Two (p, q)-Laplace transforms are introduced and their relative properties are stated and proved. Applications are made to solve some (p, q)-linear difference equations.

The work carried out in this paper focused on “Machine learning models for the prediction of turbulent combustion speed for hydrogen-natural gas spark ignition engines”. The aim of this work is to develop and verify the ability of machine learning models to solve the problem of estimating the turbulent flame speed for a spark-ignition internal combustion engine operating with a hydrogen-natural gas mixture, then evaluate the relevance of these models in relation to the usual approaches. The novelty of this work is the possibility of a direct calculation of turbulent combustion speed with a good precision, using only machine learning model. The obtained models are also compared to each other by considering in turn as a comparison criterion: the precision of the result, calculation time, and the ability to assimilate original data (which has not undergone preprocessing). An important particularity of this work is that the input variables of the machine learning models were chosen among the variables directly measurable experimentally, based on the opinion of experts in combustion in internal combustion engines and not on the usual approaches to dimensionality reduction on a dataset. The data used for this work was taken from a MINSEL 380, a 380-cc single-cylinder engine. The results show that all the machine learning models obtained are significantly faster than the usual approach and Random Forest (R²: R-squared = 0.9939 and RMSE: Root Mean Square Error = 0.4274) gives the best results. With a forecasting accuracy of over 90 %, both approaches can make reasonable predictions for most industrial applications such as designing engine monitoring and control systems, firefighting systems, simulation, and prototyping tools.

We firstly consider the fully degenerate Gould–Hopper polynomials with a q parameter and investigate some of their properties including difference rule, inversion formula and addition formula. We then introduce the Gould–Hopper-based fully degenerate poly-Bernoulli polynomials with a q parameter and provide some of their diverse basic identities and properties including not only addition property, but also difference rule properties. By the same way of mentioned polynomials, we define the Gould–Hopper-based fully degenerate $(\alpha ,q)$ -Stirling polynomials of the second kind, and then give many relations. Moreover, we derive multifarious correlations and identities for foregoing polynomials and numbers, including recurrence relations and implicit summation formulas.