Lietuvos matematikos rinkinys 2020-02-11T09:03:36+00:00 R. Leipus Open Journal Systems <p>Publish articles presenting new and important events in all areas of mathematics.</p> Editorial Board and Table of Contents 2020-02-11T09:03:28+00:00 Artūras Štikonas 2019-12-05T10:09:31+00:00 Copyright (c) 2019 Lietuvos matematikos rinkinys Lithuanian science courses in Vilnius and traces of mathematics in them 2020-02-11T09:03:36+00:00 Juozas Banionis <p><span style="background-color: #ffffff;">Lithuania and sheds light on attempts by the Lithuanian public to revive higher education studies in Vilnius from 1919 to 1921. According to the remaining sets of documents it is possible to testify about the existing traces of mathematics in the projects of the restored Vilnius University or organized higher education courses.</span></p> <p>&nbsp;</p> <p>&nbsp;</p> 2019-12-05T00:00:00+00:00 Copyright (c) 2019 Lietuvos matematikos rinkinys Modeling Baltic market benchmark index: a comparison of models 2020-02-11T09:03:35+00:00 Igoris Belovas <p><span style="background-color: #ffffff;">In this paper we perform a statistical analysis of the returns of OMX Baltic Benchmark index. We construct symmetric α-stable, non-standardized Student’s t and normal-inverse Gaussian models of daily logarithmic returns of the index, using maximum likelihood method for the estimation of the parameters of the models. The adequacy of the modeling is evaluated with the Kolmogorov-Smirnov tests for composite hypothesis. The results of the study indicate that the normal-inverse Gaussian model outperforms alternative heavy-tailed models for long periods of time, while the non-standardized Student’s t model provides the best overall fit for the data for shorter intervals. According to the likelihood-ratio test, the four-parameter models of the log-returns of OMX Baltic Benchmark index could be reduced to the three-parameter (symmetric) models without much loss.<br></span></p> <p>&nbsp;</p> 2019-12-05T00:00:00+00:00 Copyright (c) 2019 Lietuvos matematikos rinkinys Local limit theorem for coefficients of modified Borwein’s algorithm, proved by the ratio method 2020-02-11T09:03:34+00:00 Igoris Belovas <p><span style="background-color: #ffffff;">The paper continues the research of the modified Borwein method for the evaluation of the Riemann zeta-function. It provides a different perspective on the derivation of the local limit theorem for coefficients of the method. The approach is based on the ratio method, proposed by Proschan.</span></p> <p><span style="background-color: #ffffff;">&nbsp;</span></p> 2019-12-05T00:00:00+00:00 Copyright (c) 2019 Lietuvos matematikos rinkinys The distribution of minimum air temperature in Lithuania 2020-02-11T09:03:33+00:00 Arvydas Jokimaitis Darius Petronaitis <p style="color: #000000; font-family: &amp;quot; noto sans&amp;quot;,arial,helvetica,sans-serif; font-size: 14px; font-style: normal; font-variant: normal; font-weight: 400; letter-spacing: normal; orphans: 2; text-align: left; text-decoration: none; text-indent: 0px; text-transform: none; -webkit-text-stroke-width: 0px; white-space: normal; word-spacing: 0px;"><span style="background-color: #ffffff;">The article authors detected distribution estimates of minimum air temperature in Lithuania. Also estimated ultimate minimum temperature record.</span></p> <p>&nbsp;</p> 2019-12-05T00:00:00+00:00 Copyright (c) 2019 Lietuvos matematikos rinkinys About simple philosophy of solving even simpler yet interesting geometry problems 2020-02-11T09:03:32+00:00 Romualdas Kašuba Edmundas Mazėtis <p><span style="background-color: rgb(255, 255, 255);">Geometry problems are important for training of the mind, imagination and other highly valuable human abilities, however, dealing with geometry tasks is remarkably difficult even for the brightest students. There do not exist, as it seems, universal methods enabling one to solve all or even most of geometry problems. The authors share their life-long experience about some methods of approaching problems, which, when done properly, make some difficult problems not so difficult.