Results in Applied Mathematics最新文献

{"title":"On a fundamental barrier of the Wirtinger criterion for Gabor systems with odd functions","authors":"Markus Faulhuber","doi":"10.1016/j.rinam.2026.100719","DOIUrl":"10.1016/j.rinam.2026.100719","url":null,"abstract":"<div><div>We show that the Wirtinger criterion cannot be used to investigate the frame set conjecture for the first Hermite function. More generally, for odd functions, it cannot determine regions of the frame set with density less than 2.</div></div>","PeriodicalId":36918,"journal":{"name":"Results in Applied Mathematics","volume":"30 ","pages":"Article 100719"},"PeriodicalIF":1.3,"publicationDate":"2026-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148184759","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}

{"title":"Mathematical and computational study of magnetohydrodynamic flow and mass transfer past a semi-infinite vertical plate","authors":"Yves Garnard Irilan ,&nbsp;Paul André","doi":"10.1016/j.rinam.2026.100714","DOIUrl":"10.1016/j.rinam.2026.100714","url":null,"abstract":"<div><div>This study presents a resolution numerical investigation of transient magnetohydrodynamic (MHD) flow of an electrically conducting, incompressible, and viscous fluid past a semi-infinite vertical plate in the presence of mass transfer and a transverse magnetic field. Unlike previous studies, the present work simultaneously accounts for unsteady effects, buoyancy-driven convection, and species diffusion within a unified computational framework. The analysis assumes that viscous dissipation and induced magnetic field effects are negligible, which is appropriate for flows characterized by low magnetic Reynolds numbers. The governing conservation equations for momentum, energy, and species concentration are formulated in dimensionless form, resulting in a system of coupled, nonlinear, and time-dependent partial differential equations. To accurately capture the transient behavior and strong coupling between physical variables, an implicit finite difference method is employed. This numerical scheme provides unconditional stability, high computational efficiency, and rapid convergence, making it well suited for simulating complex MHD convection problems. The computational approach allows precise resolution of velocity, temperature, and concentration fields within the boundary layer region. Special attention is given to the influence of buoyancy forces associated with external cooling conditions, corresponding to positive values of the thermal Grashof number <span><math><mrow><mo>(</mo><mi>G</mi><mi>r</mi><mo>&gt;</mo><mn>0</mn><mo>)</mo></mrow></math></span>, which characterize free convection regimes where density gradients drive the flow. The effects of key governing parameters, including the magnetic field strength and buoyancy intensity, on the fluid dynamics and thermal transport characteristics are systematically examined. The results demonstrate that the presence of a magnetic field significantly alters the velocity distribution due to the Lorentz force, which acts to suppress fluid motion and modify the boundary layer thickness. Additionally, variations in buoyancy forces strongly influence the development of thermal and momentum boundary layers. Important engineering quantities, such as skin friction, are evaluated to quantify surface shear stress behavior under different physical conditions. The findings provide valuable insights into the coupled interaction between magnetic fields, heat transfer, and mass transport, with potential applications in thermal management systems, metallurgical processes, cooling technologies, and electromagnetic flow control.</div></div>","PeriodicalId":36918,"journal":{"name":"Results in Applied Mathematics","volume":"30 ","pages":"Article 100714"},"PeriodicalIF":1.3,"publicationDate":"2026-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147995252","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}

{"title":"An inverse problem of identifying an unknown coefficient in a plate vibration equation","authors":"Rashid Odinayev,&nbsp;Bobur Zikirov,&nbsp;Shaxriyor Mardonov","doi":"10.1016/j.rinam.2026.100718","DOIUrl":"10.1016/j.rinam.2026.100718","url":null,"abstract":"<div><div>We consider the direct initial–boundary value problem for the equation of transverse vibrations of a thin homogeneous rectangular plate. We also study the inverse problem of determining a time-dependent plate stiffness coefficient from an additional integral overdetermination condition. Using the eigenvalues and eigenfunctions of the corresponding plate vibration operator, we reduce both the direct and inverse problems to integral equations. The existence and uniqueness of the solution to the inverse problem are established by Banach’s contraction mapping principle.</div></div>","PeriodicalId":36918,"journal":{"name":"Results in Applied Mathematics","volume":"30 ","pages":"Article 100718"},"PeriodicalIF":1.3,"publicationDate":"2026-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148184755","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}

