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The existence of solutions to higher-order differential equations with nonhomogeneous conditions 非均质条件下高阶微分方程解的存在性
IF 0.4 4区 数学
Lithuanian Mathematical Journal Pub Date : 2024-02-16 DOI: 10.1007/s10986-024-09622-6
Boddeti Madhubabu, Namburi Sreedhar, Kapula Rajendra Prasad
{"title":"The existence of solutions to higher-order differential equations with nonhomogeneous conditions","authors":"Boddeti Madhubabu, Namburi Sreedhar, Kapula Rajendra Prasad","doi":"10.1007/s10986-024-09622-6","DOIUrl":"https://doi.org/10.1007/s10986-024-09622-6","url":null,"abstract":"<p>We prove the existence and uniqueness of solutions to the differential equations of higher order <span>({x}^{left(lright)}left(sright)+gleft(s,xleft(sright)right)=0,sin left[c,dright],)</span> satisfying three-point boundary conditions that contain a nonhomogeneous term <span>(xleft(cright)=0,{x}{prime}left(cright)=0,{x}^{^{primeprime} }left(cright)=0,dots {x}^{left(l-2right)}left(cright)=0,{x}^{left(l-2right)}left(dright)-{beta x}^{left(l-2right)}left(eta right)=upgamma ,)</span> where <span>(lge mathrm{3,0}le c&lt;eta &lt;d,)</span> the constants <span>(beta ,upgamma )</span> are real numbers, and <span>(g:left[c,dright]times {mathbb{R}}to {mathbb{R}})</span> is a continuous function. By using finer bounds on the integral of kernel, the Banach and Rus fixed point theorems on metric spaces are utilized to prove the existence and uniqueness of a solution to the problem.</p>","PeriodicalId":51108,"journal":{"name":"Lithuanian Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2024-02-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139758707","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
Limit theorems for linear processes with tapered innovations and filters 具有锥形创新和滤波器的线性过程的极限定理
IF 0.4 4区 数学
Lithuanian Mathematical Journal Pub Date : 2024-02-16 DOI: 10.1007/s10986-024-09619-1
{"title":"Limit theorems for linear processes with tapered innovations and filters","authors":"","doi":"10.1007/s10986-024-09619-1","DOIUrl":"https://doi.org/10.1007/s10986-024-09619-1","url":null,"abstract":"<h3>Abstract</h3> <p>We consider the partial-sum process <span> <span>({sum }_{k=1}^{left[ntright]}{X}_{k}^{left(nright)},)</span> </span> where <span> <span>(left{{X}_{k}^{left(nright)}={sum }_{j=0}^{infty }{alpha }_{j}^{left(nright)}{xi }_{k-j}left(bleft(nright)right), kin {mathbb{Z}}right},)</span> </span> <em>n</em> ≥ 1, is a series of linear processes with tapered filter <span> <span>({alpha }_{j}^{left(nright)}={alpha }_{j} {1}_{left{0le jlelambdaleft(nright)right}})</span> </span> and heavy-tailed tapered innovations <em>ξ</em><sub><em>j</em></sub>(<em>b</em>(<em>n</em>)), <em>j ∈</em> Z. Both tapering parameters <em>b</em>(<em>n</em>) and <em>⋋</em> (<em>n</em>) grow to <em>∞</em> as <em>n→∞</em>. The limit behavior of the partial-sum process (in the sense of convergence of finite-dimensional distributions) depends on the growth of these two tapering parameters and dependence properties of a linear process with nontapered filter <em>a</em><sub><em>i</em></sub>, <em>i</em> ≥ 0, and nontapered innovations. We consider the cases where <em>b</em>(<em>n</em>) grows relatively slowly (soft tapering) and rapidly (hard tapering) and all three cases of growth of <em>⋋</em>(<em>n</em>) (strong, weak, and moderate tapering).</p>","PeriodicalId":51108,"journal":{"name":"Lithuanian Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2024-02-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139772911","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
Rates of convergence in the strong law of large numbers for weighted averages of nonidentically distributed random variables 非同分布随机变量加权平均数的强大数定律收敛速率
IF 0.4 4区 数学
Lithuanian Mathematical Journal Pub Date : 2024-02-16 DOI: 10.1007/s10986-024-09621-7
