In this paper the local limit theorem for density of k-th maxima of independent identically distributed random variables is proved.
本文证明了独立同分布随机变量第k个极大值密度的局部极限定理。
{"title":"Nepriklausomų atsitiktinių dydžių k-tojo maksimumo tankio asimptotika","authors":"Arvydas Jokimaitis","doi":"10.15388/lmr.2006.30794","DOIUrl":"https://doi.org/10.15388/lmr.2006.30794","url":null,"abstract":"In this paper the local limit theorem for density of k-th maxima of independent identically distributed random variables is proved.","PeriodicalId":33611,"journal":{"name":"Lietuvos Matematikos Rinkinys","volume":"158 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-09-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136238440","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}
Jelena Čikun, Jonas-Vytautas Daunoravičius, Marijus Radavičius
The paper is devoted to multivariate statistical analysis of academic performance data. The phenomina of general grade inflation and the effect of the first passing of an egzam on grades of the egzam are investigated by making use of general linear (mixed) model and logistic regresion.
{"title":"Analysis of correlations between indices of academic performance","authors":"Jelena Čikun, Jonas-Vytautas Daunoravičius, Marijus Radavičius","doi":"10.15388/lmr.2006.30601","DOIUrl":"https://doi.org/10.15388/lmr.2006.30601","url":null,"abstract":"The paper is devoted to multivariate statistical analysis of academic performance data. The phenomina of general grade inflation and the effect of the first passing of an egzam on grades of the egzam are investigated by making use of general linear (mixed) model and logistic regresion.","PeriodicalId":33611,"journal":{"name":"Lietuvos Matematikos Rinkinys","volume":"58 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-09-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136238677","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}
{"title":"Explicit formulas in asymptotic expansions for Euler’s approximations of semigroups","authors":"Monika Vilkienė","doi":"10.15388/lmr.2006.30575","DOIUrl":"https://doi.org/10.15388/lmr.2006.30575","url":null,"abstract":"There is not abstract.","PeriodicalId":33611,"journal":{"name":"Lietuvos Matematikos Rinkinys","volume":"159 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-09-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136239127","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 1904 with the lifting of the ban on Lithuanian publications by Russian czar government and in 1906 with giving the permit to teach arithmetics in mother tongue at primary schools the legal publishing of Lithuanian arithmetic textbooks started. Already in 1906 even three arithmetic textbooks were published. These were two parts of ``Arithmetic Taskbook“ by Pranas Mašiotas, the first part of ``Collection of Arithmetic Tasks and Examples“ by Petras Bendorius and Pranas Daugirda and two parts of translated from Polish ``Arithmetic Tasks and Examples“ by Stanislaw Thom. All the books step by step explained in the Lithuanian language four arithmetic operations up to ten, later a hundred and finally up to a thousand.In 1909 two important books were published: the second part of the textbook by Petras Bendorius and Pranas Daugirda and ``Elementary Arithmetics“ by Petras Mikolainis. The latter textbook could be distinguished for methodical instructions.In 1909–1916 Juozas Damijonaitis prepared and published two parts of ``Arithmetic Textbook“. The book was recompiled into three parts during the period of the Republic of Lithuania (in 1918–1940). It became popular and was constantly republished.When forming of arithmetic basics was coming to end in 1916 ``The Short Science of Arithmetics“ by S. Thom (1916) appeared in the Lithuanian language, where the theory of arithmetics was presented.
1904年，随着俄罗斯沙皇政府解除对立陶宛出版物的禁令，以及1906年允许在小学用母语教授算术，立陶宛算术教科书开始合法出版。早在1906年，就已经出版了三本算术教科书。这是Pranas Mašiotas的“算术任务手册”的两个部分，Petras bendorus和Pranas Daugirda的“算术任务和示例集”的第一部分，以及Stanislaw Thom从波兰翻译的“算术任务和示例”的两个部分。所有的书都用立陶宛语一步一步地解释了从十到一百，最后到一千的四种算术运算。1909年出版了两本重要的书:佩特拉斯·本多留斯和普拉纳斯·道格达的教科书的第二部分和佩特拉斯·米科莱尼斯的《基本算术》。后一本教科书以教学有条不紊而著称。1909-1916年，达米约奈提斯编写并出版了《算术教科书》的两部分。在立陶宛共和国时期(1918-1940年)，这本书被重新编辑成三部分。这本书很受欢迎，并不断被再版。当1916年算术基础的形成即将结束时，S. Thom(1916)的《算术的简短科学》(The Short Science of Arithmetics)以立陶宛语出版，在那里提出了算术理论。
{"title":"Dešimtmečio po lietuviškos spaudos atgavimo aritmetikos vadovėlių panorama","authors":"Juozas Banionis","doi":"10.15388/lmr.2006.30629","DOIUrl":"https://doi.org/10.15388/lmr.2006.30629","url":null,"abstract":"In 1904 with the lifting of the ban on Lithuanian publications by Russian czar government and in 1906 with giving the permit to teach arithmetics in mother tongue at primary schools the legal publishing of Lithuanian arithmetic textbooks started. Already in 1906 even three arithmetic textbooks were published. These were two parts of ``Arithmetic Taskbook“ by Pranas Mašiotas, the first part of ``Collection of Arithmetic Tasks and Examples“ by Petras Bendorius and Pranas Daugirda and two parts of translated from Polish ``Arithmetic Tasks and Examples“ by Stanislaw Thom. All the books step by step explained in the Lithuanian language four arithmetic operations up to ten, later a hundred and finally up to a thousand.In 1909 two important books were published: the second part of the textbook by Petras Bendorius and Pranas Daugirda and ``Elementary Arithmetics“ by Petras Mikolainis. The latter textbook could be distinguished for methodical instructions.In 1909–1916 Juozas Damijonaitis prepared and published two parts of ``Arithmetic Textbook“. The book was recompiled into three parts during the period of the Republic of Lithuania (in 1918–1940). It became popular and was constantly republished.When forming of arithmetic basics was coming to end in 1916 ``The Short Science of Arithmetics“ by S. Thom (1916) appeared in the Lithuanian language, where the theory of arithmetics was presented.","PeriodicalId":33611,"journal":{"name":"Lietuvos Matematikos Rinkinys","volume":"96 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-09-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136240092","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 application of the dynamical dampers in the mechanical systems, when the sources of stimulation are impossible to abolish, is one of the ways to fight against the harmful vibrations. The linear dynamical damper of nonlinear systems can compensate the force of stimulation in wide diapason of frequency. The parameters of dynamical system where dynamical damper exists more effectively are determined.
