Lietuvos matematikos rinkinys
ISSN / EISSN : 0132-2818 / 0132-2818
Current Publisher: Vilnius University Press (10.15388)
Total articles ≅ 62
Latest articles in this journal
Lietuvos matematikos rinkinys, Volume 61, pp 8-14; doi:10.15388/lmr.2020.22472
We discuss different alternatives of the content of school mathematics. According to the prevalent public opinion in Lithuania school mathematics can be oriented either to the academic mathematics or to the applications of mathematics. In reality the second alternative means lowering of the level of teaching in the hope that school mathematics will be accessible to all students. While the content oriented to the academic school mathematics is accessible only to gifted students. In this article we describe a middle alternative content which we call school mathematics based on mathematical reasoning. We argue that such school mathematics serves all students and makes acquaintance with mathematical reasoning and with applications of mathematics to the real world. Reasoning makes mathematics reasonable for all.
Lietuvos matematikos rinkinys, Volume 61, pp 15-20; doi:10.15388/lmr.2020.22454
As soon as the young Lithuanian state was formed, the international situation was unfavorable (the war of independence took place) and as a result its internal life was burdened by difficulties. Therefore, the Lithuanian intelligentsia (one of their leading mathematicians Z. Žemaitis) took the initiative to organize Higher Courses (AK) in the temporary capital Kaunas. These universal courses, equivalent to the type of higher education institution (university), existed in 1920– 1922. According to the adopted statute, there were six chapters covering the basic sciences - humanities, social sciences and natural or real sciences. The existence of the latter sciences was evidenced by the Department of Mathematics and Physics, where there was an opportunity to study mathematics in Lithuanian. This article shows the circumstances of the establishment of AK, the conditions of their activity, introduces the lecturers of mathematics and shows the composition of the listeners, as well as reveals the content of mathematics studies and names the literature used for studies. During the two years of AK's existence, a solid foundation was laid for the future Lithuanian University (since 1930 – Vytautas Magnus). The staff formed consisted mainly of 1922. the core of the developing university, and the first scientific aids, books and premises were acquired - the base of the higher school. For the first time in its history, AK turned Kaunas into a university city, and the departments operating in them laid the foundations for the establishment of the university, as well as the Faculty of Mathematics.
Lietuvos matematikos rinkinys, Volume 61, pp 1-7; doi:10.15388/lmr.2020.22466
The paper extends the investigations of limit theorems for numbers satisfying a class of triangular arrays. We obtain analytical expressions for the semiexponential generating function the numbers, associated with Hermite polynomials. We apply the results to prove the asymptotic normality of the numbers and specify the convergence rate to the limiting distribution.
Lietuvos matematikos rinkinys, Volume 61, pp 21-28; doi:10.15388/lmr.2020.22717
The article introduces the reader to some amazing properties of trigonometric functions. It turns out that if the values of the arguments of the functions sin x, cos x, tg x and ctg x, expressed in radians, are algebraic numbers, then the values of these functions are transcendental numbers. Hence, it follows that the values of all angles of the pseudo-Heronian triangle, including the values of all angles of the Pythagoras or Heron triangle, expressed in radians, are transcendental numbers. If the arguments of functions sin x and cos x, expressed in radians, are equal to x = r 2 \pi, where r are rational numbers, then the values of the functions are algebraic numbers. It should be noted that in this case the argument x = r 2\pi is transcendental and, if expressed in degrees, becomes a rational.
Lietuvos matematikos rinkinys, Volume 61, pp 29-37; doi:10.15388/lmr.2020.22718
The stochastic control system is investigated. The article solves the problem of human-robot humanoid communication. The problem arises in the development of human behavior formation management systems. They describe human behavior in terms of probabilistic characteristics. Such control systems are stochastic. The management system of human behavior formation and its functioning is described quality assessment. The problem is solved by simulation modeling. The software implementing the method is described. The results of experimental research are presented.
Lietuvos matematikos rinkinys, Volume 61, pp 18-24; doi:10.15388/lmr.2020.22470
Word problems are classified to S problems and P problems by Verschaffel , classification is being specified and expanded. Reviewed word problems in Lithuanian first grade textbooks and divided to types. Submitted recommendations to use more varied types word problems, that would let to expand concepts understanding, develop mathematical reasoning, motivate to study word problem.
Lietuvos matematikos rinkinys, Volume 61, pp 13-17; doi:10.15388/lmr.2020.22468
In this article we are going to analyze market price stability with different market intensity coefficient and delay argument values. Market price is described as a scalar differential equation with a delay argument. In order to find solutions for the transcendental equation we will use method based on Lambert function. We will present examples of the applications of the method.
Lietuvos matematikos rinkinys, Volume 61, pp 25-30; doi:10.15388/lmr.2020.22521
In this paper, we present models for the analysis of the behavior of the virtual library (VL) users. Unlike the models presented in the literature, they use only the big data that is stored in the log files of virtual library servers and methods of statistics, association rules, and recommendation systems. The proposed models were implemented with R software. Using the proposed models, the analysis of the behavior of VL users of Lithuanian research and study of higher education institutions was performed for the first time. The results showed that the proposed models allow to operatively analyze the behavior of virtual library users using advanced search filters, facets, and provide suggestions for improvement of service quality.
Lietuvos matematikos rinkinys, Volume 61, pp 7-12; doi:10.15388/lmr.2020.22469
The variance of a linear statistics on multisets of necklaces is explored. The upper and lower bounds with optimal constants are obtained
Lietuvos matematikos rinkinys, Volume 61, pp 1-6; doi:10.15388/lmr.2020.22474
Sturm-Liouville problem with nonlocal boundary conditions arises in many scientific fields such as chemistry, physics, or biology. There could be found some references to graph theory in a discrete Sturm-Liouville problem, especially in investigation of spectrum curves. In this paper, relations between discrete Sturm-Liouville problem with nonlocal boundary conditions characteristics (poles, critical points, spectrum curves) and graphs characteristics (vertices, edges and faces) were found.