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Lithuanian Mathematical Journal最新文献

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On the independence of greedy expansions of certain algebraic numbers in a Pisot or Salem base 论皮索特或萨利姆基中某些代数数贪婪展开的独立性
IF 0.4 4区 数学
Lithuanian Mathematical Journal Pub Date : 2024-09-03 DOI: 10.1007/s10986-024-09643-1
Eiji Miyanohara
{"title":"On the independence of greedy expansions of certain algebraic numbers in a Pisot or Salem base","authors":"Eiji Miyanohara","doi":"10.1007/s10986-024-09643-1","DOIUrl":"https://doi.org/10.1007/s10986-024-09643-1","url":null,"abstract":"<p>Let <i>β</i> be a Pisot or Salem number with <i>β &gt;</i> 1, and let <i>α</i><sub>1</sub> and <i>α</i><sub>2</sub> be elements in <span>({mathbb{Q}})</span>(<i>β</i>) ∩ [0<i>,</i> 1). In this note, we prove that <i>α</i><sub>1</sub> and <i>α</i><sub>2</sub> have either the same tail greedy expansions in a base <i>β</i> or independent random greedy expansions in a base <i>β</i>.</p>","PeriodicalId":51108,"journal":{"name":"Lithuanian Mathematical Journal","volume":"40 1","pages":""},"PeriodicalIF":0.4,"publicationDate":"2024-09-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142200970","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Sharp bounds for the complete elliptic integral of the first kind in term of the inverse tangent hyperbolic function 反切双曲函数第一类完全椭圆积分的锐界
IF 0.4 4区 数学
Lithuanian Mathematical Journal Pub Date : 2024-09-03 DOI: 10.1007/s10986-024-09644-0
Zhen-Hang Yang, Jing-Feng Tian
{"title":"Sharp bounds for the complete elliptic integral of the first kind in term of the inverse tangent hyperbolic function","authors":"Zhen-Hang Yang, Jing-Feng Tian","doi":"10.1007/s10986-024-09644-0","DOIUrl":"https://doi.org/10.1007/s10986-024-09644-0","url":null,"abstract":"<p>Let <span>(mathcal{K})</span>(<i>r</i>) and arctanh <i>r</i> for <i>r</i> ∈ (0<i>,</i> 1) be the complete elliptic integral of the first kind and the inverse tangent hyperbolic function, respectively. In this paper, we prove that the double inequality</p><p><span>({Phi }_{p}left({r}{prime}right)frac{text{arctanh}r}{r}&lt;frac{2}{pi }mathcal{K}left(rright)&lt;{Phi }_{q}left({r}{prime}right)frac{text{arctanh}r}{r})</span></p><p>holds for <i>r</i> ∈ (0<i>,</i> 1) if and only if <i>q</i> ⩽ 56 543/20 976 and 23(90π − 233)/(10(69π − 178)) ⩽ <i>p</i> ⩽ 3, where <i>r</i>′ <span>(sqrt{1-{r}^{2}})</span> and</p><p><span>({Phi }_{q}left(xright)=60frac{left(17q-41right){x}^{2}+6qx+69-23q}{left(620q-1521right){x}^{2}+2left(580q-1079right)x+5359-1780q})</span></p><p>for <i>q</i> ⩽ 3 and <i>x</i> ∈ (0<i>,</i> 1). This improves some known results and yields several new bounds for the Gauss arithmetic–geometric mean.</p>","PeriodicalId":51108,"journal":{"name":"Lithuanian Mathematical Journal","volume":"42 1","pages":""},"PeriodicalIF":0.4,"publicationDate":"2024-09-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142225719","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Analyzing arithmetic word problems: Blink of an eye for textbooks authors 分析算术文字题：教科书作者的眨眼功夫
IF 0.4 4区 数学
Lithuanian Mathematical Journal Pub Date : 2024-08-21 DOI: 10.1007/s10986-024-09642-2
Ieva Kilienė
{"title":"Analyzing arithmetic word problems: Blink of an eye for textbooks authors","authors":"Ieva Kilienė","doi":"10.1007/s10986-024-09642-2","DOIUrl":"https://doi.org/10.1007/s10986-024-09642-2","url":null,"abstract":"<p>In this paper, we study the frequency of different types of arithmetic word problems (AWP) in Lithuanian textbooks. The results show the lack of variety among types of AWP. We propose the framework for analysis of the frequency of types of AWP in a textbook and apply it to a particular set of primary school textbooks. We use a statistical method to compare the sample from the textbook rather than from the entire textbook. Also, we compare the proportions of types of AWP in Lithuanian textbooks with those in Singaporean and Spanish textbooks. The approach adopted in the paper can be used to analyze other textbooks from different countries.</p>","PeriodicalId":51108,"journal":{"name":"Lithuanian Mathematical Journal","volume":"15 1","pages":""},"PeriodicalIF":0.4,"publicationDate":"2024-08-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142200924","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
On generalization of some theorems with absolute summability factors of infinite series 关于无穷级数绝对可求和因子的若干定理的一般化
IF 0.4 4区 数学
Lithuanian Mathematical Journal Pub Date : 2024-08-13 DOI: 10.1007/s10986-024-09640-4
Włodzimierz Łenski, Bogdan Szal
