The presented research examined the impact of using biodiesel as a fuel for existing diesel engines during the transition to the broader adoption of electric vehicles powered by renewable energy or through integrated hybrid drive systems. The authors considered previous research on this topic, which is demonstrated by a literature review. This paper will utilize the findings to further explore the potential of optimizing existing engines by using biodiesel and thus propose their continued use in the transition period as one of the clean fuels. This paper outlines the standards that define fuel quality and presents a test bench equipped with an experimental engine and specialized equipment for laboratory examination, enabling the measurement of emissions and the determination of cylinder pressure. To ensure the repeatability of the experimental conditions and facilitate future comparison of the obtained results, the engine examination was conducted according to the standard ESC 13-mode test. The examination process confirmed a significant reduction in particulate matter emissions (on average 40%) but, simultaneously, an increase in nitrogen oxide emissions (on average 25%), whose level, according to data from the literature, depends on the type of raw materials used for biodiesel production. Brake thermal efficiency is higher when operating with biodiesel (on average 1.5%). Still, it was concluded that the use of biodiesel in existing diesel engines is feasible only if the engines are equipped with variable systems for automatically adjusting the compression ratio, fuel injection time, valve timing, and so on. The outcomes from the examination conducted can be further processed by applying statistical methods and represent an essential database for further research in this scientific area.

In recent times, spare parts inventory systems have been extensively researched, but most inventory models were not fully adequate due to the stochastic nature of inventory environment. This paper proposes an approach that supports decision making process in planning and controlling of spare parts in aircraft maintenance systems. Reliability characteristics of aircraft consumable parts were analyzed in order to substantiate this approach. Moreover, the proposed reliability model was used to evaluate characteristics of subassemblies and/or assemblies these parts belong to. Finally, an innovative approach for determining the total amount of parts required in inventory and underage costs, based on observing the total unit time as a stochastic process, is presented herein.

We present a hybridization of the accelerated gradient method with two vector directions. This hybridization is based on the usage of a chosen three-term hybrid model. Derived hybrid accelerated double direction model keeps preferable properties of both included methods. Convergence analysis demonstrates at least linear convergence of the proposed iterative scheme on the set of uniformly convex and strictly convex quadratic functions. The results of numerical experiments confirm better performance profile in favor of derived hybrid accelerated double direction model when compared to its forerunners.

Performance-Based Logistics (PBL) frameworks prioritize system availability by optimizing maintenance strategies, with repair rate estimation playing a critical role in predictive maintenance planning. This study proposes a machine learning-based approach for repair rate prediction, leveraging fully connected neural networks (FCNNs) and Long Short-Term Memory (LSTM) networks trained on repair rate samples generated from a stochastic model. The FCNN estimates maximum repair rates, while the LSTM predicts minimum repair rates, capturing both steady-state and sequential dependencies in repair rate variations. By eliminating the need for complex mathematical formulations, the proposed methodology provides a scalable and computationally efficient alternative to traditional stochastic models. Extensive performance evaluations demonstrate that the neural networks achieve higher accuracy and lower computational costs compared to stochastic approaches, making them well-suited for real-time predictive maintenance applications. This research enhances decision-making in maintenance planning, optimizes resource allocation, and improves overall system reliability within PBL frameworks.

A reduction of the originally double step size iteration into the single step length scheme is derived under the proposed condition that relates two step lengths in the accelerated double step size gradient descent scheme. The proposed transformation is numerically tested. Obtained results confirm the substantial progress in comparison with the single step size accelerated gradient descent method defined in a classical way regarding all analyzed characteristics: number of iterations, CPU time, and number of function evaluations. Linear convergence of derived method has been proved.