Results in Applied Mathematics最新文献_第3页

Stability analysis of a dynamical model for sustainable Glacier ecotourism 冰川可持续生态旅游动态模型的稳定性分析

IF 1.3

Results in Applied Mathematics Pub Date : 2025-08-01 DOI: 10.1016/j.rinam.2025.100636

Jianbang He , Jiyue Zhang , Mazheze Xu , Zhongxiang Chen

{"title":"Stability analysis of a dynamical model for sustainable Glacier ecotourism","authors":"Jianbang He , Jiyue Zhang , Mazheze Xu , Zhongxiang Chen","doi":"10.1016/j.rinam.2025.100636","DOIUrl":"10.1016/j.rinam.2025.100636","url":null,"abstract":"<div><div>In this paper, we construct a system dynamics model to study the sustainable evolution of glacier ecotourism systems under environmental change. We calculate <span><math><msub><mrow><mi>R</mi></mrow><mrow><mi>C</mi></mrow></msub></math></span> based on the carbon-temperature equilibrium and <span><math><msub><mrow><mi>R</mi></mrow><mrow><mi>N</mi></mrow></msub></math></span> based on the reproduction number method in epidemiological models, and prove that the zero equilibrium is globally asymptotically stable when <span><math><mrow><msub><mrow><mi>R</mi></mrow><mrow><mi>C</mi></mrow></msub><mo><</mo><mn>1</mn></mrow></math></span> and <span><math><mrow><msub><mrow><mi>R</mi></mrow><mrow><mi>N</mi></mrow></msub><mo>≤</mo><mn>1</mn></mrow></math></span>, and the error dynamics with respect to the positive equilibrium are globally uniformly ultimately bounded when both <span><math><mrow><msub><mrow><mi>R</mi></mrow><mrow><mi>C</mi></mrow></msub><mo><</mo><mn>1</mn></mrow></math></span> and <span><math><mrow><msub><mrow><mi>R</mi></mrow><mrow><mi>N</mi></mrow></msub><mo>></mo><mn>1</mn></mrow></math></span>. Empirical validation based on data from the Mendenhall Glacier is conducted to support the theoretical analysis.</div></div>","PeriodicalId":36918,"journal":{"name":"Results in Applied Mathematics","volume":"27 ","pages":"Article 100636"},"PeriodicalIF":1.3,"publicationDate":"2025-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145010207","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}

引用次数: 0

Improved Rosenbrock method with error estimator and Jacobian approximation using complex step 改进了误差估计的Rosenbrock方法和复步逼近的Jacobian方法

IF 1.3

Results in Applied Mathematics Pub Date : 2025-08-01 DOI: 10.1016/j.rinam.2025.100629

Juan Diego Pulgarín Rivera , Daniel Turizo , Elias D. Nino-Ruiz , Oscar Danilo Montoya

引用次数: 0

The spectral Galerkin method for the differential operator eigenvalue problems based on a least-squares form and its Schur complement type implementation methods 基于最小二乘形式的微分算子特征值问题的谱伽辽金方法及其Schur补型实现方法

IF 1.3

Results in Applied Mathematics Pub Date : 2025-08-01 DOI: 10.1016/j.rinam.2025.100633

Jiaoxia Huang , Yonghui Qin

{"title":"The spectral Galerkin method for the differential operator eigenvalue problems based on a least-squares form and its Schur complement type implementation methods","authors":"Jiaoxia Huang , Yonghui Qin","doi":"10.1016/j.rinam.2025.100633","DOIUrl":"10.1016/j.rinam.2025.100633","url":null,"abstract":"<div><div>The differential operator eigenvalue problems often arise in the field of physics and engineering, such as solid band structure, electron orbitals of atoms or molecules, and quantum bound states. In this paper, the spectral Galerkin method based on a least squares setting is developed for solving the differential operator eigenvalue problems. The proposed scheme leads to a global symmetric positive definite algebraic eigenvalue problem. Two kinds of Schur complement methods are given to deal with the corresponding algebraic equation. Namely, the global block matrix can be decomposed into a local matrix eigenvalue problem. Numerical results are given to verify the effectiveness and high-order accuracy of the proposed scheme. The proposed methods are also effective for solving the three-dimensional problem. We also consider the applications of the proposed methods to solve the eigenvalue problems with a parameter and the <span><math><mrow><mi>g</mi><mi>r</mi><mi>a</mi><mi>d</mi><mrow><mo>(</mo><mi>d</mi><mi>i</mi><mi>v</mi><mo>)</mo></mrow></mrow></math></span>-differential operator eigenvalue problems</div></div>","PeriodicalId":36918,"journal":{"name":"Results in Applied Mathematics","volume":"27 ","pages":"Article 100633"},"PeriodicalIF":1.3,"publicationDate":"2025-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144920161","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}

