between heat flux and the temperature, and we obtain in this case the heat transfer equation in a new form. This leads to the transfer function that describes the dependency between the heat flux at the beginning of the beam and the temperature at a given distance. This article also presents the experimental results of modelling real plant in the frequency domain based on the obtained transfer function.

Abstract. This paper presents some recent results in the area of application of fractional order system models. After the introduction to the dynamic systems modelling with the fractional order calculus the paper concentrates on the possibilities of using this approach to the modelling of real-world phenomena. Two examples of such systems are considered. First one is the ultracapacitor where fractional order models turn out to be more precise in the wider range of frequencies than other models used so far. Another example is the beam heating problem where again the fractional order model allows to obtain better modelling accuracy. The theroetical models were tested experimentally and the results of these experiments are described in the paper.

In this article, the modeling of the ultracapacitor using different models of capacity part is shown. Two fractional order models are compared with the integer model of traditional capacitor. The identification was made using the diagram matching technique. Next, the derivation of time domain response of the ultracapacitor and system with the ultracapacitor are presented. The results of frequency domain identification were used to validate the response of the ultracapacitor in time domain. All theoretical results are compared with the response of the physical system with the ultracapacitor.

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The paper describes a deep neural network-based detector dedicated for ball and players detection in high resolution, long shot, video recordings of soccer matches. The detector, dubbed FootAndBall, has an efficient fully convolutional architecture and can operate on input video stream with an arbitrary resolution. It produces ball confidence map encoding the position of the detected ball, player confidence map and player bounding boxes tensor encoding players' positions and bounding boxes. The network uses Feature Pyramid Network desing pattern, where lower level features with higher spatial resolution are combined with higher level features with bigger receptive field. This improves discriminability of small objects (the ball) as larger visual context around the object of interest is taken into account for the classification. Due to its specialized design, the network has two orders of magnitude less parameters than a generic deep neural network-based object detector, such as SSD or YOLO. This allows real-time processing of high resolution input video stream.