Let S = ω1S1 + ω2S2 + ⋯ + ωNSN. Here Sj is the sum of identically distributed random variables and ωj > 0 denotes weight. We consider the case, when Sj is the sum of independent random variables satisfying Cramer’s condition. Upper-bounds for the accuracy of compound Poisson first and second order approximations in uniformmetric are established.
{"title":"Upper-bound estimates for weighted sums satisfying Cramer’s condition","authors":"Vydas Čekanavičius, Aistė Elijio","doi":"10.15388/lmr.2006.30784","DOIUrl":"https://doi.org/10.15388/lmr.2006.30784","url":null,"abstract":"Let S = ω1S1 + ω2S2 + ⋯ + ωNSN. Here Sj is the sum of identically distributed random variables and ωj > 0 denotes weight. We consider the case, when Sj is the sum of independent random variables satisfying Cramer’s condition. Upper-bounds for the accuracy of compound Poisson first and second order approximations in uniformmetric are established.","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":"136240088","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}
Important problem in civil engineering is obtaining optimal pile placement schemes for grillage-type foundations in order to reduce the number of piles and reactive forces arising in piles. The idealizations of problem and formulation for local and global optimization are discussed, highlighting the must for global optimization. The grillage is discretized using finite element method. Sensitivity of objective function is obtained analytically. The solution technology for a class of aforementioned problems is proposed based on the use of global optimization algorithms of package GAMS, which are implemented as ``black boxes”. Results of computational experiments are presented.
{"title":"Globaliosios sijyno optimizacijos uždaviniai","authors":"Rimantas Belevičius, Dmitrij Šešok","doi":"10.15388/lmr.2006.30740","DOIUrl":"https://doi.org/10.15388/lmr.2006.30740","url":null,"abstract":"Important problem in civil engineering is obtaining optimal pile placement schemes for grillage-type foundations in order to reduce the number of piles and reactive forces arising in piles. The idealizations of problem and formulation for local and global optimization are discussed, highlighting the must for global optimization. The grillage is discretized using finite element method. Sensitivity of objective function is obtained analytically. The solution technology for a class of aforementioned problems is proposed based on the use of global optimization algorithms of package GAMS, which are implemented as ``black boxes”. Results of computational experiments are presented.","PeriodicalId":33611,"journal":{"name":"Lietuvos Matematikos Rinkinys","volume":"80 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":"136240091","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 article some problems in test on discrete mathematics are analyzed. Using statistics of students results we present several problems that presence in test could be more or less advisable.
{"title":"Diskrečiosios matematikos testo klausimų analizė","authors":"Aleksandras Krylovas, Olga Subač","doi":"10.15388/lmr.2006.30606","DOIUrl":"https://doi.org/10.15388/lmr.2006.30606","url":null,"abstract":"In this article some problems in test on discrete mathematics are analyzed. Using statistics of students results we present several problems that presence in test could be more or less advisable.","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":"136240338","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}
Let us deal with positive i.i.d. random variables X1, . . ., Xm having a tail index α. Calculating a quotient of two biggest members in the set, we obtain a new random variable and investigate its distribution and moment properties. The method itself was proposed by prof. V. Paulauskas and co-authors in [1] and [2].
{"title":"Distribution and moment characteristics of a quotient of heavy-tailed random variables","authors":"Kęstutis Gadeikis","doi":"10.15388/lmr.2006.30724","DOIUrl":"https://doi.org/10.15388/lmr.2006.30724","url":null,"abstract":"Let us deal with positive i.i.d. random variables X1, . . ., Xm having a tail index α. Calculating a quotient of two biggest members in the set, we obtain a new random variable and investigate its distribution and moment properties. The method itself was proposed by prof. V. Paulauskas and co-authors in [1] and [2].","PeriodicalId":33611,"journal":{"name":"Lietuvos Matematikos Rinkinys","volume":"85 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":"136240344","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 DNA sequents are modelled as discrete-state Markov chains. Statistical data is presented in contingency tables form. The generalized logit model is used to test the first-order Markov property for all coding and non-coding subsequences of DNA.
{"title":"Genetinių sekų markoviškumo tyrimas","authors":"Jurgita Židanavičiūtė, Tomas Rekašius","doi":"10.15388/lmr.2006.30727","DOIUrl":"https://doi.org/10.15388/lmr.2006.30727","url":null,"abstract":"In this paper DNA sequents are modelled as discrete-state Markov chains. Statistical data is presented in contingency tables form. The generalized logit model is used to test the first-order Markov property for all coding and non-coding subsequences of DNA.","PeriodicalId":33611,"journal":{"name":"Lietuvos Matematikos Rinkinys","volume":"342 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":"136240348","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}
Aleksandras Krylovas, Juozas Raulynaitis, Olga Subač
Evaluation of students’ works where they present not only answer but solution also, can be subjective. In this article we present some exam tasks with non-correct solutions and statistics, that show wide evaluation scale dependingly on revising teacher.
{"title":"Dėstytojų nuomonės apie studentų klaidas","authors":"Aleksandras Krylovas, Juozas Raulynaitis, Olga Subač","doi":"10.15388/lmr.2006.30605","DOIUrl":"https://doi.org/10.15388/lmr.2006.30605","url":null,"abstract":"Evaluation of students’ works where they present not only answer but solution also, can be subjective. In this article we present some exam tasks with non-correct solutions and statistics, that show wide evaluation scale dependingly on revising teacher.","PeriodicalId":33611,"journal":{"name":"Lietuvos Matematikos Rinkinys","volume":"10 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":"136238266","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 article the differential geometry of the nonholonomic complex NGr(1, n, 2n − 4) in the n-dimensional affine space is studied. The classification of such complexes and geometric interpretations are given.