引用次数: 0

Optimal quadrature formulas for approximate calculation of rapidly oscillating integrals 快速振荡积分近似计算的最佳正交公式

IF 1.3

Results in Applied Mathematics Pub Date : 2025-08-01 DOI: 10.1016/j.rinam.2025.100627

Kholmat Shadimetov , Anvar Adilkhodjaev , Otabek Gulomov

引用次数: 0

Stability for linear second order vector integro-differential equations 线性二阶矢量积分微分方程的稳定性

IF 1.3

Results in Applied Mathematics Pub Date : 2025-08-01 DOI: 10.1016/j.rinam.2025.100634

Leonid Berezansky , Alexander Domoshnitsky

引用次数: 0

The proximal point algorithm with a general perturbation on geodesic spaces 在测地线空间上具有一般摄动的近点算法

IF 1.4

Results in Applied Mathematics Pub Date : 2025-07-28 DOI: 10.1016/j.rinam.2025.100618

Takuto Kajimura, Yasunori Kimura

引用次数: 0

A corrected L1 scheme for solving a tempered subdiffusion equation with nonsmooth data 求解具有非光滑数据的回火次扩散方程的修正L1格式

IF 1.4

Results in Applied Mathematics Pub Date : 2025-07-23 DOI: 10.1016/j.rinam.2025.100613

Can Li , Xin Wang , Yubin Yan , Zexin Hou

引用次数: 0

Global existence for the Vlasov–Euler–Fokker–Planck system in low-regularity space 低正则空间中Vlasov-Euler-Fokker-Planck系统的整体存在性

IF 1.4

Results in Applied Mathematics Pub Date : 2025-07-22 DOI: 10.1016/j.rinam.2025.100617

Bing Tan, Yingzhe Fan

{"title":"Global existence for the Vlasov–Euler–Fokker–Planck system in low-regularity space","authors":"Bing Tan, Yingzhe Fan","doi":"10.1016/j.rinam.2025.100617","DOIUrl":"10.1016/j.rinam.2025.100617","url":null,"abstract":"<div><div>This paper investigates the global well-posedness of the Cauchy problem for the Vlasov–Fokker–Planck equation coupled with the incompressible Euler system around a normalized global Maxwellian in a periodic spatial domain. The system describes the interaction between a fluid governed by Euler equations and a particle distribution evolving under the VFP dynamics, with coupling through a drag force. We establish the existence and uniqueness of global mild solutions for small initial data in a low regularity function space <span><math><mrow><msubsup><mrow><mi>L</mi></mrow><mrow><mi>k</mi></mrow><mrow><mn>1</mn></mrow></msubsup><msubsup><mrow><mi>L</mi></mrow><mrow><mi>T</mi></mrow><mrow><mi>∞</mi></mrow></msubsup><msubsup><mrow><mi>L</mi></mrow><mrow><mi>v</mi></mrow><mrow><mn>2</mn></mrow></msubsup></mrow></math></span> by employing Fourier analysis.</div><div>Compare to the Navier–Stokes–Vlasov-Fokker–Planck system (Tan and Fan, 2023) where velocity dissipation estimates can be directly derived from the viscous term, the Vlasov–Euler–Fokker–Planck system lacks such direct accessibility to velocity dissipation due to its inherent structural differences. To overcome this obstacle, we need to exploit the macroscopic dissipation <span><math><mi>b</mi></math></span> inherent in the macroscopic equation. Then the dissipation of velocity is indirectly captured by combining the macroscopic dissipation of <span><math><mi>b</mi></math></span> and the linear dissipation of <span><math><mrow><mi>u</mi><mo>−</mo><mi>b</mi></mrow></math></span> within the equation. Finally the uniform energy functionals of the solution can be obtained by utilizing the refined energy estimate.</div></div>","PeriodicalId":36918,"journal":{"name":"Results in Applied Mathematics","volume":"27 ","pages":"Article 100617"},"PeriodicalIF":1.4,"publicationDate":"2025-07-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144680600","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}

