Lietuvos matematikos rinkinys
https://www.journals.vu.lt/LMR
<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>Vilniaus universiteto leidykla / Vilnius University PressltLietuvos matematikos rinkinys0132-2818<p>Please read the Copyright Notice in <a href="http://www.zurnalai.vu.lt/informacijos-mokslai/journalpolicy">Journal Policy</a>. </p>Modified logistic differential equation of neutral type with time delay
https://www.journals.vu.lt/LMR/article/view/34025
<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>
ArticlesDonatas Švitra
Copyright (c) 2003 Donatas Švitra
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2003-12-222003-12-2215615810.15388/LMR.2003.34025Air quality investigation using functional data analysis methods
https://www.journals.vu.lt/LMR/article/view/33658
<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>
Articlesair pollutantsparticulate matternitrogen dioxidefunctional data analysisexploratory data analysishypothesis testingAkvilė VitkauskaitėMilda Salytė
Copyright (c) 2023 Akvilė Vitkauskaitė | Milda Salytė
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2023-11-202023-11-20365310.15388/LMR.2023.33658Editorial Board
https://www.journals.vu.lt/LMR/article/view/33612
<p>Editorial Board</p>
Front MatterArtūras Štikonas
Copyright (c) 2023 Artūras Štikonas
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2023-11-202023-11-201110.15388/LMR.22612Plateau problem and minimal surfaces: numerical methods and applications
https://www.journals.vu.lt/LMR/article/view/33611
<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>
ArticlesPlateau problemminimal surface equationnumerical methodsapplications of minimal surfacesMifodijus Sapagovas
Copyright (c) 2023 Mifodijus Sapagovas
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2023-11-202023-11-2011510.15388/LMR.2023.33611Do we need mixed numbers?
https://www.journals.vu.lt/LMR/article/view/33601
<p>Many reasons are given for not using mixed numbers.</p>
Articlesmixed numbersmixed fractionsRobertas Vilkas
Copyright (c) 2023 Robertas Vilkas
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2023-11-202023-11-2011412310.15388/LMR.2023.33601Definition of an increasing function
https://www.journals.vu.lt/LMR/article/view/33600
<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>
Articlesincreasing functiondecreasing functionnon-decreasing functionnon-increasing functionRobertas Vilkas
Copyright (c) 2023 Robertas Vilkas
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2023-11-202023-11-209811310.15388/LMD.2023.33600A critique of terms and symbols in school mathematics
https://www.journals.vu.lt/LMR/article/view/33599
<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>
Articlesnotationspolynomialelementary eventsample spaceeven numberRobertas Vilkas
Copyright (c) 2023 Robertas Vilkas
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2023-11-202023-11-20879710.15388/LMD.2023.33599Revised national mathematics curriculum: improving competence in mathematical communication through teaching methods
https://www.journals.vu.lt/LMR/article/view/33598
<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>
Articlesmathematics communicationrevised national mathematics curriculummathematics teaching methodsGabija PranaitytėVioleta KravčenkienėBronė Narkevičienė
Copyright (c) 2023 Gabija Pranaitytė | Violeta Kravčenkienė | Bronė Narkevičienė
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2023-11-202023-11-20758610.15388/LMR.2023.33598Concepts, terms and symbols in mathematics textbooks
https://www.journals.vu.lt/LMR/article/view/33597
<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>
Articlesconcept of fractionconcept of quotientnumber linetextbook school mathematicsmathematical nominalismRimas Norvaiša
Copyright (c) 2023 Rimas Norvaiša
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2023-11-202023-11-20597410.15388/LMR.2023.33597Proofs without words
https://www.journals.vu.lt/LMR/article/view/33596
<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>
Articlesmathematical propositionsproofsdrawingproof ideaEdmundas MazėtisGrigorijus Melničenko
Copyright (c) 2023 Edmundas Mazėtis | Grigorijus Melničenko
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2023-11-202023-11-20505810.15388/LMR.2023.33596sites.google.com/view/Lapinskas – Mathematical readings
https://www.journals.vu.lt/LMR/article/view/33595
<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>
Articlesmath in high schoolmath circleRemigijus Lapinskas
Copyright (c) 2023 Remigijus Lapinskas
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2023-11-202023-11-20484910.15388/LMD.2023.33595Comparison of ``What numbers make sense?'' problems solving in the Czech Republic and Lithuania
https://www.journals.vu.lt/LMR/article/view/33594
<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>
Articlesword problemsnon-standard word problemsmathematical reasoningIeva Kilienė
Copyright (c) 2023 Ieva Kilienė
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2023-11-202023-11-20414710.15388/LMR.2023.33594Local asymptotic normality of statistical models of discrete martingales
https://www.journals.vu.lt/LMR/article/view/33592
<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>
Articlesdiscrete or purely discontinuous local martingalelocal asymptotic normalitycompensatorFréchet differentiabilityVaidotas Kanišauskas
Copyright (c) 2023 Vaidotas Kanišauskas
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2023-11-202023-11-20304010.15388/LMD.2023.33592Investigation of an attack on the multi-prime RSA cryptosystem based on cubic equations
https://www.journals.vu.lt/LMR/article/view/33590
<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>
Articlesasymmetric cryptographymulti-prime RSAinteger factorization problemAleksėjus MichalkovičJokūbas Žitkevičius
