In this paper the multidimensional scaling, the principal coordinate and principal component methods for the Lithuanian population structure have investigated, taken that the proximity measures are Euclid, Gower, Bray-Curtis, Kulczynski, Jaccard and Morisita. The genome-wide single nucleotide polymorphism genetic data analyzed. A comparative analysis of proximity measures performed. The results of visualization are also presented.
The rise of the Lithuanian mathematical school in the second half of the 20th century is associated with the development of probability theory and its application, and the foundations of that school were insightfully laid by the famous Lithuanian mathematician Jonas Kubilius. However, the academician also had a second vocation – the history of mathematics. At the end of the 20th century, he purposefully researched the mathematical legacy of the poet, bishop A. Baranauskas, recognizing him as the first Lithuanian mathematician researcher of the second half of the 19th century.
At the beginning of the 21st century, J. Kubilius undertook a detailed implementation of the idea of a work in the history of Lithuanian mathematics. For this purpose, an informal group of specialists was convened, the content of the work was planned, and the research-based book series ``From the History of Lithuanian Mathematics'' was published. The fourth book in this series, Mathematics in Lithuanian Higher Education Institutions in 1921–1944, presents the research of an academic who reveals the situation of mathematics in universities in Kaunas and Vilnius.
In addition, the memoirs of mathematics history by J. Kubilius, dedicated to mathematicians Z. Žemaitis, G. Žilinskas and V. Statulevičius, should be mentioned.
The article, at the end of which fragments of the author's memories are presented, is dedicated to the centenary of the birth of Academician J. Kubilius.
In recent years, a lot of research has focused on understanding the behavior of when synchronous and asynchronous phases occur, that is, the existence of chimera states in various networks. Chimera states have wide-range applications in many disciplines including biology, chemistry, physics, or engineering.
The object of research in this paper is a coupled map lattice of matrices when each node is described by an iterative map of matrices of order two. A regular topology network of iterative maps of matrices was formed by replacing the scalar iterative map with the iterative map of matrices in each node. The coupled map of matrices is special in a way where we can observe the effect of divergence. This effect can be observed when the matrix of initial conditions is a nilpotent matrix.
Also, the evolution of the derived network is investigated. It is found that the network of the supplementary variable $\mu$ can evolve into three different modes: the quiet state, the state of divergence, and the formation of divergence chimeras. The space of parameters of node coupling including coupling strength $\varepsilon$ and coupling range $r$ is also analyzed in this study. Image entropy is applied in order to identify chimera state parameter zones.
The authors introduced the concept of a pseudo-Heron triangle, such that squares of sides are integers, and the area is an integer multiplied by $2$. The article investigates the case of pseudo-Heron triangles such that the squares of the two sides of the pseudo-Heron triangle are primes of the form $4k+1$. It is proved that for any two predetermined prime numbers of the form $4k+1$ there exist pseudo-Heron triangles with vertices on an integer lattice, such that these two primes are the sides of these triangles and such triangles have a finite number. It is also proved that for any predetermined prime number of the form $4k+1$, there are isosceles triangles with vertices on an integer lattice, such that this prime is equal to the values of two sides and there are only a finite number of such triangles.
The article presents several observations about the examination papers of the state-level Maturity Examinations in Mathematics in the years 2014–2021 in Lithuania. Some inaccuracies were observed in the appendix of the paper titled ``Mathematical formulas'', in the wordings of the problems. Also the issue of proof problems in the examination is discussed. The purpose of these observations is to draw attention to areas for improvement in the examination system. The article presents the subjective opinion of the authors.
In the context of the world health crisis, distance learning which before that was rarely used in Lithuania became practically universal, causing a number of challenges. Trying to respond to some of them, we started exploring possible advantages of between-subject integration in more effectively using on-line time and increasing interest and motivation of students. The article deals with integrating mathematics and arts in distance learning in basic school. Integrated lesson was created for grade 9, and its results and student reflection showed possibilities presented by such type of education.
Floyd's triangle is often presented to computer science students as an exercise or example to illustrate the concepts of text formatting and loop constructs. The paper proposes to look at an object from a different angle and to examine limit theorems for the numbers of generalized Floyd's triangles. Tasks of this type can be used as exercises in study programs of mathematics and informatics (couses of probability theory and combinatorics). It would help to master the appropriate proof techniques and mathematical apparatus. The article proposes a series of possible problems and their proof schemes.
This paper presents an investigation of modeling and solving of differential equations in the study of mechanical systems with holonomic constraints. The 2D and 3D mathematical models of constrained motion are made. The structure of the models consists of nonlinear first or second order differential equations. Cases of free movement and movement with resistance are investigated. Solutions of the Cauchy problem of obtained differential equations were obtained by Runge–Kutta method.
Definitions of concepts of magnitude and number used in academic mathematics are not suitable for school mathematics for reasons of their cognitive complexity. We discuss possible ways to treat magnitudes and numbers in school mathematics based on mathematical reasoning.