Results in Applied Mathematics最新文献

Weak type estimates of Hardy–Littlewood maximal operator on local Morrey spaces associated with ball quasi-Banach function spaces 与球拟banach函数空间相关的局部Morrey空间上Hardy-Littlewood极大算子的弱估计

IF 1.4

Results in Applied Mathematics Pub Date : 2025-06-25 DOI: 10.1016/j.rinam.2025.100606

HanLin Li, Jiang Zhou

引用次数: 0

The numerical solution of a Fredholm integral equation of the second kind using the Galerkin method based on optimal interpolation 基于最优插值的伽辽金方法数值解第二类Fredholm积分方程

IF 1.4

Results in Applied Mathematics Pub Date : 2025-06-23 DOI: 10.1016/j.rinam.2025.100607

Samandar Babaev , Abdullo Hayotov , Asliddin Boltaev , Surayyo Mirzoyeva , Malika Mirzaeva

{"title":"The numerical solution of a Fredholm integral equation of the second kind using the Galerkin method based on optimal interpolation","authors":"Samandar Babaev , Abdullo Hayotov , Asliddin Boltaev , Surayyo Mirzoyeva , Malika Mirzaeva","doi":"10.1016/j.rinam.2025.100607","DOIUrl":"10.1016/j.rinam.2025.100607","url":null,"abstract":"<div><div>In this paper, we study the Galerkin method for obtaining approximate solutions to linear Fredholm integral equations of the second kind. The finite element solution is represented as a linear combination of basis functions, and the construction of suitable basis functions plays a crucial role in the accuracy of the approximation. We propose an optimal interpolation formula that exactly reproduces the functions <span><math><msup><mrow><mi>e</mi></mrow><mrow><mi>x</mi></mrow></msup></math></span> and <span><math><msup><mrow><mi>e</mi></mrow><mrow><mo>−</mo><mi>x</mi></mrow></msup></math></span>, and derive basis functions from its coefficients. This interpolation formula is constructed within the Hilbert space <span><math><msubsup><mrow><mi>W</mi></mrow><mrow><mn>2</mn></mrow><mrow><mrow><mo>(</mo><mn>1</mn><mo>,</mo><mn>0</mn><mo>)</mo></mrow></mrow></msubsup></math></span>. To evaluate the effectiveness of the proposed approach, we solve several integral equations using the Galerkin method with two types of basis functions: the newly constructed exponential basis and classical piecewise linear basis functions. Numerical experiments are presented to compare the accuracy of these approaches. Graphs and tables illustrate the approximation errors, demonstrating that both basis functions achieve an error order of <span><math><mrow><mi>O</mi><mrow><mo>(</mo><mi>h</mi><mo>)</mo></mrow></mrow></math></span>, with the optimal interpolation-based basis yielding superior accuracy in certain cases.</div></div>","PeriodicalId":36918,"journal":{"name":"Results in Applied Mathematics","volume":"27 ","pages":"Article 100607"},"PeriodicalIF":1.4,"publicationDate":"2025-06-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144338603","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

TreeEM: Tree-enhanced ensemble model combining with feature selection for cancer subtype classification and survival prediction TreeEM：结合特征选择的树增强集成模型用于癌症亚型分类和生存预测

IF 1.4

Results in Applied Mathematics Pub Date : 2025-06-20 DOI: 10.1016/j.rinam.2025.100605

