AIMS Mathematics最新文献

英文中文

Efficient numerical approaches with accelerated graphics processing unit (GPU) computations for Poisson problems and Cahn-Hilliard equations. 利用图形处理器（GPU）加速计算泊松问题和卡恩-希利亚德方程的高效数值方法。

IF 1.8 3区数学 Q1 MATHEMATICS

AIMS Mathematics

Pub Date : 2024-01-01 Epub Date: 2024-09-23 DOI: 10.3934/math.20241334

Saulo Orizaga, Maurice Fabien, Michael Millard

In this computational paper, we focused on the efficient numerical implementation of semi-implicit methods for models in materials science. In particular, we were interested in a class of nonlinear higher-order parabolic partial differential equations. The Cahn-Hilliard (CH) equation was chosen as a benchmark problem for our proposed methods. We first considered the Cahn-Hilliard equation with a convexity-splitting (CS) approach coupled with a backward Euler approximation of the time derivative and tested the performance against the bi-harmonic-modified (BHM) approach in terms of accuracy, order of convergence, and computation time. Higher-order time-stepping techniques that allow for the methods to increase their accuracy and order of convergence were then introduced. The proposed schemes in this paper were found to be very efficient for 2D computations. Computed dynamics in 2D and 3D are presented to demonstrate the energy-decreasing property and overall performance of the methods for longer simulation runs with a variety of initial conditions. In addition, we also present a simple yet powerful way to accelerate the computations by using MATLAB built-in commands to perform GPU implementations of the schemes. We show that it is possible to accelerate computations for the CH equation in 3D by a factor of 80, provided the hardware is capable enough.

在这篇计算论文中，我们重点关注材料科学模型半隐式方法的高效数值实现。我们尤其对一类非线性高阶抛物线偏微分方程感兴趣。我们选择卡恩-希利亚德（Cahn-Hilliard，CH）方程作为我们所提方法的基准问题。我们首先用凸性分割（CS）方法结合时间导数的后向欧拉近似来考虑 Cahn-Hilliard 方程，并在精度、收敛阶数和计算时间方面与双谐波修正（BHM）方法进行了性能对比测试。然后介绍了高阶时间步进技术，使这些方法能够提高精度和收敛阶次。本文提出的方案在二维计算中非常高效。本文展示了二维和三维的计算动态，以证明这些方法在各种初始条件下进行较长时间模拟运行时的能量递减特性和整体性能。此外，我们还介绍了一种简单而强大的方法，通过使用 MATLAB 内置命令来执行 GPU 实现方案，从而加速计算。我们的研究表明，只要硬件足够强大，就有可能将三维 CH 方程的计算速度提高 80 倍。

{"title":"Efficient numerical approaches with accelerated graphics processing unit (GPU) computations for Poisson problems and Cahn-Hilliard equations.","authors":"Saulo Orizaga, Maurice Fabien, Michael Millard","doi":"10.3934/math.20241334","DOIUrl":"10.3934/math.20241334","url":null,"abstract":"<p><p>In this computational paper, we focused on the efficient numerical implementation of semi-implicit methods for models in materials science. In particular, we were interested in a class of nonlinear higher-order parabolic partial differential equations. The Cahn-Hilliard (CH) equation was chosen as a benchmark problem for our proposed methods. We first considered the Cahn-Hilliard equation with a convexity-splitting (CS) approach coupled with a backward Euler approximation of the time derivative and tested the performance against the bi-harmonic-modified (BHM) approach in terms of accuracy, order of convergence, and computation time. Higher-order time-stepping techniques that allow for the methods to increase their accuracy and order of convergence were then introduced. The proposed schemes in this paper were found to be very efficient for 2D computations. Computed dynamics in 2D and 3D are presented to demonstrate the energy-decreasing property and overall performance of the methods for longer simulation runs with a variety of initial conditions. In addition, we also present a simple yet powerful way to accelerate the computations by using MATLAB built-in commands to perform GPU implementations of the schemes. We show that it is possible to accelerate computations for the CH equation in 3D by a factor of 80, provided the hardware is capable enough.</p>","PeriodicalId":48562,"journal":{"name":"AIMS Mathematics","volume":"9 10","pages":"27471-27496"},"PeriodicalIF":1.8,"publicationDate":"2024-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC11466300/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142401649","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Fejér type inequalities for harmonically convex functions 调和凸函数的fejsamr型不等式

IF 2.2 3区数学 Q1 MATHEMATICS

AIMS Mathematics

Pub Date : 2023-08-18 DOI: 10.3934/math.2022835

Muhammad Amer Latif

In this study, some mappings related to the Fejér-type inequalities for harmonically convex functions are defined over $ left[ 0, 1right] $. Some Fejér-type inequalities for harmonically convex functions are proved using these mappings. Properties of these mappings are considered and consequently, refinements are obtained of some known results.