{"title":"Rates of convergence in the strong law of large numbers for weighted averages of nonidentically distributed random variables","authors":"","doi":"10.1007/s10986-024-09621-7","DOIUrl":"https://doi.org/10.1007/s10986-024-09621-7","url":null,"abstract":"<h3>Abstract</h3> <p>Integral tests are found for the convergence of two Spitzer-type series associated with a class of weighted averages introduced by Jajte [On the strong law of large numbers, <em>Ann. Probab.</em>, 31(1):409–412, 2003]. Our main theorems are valid for a large family of dependent random variables that are not necessarily identically distributed. As a byproduct, we improve the Marcinkiewicz–Zygmund strong law of large numbers for asymptotically almost negatively associated sequences due to Chandra and Ghosal [Extensions of the strong law of large numbers of Marcinkiewicz and Zygmund for dependent variables <em>Acta Math. Hung.</em>, 71(4):327–336, 1996]. We also complement two limit theorems recently derived by Anh et al. [TheMarcinkiewicz–Zygmund-type strong law of large numbers with general normalizing sequences, <em>J. Theor. Probab.</em>, 34(1):331–348, 2021] and Thành [On a new concept of stochastic domination and the laws of large numbers, <em>Test</em>, 32(1):74–106, 2023]. The obtained results are new even when the summands are independent.</p>","PeriodicalId":51108,"journal":{"name":"Lithuanian Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2024-02-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139758574","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
Complete convergence for weighted sums of random variables satisfying generalized Rosenthal-type inequalities* 满足广义罗森塔尔型不等式的随机变量加权和的完全收敛性*
IF 0.4 4区 数学
Lithuanian Mathematical Journal Pub Date : 2024-02-16 DOI: 10.1007/s10986-024-09618-2
Chang Liu, Yu Miao
{"title":"Complete convergence for weighted sums of random variables satisfying generalized Rosenthal-type inequalities*","authors":"Chang Liu, Yu Miao","doi":"10.1007/s10986-024-09618-2","DOIUrl":"https://doi.org/10.1007/s10986-024-09618-2","url":null,"abstract":"<p>In the paper, we establish the complete convergence for weighted sums of random variables satisfying generalized Rosenthal-type inequalities. Our results partially extend some known results and weaken their conditions. As statistical applications, we study the nonparametric regression model and obtain the complete consistency of the weighted regression estimator for the unknown regression functions.</p>","PeriodicalId":51108,"journal":{"name":"Lithuanian Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2024-02-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139758706","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
Second Hankel determinant of logarithmic coefficients of inverse functions in certain classes of univalent functions 某些等价函数类中反函数对数系数的第二汉克尔行列式
IF 0.4 4区 数学
Lithuanian Mathematical Journal Pub Date : 2024-02-16 DOI: 10.1007/s10986-024-09623-5
Sanju Mandal, Molla Basir Ahamed
{"title":"Second Hankel determinant of logarithmic coefficients of inverse functions in certain classes of univalent functions","authors":"Sanju Mandal, Molla Basir Ahamed","doi":"10.1007/s10986-024-09623-5","DOIUrl":"https://doi.org/10.1007/s10986-024-09623-5","url":null,"abstract":"<p>The Hankel determinant <span>({H}_{mathrm{2,1}}left({F}_{f-1}/2right))</span> of logarithmic coefficients is defined as</p><p><span>({H}_{mathrm{2,1}}left({F}_{f-1}/2right):=left|begin{array}{cc}{Gamma }_{1}&amp; {Gamma }_{2} {Gamma }_{2}&amp; {Gamma }_{3}end{array}right|={Gamma }_{1}{Gamma }_{3}-{Gamma }_{2}^{2},)</span></p><p>where <span>({Gamma }_{1},{Gamma }_{2},)</span> and <span>({Gamma }_{3})</span> are the first, second, and third logarithmic coefficients of inverse functions belonging to the class <span>(mathcal{S})</span> of normalized univalent functions. In this paper, we establish sharp inequalities <span>(left|{H}_{mathrm{2,1}}left({F}_{f-1}/2right)right|le 19/288,)</span> <span>(left|{H}_{mathrm{2,1}}left({F}_{f-1}/2right)right|le 1/144,)</span> and <span>(left|{H}_{mathrm{2,1}}left({F}_{f-1}/2right)right|le 1/36)</span> for the logarithmic coefficients of inverse functions, considering starlike and convex functions, as well as functions with bounded turning of order 1/2, respectively.</p>","PeriodicalId":51108,"journal":{"name":"Lithuanian Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2024-02-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139758522","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