{"title":"Portfolio selection based on the spectral decomposition of the sample covariance matrix: A shrinkage-motivated basis-optimization strategy","authors":"Ruili Sun ,&nbsp;Kunqi Wang ,&nbsp;Tiefeng Ma ,&nbsp;Shuangzhe Liu","doi":"10.1016/j.rinam.2026.100720","DOIUrl":"10.1016/j.rinam.2026.100720","url":null,"abstract":"<div><div>The estimation of the covariance matrix and its inverse is crucial in portfolio selection. However, non-negligible estimation errors arise in practice, which has motivated a large literature on linear and nonlinear shrinkage methods for covariance and inverse covariance estimation. Among them, nonlinear shrinkage is generally more flexible and powerful than linear shrinkage. This paper proposes two portfolio construction methods motivated by linear and nonlinear shrinkage ideas and based on the spectral decomposition of the sample covariance matrix. After reparameterization, the proposed procedures are implemented as basis-coefficient optimization rules under an internally validated out-of-sample variance criterion, rather than as classical low-dimensional shrinkage estimators of portfolio weights. The first method is a generalized spectral-shrinkage-motivated portfolio rule, and the second is a double-target spectral-shrinkage-motivated portfolio rule. Empirical results based on real data show that the proposed methods can deliver competitive, and in some cases superior, out-of-sample mean and Sharpe ratio performance. At the same time, the additional diagnostics based on out-of-sample variance, turnover, and HHI concentration reveal important trade-offs in stability and implementability.</div></div>","PeriodicalId":36918,"journal":{"name":"Results in Applied Mathematics","volume":"30 ","pages":"Article 100720"},"PeriodicalIF":1.3,"publicationDate":"2026-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148184758","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}

{"title":"A multiscale hierarchical method of fundamental solutions for severely ill-posed elliptic Cauchy problems","authors":"Wen Li","doi":"10.1016/j.rinam.2026.100710","DOIUrl":"10.1016/j.rinam.2026.100710","url":null,"abstract":"<div><div>We propose a multiscale hierarchical extension of the method of fundamental solutions (MH-MFS) for inverse Cauchy problems. The problems considered in this paper are governed by homogeneous elliptic partial differential equations and characterized by severe ill-posedness. The method hierarchically constructs the MFS solution by approximating the boundary data from coarse to fine scales, through progressive refinement of the Tikhonov regularization parameter at each level. Numerical experiments indicate that the MH-MFS, combined with adaptive stopping criteria, can recover the solution on the inaccessible boundary in severely ill-posed scenarios while improving robustness and computational efficiency compared with the standard MFS with L-curve parameter selection.</div></div>","PeriodicalId":36918,"journal":{"name":"Results in Applied Mathematics","volume":"30 ","pages":"Article 100710"},"PeriodicalIF":1.3,"publicationDate":"2026-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147995401","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}

{"title":"A reliable method for finding intersections of 2D NURBS curves","authors":"Yuqiao Gai ,&nbsp;Gangyi Li ,&nbsp;Na Lei ,&nbsp;Wei Dong ,&nbsp;Jinsan Cheng","doi":"10.1016/j.rinam.2026.100707","DOIUrl":"10.1016/j.rinam.2026.100707","url":null,"abstract":"<div><div>A reliable method is presented to compute the intersection of two-dimensional NURBS curves. Two innovative verification criteria are introduced: an intersection existence criterion based on geometric method, and an intersection uniqueness verification criterion founded on Hodograph theory. The combination of these criteria enables precise identification of parametric subintervals containing a unique intersection point. Experimental results demonstrate that compared to traditional Bézier clipping algorithms and piecewise conversion methods, our algorithm significantly improves the computational efficiency and numerical stability of NURBS curves intersection calculations. The method can find intersections in non-singular cases and shows superior robustness, particularly in scenarios with high-degree curves and dense intersections. We also discuss how to deal with singular cases stably. This approach provides both theoretical foundation and practical tools for high-precision intersection computation in complex geometric modeling, path planning, and engineering simulation applications.</div></div>","PeriodicalId":36918,"journal":{"name":"Results in Applied Mathematics","volume":"30 ","pages":"Article 100707"},"PeriodicalIF":1.3,"publicationDate":"2026-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147802960","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}

{"title":"Error estimates of FEM combined with H2N2 scheme for Schrödinger equation with Caputo time derivative","authors":"Yuelong Tang,&nbsp;Yuchun Hua","doi":"10.1016/j.rinam.2026.100723","DOIUrl":"10.1016/j.rinam.2026.100723","url":null,"abstract":"<div><div>This paper investigates a numerical solution of the linear Schrödinger equation with Caputo time derivative of order <span><math><mrow><mi>α</mi><mo>∈</mo><mrow><mo>(</mo><mn>1</mn><mo>,</mo><mn>2</mn><mo>)</mo></mrow></mrow></math></span>. We first decompose the original equation into a coupled linear system and obtain its numerical solutions by using the H2N2 scheme on graded meshes and the finite element method for temporal and spatial discretization, respectively. Subsequently, we rigorously analyze the stability and convergence of the numerical solutions under appropriate regularity conditions. Finally, we provide some numerical examples to confirm our theoretical findings.</div></div>","PeriodicalId":36918,"journal":{"name":"Results in Applied Mathematics","volume":"30 ","pages":"Article 100723"},"PeriodicalIF":1.3,"publicationDate":"2026-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148184757","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}