在本研究中，在$left[0,1right]$上定义了一些与调和凸函数的Fejér型不等式有关的映射。利用这些映射证明了调和凸函数的一些Fejér型不等式。考虑了这些映射的性质，从而得到了一些已知结果的精化。

引用次数: 3

Angle in the space of $ p $-summable sequences $ p $-可和序列空间中的角

IF 2.2 3区数学 Q1 MATHEMATICS

AIMS Mathematics

Pub Date : 2023-07-16 DOI: 10.3934/math.2022155

M. Nur, M. Bahri, A. Islamiyati, Harmanus Batkunde

The aim of this paper is to investigate completness of $ A $ that equipped with usual norm on $ p $-summable sequences space where $ A $ is subspace in $ p $-summable sequences space and $ 1le p < infty $. We also introduce a new inner product on $ A $ and prove completness of $ A $ using a new norm that corresponds this new inner product. Moreover, we discuss the angle between two vectors and two subspaces in $ A $. In particular, we discuss the angle between $ 1 $-dimensional subspace and $ (s-1) $-dimensional subspace where $ sge 2 $ of $ A $.

本文的目的是研究具有通常范数的$ A $在$ p $ -可和序列空间上的完备性，其中$ A $是$ p $ -可和序列空间和$ 1le p < infty $中的子空间。在$ A $上引入了一个新的内积，并用一个新的范数证明了$ A $的完备性。此外，我们还讨论了$ A $中两个向量与两个子空间之间的夹角。特别地，我们讨论了$ 1 $维子空间与$ (s-1) $维子空间之间的夹角，其中$ A $的$ sge 2 $。

引用次数: 0

Cohomologies of modified $ lambda $-differential Lie triple systems and applications 修正$ λ $-微分李三元系统的上同调及其应用

IF 2.2 3区数学 Q1 MATHEMATICS

AIMS Mathematics

Pub Date : 2023-07-12 DOI: 10.3934/math.20231280

Wen Teng, Fengshan Long, Yu Zhang

In this paper, we introduce the concept and representation of modified $ lambda $-differential Lie triple systems. Next, we define the cohomology of modified $ lambda $-differential Lie triple systems with coefficients in a suitable representation. As applications of the proposed cohomology theory, we study 1-parameter formal deformations and abelian extensions of modified $ lambda $-differential Lie triple systems.

在本文中，我们引入了修正的$lambda$微分李三系统的概念和表示。接下来，我们定义了系数在适当表示中的修正$lambda$微分李三系统的上同调。作为所提出的上同调理论的应用，我们研究了修正的$lambda$微分李三系统的1-参数形式变形和阿贝尔扩展。

引用次数: 0

The lifespan of classical solutions of one dimensional wave equations with semilinear terms of the spatial derivative 具有空间导数的双线性项的一维波动方程经典解的寿命

IF 2.2 3区数学 Q1 MATHEMATICS

AIMS Mathematics

Pub Date : 2023-06-12 DOI: 10.3934/math.20231300

Takiko Sasaki, Shuhei Takamatsu, H. Takamura

This paper is devoted to the lifespan estimates of small classical solutions of the initial value problems for one dimensional wave equations with semilinear terms of the spatial derivative of the unknown function. It is natural that the result is same as the one for semilinear terms of the time-derivative. But there are so many differences among their proofs. Moreover, it is meaningful to study this problem in the sense that it may help us to investigate its blow-up boundary in the near future.

