Since the order of the transfer matrix for either each pipe segment or the entire piping system is 4×4, which is independent of the number of the spans for the system, the presented approach is simpler than the existing techniques, particularly for the piping systems with large number of spans.
The time span of the Karoo System extends from the Carboniferous and Permian periods (about 359 million to 251 million years ago) to the Late Triassic Epoch (about 229 million to 200 million years ago).
The space (mathcal{H}_{mu}^{p}) is defined as the (L^{p}_{mu} -closed linear span of the orthogonal system (phi^{mathbb{Y}_{mu} -closed
The representation (2.10) results from the fact that the functions constitute a system of orthonormal functions and due to the fact that, acting as a multiplication operator, requires to be a formally symmetric linear operator on the finite linear span of the orthonormal system.
Then, from the distance matrix of the areas, we can determine the minimum spanning tree of the system, a concept introduced in the context of graph theory to find the most relevant (or more informative) connections in a network.
Design of a tunnel submarine to perform controlled maintenance and service duties within pipes, tunnels and sewers, such as water tunnels, water and oil pipelines containing hydraulic liquid substances, is proposed to extend the life span of those systems.
The use of artificial intelligence (AI) soft computing techniques is gaining acceptance in the industry to ensure efficient energy utilization, robust and accurate speed reference tracking, minimum impact on the host electric grid system, and extended life span of the motor drive system while avoiding magnetic saturation and inrush current conditions.
This arrangement fueled industrial progress in the early United States, but during the short span of the Internet revolution the system has begun to disintegrate -- by growing out of control.
