Artificial neural networks find extensive applications in various fields, including complex robotics, computer vision, and classification tasks. They are designed to mimic the highly complex, nonlinear, and parallel computational abilities of the hum...

Partial differential equations are a branch of engineering mathematics that in the last decades in the scientific field has played a very important role in solving certain engineering problems. In this paper, we have applied a kind of partial differential equations when examining the influence of microwaves. We have observed the phenomena occurring in one part of the electromagnetic spectrum in the frequency range of 1 GHz-100 GHz as an aggravating factor in signal transmission by telecommunication water, which was the starting point for research on this topic. The reason for isolating this area is contained in the specific technique that characterizes it. One of the types of partial hyperbolic equations is the telegraphic equation, whose solution eliminates problems related to the transmission line. The graphical interpolation of the telegraph equation is given in the Matlab Engineering Matrix Laboratory. Only the parts of mathematically important functions are derived in the paper and the final results are presented in order to represent our starting differential equation as telegraphic.

Wireless sensor networks play a key role in various applications such as environmental monitoring, smart cities and medical monitoring. Latency and reliability are two basic aspects that affect the efficiency and quality of service of these networks. In this research, delay and reliability analyzes of WSN were conducted through the application of mathematical models. Different parameters were analyzed such as distance, number of devices, and bandwidth to gain a deeper understanding of their impact on network performance. Mathematical models have been developed that take into account random variables and changing factors in order to conduct a more precise analysis. Through simulations and numerical experiments, Matlab codes will be used to simulate and analyze the actual process, all with the aim of achieving minimum delay and maximum reliability. This research provides a deeper insight into the characteristics of WSN and provides guidelines for the design and optimization of these networks.

This paper explores the applications of stochastic methods in the field of artificial intelligence (AI), focusing on their contribution to optimization, learning, and decision-making. By employing stochastic models, we enable AI to effectively handle uncertainty, unpredictability, and data variation. We analyze how stochastic processes can improve the convergence of algorithms in training deep neural networks and optimizing parameters. Additionally, we investigate the applications of stochastic simulations in assessing the performance of machine learning algorithms in real-world conditions. Through this study, we highlight the key advantages and challenges of stochastic methods in the field of artificial intelligence. Furthermore, we explore how stochastic methods allow artificial intelligence models to better adapt to changing circumstances and unpredictable situations, thereby increasing their robustness and applicability in the real world. We analyze the impact of stochastic elements on decision-making processes, examining how these properties contribute to the adaptability of systems in dynamic environments. By reviewing relevant studies and experiments, this research provides insight into how stochastic methods contribute to the evolution of artificial intelligence, opening new perspectives for understanding and improving the performance of models in real-world scenarios. This paper contributes to a broader understanding of the role of stochastic processes in the field of artificial intelligence, emphasizing the potential for further development and applications in various domains