The structure function is an often-used mathematical representation of the investigated system in reliability analysis. It is a binary function that models system state according to states of its components. The size of the structure function depends on the number of components and can be enormous for systems with many components. Therefore, the system reliability analysis based on the structure function needs special methods to decrease this dimension and to measure the system reliability. The concept of survival signature provides a useful transformation of the structure function to simplify reliability assessment for systems with many components of specified types. The survival signature is a complete probabilistic description of the system. The new methods and algorithms of system reliability analysis based on this mathematical representation should be developed. The Direct Partial Logic Derivative is one of approaches that are effective in system reliability evaluation based on the structure function. This approach is used to determine different aspects of system failure depending on system components breakdowns. The development of this derivative for survival signature permits to obtain the new method for the reliability analysis of system failure caused by system component breakdown depending on components types.

Semiconductor devices and binary information technology reach their limits set by the atomic size of miniaturization, calculation speed, and the fundamental principle of energy dissipation per bit processing. Therefore, new technologies in logic design and mathematical approaches must be investigated. Application of multiple-valued logic (MVL) in logic design allows developing gates and circuits with more than two stable states. This enables packing an unprecedented high-density of information. Based on this idea, a new technique of the programmable logic arrays (PLA) construction based on MVL units is considered. The unique aspect of this technique is the application of recurrent generalized Reed–Muller expression (GRME) for MVL function representation. The recurrent procedure for this expression’s construction is considered and applied in the PLA development. The proposed structure of PLA consists of two blocks that are memory and logic block. In this paper, we also consider the possibility to use the ferroelectrics for the implementation of cells of the memory block of PLA. The development of gates with multi-stable states is possible by the ferroelectrics ability to pin the polarization as a sequence of stable states.

Forests of Slovak Eastern Carpathians provide essential services to society ensuring human well-being. Primeval forests that remained there untouched have exceptional value. Unsustainable logging and climate change intensify forest disturbances and may cause substantial forest loss. The engagement of remote sensing allows timely monitoring and prediction of negative consequences. The leaf area index is selected from the other forest’s condition indicators to assess the forests’ quantity and disturbance. The conceptual approach for risk assessment of forest disturbance is proposed. This approach uses multiscale multi-temporal Earth observation data, such as synthetic aperture radar imagery and high-level satellite data products. The output response of the forest’s condition was restored by multivariate regression with radar backscattering coefficients, relative difference polarization index, and local incidence angle. The low-resolution leaf area index pre-developed Copernicus data products make it possible to characterize the forest’s condition without ground truth measurements. According to the elaborated methodology, a time series of the leaf area index was mapped, and risks analysis was performed according to hazard functions. A resulting risk’s gradations map is a good tool for future research and decision-making support in nature management. The high spatial resolution of the output maps allows getting a more detailed assessment of forest disturbance behavior.

A Multi-State System (MSS) is a mathematical model in reliability engineering that allows representing investigated system/object using several performance levels from perfect working to complete failure. A new approach for the analysis of a MSS based on mathematical methods of multiple-valued logic is proposed in this paper. In particular, the method for the calculation of critical system states is presented.