https://www.journals.vu.lt/LMR/gateway/plugin/WebFeedGatewayPlugin/atomLietuvos matematikos rinkinys2024-01-08T09:06:16+00:00Artūras Štikonasarturas.stikonas@mif.vu.ltOpen Journal Systems<p><span data-contrast="auto">Founded in 1961. Publishes articles presenting new and important events in all areas of mathematics.</span><span data-ccp-props="{"335559731":0}"> </span></p>https://www.journals.vu.lt/LMR/article/view/34025Modified logistic differential equation of neutral type with time delay2024-01-08T09:16:25+00:00Donatas Švitra
<p>The following differential equation is considered:<br><em>N</em>(<em>t</em>) =<em> rN</em>[1 + a(1 − {<em>N</em>(<em>t</em>)}/<em>K</em>) − {<em>N</em>(<em>t</em> − <em>h</em>) + <em>ρN</em>(<em>t</em> − <em>h</em>)}/<em>K</em>].<br>The stable periodic solution based on the bifurcation theory of that differential equation is constructed.</p>
2003-12-22T00:00:00+00:00Copyright (c) 2003 Donatas Švitrahttps://www.journals.vu.lt/LMR/article/view/33658Air quality investigation using functional data analysis methods2023-11-20T20:21:30+00:00Akvilė VitkauskaitėMilda Salytė
<p>In this research paper, a comprehensive analysis of particulate matter (PM10) and nitrogen dioxide (NO2) pollution concentrations in six different Lithuanian regions is presented. The analysis employs data smoothing, principal component analysis (PCA), exploratory data analysis, hypothesis testing, and time series analysis to provide a thorough examination. Functional data analysis approaches were used to find the origins and effects of these air pollutants by revealing their data patterns. The functional data analysis techniques demonstrate their effectiveness in revealing deep links within large datasets, assisting in the control of air quality problems. This research provides valuable insights into air quality challenges in Lithuanian regions. The study, aimed at comparing air quality across different regions, indicates that there are no significant differences in PM10 and NO2 between the two groups. Notably, reliable forecasts for 2023 data are attainable for PM10 in regions such as Vilnius Old Town, Vilnius Lazdynai, Šiauliai, and Klaipėda. For NO2, successful forecasting can be applied to Vilnius Old Town, Vilnius Lazdynai, and Šiauliai.</p>
2023-11-20T00:00:00+00:00Copyright (c) 2023 Akvilė Vitkauskaitė | Milda Salytėhttps://www.journals.vu.lt/LMR/article/view/33612Editorial Board2023-11-20T20:21:30+00:00Artūras Štikonas
<p>Editorial Board</p>
2023-11-20T00:00:00+00:00Copyright (c) 2023 Artūras Štikonashttps://www.journals.vu.lt/LMR/article/view/33611Plateau problem and minimal surfaces: numerical methods and applications2023-11-20T15:59:42+00:00Mifodijus Sapagovas
<p>This article presents an overview of the results of solving the minimal surface equation by numerical methods. Another research task is the application of minimal surfaces in science, technology, especially architecture. The article is illustrated with examples of the application of minimal surfaces.</p>
2023-11-20T00:00:00+00:00Copyright (c) 2023 Mifodijus Sapagovashttps://www.journals.vu.lt/LMR/article/view/33601Do we need mixed numbers?2023-11-20T15:59:43+00:00Robertas Vilkas
<p>Many reasons are given for not using mixed numbers.</p>
2023-11-20T00:00:00+00:00Copyright (c) 2023 Robertas Vilkashttps://www.journals.vu.lt/LMR/article/view/33600Definition of an increasing function2023-11-20T15:59:43+00:00Robertas Vilkas
<p>Some nuances of applications of the general definition of an increasing (decreasing, non-decreasing, non-increasing) function are discussed. The question of concern to teachers is answered: can a function be increasing not only on an open interval?</p>
2023-11-20T00:00:00+00:00Copyright (c) 2023 Robertas Vilkashttps://www.journals.vu.lt/LMR/article/view/33599A critique of terms and symbols in school mathematics2023-11-20T15:59:43+00:00Robertas Vilkas
<p>Criticism of some terms and symbols of school mathematics is presented, and recommendations are given. The problem of writing decimal fractions using a comma and the resulting semicolon when separating such numbers, which contradicts not only the international symbols of mathematics, but also the general rules of the Lithuanian language, is discussed separately. The incorrect use of the concept of an elementary event not only in schools, but also in universities, is discussed in more detail.</p>
