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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 Q3 MATHEMATICS Pub Date : 2024-02-16 DOI: 10.1007/s10986-024-09623-5
Sanju Mandal, Molla Basir Ahamed

The Hankel determinant ({H}_{mathrm{2,1}}left({F}_{f-1}/2right)) of logarithmic coefficients is defined as

({H}_{mathrm{2,1}}left({F}_{f-1}/2right):=left|begin{array}{cc}{Gamma }_{1}& {Gamma }_{2} {Gamma }_{2}& {Gamma }_{3}end{array}right|={Gamma }_{1}{Gamma }_{3}-{Gamma }_{2}^{2},)

where ({Gamma }_{1},{Gamma }_{2},) and ({Gamma }_{3}) are the first, second, and third logarithmic coefficients of inverse functions belonging to the class (mathcal{S}) of normalized univalent functions. In this paper, we establish sharp inequalities (left|{H}_{mathrm{2,1}}left({F}_{f-1}/2right)right|le 19/288,) (left|{H}_{mathrm{2,1}}left({F}_{f-1}/2right)right|le 1/144,) and (left|{H}_{mathrm{2,1}}left({F}_{f-1}/2right)right|le 1/36) for the logarithmic coefficients of inverse functions, considering starlike and convex functions, as well as functions with bounded turning of order 1/2, respectively.

对数系数的汉克尔行列式({H}_{mathrm{2,1}}left({F}_{f-1}/2right))定义为: ({H}_{mathrm{2,1}}left({F}_{f-1}/2right):=left|begin{array}{cc}{Gamma }_{1}& {Gamma }_{2} {Gamma }_{2}&;{Gamma }_{3}end{array}right|={Gamma }_{1}{Gamma }_{3}-{Gamma }_{2}^{2},)where ({Gamma }_{1},{Gamma }_{2},) and({Gamma }_{3}) are the first、属于归一化单值函数类 (mathcal{S}) 的反函数的第一、第二和第三对数系数。在本文中,我们建立了尖锐的不等式 ((left|{H}_{mathrm{2,1}}left({F}_{f-1}/2right)right|le 19/288,)(left|{H}_{mathrm{2,1}left({F}_{f-1}/2right)right|le 1/144,)和 (left|{H}_{mathrm{2,1}left({F}_{f-1}/2right)right|le 1/36)为反函数的对数系数、分别考虑星形函数和凸函数,以及阶数为 1/2 的有界转折函数。
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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 Q3 MATHEMATICS Pub Date : 2024-01-15 DOI: 10.1007/s10986-023-09614-y
Xiulian Shi, Keyan Wang, Hui Sun

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 [1, 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 L2 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.

在本文中,我们提出并分析了一种用于分数多延时微分方程数值求解的谱配位法。分数导数是在卡普托意义上描述的。我们提出,一些合适的变量变换可以将方程转换为定义在标准区间 [-1, 1] 上的 Volterra 积分方程。然后以 Jacobi-Gauss 点作为配位节点,利用 Jacobi-Gauss 正交公式对积分方程进行逼近。随后,研究了所提方法在无穷规范和加权 L2 规范下的收敛性分析。为了进行数值模拟,我们研究了一些测试实例,并给出了数值结果。此外,我们还提供了所提方法与一些现有数值方法的比较研究。
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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 Q3 MATHEMATICS Pub Date : 2024-01-09 DOI: 10.1007/s10986-023-09616-w

Abstract

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 fluid dynamic and electromagnetic problems.

摘要 我们提出并分析了一个抽象框架,用于研究线性退化抛物线增强混合方程组的良好求解性。我们将线性退化抛物线问题的理论与有关静态二重鞍点方程的结果相结合,推导出该问题解的存在性和唯一性的充分条件。最后,我们通过流体动力学和电磁问题的实例展示了所开发理论的一些应用。
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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 Q3 MATHEMATICS Pub Date : 2024-01-06 DOI: 10.1007/s10986-023-09617-9
Rima Chetouane, Brahim Dridi, Rached Jaidane

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 B of ℝ4. The potential V is a continuous positive function bounded away from zero in B. 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.