Guoqiang Zhao, Dongxi Li

{"title":"TreeEM: Tree-enhanced ensemble model combining with feature selection for cancer subtype classification and survival prediction","authors":"Guoqiang Zhao, Dongxi Li","doi":"10.1016/j.rinam.2025.100605","DOIUrl":"10.1016/j.rinam.2025.100605","url":null,"abstract":"<div><div>Cancer subtype analysis faces challenges due to limited availability of gene samples and the complexity of cancer gene expression data. The imbalance of Positive and negative category ratio and high-dimensional redundant information degrade prediction performance. This paper proposes an integrated extreme random forest with feature selection model TreeEM(Tree-enhanced Ensemble Model combining with feature selection) to enhance prediction ability and reduce computational costs. The TreeEM model combines the Max-Relevance and Min-Redundancy(MRMR) feature selection method with improved fusion undersampling random forest and extreme tree forest. The TreeEM model achieves excellent performance on three cancer datasets, especially on the multi-omics datasets BRCA(Breast Cancer) and ARCENE datasets, with average improvements of 7.90% and 1.90% in prediction accuracy, respectively. This model also uses TCGA data with known survival time for survival analysis and prediction, demonstrating the reliability of the TreeEM model. This work contributes to advancements in computational tools for cancer research, facilitating precision medicine approaches and improving decision-making. The above results provide new ideas for cancer subtype classification, but the existing methods still have limitations in data imbalance and high-dimensional feature processing. In the following section, the shortcomings of the current research and the innovative solutions of this paper are systematically described.</div></div>","PeriodicalId":36918,"journal":{"name":"Results in Applied Mathematics","volume":"27 ","pages":"Article 100605"},"PeriodicalIF":1.4,"publicationDate":"2025-06-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144321581","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

Global boundedness of a three-species spatial intraguild predation model with alarm-taxis 具有报警趋向性的三种空间捕食模型的全局有界性

IF 1.4

Results in Applied Mathematics Pub Date : 2025-06-18 DOI: 10.1016/j.rinam.2025.100602

Pengfei Luo , Yun Zhang , Lu Xu

引用次数: 0

Analytical computation of five unresolved integrals in the linear theory of partially cavitating hydrofoils 部分空化水翼线性理论中五个未解析积分的解析计算

IF 1.4

Results in Applied Mathematics Pub Date : 2025-06-16 DOI: 10.1016/j.rinam.2025.100599

Jean-Baptiste Leroux, Matthieu Sacher

引用次数: 0

A kind of adaptive variable stepsize embedded Runge–Kutta pairs coupled with the Sinc collocation method for solving the KdV equation 一种自适应变步长嵌入龙格-库塔对并结合Sinc配置法求解KdV方程

IF 1.4

Results in Applied Mathematics Pub Date : 2025-06-16 DOI: 10.1016/j.rinam.2025.100604

Cheng Chen , Wenting Shao

{"title":"A kind of adaptive variable stepsize embedded Runge–Kutta pairs coupled with the Sinc collocation method for solving the KdV equation","authors":"Cheng Chen , Wenting Shao","doi":"10.1016/j.rinam.2025.100604","DOIUrl":"10.1016/j.rinam.2025.100604","url":null,"abstract":"<div><div>For solving the KdV equation, a novel numerical method with high order accuracy in both space and time is proposed. In the spatial direction, Sinc collocation method, which has the property of exponential convergence, is adopted. In the temporal direction, the variable stepsize Runge–Kutta-embedded pair RKq(p) is utilized. Sinc collocation method is applicable when the approximated function satisfies the exponential decay as the spatial variable tends to infinity, this characteristic is consistent with the one of the soliton solution of the KdV equation. For practical computation, a sufficiently large finite domain is taken, on which the differential matrices with respect to the discrete points are constructed. A new adaptive strategy is proposed to enhance the robustness of the variable stepsize algorithm. In the numerical experiment, four embedded pairs including RK5(4), RK6(5), RK8(7) and RK9(8) are investigated in terms of accuracy, CPU time, the minimum, average and maximum time stepsizes. The numerical results show that RK8(7) has a better performance in the computational efficiency, it achieves higher accuracy with significantly less CPU time. Besides, the KdV-Burgers equation with nonhomogeneous Dirichlet boundary condition imposed on a general interval is considered. The single-exponential transformation and double-exponential transformation are involved. We show that Sinc collocation method, enhanced by exponential transformations, provides an effective numerical approximation for this problem.</div></div>","PeriodicalId":36918,"journal":{"name":"Results in Applied Mathematics","volume":"27 ","pages":"Article 100604"},"PeriodicalIF":1.4,"publicationDate":"2025-06-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144291511","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

A numerical method based on the shifted Jacobi polynomials for a class of tempered fractional quadratic integro-differential equations 一类缓变分数阶二次积分微分方程的基于移位Jacobi多项式的数值解法

IF 1.4

Results in Applied Mathematics Pub Date : 2025-06-13 DOI: 10.1016/j.rinam.2025.100601

