A hyperbolic system of first order partial differential equations with small parameter and periodical initial conditions is obtained. The uniformly valid in a long time interval asymptotical solution can be constructed using the averaging along characteristics of the system. The asymptotical estimation of the approximation is made in the paper. Some aspects of practical realization of the method are discussed in the work too.
{"title":"Substantiation of asymptotical solution of weakly nonlinear hyperbolic system","authors":"Aleksandras Krylovas","doi":"10.15388/lmr.2006.30572","DOIUrl":"https://doi.org/10.15388/lmr.2006.30572","url":null,"abstract":"A hyperbolic system of first order partial differential equations with small parameter and periodical initial conditions is obtained. The uniformly valid in a long time interval asymptotical solution can be constructed using the averaging along characteristics of the system. The asymptotical estimation of the approximation is made in the paper. Some aspects of practical realization of the method are discussed in the work too.","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":"136238676","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 we present estimated generalized least squares (EGLS) estimator for the coefficient vector β in the linear regression model y = βX + ε, where disturbance term can be heteroskedastic. For the heteroskedasticity of the changed segment type, using Monte-Carlo method, we investigate empirical properties of the proposed and ordinary least squares (OLS) estimators. The results show that the empirical covariance of the EGLS estimators is smaller than that of OLS estimators.
本文给出了y = β x + ε线性回归模型中干扰项可以是异方差的系数向量β的估计广义最小二乘估计。对于变化段类型的异方差，我们使用蒙特卡罗方法研究了所提出的最小二乘(OLS)估计量和普通最小二乘估计量的经验性质。结果表明，EGLS估计量的经验协方差小于OLS估计量。
{"title":"Properties of the coefficient estimators for the linear regression model with heteroskedastic error term","authors":"Alfredas Račkauskas, Danas Zuokas","doi":"10.15388/lmr.2006.30725","DOIUrl":"https://doi.org/10.15388/lmr.2006.30725","url":null,"abstract":"In this paper we present estimated generalized least squares (EGLS) estimator for the coefficient vector β in the linear regression model y = βX + ε, where disturbance term can be heteroskedastic. For the heteroskedasticity of the changed segment type, using Monte-Carlo method, we investigate empirical properties of the proposed and ordinary least squares (OLS) estimators. The results show that the empirical covariance of the EGLS estimators is smaller than that of OLS estimators.","PeriodicalId":33611,"journal":{"name":"Lietuvos Matematikos Rinkinys","volume":"25 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":"136238829","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}
Loop-check-free decidable specialization of sequent calculus for modal logic S5 is presented. Soundness and completness of this calculus is proved.
给出了模态逻辑S5的序列演算的无环检可定专门化。证明了该演算的完备性和正确性。
{"title":"Įrodymų specializacija modalumo logikai S5","authors":"Aida Pliuškevičienė","doi":"10.15388/lmr.2006.30718","DOIUrl":"https://doi.org/10.15388/lmr.2006.30718","url":null,"abstract":"Loop-check-free decidable specialization of sequent calculus for modal logic S5 is presented. Soundness and completness of this calculus is proved.","PeriodicalId":33611,"journal":{"name":"Lietuvos Matematikos Rinkinys","volume":"75 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":"136239007","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}
Investigation of the mutual synchronizatin system with delays, composed of n (n= 2p +1, p ∈ N) oscillators joined into a onedirectional ring, is carried out. The investigation is based on the use of eigenvectors of the matrix, which describes the structure of the internal links of the system.
{"title":"Sistemos su vėlavimais ir struktūros matrica su tikrinėmis reikšmėmis vienetiniame apskritime analizinis tyrimas","authors":"Gintarė Leonaitė, Jonas Rimas","doi":"10.15388/lmr.2006.30760","DOIUrl":"https://doi.org/10.15388/lmr.2006.30760","url":null,"abstract":"Investigation of the mutual synchronizatin system with delays, composed of n (n= 2p +1, p ∈ N) oscillators joined into a onedirectional ring, is carried out. The investigation is based on the use of eigenvectors of the matrix, which describes the structure of the internal links of the system.","PeriodicalId":33611,"journal":{"name":"Lietuvos Matematikos Rinkinys","volume":"51 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":"136239139","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}
Large-scale aggregation and its inverse, disaggregation, problems are important in many fields of studies like macroeconomics, astronomy, hydrology and sociology. It was shown in Granger (1980) that a certain aggregation of random coefficient AR(1) models can lead to long memory output. Dacunha-Castelle and Oppenheim (2001) explored the topic further, answering when and if a predefined long memory process could be obtained as the result of aggregation of a specific class of individual processes. In this paper, the disaggregation scheme of Leipus et al. (2006) is briefly discussed. Then disaggregation into AR(1) is analyzed further, resulting in a theorem that helps, under corresponding assumptions, to construct a mixture density for a given aggregated by AR(1) scheme process. Finally the theorem is illustrated by FARUMA mixture densityÆs example.