Copyright (c) 2023 Aleksėjus Michalkovič | Jokūbas Žitkevičius
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2023-11-202023-11-20253510.15388/LMR.2023.33590fANOVA application for comparison of companies by the CEO turnover rates
https://www.journals.vu.lt/LMR/article/view/33589
<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>
ArticlesprofitabilityCEO turnoverfunctional datafANOVAUrtė DeinoravičiūtėAnna Yasyreva
Copyright (c) 2023 Urtė Deinoravičiūtė | Anna Yasyreva
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2023-11-202023-11-20122410.15388/LMR.2023.33589On using a non-probability sample for the estimation of population parameters
https://www.journals.vu.lt/LMR/article/view/33587
<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>
Articlesdata integrationnot missing at randompropensity score adjustmentpopulation censusIeva BurakauskaitėAndrius Čiginas
Copyright (c) 2023 Ieva Burakauskaitė | Andrius Čiginas
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2023-11-202023-11-2011110.15388/LMR.2003.33587On the calculation of integer sequences, associated with twin primes
https://www.journals.vu.lt/LMR/article/view/33586
<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>
Articlesinteger sequencesHardy-Littlewood conjectureprime k-tuplesIgoris BelovasMartynas SabaliauskasPaulius Mykolaitis
Copyright (c) 2023 Igoris Belovas | Martynas Sabaliauskas | Paulius Mykolaitis
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2023-11-202023-11-20232910.15388/LMR.2023.33586Editorial Board
https://www.journals.vu.lt/LMR/article/view/33580
Front MatterArtūras Štikonas
Copyright (c) 2023 Artūras Štikonas
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2023-11-202023-11-201110.15388/LMR.2023.33580Problems for combinatorial numbers satisfying a class of triangular arrays
https://www.journals.vu.lt/LMR/article/view/33577
<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>
Articlescombinatorial numberslimit theoremsasymptotic normalityIgoris Belovas
Copyright (c) 2023 Igoris Belovas
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2023-11-202023-11-20162210.15388/LMR.2023.33577Data mining technologies based on IBM intelligent miner
https://www.journals.vu.lt/LMR/article/view/33576
<p>There is not abstract.</p>
ArticlesRegina KulvietienėJelena Mamčenko
Copyright (c) 2002 Regina Kulvietienė | Jelena Mamčenko
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2002-12-202002-12-2062162910.15388/LMR.2002.33576Optimal allocation of means for trauma prevention using stochastic programming
https://www.journals.vu.lt/LMR/article/view/33575
<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>
ArticlesSigutė VakrinienėPetras Čyras
Copyright (c) 2002 Sigutė Vakrinienė | Petras Čyras
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2002-12-202002-12-2059159610.15388/LMR.2002.33575Data mining approach on information detection using intelligent miner for data
https://www.journals.vu.lt/LMR/article/view/33574
<p>There is not abstract.</p>
ArticlesRegina KulvietienėJelena Mamčenko
Copyright (c) 2003 Regina Kulvietienė | Jelena Mamčenko
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2003-12-222003-12-2224825310.15388/LMR.2003.33574About "Practical Informatics" course
https://www.journals.vu.lt/LMR/article/view/33573
<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>
ArticlesSigitas Dapkūnas
Copyright (c) 2003 Sigitas Dapkūnas
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2003-12-222003-12-2221521710.15388/LMR.2003.33573Changing of the school-leaving exam in information technology
https://www.journals.vu.lt/LMR/article/view/33224
<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>
ArticlesValentina Dagienė
Copyright (c) 2003 Valentina Dagienė
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2003-12-222003-12-2220420810.15388/LMR.2003.33224Editorial Board and Table of Contents
https://www.journals.vu.lt/LMR/article/view/15318
Front MatterArtūras Štikonas
Copyright (c) 2002 Lietuvos matematikos rinkinys
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2002-12-202002-12-2011010.15388/LMR.2002.15318On approximation by the Poisson law
https://www.journals.vu.lt/LMR/article/view/33057
<p>There is not abstract.</p>
ArticlesVydas Čekanavičius
Copyright (c) 2002 Lietuvos matematikos rinkinys
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2002-12-202002-12-2068669010.15388/LMR.2002.33057Asymptotic expansion for the distribution function of the series scheme of random variables in the large deviation Cramer zone
https://www.journals.vu.lt/LMR/article/view/33058
<p>There is not abstract.</p>
ArticlesDovilė Deltuvienė
Copyright (c) 2002 Lietuvos matematikos rinkinys
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2002-12-202002-12-2069169610.15388/LMR.2002.33058Convergence of products of independent random variables to the log-Poisson law
https://www.journals.vu.lt/LMR/article/view/33061
<p>There is not abstract.</p>
ArticlesReda LileikytėJonas Šiaulys
Copyright (c) 2002 Lietuvos matematikos rinkinys
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2002-12-202002-12-2070170410.15388/LMR.2002.33061Discrete limit theorems for general Dirichlet polynomials
https://www.journals.vu.lt/LMR/article/view/33062
<p>There is not abstract.</p>
ArticlesRenata Macaitienė
Copyright (c) 2002 Lietuvos matematikos rinkinys
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2002-12-202002-12-2070570910.15388/LMR.2002.33062Large deviation theorems for weighted summation of Gamma-distribution random variables
https://www.journals.vu.lt/LMR/article/view/33064
<p>There is not abstract.</p>
ArticlesLeonas Saulis
Copyright (c) 2002 Lietuvos matematikos rinkinys
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2002-12-202002-12-2071471810.15388/LMR.2002.33064