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.
{"title":"Monotoniškųjų sekų metodo taikymas","authors":"Juozas Juvencijus Mačys","doi":"10.15388/lmr.2005.26664","DOIUrl":"https://doi.org/10.15388/lmr.2005.26664","url":null,"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.","PeriodicalId":33611,"journal":{"name":"Lietuvos Matematikos Rinkinys","volume":"17 2","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-11-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139254803","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}
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.
{"title":"Oro kokybės tyrimas naudojant funkcinės duomenų analizės metodus","authors":"Akvilė Vitkauskaitė, Milda Salytė","doi":"10.15388/lmr.2023.33658","DOIUrl":"https://doi.org/10.15388/lmr.2023.33658","url":null,"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.","PeriodicalId":33611,"journal":{"name":"Lietuvos Matematikos Rinkinys","volume":"40 4","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-11-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139255784","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}
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.
{"title":"Problems for combinatorial numbers satisfying a class of triangular arrays","authors":"I. Belovas","doi":"10.15388/lmr.2023.33577","DOIUrl":"https://doi.org/10.15388/lmr.2023.33577","url":null,"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.","PeriodicalId":33611,"journal":{"name":"Lietuvos Matematikos Rinkinys","volume":"38 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-11-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139258907","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}
Many reasons are given for not using mixed numbers.
不使用混合数的理由有很多。
{"title":"Do we need mixed numbers?","authors":"Robertas Vilkas","doi":"10.15388/lmr.2023.33601","DOIUrl":"https://doi.org/10.15388/lmr.2023.33601","url":null,"abstract":"Many reasons are given for not using mixed numbers.","PeriodicalId":33611,"journal":{"name":"Lietuvos Matematikos Rinkinys","volume":"38 9","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-11-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139255561","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}
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.
{"title":"Comparison of ``What numbers make sense?'' problems solving in the Czech Republic and Lithuania","authors":"Ieva Kilienė","doi":"10.15388/lmr.2023.33594","DOIUrl":"https://doi.org/10.15388/lmr.2023.33594","url":null,"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.","PeriodicalId":33611,"journal":{"name":"Lietuvos Matematikos Rinkinys","volume":"122 4","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-11-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139257170","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 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.
{"title":"fANOVA taikymas kompanijų su dažnu ir retu generalinio direktoriaus pasikeitimu palyginimui","authors":"Urtė Deinoravičiūtė, Anna Yasyreva","doi":"10.15388/lmr.2023.33589","DOIUrl":"https://doi.org/10.15388/lmr.2023.33589","url":null,"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.","PeriodicalId":33611,"journal":{"name":"Lietuvos Matematikos Rinkinys","volume":"54 8","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-11-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139258662","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 processes of growth play an important role in different fields of science, such as ecology, economics, finance etc. In applications the averaged trend kinetics is represented by means of one of the types of logistic forms (Verhulst, Gompertz, Mitscherlich, Richards et al.). The article deals with the numerical solutions of the Fokker–Plank equation.
{"title":"Stochastinių logistinių dėsnių ir tankio mišinių taikymas medynų augimo analizėje","authors":"Petras Rupšys, Danutė Raškinienė","doi":"10.15388/lmr.2005.29316","DOIUrl":"https://doi.org/10.15388/lmr.2005.29316","url":null,"abstract":"The processes of growth play an important role in different fields of science, such as ecology, economics, finance etc. In applications the averaged trend kinetics is represented by means of one of the types of logistic forms (Verhulst, Gompertz, Mitscherlich, Richards et al.). The article deals with the numerical solutions of the Fokker–Plank equation.","PeriodicalId":33611,"journal":{"name":"Lietuvos Matematikos Rinkinys","volume":"102 3","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-11-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139258794","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}
In this paper the error estimation for n-th order Filon quadrature formula is discussed.
本文讨论了 n 阶菲隆正交公式的误差估计。
{"title":"n-os eilės Filono kvadratūrinės formulės paklaidos įvertinimas","authors":"Kostas Plukas, Danutė Plukienė","doi":"10.15388/lmr.2005.29206","DOIUrl":"https://doi.org/10.15388/lmr.2005.29206","url":null,"abstract":"In this paper the error estimation for n-th order Filon quadrature formula is discussed.","PeriodicalId":33611,"journal":{"name":"Lietuvos Matematikos Rinkinys","volume":"7 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-11-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139259123","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 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.
本文介绍的是作者的在线书籍《数学读本》[2]。本书介绍高中数学课程的方式与传统教科书略有不同，作品较少关注常规问题，而是试图在更广阔的背景下考察数学概念。书中经常使用移动数学应用程序和 R 程序，并经常提供在线资源链接。这本教科书可能对自学和数学圈子有用。
{"title":"sites.google.com/view/Lapinskas – Mathematical readings","authors":"Remigijus Lapinskas","doi":"10.15388/lmd.2023.33595","DOIUrl":"https://doi.org/10.15388/lmd.2023.33595","url":null,"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.","PeriodicalId":33611,"journal":{"name":"Lietuvos Matematikos Rinkinys","volume":"15 5","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-11-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139259546","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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