Aliens attack – population dynamics and density control of American mink Neovison vison in four National Parks in Poland

Niemczynowicz, A., Brzeziński, M., Zalewski, A

Chemometric approach to characterization of the selected grape seed oils based on their fatty acids composition and FTIR spectroscopy

Addressing the issues arising from the production and trade of low-quality foods necessitates developing new quality control methods. Cooking oils, especially those produced from the grape seeds, are an example of food products that often suffer from questionable quality due to various adulterations and low-quality fruits used for their production. Among many methods allowing for fast and efficient food quality control, the combination of experimental and advanced mathematical approaches seems most reliable. In this work a method for grape seed oils compositional characterization based on the infrared (FTIR) spectroscopy and fatty acids profile is reported. Also, the relevant parameters of oils are characterized using a combination of standard techniques such as the Principal Component Analysis, k-Means, and Gaussian Mixture Model (GMM) fitting parameters. Two different approaches to perform unsupervised clustering using GMM were investigated. The first approach relies on the profile of fatty acids, while the second is FT-IR spectroscopy-based. The GMM fitting parameters in both approaches were compared. The results obtained from both approaches are consistent and complementary and provide the tools to address the characterization and clustering issues in grape seed oils.O

Selected aspects of complex, hypercomplex and fuzzy neural networks

This short report reviews the current state of the research and methodology on theoretical and practical aspects of Artificial Neural Networks (ANN). It was prepared to gather state-of-the-art knowledge needed to construct complex, hypercomplex and fuzzy neural networks. The report reflects the individual interests of the authors and, by now means, cannot be treated as a comprehensive review of the ANN discipline. Considering the fast development of this field, it is currently impossible to do a detailed review of a considerable number of pages. The report is an outcome of the Project 'The Strategic Research Partnership for the mathematical aspects of complex, hypercomplex and fuzzy neural networks' meeting at the University of Warmia and Mazury in Olsztyn, Poland, organized in September 2022.Comment: 46 page

An Approach to Models of Order-Disorder and Ising Lattices

The present paper develops the approach to the famous problem presented by L. Onsager (1944) and its further investigation proposed in a recent work by Z.-D. Zhang (2007). The above works give quaternion-based two- and three-dimensional (quantum) models of order-disorder transition and simple orthorhombic Ising lattices (1925). The general methods applied by Zhang refer to opening knots by a rotation in a higher dimensional space, introduction of weight factor (his Conjecture 1 and 2) and important commutators. The main objective of the present paper is to reformulate the algebraic part of the theory in terms of the quaternionic sequence of Jordan algebras and to look at some of the geometrical aspects of simple orthorhombic Ising-Onsager-Zhang lattices. The present authors discuss the relationship with Bethe-type fractals, Kikuchi-type fractals, and fractals of the algebraic structure and, moreover, the duality for fractal sets and lattice models on fractal sets. A simple description in terms of fractals corresponding to algebraic structure involving the quaternionic sequence (H(q)(4)) of P. Jordan's algebras appears to be possible. Physically we obtain models of (H(q)(4)) for q = 5 . 2(2) = 20 for the melting, q = 9 . 2(6) = 576 for binary alloys, and q = 13 . 2(10) = 13 312 for ternary alloys

Elastodynamical properties of Sturmian structured media

[EN] In this paper, wave propagation in structured media with quasiperiodic patterns is investigated. We propose a methodology based on Sturmian sequences for the generation of structured mechanical systems from a given parameter. The approach is presented in a general form so that it can be applied to waveguides of different nature, as long as they can be modeled with the transfer matrix method. The bulk spectrum is obtained and its fractal nature analyzed. For validation of the theoretical results, three numerical examples are presented. The obtained bulk spectra show different shapes for the studied examples, but they share features which can be explained from the proposed theoretical setting.This research was partially supported by the Grant PID2020-112759GB-I00 funded by MCIN/AEI/10.13039/501100011033 and by ``ERDF A way of making Europe''. It has also been supported by the project HYPERMETA funded under the program Etoiles Montantes of the Region Pays de la Loire (France). The part of research of Agnieszka Niemczynowicz in this publication was written as a result of internship in Valencia, Spain, co-financed by the European Union under the European Social Fund (Operational Program Knowledge Education Development), carried out in the project Development Program at the University of Warmia and Mazury in Olsztyn (POWR.03.05. 00-00-Z310/17). Funding for open access charge: CRUE-Universitat Politecnica de Valencia.Lázaro, M.; Niemczynowicz, A.; Siemaszko, A.; García-Raffi, LM. (2022). Elastodynamical properties of Sturmian structured media. Journal of Sound and Vibration. 517:1-21. https://doi.org/10.1016/j.jsv.2021.11653912151

Measure Theory in Condensed Matter

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