2023-11-20T00:00:00+00:00Copyright (c) 2023 Robertas Vilkashttps://www.journals.vu.lt/LMR/article/view/33598Revised national mathematics curriculum: improving competence in mathematical communication through teaching methods2023-11-20T15:59:43+00:00Gabija PranaitytėVioleta KravčenkienėBronė Narkevičienė
<p>The article delves into the topic of mathematical communication development, a key competence outlined in the updated National Mathematics Curriculum. It explores the integration of this competence within the context of the revised curriculum, examining relevant research on mathematical communication and teaching methodologies to foster its growth. Suggestions for pedagogical strategies aimed at enhancing mathematical communication are presented.</p>
2023-11-20T00:00:00+00:00Copyright (c) 2023 Gabija Pranaitytė | Violeta Kravčenkienė | Bronė Narkevičienėhttps://www.journals.vu.lt/LMR/article/view/33597Concepts, terms and symbols in mathematics textbooks2023-11-20T15:59:43+00:00Rimas Norvaiša
<p>The article discusses the problems of definitions of concepts of school mathematics in textbooks. Excerpts from textbooks show how interpretations of a fraction having no necessary properties of a mathematical definition have changed over the decades. The alternative of a concept of a fraction based on the number line is discussed.</p>
2023-11-20T00:00:00+00:00Copyright (c) 2023 Rimas Norvaišahttps://www.journals.vu.lt/LMR/article/view/33596Proofs without words2023-11-20T15:59:43+00:00Edmundas MazėtisGrigorijus Melničenko
<p>Usually, proofs of mathematical statements involve both algebraic rearrangements and logical reasoning. But there are mathematical statements whose truth is obvious at first glance when there is a diagram illustrating that proof. Although the proofs based on the drawing are not necessarily full and complete, but the drawing helps to notice facts that are then easily supported by algebra and logic. The paper presents proofs of mathematical propositions where, upon careful study of the drawing, the main idea of the proof can be seen from the drawing, and the proof itself becomes beautiful and clear.</p>
2023-11-20T00:00:00+00:00Copyright (c) 2023 Edmundas Mazėtis | Grigorijus Melničenkohttps://www.journals.vu.lt/LMR/article/view/33595sites.google.com/view/Lapinskas – Mathematical readings2023-11-20T15:59:43+00:00Remigijus Lapinskas
<p>This article is about the author's online book "Mathematical Readings" [2]. The book presents the high school math course in a slightly different way than conventional textbooks, the work focuses less on routine problems and tries to examine mathematical concepts in a broader context. The book makes frequent use of mobile math apps and the R program, and links to online sources are often provided. The text may be useful for self-study and math circles.</p>
2023-11-20T00:00:00+00:00Copyright (c) 2023 Remigijus Lapinskashttps://www.journals.vu.lt/LMR/article/view/33594Comparison of ``What numbers make sense?'' problems solving in the Czech Republic and Lithuania2023-11-20T15:59:43+00:00Ieva Kilienė
<p>Word problems pose many challenges for students. One of them is the failure to understand the task conditions and the mechanical solution of the problem. This problem can be addressed by incorporating non-standard word problems into the learning process. The article reviews the type of non-standard word problems called ``Where numbers make sense?'' and discusses its potential applications. It also presents the results of a study conducted with students from Lithuania and the Czech Republic.</p>
2023-11-20T00:00:00+00:00Copyright (c) 2023 Ieva Kilienėhttps://www.journals.vu.lt/LMR/article/view/33592Local asymptotic normality of statistical models of discrete martingales2023-11-20T15:59:43+00:00Vaidotas Kanišauskas
<p>We establish general conditions assuring the local asymptotic normality of statistical experiments of discrete or purely discontinuous local martingales obtained models of point processes of all types were found out. The general conditions include the Fréchet differentiability of parameters in probability in normed spaces with regard to a continuous compensator.</p>
2023-11-20T00:00:00+00:00Copyright (c) 2023 Vaidotas Kanišauskashttps://www.journals.vu.lt/LMR/article/view/33590Investigation of an attack on the multi-prime RSA cryptosystem based on cubic equations2023-11-20T20:21:30+00:00Aleksėjus MichalkovičJokūbas Žitkevičius
