The fundamental solution and the heat semigroup of the Vladimirov-Taibleson operator on constant-order noncommutative Vilenkin groups are obtained, together with some estimates on the associated heat kernel. We also show the existence of a fundamental solution for the "Vladimirov Laplacian" on the -adic Heisenberg group and the -adic Engel group, and discuss possible extensions of our results to more general homogeneous operators on graded -adic Lie groups.

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RESUMEN I SuMMARYTheproject presents some singularpoints in which ihe solu~ions adopted are structurally extraordinary. INTRODUCCI~NDicho túnel viario se convertirá en un elemento singular dentro de la infraestructura viaria de la ciudad de Madrid. El túnel Viario de María de Molina, que unirá el Paseo de Con sus 2.271 metros, incluyendo ramales será el paso la Castellana y la calle Velázquez con la Autovía N-11 subterráneo urbano más largo de España, y servirá para Madrid-Barcelona, constituirá la mayor obra municipal en unir el paseo de la Castellana y las calles de José Abascal el conjunto de pasos subterráneos, representando una iny Velázquez con la N-11 en la proximidad de la M-30, en versión de mas de 42 millones de euros.

The purpose of this article is to analyze the vibrations and behavior of an internal combustion engine of three vehicles: A1, J1, K1 which are exposed to both the geography, relief and road conditions of the Metropolitan District of Quito. To implement the quantitative methodology in the research it is important to perform a complete analysis of the vehicle based on its technical data sheet: A1, J1, K1, in order to identify both fuel consumption and the use of additives to reduce the friction that cause vibrations in the engine, especially the condition of the road. In addition, it is important to check how the level of vibrations can be reduced, the percentage of fuel when using additives and to verify the data provided by the vibration study of each vehicle. The results show that the tests carried out at 3500 RPM in vehicle A1 show a value of 27%, in vehicle J1 a value of 17% and vehicle K1 a value of 15%, these values are related to the use of additives. The results of the research are linked to field tests, individual tests, comparison of results and discussion of the feasibility of each of the tests performed on each vehicle to find similarities or marked differences.

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