{"title":"n-matės afininės erdvės neholonominių kompleksų diferencialinė geometrija","authors":"Kazimieras Navickis","doi":"10.15388/lmr.2006.30578","DOIUrl":"https://doi.org/10.15388/lmr.2006.30578","url":null,"abstract":"In this article the differential geometry of the nonholonomic complex NGr(1, n, 2n − 4) in the n-dimensional affine space is studied. The classification of such complexes and geometric interpretations are given.","PeriodicalId":33611,"journal":{"name":"Lietuvos Matematikos Rinkinys","volume":"84 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":"136238441","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}
Modelling of Ignalina NPP RBMK-1500 reactor control and protection system cooling circuit (CPSCC) voiding logic, which was implemented in code QUABOX/CUBBOX-HYCA, is described. Analysis of numerical simulation results shows, that this logic is correct, the results are comparable to analogous modelling data obtained by Russian code STEPAN/KOBRA. The improved QUABOX/CUBBOX-HYCA code version allows to simulate the CPSCC voiding for RBMK-1500 reactor operation at any power level. Together with implemented and validated full CPS operation logic it could be used for simulation of various transitional processes, which can occur in nuclear reactors of Ignalina NPP, or during analyses when the safety substantiation of reactor unit operation is performed.
{"title":"Branduolinio reaktoriaus valdymo ir apsaugos sistemos aušinimo kontūro nusausėjimo modeliavimas","authors":"Narimantas Listopadskis, Raimondas Pabarčius, Aurimas Tonkūnas","doi":"10.15388/lmr.2006.30761","DOIUrl":"https://doi.org/10.15388/lmr.2006.30761","url":null,"abstract":"Modelling of Ignalina NPP RBMK-1500 reactor control and protection system cooling circuit (CPSCC) voiding logic, which was implemented in code QUABOX/CUBBOX-HYCA, is described. Analysis of numerical simulation results shows, that this logic is correct, the results are comparable to analogous modelling data obtained by Russian code STEPAN/KOBRA. The improved QUABOX/CUBBOX-HYCA code version allows to simulate the CPSCC voiding for RBMK-1500 reactor operation at any power level. Together with implemented and validated full CPS operation logic it could be used for simulation of various transitional processes, which can occur in nuclear reactors of Ignalina NPP, or during analyses when the safety substantiation of reactor unit operation is performed.","PeriodicalId":33611,"journal":{"name":"Lietuvos Matematikos Rinkinys","volume":"84 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":"136238675","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}
For most institutions information technologies represent a hole of additional expense. Most campuses have simply bolted new technologies onto a fixed plant, a fixed faculty, and a fixed notion of classroom instruction. Presented results show that all thirty institutions of course redesign online learning program reduced cost by about forty percent on average, increased course-completion rates, improved retention, better student attitudes toward the subject matter.All universities and colleges of this program have realized promise of technology by means of whole course redesign, active learning, computer-based learning resources, mastery learning, on-demand help, alternative staffing.
{"title":"Elearning levels","authors":"Antanas Baskas","doi":"10.15388/lmr.2006.30582","DOIUrl":"https://doi.org/10.15388/lmr.2006.30582","url":null,"abstract":"For most institutions information technologies represent a hole of additional expense. Most campuses have simply bolted new technologies onto a fixed plant, a fixed faculty, and a fixed notion of classroom instruction. Presented results show that all thirty institutions of course redesign online learning program reduced cost by about forty percent on average, increased course-completion rates, improved retention, better student attitudes toward the subject matter.All universities and colleges of this program have realized promise of technology by means of whole course redesign, active learning, computer-based learning resources, mastery learning, on-demand help, alternative staffing.","PeriodicalId":33611,"journal":{"name":"Lietuvos Matematikos Rinkinys","volume":"32 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":"136239926","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}
Juozas Revuckas (1924–1991) lectured didactics of mathematicsa at Šiauliai Pedagogical Institute (at present – Šiauliai Pedagogical University) for 35 years. He investigated development of logical thinking of pupils in teaching geometry. On this subject, he had published 4 articles and maintained a thesis.
Juozas Revuckas(1924-1991)在Šiauliai教育学院(现Šiauliai教育大学)讲授数学教学35年。他研究了学生在几何教学中逻辑思维的发展。在这个课题上，他已经发表了4篇文章，并持有一篇论文。
{"title":"Juozas Revuckas on development of logical thinking of pupils in teaching geometry","authors":"Algirdas Ažubalis","doi":"10.15388/lmr.2006.30628","DOIUrl":"https://doi.org/10.15388/lmr.2006.30628","url":null,"abstract":"Juozas Revuckas (1924–1991) lectured didactics of mathematicsa at Šiauliai Pedagogical Institute (at present – Šiauliai Pedagogical University) for 35 years. He investigated development of logical thinking of pupils in teaching geometry. On this subject, he had published 4 articles and maintained a thesis.","PeriodicalId":33611,"journal":{"name":"Lietuvos Matematikos Rinkinys","volume":"6 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":"136240347","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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