在本文中,我们确定了在ℝ4 的单位球 B 中边界狄利克特条件下薛定谔型加权四阶方程的基态解的存在性。由于亚当斯型不等式与多项式项相结合,方程的非线性假定为指数增长。我们使用了 Nehari 集合中的约束最小化、定量变形 Lemma 和度理论结果。
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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 Q3 MATHEMATICS Pub Date : 2023-12-23 DOI: 10.1007/s10986-023-09613-z
Andrius Grigutis, Jonas Jankauskas, Jonas Šiaulys

In this work, we set up the distribution function of (mathcal{M}:={mathrm{sup}}_{nge 1}{sum }_{i=1}^{n}left({X}_{i}-1right),) where the random walk ({sum }_{i=1}^{n}{X}_{i},nin {mathbb{N}},) is generated by N periodically occurring distributions, and the integer-valued and nonnegative random variablesX1,X2, . . . are independent. The considered random walk generates a so-called multiseasonal discrete-time risk model, and a known distribution of random variable M enables us to calculate the ultimate time ruin or survival probability. Verifying obtained theoretical statements, we demonstrate several computational examples for survival probability P(M < u) when N = 2, 3, or 10.

在这项工作中,我们设定了分布函数({M}:={mathrm{sup}}_{nge 1}{sum }_{i=1}^{n}left({X}_{i}-1right),) 其中随机行走 ({sum }_{i=1}^{n}{X}_{i},nin {mathbb{N}},) 是由 N 个周期性出现的分布生成的,且整数值和非负随机变量 X1,X2, ....是独立的。所考虑的随机漫步生成了一个所谓的多季节离散时间风险模型,已知随机变量 M 的分布使我们能够计算最终时间毁灭或生存概率。为了验证所获得的理论陈述,我们演示了几个计算实例,说明当 N = 2、3 或 10 时的生存概率 P(M < u)。
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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 Q3 MATHEMATICS Pub Date : 2023-12-23 DOI: 10.1007/s10986-023-09615-x
Viktor Skorniakov

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 Large Sample Inference for Long Memory Processes, 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&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.

为纪念立陶宛数学家约纳斯-库比留斯(Jonas Kubilius)、多纳塔斯-苏尔盖里斯(Donatas Surgailis)、安塔纳斯-劳林ˇ西卡斯(Antanas Laurinˇcikas)、尤金尼尤斯-曼斯塔维ˇ西乌斯(Eugenijus Manstaviˇcius)、库比留斯-库比留斯(K˛estutis Kubilius)和阿尔弗雷达斯-拉ˇ克劳斯卡斯(Alfredas Raˇckauskas)诞辰,数论与概率论国际会议于2023年9月11日至15日在帕兰加举行。这是一篇对其中一位欢庆者 D. Surgailis 的访谈文章,他因在随机过程方面的工作而闻名,对长程依赖性、分数积分时间序列、统计推断、空间模型、随机场及其缩放极限等领域很感兴趣。D. Surgailis 是专著《长记忆过程的大样本推断》(Large Sample Inference for Long Memory Processes)的作者,该书于 2012 年由伦敦帝国学院出版社出版(与 Liudas Giraitis 和 Hira L. Koul 合著),他还发表了 150 篇期刊论文。他发表的全部论文可在 http://lma.lt/asmsv/intranetas/index.php?m=profile&user=1577 上查阅。D. Surgailis 曾担任数学与信息学研究所(MII)随机过程系主任。他是立陶宛科学院(LAS)荣誉院士和维尔纽斯大学(VU)荣誉教授。这次访谈于 2023 年 10 月进行,重点是 D. Surgailis 鲜为人知但却引人入胜的个人生活和科学生涯。
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引用次数: 0
On normal approximation for φ-mixing and m-dependent random variables φ-混合和m-相关随机变量的正态逼近
IF 0.4 4区 数学 Q3 MATHEMATICS Pub Date : 2023-12-05 DOI: 10.1007/s10986-023-09612-0
Jonas Kazys Sunklodas