{"title":"On generalization of some theorems with absolute summability factors of infinite series","authors":"Włodzimierz Łenski, Bogdan Szal","doi":"10.1007/s10986-024-09640-4","DOIUrl":"https://doi.org/10.1007/s10986-024-09640-4","url":null,"abstract":"<p>The generalizations of some results of H. Bor, L. Leindler, and H. Sevli pertaining to absolute summability are examined.</p>","PeriodicalId":51108,"journal":{"name":"Lithuanian Mathematical Journal","volume":"4 1","pages":""},"PeriodicalIF":0.4,"publicationDate":"2024-08-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142200926","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
On some uniformly distributed subsets of rationals 关于一些均匀分布的有理子集
IF 0.4 4区 数学
Lithuanian Mathematical Journal Pub Date : 2024-08-06 DOI: 10.1007/s10986-024-09641-3
Vilius Stakėnas
{"title":"On some uniformly distributed subsets of rationals","authors":"Vilius Stakėnas","doi":"10.1007/s10986-024-09641-3","DOIUrl":"https://doi.org/10.1007/s10986-024-09641-3","url":null,"abstract":"<p>Subsets of rational numbers are specified as preimages of values of arithmetical functions. The uniformity of distribution of elements of these sets is proved and interpreted in the context of Diophantine approximation to real numbers.</p>","PeriodicalId":51108,"journal":{"name":"Lithuanian Mathematical Journal","volume":"46 1","pages":""},"PeriodicalIF":0.4,"publicationDate":"2024-08-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141945452","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
On multidimensional locally perturbed standard random walks 关于多维局部扰动标准随机游走
IF 0.4 4区 数学
Lithuanian Mathematical Journal Pub Date : 2024-07-25 DOI: 10.1007/s10986-024-09639-x
Congzao Dong, Alexander Iksanov, Andrey Pilipenko
{"title":"On multidimensional locally perturbed standard random walks","authors":"Congzao Dong, Alexander Iksanov, Andrey Pilipenko","doi":"10.1007/s10986-024-09639-x","DOIUrl":"https://doi.org/10.1007/s10986-024-09639-x","url":null,"abstract":"<p>Let <i>d</i> be a positive integer, and let <i>A</i> be a set in <span>({mathbb{Z}}^{d})</span> that contains finitely many points with integer coordinates. We consider a standard random walk <i>X</i> perturbed on the set <i>A</i>. This means that <i>X</i> is a Markov chain whose transition probabilities from the points outside <i>A</i> coincide with those of a standard random walk on <span>({mathbb{Z}}^{d})</span>, whereas the transition probabilities from the points inside <i>A</i> are different. We investigate the impact of the perturbation on a scaling limit of <i>X</i>. It turns out that if <i>d</i> ⩾ 2, then in a typical situation the scaling limit of <i>X</i> coincides with that of the underlying standard random walk. This is unlike the case <i>d</i> = 1<i>,</i> in which the scaling limit of <i>X</i> is usually a skew Brownian motion, a skew stable Lévy process, or some other “skew” process. The distinction between the one-dimensional and multidimensional cases under comparable assumptions may simply be caused by transience of the underlying standard random walk in <span>({mathbb{Z}}^{d})</span> for <i>d</i> ⩾ 3. More interestingly, in the situation where the standard random walk in <span>({mathbb{Z}}^{2})</span> is recurrent, the preservation of its Donsker scaling limit is secured by the fact that the number of visits of <i>X</i> to the set <i>A</i> is much smaller than in the one-dimensional case. As a consequence, the influence of the perturbation vanishes upon the scaling. On the other edge of the spectrum, we have the situation in which the standard random walk admits a Donsker’s scaling limit, whereas its locally perturbed version does not because of huge jumps from the set <i>A,</i> which occur early enough.</p>","PeriodicalId":51108,"journal":{"name":"Lithuanian Mathematical Journal","volume":"11 1","pages":""},"PeriodicalIF":0.4,"publicationDate":"2024-07-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141777265","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Julius Kruopis: Pioneer of the applications of mathematical statistics in Lithuania 朱利叶斯-克鲁奥皮斯立陶宛数理统计应用的先驱
IF 0.4 4区 数学
Lithuanian Mathematical Journal Pub Date : 2024-07-25 DOI: 10.1007/s10986-024-09638-y
Vilijandas Bagdonavičius, Vydas Čekanavičius, Rūta Levulienė, Pranas Vaitkus