Spectral collocation methods for fractional multipantograph delay differential equations* 分数多图延迟微分方程的谱配位法*
IF 0.4 4区 数学
Lithuanian Mathematical Journal Pub Date : 2024-01-15 DOI: 10.1007/s10986-023-09614-y
Xiulian Shi, Keyan Wang, Hui Sun
{"title":"Spectral collocation methods for fractional multipantograph delay differential equations*","authors":"Xiulian Shi, Keyan Wang, Hui Sun","doi":"10.1007/s10986-023-09614-y","DOIUrl":"https://doi.org/10.1007/s10986-023-09614-y","url":null,"abstract":"<p>In this paper, we propose and analyze a spectral collocation method for the numerical solutions of fractional multipantograph delay differential equations. The fractional derivatives are described in the Caputo sense. We present that some suitable variable transformations can convert the equations to a Volterra integral equation defined on the standard interval [<i>−</i>1<i>,</i> 1]. Then the Jacobi–Gauss points are used as collocation nodes, and the Jacobi–Gauss quadrature formula is used to approximate the integral equation. Later, the convergence analysis of the proposed method is investigated in the infinity norm and weighted <i>L</i><sup>2</sup> norm. To perform the numerical simulations, some test examples are investigated, and numerical results are presented. Further, we provide the comparative study of the proposed method with some existing numerical methods.</p>","PeriodicalId":51108,"journal":{"name":"Lithuanian Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2024-01-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139476226","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
Existence results for a class of two-fold saddle point parabolic differential equations 一类两折鞍点抛物微分方程的存在性结果
IF 0.4 4区 数学
Lithuanian Mathematical Journal Pub Date : 2024-01-09 DOI: 10.1007/s10986-023-09616-w
{"title":"Existence results for a class of two-fold saddle point parabolic differential equations","authors":"","doi":"10.1007/s10986-023-09616-w","DOIUrl":"https://doi.org/10.1007/s10986-023-09616-w","url":null,"abstract":"<h3>Abstract</h3> <p>We propose and analyze an abstract framework to study the well-posedness for a family of linear degenerate parabolic augmentedmixed equations.We combine the theory for linear degenerate parabolic problems with results about stationary two-fold saddle point equations to deduce sufficient conditions for the existence and uniqueness of a solution for the problem. Finally, we show some applications of the developed theory through examples that come from <em>fluid dynamic</em> and <em>electromagnetic</em> problems.</p>","PeriodicalId":51108,"journal":{"name":"Lithuanian Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2024-01-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139410136","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 solution for a weighted fourth-order Schrödinger equation with exponential growth nonlinearity 具有指数增长非线性的加权四阶薛定谔方程的基态解
IF 0.4 4区 数学
Lithuanian Mathematical Journal Pub Date : 2024-01-06 DOI: 10.1007/s10986-023-09617-9
Rima Chetouane, Brahim Dridi, Rached Jaidane
{"title":"Ground state solution for a weighted fourth-order Schrödinger equation with exponential growth nonlinearity","authors":"Rima Chetouane, Brahim Dridi, Rached Jaidane","doi":"10.1007/s10986-023-09617-9","DOIUrl":"https://doi.org/10.1007/s10986-023-09617-9","url":null,"abstract":"<p>In this paper, we establish the existence of a ground state solution for a weighted fourth-order equation of Shrödinger type under boundary Dirichlet condition in the unit ball <i>B</i> of ℝ<sup>4</sup>. The potential <i>V</i> is a continuous positive function bounded away from zero in <i>B</i>. The nonlinearity of the equation is assumed to have exponential growth due to Adams-type inequalities combined with polynomial term. We use the constrained minimization in the Nehari set, the quantitative deformation lemma, and degree theory results.</p>","PeriodicalId":51108,"journal":{"name":"Lithuanian Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2024-01-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139374553","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