本文致力于具有未知函数空间导数的双线性项的一维波动方程初值问题的小经典解的寿命估计。这个结果和时间导数的双线性项的结果是一样的，这是很自然的。但他们的证明之间有很多不同之处。此外，研究这一问题有意义，因为它可能有助于我们在不久的将来研究其爆炸边界。

引用次数: 1

Stability of stochastic dynamic systems of a random structure with Markov switching in the presence of concentration points 具有马尔可夫切换的随机结构动态系统在集中点下的稳定性

IF 2.2 3区数学 Q1 MATHEMATICS

AIMS Mathematics

Pub Date : 2023-05-19 DOI: 10.3934/math.20231245

T. Lukashiv, I. Malyk, Maryna K. Chepeleva, P. Nazarov

This article aims to investigate sufficient conditions for the stability of the trivial solution of stochastic differential equations with a random structure, particularly in contexts involving the presence of concentration points. The proof of asymptotic stability leverages the use of Lyapunov functions, supplemented by additional constraints on the magnitudes of jumps and jump times, as well as the Markov property of the system solutions. The findings are elucidated with an example, demonstrating both stable and unstable conditions of the system. The novelty of this work is in the consideration of jump concentration points, which are not considered in classical works. The assumption of the existence of concentration points leads to additional constraints on jumps, jump times and relations between them.

本文旨在研究具有随机结构的随机微分方程平凡解的稳定性的充分条件，特别是在涉及存在集中点的情况下。渐近稳定性的证明利用了李雅普诺夫函数的使用，辅以对跳跃幅度和跳跃时间的附加约束，以及系统解的马尔可夫性质。通过一个算例说明了系统的稳定和不稳定情况。这部作品的新颖之处在于考虑了跳跃集中点，这在经典作品中是没有考虑到的。集中点存在的假设导致了对跳跃、跳跃时间和它们之间关系的附加约束。

引用次数: 0

Mixed radial-angular bounds for Hardy-type operators on Heisenberg group Heisenberg群上hardy型算子的混合径向-角界

IF 2.2 3区数学 Q1 MATHEMATICS

AIMS Mathematics

Pub Date : 2023-04-24 DOI: 10.3934/math.20231070

Zhongci Hang, Xiang Li, D. Yan

In this paper, we study $ n $-dimensional Hardy operator and its dual in mixed radial-angular spaces on Heisenberg group and obtain their sharp bounds by using the rotation method. Furthermore, the sharp bounds of $ n $-dimensional weighted Hardy operator and weighted Cesàro operator are also obtained.

本文研究了海森堡群上混合径向角空间中的$n$维Hardy算子及其对偶，并利用旋转方法得到了它们的锐界。此外，还得到了$n$维加权Hardy算子和加权Cesàro算子的锐界。

引用次数: 1

Exact solutions and superposition rules for Hamiltonian systems generalizing time-dependent SIS epidemic models with stochastic fluctuations 具有随机波动的时变SIS流行病模型的hamilton系统的精确解和叠加规则

IF 2.2 3区数学 Q1 MATHEMATICS

AIMS Mathematics

Pub Date : 2023-04-18 DOI: 10.3934/math.20231225

R. Campoamor-Stursberg, Eduardo Fernández-Saiz, F. J. Herranz

Using the theory of Lie-Hamilton systems, formal generalized time-dependent Hamiltonian systems that extend a recently proposed SIS epidemic model with a variable infection rate are considered. It is shown that, independently on the particular interpretation of the time-dependent coefficients, these systems generally admit an exact solution, up to the case of the maximal extension within the classification of Lie-Hamilton systems, for which a superposition rule is constructed. The method provides the algebraic frame to which any SIS epidemic model that preserves the above-mentioned properties is subjected. In particular, we obtain exact solutions for generalized SIS Hamiltonian models based on the book and oscillator algebras, denoted by $ mathfrak{b}_2 $ and $ mathfrak{h}_4 $, respectively. The last generalization corresponds to an SIS system possessing the so-called two-photon algebra symmetry $ mathfrak{h}_6 $, according to the embedding chain $ mathfrak{b}_2subset mathfrak{h}_4subset mathfrak{h}_6 $, for which an exact solution cannot generally be found but a nonlinear superposition rule is explicitly given.