{"title":"Supression of mechanical oscillations in a nonlinear systems with restriction","authors":"Genovaitė Zaksienė","doi":"10.15388/lmr.2006.30781","DOIUrl":"https://doi.org/10.15388/lmr.2006.30781","url":null,"abstract":"The application of the dynamical dampers in the mechanical systems, when the sources of stimulation are impossible to abolish, is one of the ways to fight against the harmful vibrations. The linear dynamical damper of nonlinear systems can compensate the force of stimulation in wide diapason of frequency. The parameters of dynamical system where dynamical damper exists more effectively are determined.","PeriodicalId":33611,"journal":{"name":"Lietuvos Matematikos Rinkinys","volume":"12 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-09-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136238695","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}
How to decrease the redundancy in the textbooks of mathematics? How to improve the math curricula? Overlapping of topics is the source for improvement. Proposals of this article are based on the experience acquired in the process of writing a book of math examples for high school and university students.
{"title":"Basic course of mathematics created by overlapping methodology of topics","authors":"Bronislovas Burgis","doi":"10.15388/lmr.2006.30591","DOIUrl":"https://doi.org/10.15388/lmr.2006.30591","url":null,"abstract":"How to decrease the redundancy in the textbooks of mathematics? How to improve the math curricula? Overlapping of topics is the source for improvement. Proposals of this article are based on the experience acquired in the process of writing a book of math examples for high school and university students.","PeriodicalId":33611,"journal":{"name":"Lietuvos Matematikos Rinkinys","volume":"26 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-09-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136240349","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 provide precise upper bounds for the survival function of bounded unimodal random variables.
给出了有界单峰随机变量生存函数的精确上界。
{"title":"Chebyshev inequalities for unimodal distributions","authors":"Tomas Juškevičius","doi":"10.15388/lmr.2006.30798","DOIUrl":"https://doi.org/10.15388/lmr.2006.30798","url":null,"abstract":"We provide precise upper bounds for the survival function of bounded unimodal random variables.","PeriodicalId":33611,"journal":{"name":"Lietuvos Matematikos Rinkinys","volume":"12 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-09-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136238837","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 problems of the olympiad are considered. One of them is solved.
对奥运会的一些问题进行了思考。其中一个已经解了。
{"title":"Students’ olympiad of Vilnius University","authors":"Dainius Dzindzalieta","doi":"10.15388/lmr.2006.30603","DOIUrl":"https://doi.org/10.15388/lmr.2006.30603","url":null,"abstract":"Some problems of the olympiad are considered. One of them is solved.","PeriodicalId":33611,"journal":{"name":"Lietuvos Matematikos Rinkinys","volume":"26 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-09-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136238840","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}
{"title":"Rymano dzeta funkcijos kvadrato Melino tranformacijos kritinėje juostoje","authors":"Mindaugas Stoncelis","doi":"10.15388/lmr.2006.30567","DOIUrl":"https://doi.org/10.15388/lmr.2006.30567","url":null,"abstract":"There is not abstract","PeriodicalId":33611,"journal":{"name":"Lietuvos Matematikos Rinkinys","volume":"12 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-09-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136239922","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}
Romas Baronas, Sigitas Būda, Feliksas Ivanauskas, Pranas Vaitkus
This paper deals with an analysis of the electrochemical biosensors and their response to multi-component mixtures. The main task is to build a mathematical model for estimation the concentration of each mixture component from the biosensor response data. Two different types of biosensors: amperometric and potenciometric are analysed. Due to high dimensionality of biosensor output data the principal component analysis is applied. Additional multivariate analysis of variance is used to analyze the response sensitivity of each biosensor type. Finally a concentration estimation model based on ensemble of neural networks is presented.
{"title":"Biosensor response to multi-component mixtures statistical analysis and forecasting","authors":"Romas Baronas, Sigitas Būda, Feliksas Ivanauskas, Pranas Vaitkus","doi":"10.15388/lmr.2006.30739","DOIUrl":"https://doi.org/10.15388/lmr.2006.30739","url":null,"abstract":"This paper deals with an analysis of the electrochemical biosensors and their response to multi-component mixtures. The main task is to build a mathematical model for estimation the concentration of each mixture component from the biosensor response data. Two different types of biosensors: amperometric and potenciometric are analysed. Due to high dimensionality of biosensor output data the principal component analysis is applied. Additional multivariate analysis of variance is used to analyze the response sensitivity of each biosensor type. Finally a concentration estimation model based on ensemble of neural networks is presented.","PeriodicalId":33611,"journal":{"name":"Lietuvos Matematikos Rinkinys","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-09-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136239924","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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