<p>In this paper we consider a modification of the attack on the classic RSA cryptosystem aimed at factoring the public modulus <em>n</em>, which is a product of three primes. To improve the performance of the modified attack we introduce additional parameters. We present the theoretical upper bound on the search range parameter and define a shifting parameter based on the empirical results. Since these changes make our attack probabilistic, we investigate the dependence of the success on the values of the newly defined parameters.</p>
2023-11-20T00:00:00+00:00Copyright (c) 2023 Aleksėjus Michalkovič | Jokūbas Žitkevičiushttps://www.journals.vu.lt/LMR/article/view/33589fANOVA application for comparison of companies by the CEO turnover rates2023-11-20T20:21:30+00:00Urtė DeinoravičiūtėAnna Yasyreva
<p>The aim of this study was to analyze the data from the Nasdaq Baltic listed companies’ financial statements and to estimate if the CEO changes have a significant influence on the financial performance: profitability, indebtedness and stock price. Data was collected and financial ratios were computed for 34 companies during 2006 to 2021 (2008 to 2022 for stock prices). The companies were divided into 3 groups: ones that had no CEO changes over the period; those that had 1 or 2 and those with 3 or more. Point-wise ANOVA, fANOVA and fMANOVA were conducted. Both point-wise and functional ANOVA indicated that there is a significant difference of at least one group from the others in terms of ROA and EBITDA margin. After conducting two-sample tests, the group with 3 or more CEO changes was identified as having a significantly higher EBITDA margin than the others. Furthermore, a significant positive relationship between the stock price and the CEO turnover was uncovered in the function-on-scalar regression results.</p>
2023-11-20T00:00:00+00:00Copyright (c) 2023 Urtė Deinoravičiūtė | Anna Yasyrevahttps://www.journals.vu.lt/LMR/article/view/33587On using a non-probability sample for the estimation of population parameters2023-11-20T20:21:31+00:00Ieva BurakauskaitėAndrius Čiginas
<p>We aim to find a way to effectively integrate a non-probability (voluntary) sample under the data framework, where the study variable is also observed in a probability sample of some statistical survey. The selection bias that arises from voluntary participation in the survey is corrected by estimating the inclusion into the sample probabilities (propensity scores) for the units in the non-probability sample. The estimators for the propensity scores are constructed using a parametric logistic regression model. We consider two modeling scenarios: with an assumption that the willingness to participate in the voluntary survey does not depend on the survey variable itself and that such a variable does contribute to whether the individual responds or not. The maximum likelihood method is applied in both scenarios to estimate the propensity scores. The estimators of the population mean based on the estimated propensity scores are linearly combined with the unbiased estimator using the probability sample data. We compare the constructed estimators in the simulation study, where we estimate the population proportions using data from the Population and Housing Census surveys.</p>
2023-11-20T00:00:00+00:00Copyright (c) 2023 Ieva Burakauskaitė | Andrius Čiginashttps://www.journals.vu.lt/LMR/article/view/33586On the calculation of integer sequences, associated with twin primes2023-11-20T15:59:43+00:00Igoris BelovasMartynas SabaliauskasPaulius Mykolaitis
<p>The twin primes conjecture states that there are infinitely many twin primes. While studying this hypothesis, many important results were obtained, but the problem remains unsolved. In this work, the problem is studied from the side of experimental mathematics. Using the probabilistic Miller–Rabin primality test and parallel computing technologies, the distribution of prime pairs in the intervals (2<em><sup>n</sup></em>; 2<sup><em>n</em>+1</sup>] is studied experimentally.</p>
2023-11-20T00:00:00+00:00Copyright (c) 2023 Igoris Belovas | Martynas Sabaliauskas | Paulius Mykolaitishttps://www.journals.vu.lt/LMR/article/view/33580Editorial Board2023-11-21T17:39:34+00:00Artūras Štikonas2023-11-20T00:00:00+00:00Copyright (c) 2023 Artūras Štikonashttps://www.journals.vu.lt/LMR/article/view/33577Problems for combinatorial numbers satisfying a class of triangular arrays2023-11-20T15:59:44+00:00Igoris Belovas
