Let P be a set of primary irreducible polynomials and Qm = {p + 1; p ∈ P , ∂(p) = m}. Kubilius inequality for additive functions f : Qm → C is proved.
设 P 是初等不可约多项式集合，Qm = {p + 1; p∈ P , ∂(p) = m}。加法函数 f 的库比留斯不等式 ：Qm → C 的库比留斯不等式得到证明。
{"title":"Kubiliaus nelygybės analogas polinomų pusgrupėje","authors":"Gintautas Bareikis","doi":"10.15388/lmr.2000.34895","DOIUrl":"https://doi.org/10.15388/lmr.2000.34895","url":null,"abstract":"Let P be a set of primary irreducible polynomials and Qm = {p + 1; p ∈ P , ∂(p) = m}. Kubilius inequality for additive functions f : Qm → C is proved.\u0000 ","PeriodicalId":33611,"journal":{"name":"Lietuvos Matematikos Rinkinys","volume":"64 6","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-05-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140973037","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 we define the canonical forms on the principal bundle of holonomic frames of order r, give structure equations for these forms and determine the connection of order r.
在本文中，我们定义了阶数为 r 的整体框架主束上的典型形式，给出了这些形式的结构方程，并确定了阶数为 r 的连接。
{"title":"Geometry of frame bundles","authors":"Kazimeras Navickis","doi":"10.15388/lmr.2000.35084","DOIUrl":"https://doi.org/10.15388/lmr.2000.35084","url":null,"abstract":"In this article we define the canonical forms on the principal bundle of holonomic frames of order r, give structure equations for these forms and determine the connection of order r.","PeriodicalId":33611,"journal":{"name":"Lietuvos Matematikos Rinkinys","volume":"142 13","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-05-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140976475","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 deals with the possibilities of computerized comparative legal analysis. Legal documents are formalized using frame logic (F-logic) and are stored in knowledge bases. Their difference is defined as the difference between conclusions made from possible cases. This article presents an elaborated rule of knowledge base model generation designed for F-logic expressions.
文章论述了计算机化比较法律分析的可能性。法律文件使用框架逻辑（F-逻辑）进行形式化，并存储在知识库中。它们之间的差异被定义为从可能的案例中得出的结论之间的差异。本文详细介绍了为 F 逻辑表达式设计的知识库模型生成规则。
{"title":"Model generation and comparative analysis of legal knowledge bases","authors":"L. Paliulioniene","doi":"10.15388/lmr.2003.32417","DOIUrl":"https://doi.org/10.15388/lmr.2003.32417","url":null,"abstract":"The article deals with the possibilities of computerized comparative legal analysis. Legal documents are formalized using frame logic (F-logic) and are stored in knowledge bases. Their difference is defined as the difference between conclusions made from possible cases. This article presents an elaborated rule of knowledge base model generation designed for F-logic expressions.","PeriodicalId":33611,"journal":{"name":"Lietuvos Matematikos Rinkinys","volume":"95 ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-12-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139175550","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 establish general conditions assuring the local asymptotic normality of statistical experiments of discrete or purely discontinuous local martingales obtained models of point processes of all types were found out. The general conditions include the Fréchet differentiability of parameters in probability in normed spaces with regard to a continuous compensator.
{"title":"Diskrečiųjų martingalų statistinių modelių lokalus asimptotinis normalumas","authors":"Vaidotas Kanišauskas","doi":"10.15388/lmd.2023.33592","DOIUrl":"https://doi.org/10.15388/lmd.2023.33592","url":null,"abstract":"We establish general conditions assuring the local asymptotic normality of statistical experiments of discrete or purely discontinuous local martingales obtained models of point processes of all types were found out. The general conditions include the Fréchet differentiability of parameters in probability in normed spaces with regard to a continuous compensator.","PeriodicalId":33611,"journal":{"name":"Lietuvos Matematikos Rinkinys","volume":"29 5","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-11-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139256075","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 examines the factors that describe homework policy and characterize their influence on students' achievements in learning mathematics. The data of national research of 2004 is analyzed on the basis of statistic methods. 346 mathematics teachers and 2030 students of the 6th form and 1827 students of the 10th form took part in the research.Most teachers recognize that the main function of homework is to review the knowledge and skills acquired in the classroom. However, the results of the research show that this object is achievable in case students are responsibly trained for homework, and the teacher develops the right students' attitude towards their duties by constant and moderate insistence.
{"title":"The importance of homework in the system of mathematical education","authors":"Viktorija Sičiūnienė","doi":"10.15388/lmr.2005.26667","DOIUrl":"https://doi.org/10.15388/lmr.2005.26667","url":null,"abstract":"The article examines the factors that describe homework policy and characterize their influence on students' achievements in learning mathematics. The data of national research of 2004 is analyzed on the basis of statistic methods. 346 mathematics teachers and 2030 students of the 6th form and 1827 students of the 10th form took part in the research.Most teachers recognize that the main function of homework is to review the knowledge and skills acquired in the classroom. However, the results of the research show that this object is achievable in case students are responsibly trained for homework, and the teacher develops the right students' attitude towards their duties by constant and moderate insistence.","PeriodicalId":33611,"journal":{"name":"Lietuvos Matematikos Rinkinys","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-11-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139257439","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}
There is considered the Schrödinger equation ∂u/∂t= i Δu+ i|u|p , u, t > 0, with initial condition u(0, x)= u0(x), x ∈ Rn, n = 1. We prove the existence of the u0(x) such, that the blow up time estimation increases if p increases in the intervale 4 < p < p0.