{"title":"Julius Kruopis: Pioneer of the applications of mathematical statistics in Lithuania","authors":"Vilijandas Bagdonavičius, Vydas Čekanavičius, Rūta Levulienė, Pranas Vaitkus","doi":"10.1007/s10986-024-09638-y","DOIUrl":"https://doi.org/10.1007/s10986-024-09638-y","url":null,"abstract":"<p>The paper reviews the scientific and pedagogical activities of Julius Kruopis, the pioneer of Lithuanian applied statistics. His contribution to statistics and cooperation with Lithuanian companies in the application of statistical methods in various fields of human activity is described in the most detail, especially in the quality control area and industrial process optimization. His works in probability theory are also mentioned, emphasizing important contributions to approximations of distributions. Peculiarities of his pedagogical activity, textbooks and monographs, and supervision of students’ theses and dissertations are discussed.</p>","PeriodicalId":51108,"journal":{"name":"Lithuanian Mathematical Journal","volume":"8 1","pages":""},"PeriodicalIF":0.4,"publicationDate":"2024-07-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141777266","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Asymptotics for the second moment of the Dirichlet coefficients of symmetric power L-functions 对称幂 L 函数 Dirichlet 系数第二矩的渐近线
IF 0.4 4区 数学
Lithuanian Mathematical Journal Pub Date : 2024-06-24 DOI: 10.1007/s10986-024-09636-0
Xue Han, Huafeng Liu
{"title":"Asymptotics for the second moment of the Dirichlet coefficients of symmetric power L-functions","authors":"Xue Han, Huafeng Liu","doi":"10.1007/s10986-024-09636-0","DOIUrl":"https://doi.org/10.1007/s10986-024-09636-0","url":null,"abstract":"<p>Let <i>m</i> ≥ 2 be an integer. Let <i>f</i> be a holomorphic Hecke eigenform of even weight <i>k</i> for the full modular group <i>SL</i>(2, ℤ). Denote by <i>λ</i><sub>Sym</sub><sup><i>m</i></sup> <sub><i>f</i></sub> (<i>n</i>) the <i>n</i>th normalized Dirichlet coefficient of the corresponding symmetric power <i>L</i>-function <i>L</i>(<i>s</i>, Sym<sup><i>m</i></sup><i> f</i>) related to <i>f</i>. In this paper, we study the average behavior of the second moment of the Dirichlet coefficients <i>λ</i><sub>Sym</sub><sup><i>m</i></sup> <sub><i>f</i></sub> (<i>n</i>) and establish its asymptotic formula.</p>","PeriodicalId":51108,"journal":{"name":"Lithuanian Mathematical Journal","volume":"84 1","pages":""},"PeriodicalIF":0.4,"publicationDate":"2024-06-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141506994","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Variance of a strongly additive function defined on random permutations 定义在随机排列上的强加法函数的方差
IF 0.4 4区 数学
Lithuanian Mathematical Journal Pub Date : 2024-06-24 DOI: 10.1007/s10986-024-09637-z
Arvydas Karbonskis, Eugenijus Manstavičius
{"title":"Variance of a strongly additive function defined on random permutations","authors":"Arvydas Karbonskis, Eugenijus Manstavičius","doi":"10.1007/s10986-024-09637-z","DOIUrl":"https://doi.org/10.1007/s10986-024-09637-z","url":null,"abstract":"<p>Inspired by unfading popularity of the Turán–Kubilius inequality for additive number theoretic functions within the last decades, we examine the variance of additive functions defined on random permutations uniformly taken from the symmetric group. Extending the optimal estimate achieved in 2018 by Klimavičius and Manstavičius for the case of completely additive functions, we obtain asymptotically sharp upper and lower bounds when the functions are strongly additive. The upper estimates are analogous to that established in number theory by Kubilius in 1985.</p>","PeriodicalId":51108,"journal":{"name":"Lithuanian Mathematical Journal","volume":"85 1","pages":""},"PeriodicalIF":0.4,"publicationDate":"2024-06-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141506995","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Ground state solutions for quasilinear Schrödinger equations with critical Berestycki–Lions nonlinearities 具有临界贝里斯基-狮子非线性的准线性薛定谔方程的基态解
IF 0.4 4区 数学
Lithuanian Mathematical Journal Pub Date : 2024-05-28 DOI: 10.1007/s10986-024-09635-1
Jian-Xin Han, Ming-Chao Chen, Yan-Fang Xue
{"title":"Ground state solutions for quasilinear Schrödinger equations with critical Berestycki–Lions nonlinearities","authors":"Jian-Xin Han, Ming-Chao Chen, Yan-Fang Xue","doi":"10.1007/s10986-024-09635-1","DOIUrl":"https://doi.org/10.1007/s10986-024-09635-1","url":null,"abstract":"<p>We consider the quasilinear Schrödinger equation involving a general nonlinearity at critical growth. By using Jeanjean’s monotonicity trick and the Pohozaev identity we get the existence results that generalize an earlier work [H. Liu and L. Zhao, Existence results for quasilinear Schrödinger equations with a general nonlinearity, <i>Commun. Pure Appl. Anal.</i>, 19(6):3429–3444, 2020] about the subcritical case to the critical case.</p>","PeriodicalId":51108,"journal":{"name":"Lithuanian Mathematical Journal","volume":"29 1","pages":""},"PeriodicalIF":0.4,"publicationDate":"2024-05-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141165852","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
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