In this paper, we estimate the difference |Eh(Zn) Eh(Y)| between the expectations of real finite Lipschitz function h of the sum Zn = (X1 + ⋯ + Xn)/Bn, where ({B}_{n}^{2}) = E(X1 + ⋯ + Xn)2 > 0, and a standard normal random variable Y, where real centered random variables X1,X2,… satisfy the φ-mixing condition, defined between the “past” and “ future”, or are m-dependent. In particular cases, under the condition ({sum }_{r=1}^{infty }rvarphi (r)<infty ) or ({sum }_{r=1}^{infty }{rvarphi }^{1/2}(r)<infty ), the obtained upper bounds for φ-mixing random variables are of order O(n1/2). In addition, we refine the previously known upper bounds of order O((m + 1)1+δL2+δ,n), where L2+δ,n is the Lyapunov fraction of order 2 + δ, for m-dependent random variables, supplementing them with explicit constants. We also separately present the case of independent r.v.s.

在本文中,我们估计了和Zn = (X1 +⋯⋯+ Xn)/Bn的实有限Lipschitz函数h的期望之间的差|Eh(Zn)−Eh(Y)|,其中({B}_{n}^{2}) = E(X1 +⋯+ Xn)2 &gt;0和标准正态随机变量Y,其中实中心随机变量X1,X2,…满足φ-混合条件,定义在“过去”和“未来”之间,或者与m相关。在特殊情况下,在({sum }_{r=1}^{infty }rvarphi (r)<infty )或({sum }_{r=1}^{infty }{rvarphi }^{1/2}(r)<infty )条件下,φ-混合随机变量的上界为O(n−1/2)阶。此外,我们改进了先前已知的阶O((m + 1)1+δL2+δ,n)的上界,其中L2+δ,n是阶2+δ的Lyapunov分数,对于m相关随机变量,补充了显式常数。我们还分别介绍了独立rv的情况。
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引用次数: 0
Solvability of a nonlinear parabolic problem arising in modeling surface reactions 表面反应模型中非线性抛物型问题的可解性
IF 0.4 4区 数学 Q3 MATHEMATICS Pub Date : 2023-11-28 DOI: 10.1007/s10986-023-09609-9
Algirdas Ambrazevičius, Vladas Skakauskas

We investigate the existence, uniqueness, and long-time behavior of classical solutions to a coupled system of seven nonlinear parabolic equations. Four of them are determined in the interior of a region, and the other three are solved on a part of the boundary. In particular, such systems arise in modeling of surface reactions that involve the bulk diffusion of reactants toward and reaction products from the biocatalyst surface and surface diffusion of the intermediate reaction products.

研究了一类非线性抛物方程耦合系统经典解的存在性、唯一性和长时性。其中四个是在区域内部确定的,另外三个是在边界的一部分上解决的。特别是,这种系统出现在涉及反应物向生物催化剂表面的大量扩散和反应产物从生物催化剂表面和中间反应产物的表面扩散的表面反应的建模中。
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引用次数: 0
Sharp bounds on the third Hankel determinant for the Ozaki close-to-convex and convex functions Ozaki近凸函数和凸函数的第三个Hankel行列式的尖锐界
4区 数学 Q3 MATHEMATICS Pub Date : 2023-11-08 DOI: 10.1007/s10986-023-09610-2
Lei Shi, Muhammad Arif
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引用次数: 0
On general sums involving the floor function with applications to k-free numbers 关于涉及底函数的一般和及其在无k数上的应用
4区 数学 Q3 MATHEMATICS Pub Date : 2023-11-08 DOI: 10.1007/s10986-023-09611-1
Wei Zhang
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引用次数: 2
期刊
Lithuanian Mathematical Journal
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