薛定谔方程 ∂u/∂t= i Δu+ i|u|p , u, t > 0，初始条件为 u(0, x)= u0(x), x∈ Rn, n = 1。我们证明了 u0(x) 的存在性，即如果 p 在 4 < p < p0 的区间内增加，炸毁时间估计值会增加。
{"title":"Apie Šrėdingerio lygties sprendinio sprogimo laiko įvertį","authors":"Gintaras Puriuškis","doi":"10.15388/lmr.2005.24559","DOIUrl":"https://doi.org/10.15388/lmr.2005.24559","url":null,"abstract":"There is considered the Schrödinger equation ∂u/∂t= i Δu+ i|u|p , u, t > 0, with initial condition u(0, x)= u0(x), x ∈ Rn, n = 1. We prove the existence of the u0(x) such, that the blow up time estimation increases if p increases in the intervale 4 < p < p0.","PeriodicalId":33611,"journal":{"name":"Lietuvos Matematikos Rinkinys","volume":"58 2","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-11-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139258735","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 consider a modification of the attack on the classic RSA cryptosystem aimed at factoring the public modulus n, which is a product of three primes. To improve the performance of the modified attack we introduce additional parameters. We present the theoretical upper bound on the search range parameter and define a shifting parameter based on the empirical results. Since these changes make our attack probabilistic, we investigate the dependence of the success on the values of the newly defined parameters.
在本文中，我们考虑对经典 RSA 密码系统的攻击进行修改，目的是对公共模 n 进行因式分解，而公共模 n 是三个素数的乘积。为了提高修改后攻击的性能，我们引入了额外的参数。我们提出了搜索范围参数的理论上限，并根据经验结果定义了移动参数。由于这些变化使得我们的攻击具有概率性，因此我们研究了成功与否取决于新定义的参数值。
{"title":"Investigation of an attack on the multi-prime RSA cryptosystem based on cubic equations","authors":"Aleksėjus Michalkovič, Jokūbas Žitkevičius","doi":"10.15388/lmr.2023.33590","DOIUrl":"https://doi.org/10.15388/lmr.2023.33590","url":null,"abstract":"In this paper we consider a modification of the attack on the classic RSA cryptosystem aimed at factoring the public modulus n, which is a product of three primes. To improve the performance of the modified attack we introduce additional parameters. We present the theoretical upper bound on the search range parameter and define a shifting parameter based on the empirical results. Since these changes make our attack probabilistic, we investigate the dependence of the success on the values of the newly defined parameters.","PeriodicalId":33611,"journal":{"name":"Lietuvos Matematikos Rinkinys","volume":"5 2","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-11-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139258392","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":"Testing for a changed segment in variance with application","authors":"D. Zuokas","doi":"10.15388/lmr.2005.27393","DOIUrl":"https://doi.org/10.15388/lmr.2005.27393","url":null,"abstract":"There is not abstract","PeriodicalId":33611,"journal":{"name":"Lietuvos Matematikos Rinkinys","volume":"277 3","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-11-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139256557","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 brief biography of the mathematician prof. J. Matulionis is presented. The accent is made on the most significant links of his life – the study period and the longevous work at the Kaunas University of Technology.The textbook ` ` Higher mathematics'', prepared by J. Matulionis, is analysed. The textbook appears to be the very first (after the war) means on mathematics in Lithuanian, for higher technical schools.
介绍了数学家 Prof.J. Matulionis 的简介。对 J. Matulionis 编写的教科书 "高等数学 "进行了分析。这本教科书似乎是（战后）第一本用立陶宛语编写的高等技术学校数学教材。
{"title":"The life and activities of Jonas Matulionis","authors":"V. Pekarskas, A. Pekarskienė","doi":"10.15388/lmr.2005.26652","DOIUrl":"https://doi.org/10.15388/lmr.2005.26652","url":null,"abstract":"A brief biography of the mathematician prof. J. Matulionis is presented. The accent is made on the most significant links of his life – the study period and the longevous work at the Kaunas University of Technology.The textbook ` ` Higher mathematics'', prepared by J. Matulionis, is analysed. The textbook appears to be the very first (after the war) means on mathematics in Lithuanian, for higher technical schools.","PeriodicalId":33611,"journal":{"name":"Lietuvos Matematikos Rinkinys","volume":"39 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-11-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139258892","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":"Completeness classes for intuitionistic first-order temporal logic with time gaps","authors":"R. Alonderis","doi":"10.15388/lmr.2005.26671","DOIUrl":"https://doi.org/10.15388/lmr.2005.26671","url":null,"abstract":"There is not abstract.","PeriodicalId":33611,"journal":{"name":"Lietuvos Matematikos Rinkinys","volume":"289 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-11-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139257222","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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