</span></p> 2019-12-05T00:00:00+00:00 Copyright (c) 2019 Lietuvos matematikos rinkinys Equations of higher orders 2020-02-11T09:03:31+00:00 Juozas Juvencijus Mačys <p><span style="background-color: #ffffff;">A complicated system of two equations with two variables is considered. The theory of equations of higher orders required for solution is given. Many different methods of solution are indicated. </span></p> <p>&nbsp;</p> <p>&nbsp;</p> 2019-12-05T00:00:00+00:00 Copyright (c) 2019 Lietuvos matematikos rinkinys Rational cuboids and Heron triangles II 2020-02-11T09:03:30+00:00 Edmundas Mazėtis Grigorijus Melničenko <p><span style="background-color: #ffffff;">We study the connection of Heronian triangles with the problem of the existence of rational cuboids. It is proved that the existence of a rational cuboid is equivalent to the existence of a rectangular tetrahedron, which all sides are rational and the base is a Heronian triangle. Examples of rectangular tetrahedra are given, in which all sides are integer numbers, but the area of the base is irrational. The example of the rectangular tetrahedron is also given, which has lengths of one side irrational and the other integer, but the area of the base is integer.</span></p> <p>&nbsp;</p> 2019-12-05T00:00:00+00:00 Copyright (c) 2019 Lietuvos matematikos rinkinys Direct and inverse factorization algorithms of numbers 2020-02-11T09:03:29+00:00 Grigorijus Melničenko <p><span style="background-color: #ffffff;">The factoring natural numbers into factors is a complex computational task. The complexity of solving this problem lies at the heart of RSA security, one of the most famous cryptographic methods. The classical trial division algorithm divides a given number <em>N</em> into all divisors, starting from 2 and to integer part of <strong>√</strong><em>N</em>. Therefore, this algorithm can be called the direct trial division algorithm. We present the inverse trial division algorithm, which divides a given number N into all divisors,<br>starting from the integer part of <em>√N</em> to 2.</span></p> <p>&nbsp;</p> 2019-12-05T00:00:00+00:00 Copyright (c) 2019 Lietuvos matematikos rinkinys Analysis of reasons for graduation from students of the Faculty of Mathematics and Science KTU 2020-02-11T09:03:27+00:00 Miglė Morkevičiūtė Violeta Kravčenkienė <p><span style="background-color: #ffffff;">This article provides an overview of data from the Ministry of Education, Science and Sport of the Republic of Lithuania on students of Lithuanian higher education institutions. Data from Kaunas University of Technology studies department in 2016–2018 on student graduation, maturity exam and study module results has been analyzed. Using descriptive statistics, correlation, logistic regression analysis, and analyzing student interviews and interviews with the employees from the Faculty of Mathematics and Natural Sciences, it has been clarified how achievements in school influence the final marks of study modules and the success of studies overall.<br></span></p> <p>&nbsp;</p> 2019-12-06T00:00:00+00:00 Copyright (c) 2019 Lietuvos matematikos rinkinys Professor of matematics Aurel Edmund Voss and University of Lithuania 2020-02-11T09:03:26+00:00 Judita Puišo Dalia Larionovienė <p><span style="background-color: #ffffff;">Professor Aurel Edmund Voss was a German mathematician, best known for his contributions to application of geometry in natural science and mechanics. The collection of books of professor A.E. Voss was bought and used by Faculty of Matematics and Nature of Univerity of Lithuania. In 1940’s the collection of books of prof. A.E. Voss was transfered to Vilnius University. The aim of the work was to investigate collections of books of libraries of Lithuania and to present books of prof. A.E Voss to scientific society of Lithuania.</span></p> <p>&nbsp;</p> 2019-12-06T00:00:00+00:00 Copyright (c) 2019 Lietuvos matematikos rinkinys Comparison of intermediate Lithuanian mathematics programs with the 1912 Viurtemberg mathematics program in Germany 2020-02-11T09:03:25+00:00 Birutė Ragalytė Alma Paukštienė <p><span style="background-color: #ffffff;">The article compares interwar Lithuanian mathematics programs with Württemberg mathematics programs in German land. The influence of Klein’s ideas on the content of the programs is presented.</span>&nbsp;</p> <p>&nbsp;</p> 2019-12-06T00:00:00+00:00 Copyright (c) 2019 Lietuvos matematikos rinkinys