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Lietuvos Matematikos Rinkinys
Number of Followers: 0  Open Access journalISSN (Print) 0132-2818 - ISSN (Online) 2335-898X Published by Vilnius University  [38 journals]
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- Plateau problem and minimal surfaces: numerical methods and applications
Authors: Mifodijus Sapagovas
Pages: 1 - 15
Abstract: 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.
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parameters
Authors: Ieva Burakauskaitė, Andrius Čiginas
Pages: 1 - 11
Abstract: 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.
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Authors: Urtė Deinoravičiūtė, Anna Yasyreva
Pages: 12 - 24
Abstract: 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.
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Authors: Igoris Belovas
Pages: 16 - 22
Abstract: 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.
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Authors: Birutė Kryžienė, Gintautas Misevičius
Pages: 19 - 23
Abstract: There is not abstract.
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PubDate: 2023-09-21
DOI: 10.15388/LMR.2006.30565
- On the calculation of integer sequences, associated with twin primes
Authors: Igoris Belovas, Martynas Sabaliauskas, Paulius Mykolaitis
Pages: 23 - 29
Abstract: 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 (2n; 2n+1] is studied experimentally.
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cubic equations
Authors: Aleksėjus Michalkovič, Jokūbas Žitkevičius
Pages: 25 - 35
Abstract: In this paper we consider a modification of the attack on the classic RSA cryptosystem aimed at factoring the public modulus n, 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.
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critical strip
Authors: Mindaugas Stoncelis
Pages: 28 - 31
Abstract: There is not abstract
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PubDate: 2023-09-21
DOI: 10.15388/LMR.2006.30567
- Local asymptotic normality of statistical models of discrete martingales
Authors: Vaidotas Kanišauskas
Pages: 30 - 40
Abstract: 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.
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Authors: Akvilė Vitkauskaitė, Milda Salytė
Pages: 36 - 53
Abstract: 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.
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Republic and Lithuania
Authors: Ieva Kilienė
Pages: 41 - 47
Abstract: 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.
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Authors: Remigijus Lapinskas
Pages: 48 - 49
Abstract: 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.
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Authors: Edmundas Mazėtis, Grigorijus Melničenko
Pages: 50 - 58
Abstract: 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.
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Authors: Rimas Norvaiša
Pages: 59 - 74
Abstract: 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.
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mathematical communication through teaching methods
Authors: Gabija Pranaitytė, Violeta Kravčenkienė, Bronė Narkevičienė
Pages: 75 - 86
Abstract: 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.
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Authors: Robertas Vilkas
Pages: 87 - 97
Abstract: 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.
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Authors: Robertas Vilkas
Pages: 98 - 113
Abstract: 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'
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Authors: Robertas Vilkas
Pages: 114 - 123
Abstract: Many reasons are given for not using mixed numbers.
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Authors: Juozas Juvencijus Mačys
Pages: 270 - 274
Abstract: The method of monotonic sequences (see [1], [2]) is considered and the issue of its exactness is discussed. It is shown how the method can be applied to finite sums with a large number of summands.
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Authors: Igoris Belovas, Audrius Kabašinskas, Leonidas Sakalauskas
Pages: 289 - 294
Abstract: The Baltic States equity market is a challenge for investors and financial analysts. Unfortunately strong assivity is observed in ``young'' markets, therefore any (Gaussian, α-stable etc) distribution fitting tests (Anderson–Darling, Kolmogorov–Smirnov, etc.) are poorly applicable. Improvement based on mixed distributions is proposed and its adequacy in the Baltic States market is tested. In this paper we use Koutrouvelis goodness-of-fit test and modified χ2 test.
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Authors: Eimutis Valakevičius
Pages: 295 - 302
Abstract: In the article is proposed the algorithm how to model the dynamics of asset prices by Markov process with continuous time and countable set of states.
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