P. Senfiazad , M.H. Heydari , M. Bayram , D. Baleanu

{"title":"A numerical method based on the shifted Jacobi polynomials for a class of tempered fractional quadratic integro-differential equations","authors":"P. Senfiazad , M.H. Heydari , M. Bayram , D. Baleanu","doi":"10.1016/j.rinam.2025.100601","DOIUrl":"10.1016/j.rinam.2025.100601","url":null,"abstract":"<div><div>This paper introduces a new class of tempered fractional quadratic integro-differential equations using the Caputo fractional derivative. The existence and uniqueness of solutions to these equations are analyzed. A numerical method based on the shifted Jacobi polynomials is developed to solve these equations. To execute the proposed method, two operational matrices corresponding to the ordinary and Riemann–Liouville tempered fractional integrals of these polynomials are extracted. In the developed method, the tempered fractional derivative term is initially represented as a linear combination of the aforementioned polynomials with some unknown coefficients. Then, by applying the Riemann–Liouville tempered fractional integral to the expressed polynomials and utilizing their fractional integral operational matrix, an approximation of the unknown solution is defined based on these polynomials and the introduced coefficients. Subsequently, by substituting these approximations into the problem under consideration, and applying the operational matrix of ordinary integral to the shifted Jacobi polynomials, along with utilizing their orthogonality, an approximate solution to the original problem is obtained by solving a nonlinear system of algebraic equations. The convergence of the proposed method is analyzed theoretically and demonstrated through numerical examples. Furthermore, the stability of the solutions is analyzed.</div></div>","PeriodicalId":36918,"journal":{"name":"Results in Applied Mathematics","volume":"27 ","pages":"Article 100601"},"PeriodicalIF":1.4,"publicationDate":"2025-06-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144270417","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

Convergence analysis of option drift rate inverse problem based on degenerate parabolic equation 基于退化抛物方程的期权漂移率反问题收敛性分析

IF 1.4

Results in Applied Mathematics Pub Date : 2025-05-01 DOI: 10.1016/j.rinam.2025.100561

Miao-miao Song , Zui-cha Deng , Xiang Li , Qiu Cui

引用次数: 0

A condition for the finite time blow up of the incompressible Navier–Stokes equations in the whole space 全空间不可压缩Navier-Stokes方程有限时间爆破的条件

IF 1.4

Results in Applied Mathematics Pub Date : 2025-05-01 DOI: 10.1016/j.rinam.2025.100590

Abdelhafid Younsi

引用次数: 0

Study of nonlinear anisotropic elliptic problems with non-local boundary conditions in weighted variable exponent Sobolev spaces 加权变指数Sobolev空间中具有非局部边界条件的非线性各向异性椭圆问题的研究

IF 1.4

Results in Applied Mathematics Pub Date : 2025-05-01 DOI: 10.1016/j.rinam.2025.100597

Soumia EL OMARI, Said Melliani

{"title":"Study of nonlinear anisotropic elliptic problems with non-local boundary conditions in weighted variable exponent Sobolev spaces","authors":"Soumia EL OMARI, Said Melliani","doi":"10.1016/j.rinam.2025.100597","DOIUrl":"10.1016/j.rinam.2025.100597","url":null,"abstract":"<div><div>This study investigates the existence of weak solutions for nonlinear anisotropic elliptic equations characterized by non-local boundary conditions within anisotropic weighted variable exponent Sobolev spaces. By employing variational methods and compact embedding theorems tailored to anisotropic Sobolev spaces, the research focuses on understanding the impact of anisotropy, non-locality, and weighted structures on the solution behavior. We establish sufficient conditions for the existence of solutions under various boundary conditions. These results deepen the understanding of anisotropic elliptic problems by highlighting the role of weighted structures and variable exponents in the interaction between anisotropy and non-locality. The study also explores non-local boundary conditions, which may include integrals of the unknown function over parts of the domain or non-local operators, often encountered in applications such as well modeling in 3D stratified petroleum reservoirs with arbitrary geometries. This work provides a solid theoretical foundation for broader applications in engineering and physics.</div></div>","PeriodicalId":36918,"journal":{"name":"Results in Applied Mathematics","volume":"26 ","pages":"Article 100597"},"PeriodicalIF":1.4,"publicationDate":"2025-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144241790","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