<p>Numbers satisfying a class of triangular arrays, defined by a bivariate first-order linear difference equation with linear coefficients, include a wide range of combinatorial numbers: binomial coefficients, Morgan numbers, Stirling numbers of the first and the second types, non-central Stirling numbers, Eulerian numbers, Lah numbers, and their generalizations. In this work, we derive the general analytic expression of the numbers satisfying a class of triangular arrays and propose problems (both teaching and unsolved ones) for undergraduates studying probability theory and analytical combinatorics subjects in the study programs of the fields of mathematics and computer science. Some of the unsolved challenges can also be used as the basis for a thesis.</p>
2023-11-20T00:00:00+00:00Copyright (c) 2023 Igoris Belovashttps://www.journals.vu.lt/LMR/article/view/33576Data mining technologies based on IBM intelligent miner2024-01-22T10:08:52+00:00Regina KulvietienėJelena Mamčenko
<p>There is not abstract.</p>
2002-12-20T00:00:00+00:00Copyright (c) 2002 Regina Kulvietienė | Jelena Mamčenkohttps://www.journals.vu.lt/LMR/article/view/33575Optimal allocation of means for trauma prevention using stochastic programming2024-01-22T10:08:52+00:00Sigutė VakrinienėPetras Čyras
<p>Optimal criterion for allocation of means necessary for trauma prevention is proposed. The problem is simulated as a matrix game with random elements.</p>
2002-12-20T00:00:00+00:00Copyright (c) 2002 Sigutė Vakrinienė | Petras Čyrashttps://www.journals.vu.lt/LMR/article/view/33574Data mining approach on information detection using intelligent miner for data2023-12-19T06:41:58+00:00Regina KulvietienėJelena Mamčenko
<p>There is not abstract.</p>
2003-12-22T00:00:00+00:00Copyright (c) 2003 Regina Kulvietienė | Jelena Mamčenkohttps://www.journals.vu.lt/LMR/article/view/33573About "Practical Informatics" course2023-12-19T06:43:41+00:00Sigitas Dapkūnas
<p>The paper describes the contents of course “Practical Informatics” for underclassman. It deals also with the problems of that course. The course is based on ECDL requirements.</p>
2003-12-22T00:00:00+00:00Copyright (c) 2003 Sigitas Dapkūnashttps://www.journals.vu.lt/LMR/article/view/33224Changing of the school-leaving exam in information technology2023-12-19T06:43:42+00:00Valentina Dagienė
<p>This paper deals with the main problem of the school-leaving exam in information technology – design and contents of exam for 2004. The first school-leaving exam in informatics was organized in 1994/1995.<br>Since the 1999/2000 school year, a profiled model was implemented on all the secondary education levels. Following that two types of the exam in information technology are proposed. The first one – information technology – is intended for students whose learning aim is to acquire skills for using computers in every day life. The second one – information technology (programming) –<br>for those who want to be advanced users and programmers. The main attention is paid to the aims, structure, and contents of exam.</p>
2003-12-22T00:00:00+00:00Copyright (c) 2003 Valentina Dagienėhttps://www.journals.vu.lt/LMR/article/view/15318Editorial Board and Table of Contents2024-01-22T10:08:59+00:00Artūras Štikonas2002-12-20T00:00:00+00:00Copyright (c) 2002 Lietuvos matematikos rinkinyshttps://www.journals.vu.lt/LMR/article/view/33057On approximation by the Poisson law2024-01-22T10:08:52+00:00Vydas Čekanavičius
<p>There is not abstract.</p>
2002-12-20T00:00:00+00:00Copyright (c) 2002 Lietuvos matematikos rinkinyshttps://www.journals.vu.lt/LMR/article/view/33058Asymptotic expansion for the distribution function of the series scheme of random variables in the large deviation Cramer zone2024-01-22T10:08:52+00:00Dovilė Deltuvienė
<p>There is not abstract.</p>
2002-12-20T00:00:00+00:00Copyright (c) 2002 Lietuvos matematikos rinkinyshttps://www.journals.vu.lt/LMR/article/view/33061Convergence of products of independent random variables to the log-Poisson law2024-01-22T10:08:52+00:00Reda LileikytėJonas Šiaulys
<p>There is not abstract.</p>
2002-12-20T00:00:00+00:00Copyright (c) 2002 Lietuvos matematikos rinkinyshttps://www.journals.vu.lt/LMR/article/view/33062Discrete limit theorems for general Dirichlet polynomials2024-01-22T10:08:52+00:00Renata Macaitienė
<p>There is not abstract.</p>
2002-12-20T00:00:00+00:00Copyright (c) 2002 Lietuvos matematikos rinkinyshttps://www.journals.vu.lt/LMR/article/view/33064Large deviation theorems for weighted summation of Gamma-distribution random variables2024-01-22T10:08:52+00:00Leonas Saulis
<p>There is not abstract.</p>
2002-12-20T00:00:00+00:00Copyright (c) 2002 Lietuvos matematikos rinkinys