Groundwater hydrochemistry of Algerian Sahara (Southwest, Algeria) was used to assess groundwater quality to de-termine its suitability for drinking and agricultural purposes. A total of 26 groundwater samples were analysed for 14 para-meters. Standards laboratory methods were used to determine physicochemical groundwater properties. This study shows that these pH, electric conductivity, total hardness, bicarbonate, and phosphate were within WHO limits. The concentration of magnesium ranging from 30.49 to 120 mg∙dm–3 with an average value of 67.21 mg∙dm–3. 38.56% of the water points analysed have a concentration lower than the value set by the WHO at 75.00 mg∙dm–3. It also showed that 70% of the points studied have potassium concentrations that exceed World Health Organization standards. Groundwater of Algerian Sahara is low in nitrogen (NO3–) and the higher concentration may result in various health risks. The result for this study showed that the water was to be found suitable for drinking purposes except for few samples. Piper diagram indicates that groundwater in Adrar belongs to chlorinated-sulphated, sodium and magnesium facies. The groundwater samples of Adrar present high salinity and low alkalinity fall into the field of C3S1 and C3S2. Based on the RSC values, all samples had values less than 1.25 and were good for irrigation.

Schemes are presented for calculating tuples of solutions of matrix polynomial equations using continued fractions. Despite the fact that the simplest matrix equations were solved in the second half of the 19th century, and the problem of multiplier decomposition was then deeply analysed, many tasks in this area have not yet been solved. Therefore, the construction of computer schemes for calculating the sequences of solutions is proposed in this work. The second-order matrix equations can be solved by a matrix chain function or iterative method. The results of the numerical experiment using the MatLab package for a given number of iterations are presented. A similar calculation is done for a symmetric square matrix equation of the 2nd order. Also, for the discrete (time) Riccati equation, as its analytical solution cannot be performed yet, we propose constructing its own special scheme of development of the solution in the matrix continued fraction. Next, matrix equations of the n-th order, matrix polynomial equations of the order of non-canonical form, and finally, the conditions for the termination of the iterative process in solving matrix equations by branched continued fractions and the criteria of convergence of matrix branching chain fractions to solutions are discussed.

The following paper provides an insight into application of the contemporary heuristic methods to graph coloring problem. Variety of algorithmic solutions for the Graph Coloring Problem (GCP) are discussed and recommendations for their implementation provided. The GCP is the NP-hard problem, aiming at finding the minimum number of colors for vertices in such a way that none of two adjacent vertices are marked with the same color. With the advent of modern processing units metaheuristic approaches to solve GCP were extended to discrete optimization here. To explain the phenomenon of these methods, a thorough survey of AI-based algorithms for GCP is provided, with the main differences between specific techniques pointed out.

During an inventory carried out in the Kórnik Library in October 2016, the author of this article found an unknown parchment document drawn up in 1415, which was purchased to be included in the library collections in 1954, but was not described or provided with a call number at the time and nobody knew about its existence for almost 60 years. In the document, brothers Stanisław and Jakusza, heads and owners of the Lgota village, confirm their sale of a part of their estate, i.e. a certain part of their land at Lgota, which could be flooded by the local pond-stream, to Mikołaj – the Provincial Superior, and the convent of the Pauline Fathers in Jasna Góra. At the same time, both brothers release the Pauline monks from any claims from their mother Katarzyna, and their sisters Jachna, Helena, and Dobrochna. The sale of the land meant for a flooded area should be related to the fact that in 1414 King Ladislaus Jagiello granted the village of Kalej neighbouring with the village of Lgota to the Pauline monks and possibly with their intention to erect a water mill. The document provides us with some new information for genealogical research on Polish nobility in the Middle Ages, and mentions the previously unknown name of the Provincial Superior of the Polish Province of Pauline Fathers – Mikołaj, who served this function in 1415.