利用Lie-Hamilton系统理论，考虑了形式的广义含时Hamilton体系，该体系扩展了最近提出的具有可变感染率的SIS流行病模型。结果表明，独立于对含时系数的特殊解释，这些系统通常允许精确解，直到Lie-Hamilton系统分类中的最大扩张的情况，并为此构造了叠加规则。该方法提供了代数框架，任何保留上述性质的SIS流行病模型都要服从该代数框架。特别地，我们获得了基于书和振子代数的广义SIS哈密顿模型的精确解，用$mathfrak表示{b}_2$和$mathfrak{h}_4美元。最后一个推广对应于具有所谓双光子代数对称性$mathfrak的SIS系统{h}_6$，根据嵌入链$mathfrak{b}_2子集mathfrak{h}_4子集mathfrak{h}_6$，通常不能找到其精确解，但明确给出了非线性叠加规则。

{"title":"Exact solutions and superposition rules for Hamiltonian systems generalizing time-dependent SIS epidemic models with stochastic fluctuations","authors":"R. Campoamor-Stursberg, Eduardo Fernández-Saiz, F. J. Herranz","doi":"10.3934/math.20231225","DOIUrl":"https://doi.org/10.3934/math.20231225","url":null,"abstract":"Using the theory of Lie-Hamilton systems, formal generalized time-dependent Hamiltonian systems that extend a recently proposed SIS epidemic model with a variable infection rate are considered. It is shown that, independently on the particular interpretation of the time-dependent coefficients, these systems generally admit an exact solution, up to the case of the maximal extension within the classification of Lie-Hamilton systems, for which a superposition rule is constructed. The method provides the algebraic frame to which any SIS epidemic model that preserves the above-mentioned properties is subjected. In particular, we obtain exact solutions for generalized SIS Hamiltonian models based on the book and oscillator algebras, denoted by $ mathfrak{b}_2 $ and $ mathfrak{h}_4 $, respectively. The last generalization corresponds to an SIS system possessing the so-called two-photon algebra symmetry $ mathfrak{h}_6 $, according to the embedding chain $ mathfrak{b}_2subset mathfrak{h}_4subset mathfrak{h}_6 $, for which an exact solution cannot generally be found but a nonlinear superposition rule is explicitly given.","PeriodicalId":48562,"journal":{"name":"AIMS Mathematics","volume":" ","pages":""},"PeriodicalIF":2.2,"publicationDate":"2023-04-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43783486","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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: 1

Further characterizations and representations of the Minkowski inverse in Minkowski space 闵可夫斯基逆在闵可夫斯基空间中的进一步表征与表示

IF 2.2 3区数学 Q1 MATHEMATICS

AIMS Mathematics

Pub Date : 2023-03-24 DOI: 10.3934/math.20231189

Jiale Gao, Qingwen Wang, Kezheng Zuo, Jiabao Wu

This paper serves to identify some new characterizations and representations of the Minkowski inverse in Minkowski space. First of all, a few representations of $ {1, 3^{mathfrak{m}}} $-, $ {1, 2, 3^{mathfrak{m}}} $-, $ {1, 4^{mathfrak{m}}} $- and $ {1, 2, 4^{mathfrak{m}}} $-inverses are given in order to represent the Minkowski inverse. Second, some famous characterizations of the Moore-Penrose inverse are extended to that of the Minkowski inverse. Third, using the Hartwig-Spindelböck decomposition, we present a representation of the Minkowski inverse. And, based on this result, an interesting characterization of the Minkowski inverse is showed by a rank equation. Finally, we obtain several new representations of the Minkowski inverse in a more general form, by which the Minkowski inverse of a class of block matrices is given.

本文给出了Minkowski空间中Minkowsky逆的一些新的刻画和表示。首先，为了表示Minkowski逆，给出了$｛1，3^｛mathfrak｛m｝｝｝$-，$｛1,2,3^｛ mathfrak｛m}｝}$，${1,2,4^｛mathfrak｛m}｝$和${1,24,^{mathfrak{m｝｝}$逆的几个表示。其次，将Moore-Penrose逆的一些著名性质推广到Minkowski逆的性质。第三，使用Hartwig-Spindelböck分解，我们给出了Minkowski逆的一个表示。在此基础上，用秩方程给出了Minkowski逆的一个有趣的性质。最后，我们以更一般的形式得到了Minkowski逆的几个新表示，并由此给出了一类块矩阵的Minkowsky逆。