{"title":"Bifurcation of a fractional-order BAM neural network with inertia terms and double delays: Stability switching curves","authors":"Hongfei Xu ,&nbsp;Liping Zhou ,&nbsp;Chengdai Huang","doi":"10.1016/j.rinam.2026.100717","DOIUrl":"10.1016/j.rinam.2026.100717","url":null,"abstract":"<div><div>This paper is concerned with the dynamics of a four-neuron inertial fractional-order neural network with non-identical time delays. By reducing the original multiple delays to two independent delays, we first establish two new sufficient conditions for the asymptotic stability of the delay-free system via a matrix-operator method. For the delayed system, the stability switching curve in the <span><math><mrow><mo>(</mo><msub><mrow><mi>ϵ</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>,</mo><msub><mrow><mi>ϵ</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>)</mo></mrow></math></span>-plane is derived explicitly, and the corresponding crossing direction is determined. Moreover, a criterion for Hopf bifurcation is obtained when the delay pair crosses the stability switching curve. Numerical examples are given to illustrate the theoretical results and show that a smaller fractional order of the inertial term leads to a larger stability region in the delay plane. These results reveal the stabilizing effect of the inertial term on the network dynamics.</div></div>","PeriodicalId":36918,"journal":{"name":"Results in Applied Mathematics","volume":"30 ","pages":"Article 100717"},"PeriodicalIF":1.3,"publicationDate":"2026-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148184756","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}

{"title":"A hybrid Haar wavelet approximation of linear and nonlinear heat-type equations","authors":"Hina Sajid ,&nbsp;Sidra Saleem ,&nbsp;Ayesha Shakeel ,&nbsp;Hadi Rezazadeh ,&nbsp;Ahmad Sharif","doi":"10.1016/j.rinam.2026.100725","DOIUrl":"10.1016/j.rinam.2026.100725","url":null,"abstract":"<div><div>In this article, a hybrid technique (Saleem et al., 2020), established on Haar wavelet collocation method (HWCM) and finite difference (FD) scheme is used to estimate linear and nonlinear heat-type equations. The formulated hybrid technique is applied to heat-type equations to reduce the computational complexity of FDM or HWCM (caused by implementing the FDM or HW methods separately, and increase accuracy. The proposed technique is utilized to different test problems and numerical approximations are shown in the form of tables and figures. These numerical approximations are compared with exact solutions and maximum absolute errors are calculated. Also, the experimental rate of convergence is investigated for distinct numbers of collocation points in a reasonable CPU time. The numerical approximations show the adaptability and accuracy of the formulated technique. In future, the fractional heat-type equations can be solved by hybrid Haar wavelet collocation method in two dimensions.</div></div>","PeriodicalId":36918,"journal":{"name":"Results in Applied Mathematics","volume":"30 ","pages":"Article 100725"},"PeriodicalIF":1.3,"publicationDate":"2026-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148241870","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}

{"title":"Optimal transport convergence of conditional distribution estimation for single-indexed locally stationary functional time series","authors":"Jan Nino G. Tinio ,&nbsp;Mokhtar Z. Alaya ,&nbsp;Salim Bouzebda","doi":"10.1016/j.rinam.2026.100709","DOIUrl":"10.1016/j.rinam.2026.100709","url":null,"abstract":"<div><div>Modeling nonstationary functional time series has become increasingly important in applications where both temporal dynamics and functional structure play central roles. The framework of locally stationary functional time series (LSFTS) provides a flexible representation for such data by allowing their probabilistic features to evolve smoothly over time. At the same time, the infinite-dimensional nature of functional predictors motivates the use of functional single index models (FSIM) as an effective dimension-reduction strategy. In this paper, we develop a methodology for estimating the conditional distribution of LSFTS within the FSIM framework. We introduce a Nadaraya–Watson (NW) kernel estimator that simultaneously smooths across time and along a data-driven single index. Using tools from optimal transport, we derive uniform convergence rates under the 1-Wasserstein distance, accounting for small ball probabilities and weak dependence through <span><math><mi>β</mi></math></span>-mixing conditions. We further propose a practical procedure for estimating both the single index and the bandwidth via cross-validation. Extensive simulations confirm the theoretical convergence behavior, and applications to real datasets — including financial and physiological time series — demonstrate the effectiveness of the approach for distributional forecasting. An additional case study on electricity price data illustrates how the proposed estimator can deliver competitive predictive accuracy in complex nonstationary environments.</div></div>","PeriodicalId":36918,"journal":{"name":"Results in Applied Mathematics","volume":"30 ","pages":"Article 100709"},"PeriodicalIF":1.3,"publicationDate":"2026-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147951761","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}