I. Belovas, Martynas Sabaliauskas, Paulius Mykolaitis
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.
{"title":"Apie sveikųjų skaičių sekų, asocijuotų su pirminiais dvyniais, apskaičiavimą","authors":"I. Belovas, Martynas Sabaliauskas, Paulius Mykolaitis","doi":"10.15388/lmr.2023.33586","DOIUrl":"https://doi.org/10.15388/lmr.2023.33586","url":null,"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.","PeriodicalId":33611,"journal":{"name":"Lietuvos Matematikos Rinkinys","volume":"6 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-11-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139258039","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Gabija Pranaitytė, V. Kravcenkiene, B. Narkeviciene
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.
{"title":"Revised national mathematics curriculum: improving competence in mathematical communication through teaching methods","authors":"Gabija Pranaitytė, V. Kravcenkiene, B. Narkeviciene","doi":"10.15388/lmr.2023.33598","DOIUrl":"https://doi.org/10.15388/lmr.2023.33598","url":null,"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.","PeriodicalId":33611,"journal":{"name":"Lietuvos Matematikos Rinkinys","volume":"29 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-11-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139258340","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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.
{"title":"Sąvokos, terminai ir simboliai matematikos vadovėliuose","authors":"R. Norvaiša","doi":"10.15388/lmr.2023.33597","DOIUrl":"https://doi.org/10.15388/lmr.2023.33597","url":null,"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.","PeriodicalId":33611,"journal":{"name":"Lietuvos Matematikos Rinkinys","volume":"14 7","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-11-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139256394","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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.
{"title":"Savanoriškosios imties panaudojimas populiacijos parametrams vertinti","authors":"Ieva Burakauskaitė, Andrius Čiginas","doi":"10.15388/lmr.2003.33587","DOIUrl":"https://doi.org/10.15388/lmr.2003.33587","url":null,"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.","PeriodicalId":33611,"journal":{"name":"Lietuvos Matematikos Rinkinys","volume":"8 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-11-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139256275","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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.
{"title":"Įrodymai be žodžių","authors":"Edmundas Mazėtis, Grigorijus Melničenko","doi":"10.15388/lmr.2023.33596","DOIUrl":"https://doi.org/10.15388/lmr.2023.33596","url":null,"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.","PeriodicalId":33611,"journal":{"name":"Lietuvos Matematikos Rinkinys","volume":"58 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-11-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139258971","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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.
{"title":"Plateau uždavinys ir minimalieji paviršiai: skaitiniai metodai ir taikymai","authors":"Mifodijus Sapagovas","doi":"10.15388/lmr.2023.33611","DOIUrl":"https://doi.org/10.15388/lmr.2023.33611","url":null,"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.","PeriodicalId":33611,"journal":{"name":"Lietuvos Matematikos Rinkinys","volume":"56 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-11-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139259139","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
A method of automatic detection of human brain symmetry plain in computed tomography (CT) images is described. An algorithm consists of four steps: region of interest, symmetry curve detection, symmetry axis evaluation and calculation of symmetry plane. Symmetry plane are calculated using vertex slices of human brain CT images. There are approximately 40 which has symmetry curve `` ` Falx cerebri'' property. In the first, using this feature symmetry axis in slice detected. In second, coordinates of detected symmetry axis and least square method are used to calculate symmetry plane. In others images where symmetry property is not available symmetry axis is projection of calculated plane.
{"title":"Determination of symmetry plane on human brain CT images","authors":"D. Grigaitis, Mečys Meilūnas","doi":"10.15388/lmr.2005.29213","DOIUrl":"https://doi.org/10.15388/lmr.2005.29213","url":null,"abstract":"A method of automatic detection of human brain symmetry plain in computed tomography (CT) images is described. An algorithm consists of four steps: region of interest, symmetry curve detection, symmetry axis evaluation and calculation of symmetry plane. Symmetry plane are calculated using vertex slices of human brain CT images. There are approximately 40 which has symmetry curve `` ` Falx cerebri'' property. In the first, using this feature symmetry axis in slice detected. In second, coordinates of detected symmetry axis and least square method are used to calculate symmetry plane. In others images where symmetry property is not available symmetry axis is projection of calculated plane.","PeriodicalId":33611,"journal":{"name":"Lietuvos Matematikos Rinkinys","volume":"52 6","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-11-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139257461","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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.
{"title":"A critique of terms and symbols in school mathematics","authors":"Robertas Vilkas","doi":"10.15388/lmd.2023.33599","DOIUrl":"https://doi.org/10.15388/lmd.2023.33599","url":null,"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.","PeriodicalId":33611,"journal":{"name":"Lietuvos Matematikos Rinkinys","volume":"133 3","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-11-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139256011","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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?
{"title":"Didėjančios funkcijos apibrėžimas","authors":"Robertas Vilkas","doi":"10.15388/lmd.2023.33600","DOIUrl":"https://doi.org/10.15388/lmd.2023.33600","url":null,"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?","PeriodicalId":33611,"journal":{"name":"Lietuvos Matematikos Rinkinys","volume":"14 6","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-11-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139258123","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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