Multiseasonal discrete-time risk model revisited 多季节离散时间风险模型再探讨
IF 0.4 4区 数学
Lithuanian Mathematical Journal Pub Date : 2023-12-23 DOI: 10.1007/s10986-023-09613-z
Andrius Grigutis, Jonas Jankauskas, Jonas Šiaulys
{"title":"Multiseasonal discrete-time risk model revisited","authors":"Andrius Grigutis, Jonas Jankauskas, Jonas Šiaulys","doi":"10.1007/s10986-023-09613-z","DOIUrl":"https://doi.org/10.1007/s10986-023-09613-z","url":null,"abstract":"<p>In this work, we set up the distribution function of <span>(mathcal{M}:={mathrm{sup}}_{nge 1}{sum }_{i=1}^{n}left({X}_{i}-1right),)</span> where the random walk <span>({sum }_{i=1}^{n}{X}_{i},nin {mathbb{N}},)</span> is generated by <i>N</i> periodically occurring distributions, and the integer-valued and nonnegative random variables<i>X</i><sub>1</sub><i>,X</i><sub>2</sub><i>, . . .</i> are independent. The considered random walk generates a so-called multiseasonal discrete-time risk model, and a known distribution of random variable <i>M</i> enables us to calculate the ultimate time ruin or survival probability. Verifying obtained theoretical statements, we demonstrate several computational examples for survival probability <b>P</b>(<i>M &lt; u</i>) when <i>N</i> = 2<i>,</i> 3<i>,</i> or 10.</p>","PeriodicalId":51108,"journal":{"name":"Lithuanian Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2023-12-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139027915","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
An interview with Donatas Surgailis 采访多纳塔斯-苏尔盖里斯
IF 0.4 4区 数学
Lithuanian Mathematical Journal Pub Date : 2023-12-23 DOI: 10.1007/s10986-023-09615-x
Viktor Skorniakov
{"title":"An interview with Donatas Surgailis","authors":"Viktor Skorniakov","doi":"10.1007/s10986-023-09615-x","DOIUrl":"https://doi.org/10.1007/s10986-023-09615-x","url":null,"abstract":"<p>The International Conference on Number Theory and Probability Theory took place in Palanga from September 11 to 15, 2023, in commemoration of the anniversaries of Lithuanian mathematicians Jonas Kubilius, Donatas Surgailis, Antanas Laurinˇcikas, Eugenijus Manstaviˇcius, K˛estutis Kubilius, and Alfredas Raˇckauskas. This is an interview article with one the jubilarians, D. Surgailis, known for his work in stochastic processes, with interests in long-range dependence, fractionally integrated time series, statistical inference, spatial models, random fields, and their scaling limits. D. Surgailis is the author of the monograph <i>Large Sample Inference for Long Memory Processes</i>, published by Imperial College Press, London, in 2012 (coauthored with Liudas Giraitis and Hira L. Koul), and 150 journal papers. A complete list of his publications is available on http://lma.lt/asmsv/intranetas/index.php?m=profile&amp;user=1577. D. Surgailis has served as the head of the Department of Random Processes at the Institute of Mathematics and Informatics (MII). He is Member Emeritus of the Lithuanian Academy of Sciences (LAS) and Professor Emeritus at Vilnius University (VU). This interview, conducted in October 2023, focuses on personal aspects of life and scientific career of D. Surgailis, that are less widely known but nonetheless captivating.</p>","PeriodicalId":51108,"journal":{"name":"Lithuanian Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2023-12-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139027951","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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