Forests are important because they contribute to biodiversity, regulation of carbon dioxide, protection of hydrographic basins, wood production. This article presents a methodology for fast and effective counting of treetops using the mathematical symmetry of the grayscale image. For the treetop counting, the unsupervised k-means classification Algorithm was used with two groups or centroids: treetop and not-treetop. By using these groups and the mathematical symmetry of the image, a fast k-means classification Algorithm is generated. To solve the problem of treetop overlapping and perform a more accurate counting, the watershed Algorithm was used. This methodology has a mean treetop count accuracy of 98.3% with a confidence level of 99% in the interval (97.31, 99.7). Aerial images of the coniferous forest of Alcudia, Mallorca, Spain were used. Forests attenuate climatic changes originated by global warming. Drastic climatic changes cause catastrophes to humanity. This research would help the automatic, massive and recurring counting of treetops with the aim of obtaining forest inventories in order to take care of forests.

There are many applications where it is necessary to model queuing systems that involve finite queue size. Most of the models consider traffic with Poisson arrivals and exponentially distributed service times. Unfortunately, when the traffic behavior does not consider Poisson arrivals and exponentially distributed service times, closed‐form solutions are not always available or have high mathematical complexity. Based on Lindley’s recursion, this paper presents a fast simulation model for an accurate estimation of the performance metrics of G/G/1/K queues. One of the main characteristics of this approach is the support for long‐range dependence traffic models. The model can be used to model queuing systems in the same way that a discrete event simulator would do it. This model has a speedup of at least two orders of magnitude concerning implementations in conventional discrete event simulators.

The aim of this work is to present a model for heat transfer, desorbed refrigerant, and pressure of an intermittent solar cooling systems thermochemical reactor based on backpropagation neural networks and mathematical symmetry groups. In order to achieve this, a reactor was designed and built based on the reaction of BaCl₂-NH₃. Experimental data from this reactor were collected, where barium chloride was used as a solid absorbent and ammonia as a refrigerant. The neural network was trained using the LevenbergMarquardt algorithm. The correlation coefficient between experimental data and data simulated by the neural network was r=0.9957. In the neural networks sensitivity analysis, it was found that the inputs, reactors heating temperature and sorption time, influence neural networks learning by 35 and 20, respectively. It was also found that, by applying permutations to experimental data and using multibase mathematical symmetry groups, the neural network training algorithm converges faster.

This work presents an algorithm to reduce the multiplicative computational complexity in the creation of digital holograms, where an object is considered as a set of point sources using mathematical symmetry properties of both the core in the Fresnel integral and the image. The image is modeled using group theory. This algorithm has multiplicative complexity equal to zero and an additive complexity (k − 1)N² for the case of sparse matrices or binary images, where k is the number of pixels other than zero and N² is the total of points in the image.