大规模聚集及其逆向分解问题是宏观经济学、天文学、水文学和社会学等诸多研究领域的重要问题。Granger(1980)表明，随机系数AR(1)模型的一定聚合可以导致长记忆输出。Dacunha-Castelle和Oppenheim(2001)进一步探讨了这一主题，回答了何时以及是否可以通过特定类别的单个过程的聚合获得预定义的长记忆过程。本文简要讨论了Leipus et al.(2006)的分解方案。然后进一步分析分解为AR(1)，得到一个定理，该定理有助于在相应的假设下构造给定AR(1)方案聚合过程的混合密度。最后用FARUMA混合densityÆs实例说明了该定理。
{"title":"Time series aggregation, disaggregation and long memory","authors":"Dmitrij Celov, Remigijus Leipus","doi":"10.15388/lmr.2006.30723","DOIUrl":"https://doi.org/10.15388/lmr.2006.30723","url":null,"abstract":"Large-scale aggregation and its inverse, disaggregation, problems are important in many fields of studies like macroeconomics, astronomy, hydrology and sociology. It was shown in Granger (1980) that a certain aggregation of random coefficient AR(1) models can lead to long memory output. Dacunha-Castelle and Oppenheim (2001) explored the topic further, answering when and if a predefined long memory process could be obtained as the result of aggregation of a specific class of individual processes. In this paper, the disaggregation scheme of Leipus et al. (2006) is briefly discussed. Then disaggregation into AR(1) is analyzed further, resulting in a theorem that helps, under corresponding assumptions, to construct a mixture density for a given aggregated by AR(1) scheme process. Finally the theorem is illustrated by FARUMA mixture densityÆs example.","PeriodicalId":33611,"journal":{"name":"Lietuvos Matematikos Rinkinys","volume":"4 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":"136239910","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 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.
本文提出了一种用连续时间、状态集可数的马尔可夫过程对资产价格动态建模的算法。
{"title":"Finansinių aktyvų dinamikos skaitmeninis modelis","authors":"Eimutis Valakevičius","doi":"10.15388/lmr.2006.30730","DOIUrl":"https://doi.org/10.15388/lmr.2006.30730","url":null,"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.","PeriodicalId":33611,"journal":{"name":"Lietuvos Matematikos Rinkinys","volume":"4 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":"136240094","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}
Multiple criteria decision-making methods enable to choose the optimal decision, if his criterions is contradictorys. In herein paper is describe MAUT – multiattribute utility theory. This method is reasoned in theory. MAUT up for indeterminations situations, but can to use for determinations situations. In this method multiple criteria problem solvable with the help of unitary utility functions.
{"title":"MAUT method – one in a multiple criteria decision-making methods","authors":"Rūta Simanavičienė","doi":"10.15388/lmr.2006.30777","DOIUrl":"https://doi.org/10.15388/lmr.2006.30777","url":null,"abstract":"Multiple criteria decision-making methods enable to choose the optimal decision, if his criterions is contradictorys. In herein paper is describe MAUT – multiattribute utility theory. This method is reasoned in theory. MAUT up for indeterminations situations, but can to use for determinations situations. In this method multiple criteria problem solvable with the help of unitary utility functions.","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":"136240098","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}
One of the ways to improve the accuracy of probability density estimation is multi-mode density treating as the mixture of single-mode one. In this paper we offer to use data clustering in the first place and to estimate density in every cluster separately. To objectively compare the performance, Monte Carlo approximation is used. While using various methods to evaluate the accuracy of probability density estimations we tried to use clustered and not clustered data. In this paper we also tried to reveal the usefulness of using clustering for data generated by single-mode and multi-mode distributions.
{"title":"Research of nonparametric density estimation algorithms by applying clustering methods","authors":"Rasa Šmidtaitė, Tomas Ruzgas","doi":"10.15388/lmr.2006.30726","DOIUrl":"https://doi.org/10.15388/lmr.2006.30726","url":null,"abstract":"One of the ways to improve the accuracy of probability density estimation is multi-mode density treating as the mixture of single-mode one. In this paper we offer to use data clustering in the first place and to estimate density in every cluster separately. To objectively compare the performance, Monte Carlo approximation is used. While using various methods to evaluate the accuracy of probability density estimations we tried to use clustered and not clustered data. In this paper we also tried to reveal the usefulness of using clustering for data generated by single-mode and multi-mode distributions.","PeriodicalId":33611,"journal":{"name":"Lietuvos Matematikos Rinkinys","volume":"147 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":"136240099","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}
Vytautas Jurkus, Feliksas Ivanauskas, Aleksas Pikturna
In this work a computer simulation of Vilnius University financial management is completed. The purpose of the simulation is to calculate optimal distribution of monetary reserves for each VU faculty. In addition, the conclusion is made, which budget is oriented to quality of studies and which has social aspect.
{"title":"VU studijų proceso finansų valdymo kompiuterinis modeliavimas","authors":"Vytautas Jurkus, Feliksas Ivanauskas, Aleksas Pikturna","doi":"10.15388/lmr.2006.30755","DOIUrl":"https://doi.org/10.15388/lmr.2006.30755","url":null,"abstract":"In this work a computer simulation of Vilnius University financial management is completed. The purpose of the simulation is to calculate optimal distribution of monetary reserves for each VU faculty. In addition, the conclusion is made, which budget is oriented to quality of studies and which has social aspect.","PeriodicalId":33611,"journal":{"name":"Lietuvos Matematikos Rinkinys","volume":"18 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":"136240100","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}
Cut-free sequent calculus for logic of knowledge with infinitely many agents, based on multimodul S5n.
无穷多智能体知识逻辑的无切序演算，基于多模S5n。
{"title":"Logic of knowledge with infinitely many agents","authors":"Regimantas Pliuškevičius","doi":"10.15388/lmr.2006.30719","DOIUrl":"https://doi.org/10.15388/lmr.2006.30719","url":null,"abstract":"Cut-free sequent calculus for logic of knowledge with infinitely many agents, based on multimodul S5n.","PeriodicalId":33611,"journal":{"name":"Lietuvos Matematikos Rinkinys","volume":"39 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":"136240345","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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