引用次数: 0

Some identities on degenerate hyperbolic functions arising from $ p $-adic integrals on $ mathbb{Z}_p $ $mathbb上$p$-dic积分引起的退化双曲函数的一些恒等式{Z}_p$

IF 2.2 3区数学 Q1 MATHEMATICS

AIMS Mathematics

Pub Date : 2023-03-04 DOI: 10.3934/math.20231298

Taekyun Kim, Dae San Kim, H. Kim

The aim of this paper is to introduce several degenerate hyperbolic functions as degenerate versions of the hyperbolic functions, to evaluate Volkenborn and the fermionic $ p $-adic integrals of the degenerate hyperbolic cosine and the degenerate hyperbolic sine functions and to derive from them some identities involving the degenerate Bernoulli numbers, the degenerate Euler numbers and the Cauchy numbers of the first kind.

本文的目的是引入几个退化双曲函数作为双曲函数的退化形式，评估退化双曲余弦和退化双曲正弦函数的Volkenborn积分和Fermion$p$-dic积分，并从中导出一些涉及退化伯努利数的恒等式，退化欧拉数和第一类柯西数。

引用次数: 0

下一页尾页

类型

全部化学•材料生命科学医学物理工程技术环境•农林材料科学地球科学法学管理学化学环境科学与生态学计算机科学教育学经济学农林科学人文科学生物学数学物理与天体物理心理学综合性期刊其他工业工程理学历史学农学文学信息工程

数据库

全部 ACS Publications Elsevier ieeexplore Springer The Royal Society of Chemistry Wiley

期刊

AIMS Mathematics

全部 Acc. Chem. Res. ACS Applied Bio Materials ACS Appl. Electron. Mater. ACS Appl. Energy Mater. ACS Appl. Mater. Interfaces ACS Appl. Nano Mater. ACS Appl. Polym. Mater. ACS BIOMATER-SCI ENG ACS Catal. ACS Cent. Sci. ACS Chem. Biol. ACS Chemical Health & Safety ACS Chem. Neurosci. ACS Comb. Sci. ACS Earth Space Chem. ACS Energy Lett. ACS Infect. Dis. ACS Macro Lett. ACS Mater. Lett. ACS Med. Chem. Lett. ACS Nano ACS Omega ACS Photonics ACS Sens. ACS Sustainable Chem. Eng. ACS Synth. Biol. Anal. Chem. BIOCHEMISTRY-US Bioconjugate Chem. BIOMACROMOLECULES Chem. Res. Toxicol. Chem. Rev. Chem. Mater. CRYST GROWTH DES ENERG FUEL Environ. Sci. Technol. Environ. Sci. Technol. Lett. Eur. J. Inorg. Chem. IND ENG CHEM RES Inorg. Chem. J. Agric. Food. Chem. J. Chem. Eng. Data J. Chem. Educ. J. Chem. Inf. Model. J. Chem. Theory Comput. J. Med. Chem. J. Nat. Prod. J PROTEOME RES J. Am. Chem. Soc. LANGMUIR MACROMOLECULES Mol. Pharmaceutics Nano Lett. Org. Lett. ORG PROCESS RES DEV ORGANOMETALLICS J. Org. Chem. J. Phys. Chem. J. Phys. Chem. A J. Phys. Chem. B J. Phys. Chem. C J. Phys. Chem. Lett. Analyst Anal. Methods Biomater. Sci. Catal. Sci. Technol. Chem. Commun. Chem. Soc. Rev. CHEM EDUC RES PRACT CRYSTENGCOMM Dalton Trans. Energy Environ. Sci. ENVIRON SCI-NANO ENVIRON SCI-PROC IMP ENVIRON SCI-WAT RES Faraday Discuss. Food Funct. Green Chem. Inorg. Chem. Front. Integr. Biol. J. Anal. At. Spectrom. J. Mater. Chem. A J. Mater. Chem. B J. Mater. Chem. C Lab Chip Mater. Chem. Front. Mater. Horiz. MEDCHEMCOMM Metallomics Mol. Biosyst. Mol. Syst. Des. Eng. Nanoscale Nanoscale Horiz. Nat. Prod. Rep. New J. Chem. Org. Biomol. Chem. Org. Chem. Front. PHOTOCH PHOTOBIO SCI PCCP Polym. Chem.

﹀