引用次数: 0

Discrete ILQG method based on high-order exponential Runge–Kutta discretization 基于高阶指数龙格-库塔离散化的离散ILQG方法

IF 1.4

Results in Applied Mathematics Pub Date : 2025-07-22 DOI: 10.1016/j.rinam.2025.100608

Yujie Yun, Tieqiang Gang, Lijie Chen

引用次数: 0

Multiscale wave resonance in composite sinusoidal-elliptical topographies: Critical transitions and analytical control 复合正弦波-椭圆地形中的多尺度波共振：临界跃迁和分析控制

IF 1.4

Results in Applied Mathematics Pub Date : 2025-07-18 DOI: 10.1016/j.rinam.2025.100615

Xiaofeng Li

{"title":"Multiscale wave resonance in composite sinusoidal-elliptical topographies: Critical transitions and analytical control","authors":"Xiaofeng Li","doi":"10.1016/j.rinam.2025.100615","DOIUrl":"10.1016/j.rinam.2025.100615","url":null,"abstract":"<div><div>This study presents the first analytical solution for wave propagation over composite seabeds integrating sinusoidal sandbars with truncated semi-elliptical topographies, overcoming limitations of conventional mild-slope equations in handling elliptical curvature effects, coupled Bragg scattering, and singularities at truncated boundaries. Utilizing Frobenius series expansion and multi-region field matching, we systematically quantify how geometric parameters—<span><math><mrow><mi>a</mi><mo>/</mo><mi>b</mi></mrow></math></span> ratio, <span><math><mrow><mi>δ</mi><mo>/</mo><mi>a</mi></mrow></math></span>, and <span><math><mrow><msub><mrow><mi>h</mi></mrow><mrow><mn>0</mn></mrow></msub><mo>/</mo><mi>b</mi></mrow></math></span>—govern wave reflection coefficients (<span><math><msub><mrow><mi>K</mi></mrow><mrow><mi>R</mi></mrow></msub></math></span>). Key discoveries reveal that the <span><math><mrow><mi>a</mi><mo>/</mo><mi>b</mi></mrow></math></span> ratio controls resonance peak frequencies (inducing 12% shifts per 0.1 change), the radius parameter <span><math><mrow><mi>r</mi><mo>=</mo><mrow><mo>(</mo><msub><mrow><mi>h</mi></mrow><mrow><mn>0</mn></mrow></msub><mo>−</mo><msub><mrow><mi>h</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>)</mo></mrow><mo>/</mo><msub><mrow><mi>h</mi></mrow><mrow><mn>0</mn></mrow></msub></mrow></math></span> triggers complete reflection (<span><math><mrow><msub><mrow><mi>K</mi></mrow><mrow><mi>R</mi></mrow></msub><mo>→</mo><mn>1</mn></mrow></math></span>) at a critical value of 0.5, and optimal <span><math><mrow><mi>δ</mi><mo>/</mo><mi>a</mi></mrow></math></span> expands reflection bandwidth by up to 22%. This work transcends classical studies on singular seabed types, establishes a theoretical foundation for designing wave-control metamaterials via multiscale resonances, and bridges classical potential flow theory with modern coastal engineering applications in wave energy harvesting, coastal protection, and offshore structure design.</div></div>","PeriodicalId":36918,"journal":{"name":"Results in Applied Mathematics","volume":"27 ","pages":"Article 100615"},"PeriodicalIF":1.4,"publicationDate":"2025-07-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144654180","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}

引用次数: 0