Lietuvos matematikos rinkinys https://www.journals.vu.lt/LMR <p>Publish articles presenting new and important events in all areas of mathematics.</p> Vilniaus universiteto leidykla / Vilnius University Press lt-LT Lietuvos matematikos rinkinys 0132-2818 <p>Please read the Copyright Notice in&nbsp;<a href="http://www.zurnalai.vu.lt/informacijos-mokslai/journalpolicy">Journal Policy</a>.&nbsp;</p> Editorial Board and Table of Contents https://www.journals.vu.lt/LMR/article/view/15205 Artūras Štikonas Copyright (c) 2019 Lietuvos matematikos rinkinys http://creativecommons.org/licenses/by/4.0 2019-12-05 2019-12-05 60 1 1 Lithuanian science courses in Vilnius and traces of mathematics in them https://www.journals.vu.lt/LMR/article/view/15188 <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> Juozas Banionis Copyright (c) 2019 Lietuvos matematikos rinkinys http://creativecommons.org/licenses/by/4.0 2019-12-05 2019-12-05 60 1 5 10.15388/LMR.B.2019.15188 Modeling Baltic market benchmark index: a comparison of models https://www.journals.vu.lt/LMR/article/view/15207 <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> Igoris Belovas Copyright (c) 2019 Lietuvos matematikos rinkinys http://creativecommons.org/licenses/by/4.0 2019-12-05 2019-12-05 60 6 10 10.15388/LMR.B.2019.15207 Local limit theorem for coefficients of modified Borwein’s algorithm, proved by the ratio method https://www.journals.vu.lt/LMR/article/view/15208 <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> Igoris Belovas Copyright (c) 2019 Lietuvos matematikos rinkinys http://creativecommons.org/licenses/by/4.0 2019-12-05 2019-12-05 60 11 14 10.15388/LMR.B.2019.15208 The distribution of minimum air temperature in Lithuania https://www.journals.vu.lt/LMR/article/view/15229 <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> Arvydas Jokimaitis Darius Petronaitis Copyright (c) 2019 Lietuvos matematikos rinkinys http://creativecommons.org/licenses/by/4.0 2019-12-05 2019-12-05 60 15 19 10.15388/LMR.B.2019.15229 About simple philosophy of solving even simpler yet interesting geometry problems https://www.journals.vu.lt/LMR/article/view/15230 <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> Romualdas Kašuba Edmundas Mazėtis Copyright (c) 2019 Lietuvos matematikos rinkinys http://creativecommons.org/licenses/by/4.0 2019-12-05 2019-12-05 60 20 27 10.15388/LMR.B.2019.15230 Equations of higher orders https://www.journals.vu.lt/LMR/article/view/15232 <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> Juozas Juvencijus Mačys Copyright (c) 2019 Lietuvos matematikos rinkinys http://creativecommons.org/licenses/by/4.0 2019-12-05 2019-12-05 60 28 33 10.15388/LMR.B.2019.15232 Rational cuboids and Heron triangles II https://www.journals.vu.lt/LMR/article/view/15233 <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> Edmundas Mazėtis Grigorijus Melničenko Copyright (c) 2019 Lietuvos matematikos rinkinys http://creativecommons.org/licenses/by/4.0 2019-12-05 2019-12-05 60 34 38 10.15388/LMR.B.2019.15233 Direct and inverse factorization algorithms of numbers https://www.journals.vu.lt/LMR/article/view/15234 <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> Grigorijus Melničenko Copyright (c) 2019 Lietuvos matematikos rinkinys http://creativecommons.org/licenses/by/4.0 2019-12-05 2019-12-05 60 39 45 10.15388/LMR.B.2019.15234 Analysis of reasons for graduation from students of the Faculty of Mathematics and Science KTU https://www.journals.vu.lt/LMR/article/view/15235 <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> Miglė Morkevičiūtė Violeta Kravčenkienė Copyright (c) 2019 Lietuvos matematikos rinkinys http://creativecommons.org/licenses/by/4.0 2019-12-06 2019-12-06 60 46 54 10.15388/LMR.B.2019.15235 Professor of matematics Aurel Edmund Voss and University of Lithuania https://www.journals.vu.lt/LMR/article/view/15236 <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> Judita Puišo Dalia Larionovienė Copyright (c) 2019 Lietuvos matematikos rinkinys http://creativecommons.org/licenses/by/4.0 2019-12-06 2019-12-06 60 55 62 10.15388/LMR.B.2019.15236 Comparison of intermediate Lithuanian mathematics programs with the 1912 Viurtemberg mathematics program in Germany https://www.journals.vu.lt/LMR/article/view/15237 <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> Birutė Ragalytė Alma Paukštienė Copyright (c) 2019 Lietuvos matematikos rinkinys http://creativecommons.org/licenses/by/4.0 2019-12-06 2019-12-06 60 63 69 10.15388/LMR.B.2019.15237