Pub Date : 2025-08-01DOI: 10.1016/j.rinam.2025.100633
Jiaoxia Huang , Yonghui Qin
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 -differential operator eigenvalue problems
{"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}
Pub Date : 2025-08-01DOI: 10.1016/j.rinam.2025.100629
Juan Diego Pulgarín Rivera , Daniel Turizo , Elias D. Nino-Ruiz , Oscar Danilo Montoya
This paper proposes an A-stable one-stage Rosenbrock method for the solution of Ordinary Differential Equations (ODEs). In this method, Jacobians are approximated via complex step finite differences. An asymptotically accurate estimator of the truncation error is also provided. This error estimator can be employed to control step sizes and to perform extrapolation, which increases the accuracy of the method and yields L-stability. Numerical experiments are conducted to assess the performance of the proposed method. ODE solvers and several stiff ODE problems from the current literature are employed as references during experiments. Experimental results reveal that the proposed method exhibits superior performance with respect to the other compared methods, especially for crude error tolerances.
{"title":"Improved Rosenbrock method with error estimator and Jacobian approximation using complex step","authors":"Juan Diego Pulgarín Rivera , Daniel Turizo , Elias D. Nino-Ruiz , Oscar Danilo Montoya","doi":"10.1016/j.rinam.2025.100629","DOIUrl":"10.1016/j.rinam.2025.100629","url":null,"abstract":"<div><div>This paper proposes an A-stable one-stage Rosenbrock method for the solution of Ordinary Differential Equations (ODEs). In this method, Jacobians are approximated via complex step finite differences. An asymptotically accurate estimator of the truncation error is also provided. This error estimator can be employed to control step sizes and to perform extrapolation, which increases the accuracy of the method and yields L-stability. Numerical experiments are conducted to assess the performance of the proposed method. ODE solvers and several stiff ODE problems from the current literature are employed as references during experiments. Experimental results reveal that the proposed method exhibits superior performance with respect to the other compared methods, especially for crude error tolerances.</div></div>","PeriodicalId":36918,"journal":{"name":"Results in Applied Mathematics","volume":"27 ","pages":"Article 100629"},"PeriodicalIF":1.3,"publicationDate":"2025-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144889781","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}
Pub Date : 2025-08-01DOI: 10.1016/j.rinam.2025.100627
Kholmat Shadimetov , Anvar Adilkhodjaev , Otabek Gulomov
In this paper, we study the problem of constructing optimal formulas for approximate integration in the Sobolev space of periodic functions. Using the functional approach, we obtain optimal quadrature formulas for the approximate calculation of rapidly oscillating integrals. Then, we obtain explicit formulas for the coefficients of the optimal quadrature formulas and we get the sharp estimation of the error of the constructed formulas.
{"title":"Optimal quadrature formulas for approximate calculation of rapidly oscillating integrals","authors":"Kholmat Shadimetov , Anvar Adilkhodjaev , Otabek Gulomov","doi":"10.1016/j.rinam.2025.100627","DOIUrl":"10.1016/j.rinam.2025.100627","url":null,"abstract":"<div><div>In this paper, we study the problem of constructing optimal formulas for approximate integration in the Sobolev space <span><math><mrow><mover><mrow><msubsup><mrow><mi>L</mi></mrow><mrow><mn>2</mn></mrow><mrow><mfenced><mrow><mi>m</mi></mrow></mfenced></mrow></msubsup></mrow><mrow><mo>˜</mo></mrow></mover><mfenced><mrow><mn>0</mn><mo>,</mo><mn>1</mn></mrow></mfenced></mrow></math></span> of periodic functions. Using the functional approach, we obtain optimal quadrature formulas for the approximate calculation of rapidly oscillating integrals. Then, we obtain explicit formulas for the coefficients of the optimal quadrature formulas and we get the sharp estimation of the error of the constructed formulas.</div></div>","PeriodicalId":36918,"journal":{"name":"Results in Applied Mathematics","volume":"27 ","pages":"Article 100627"},"PeriodicalIF":1.3,"publicationDate":"2025-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144908279","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}
Pub Date : 2025-08-01DOI: 10.1016/j.rinam.2025.100634
Leonid Berezansky , Alexander Domoshnitsky
Explicit sufficient conditions for uniform exponential stability of two-dimensional linear vector integro-differential equations have been established. These criteria are novel and remain valid even in the special case of second-order linear ordinary vector differential equations. The proofs leverage the Bohl–Perron theorem, incorporate a priori estimates of solutions. An illustrative example is provided to demonstrate the applicability of the results.
{"title":"Stability for linear second order vector integro-differential equations","authors":"Leonid Berezansky , Alexander Domoshnitsky","doi":"10.1016/j.rinam.2025.100634","DOIUrl":"10.1016/j.rinam.2025.100634","url":null,"abstract":"<div><div>Explicit sufficient conditions for uniform exponential stability of two-dimensional linear vector integro-differential equations have been established. These criteria are novel and remain valid even in the special case of second-order linear ordinary vector differential equations. The proofs leverage the Bohl–Perron theorem, incorporate a priori estimates of solutions. An illustrative example is provided to demonstrate the applicability of the results.</div></div>","PeriodicalId":36918,"journal":{"name":"Results in Applied Mathematics","volume":"27 ","pages":"Article 100634"},"PeriodicalIF":1.3,"publicationDate":"2025-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145044574","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}
Pub Date : 2025-07-28DOI: 10.1016/j.rinam.2025.100618
Takuto Kajimura, Yasunori Kimura
In this paper, we show some properties of a proximal mapping with a general perturbation for convex functions. We further investigate the existence and approximation of minimizers of a given convex function by using the proximal point algorithm with a general perturbation in complete geodesic spaces.
{"title":"The proximal point algorithm with a general perturbation on geodesic spaces","authors":"Takuto Kajimura, Yasunori Kimura","doi":"10.1016/j.rinam.2025.100618","DOIUrl":"10.1016/j.rinam.2025.100618","url":null,"abstract":"<div><div>In this paper, we show some properties of a proximal mapping with a general perturbation for convex functions. We further investigate the existence and approximation of minimizers of a given convex function by using the proximal point algorithm with a general perturbation in complete geodesic spaces.</div></div>","PeriodicalId":36918,"journal":{"name":"Results in Applied Mathematics","volume":"27 ","pages":"Article 100618"},"PeriodicalIF":1.4,"publicationDate":"2025-07-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144712995","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}
Pub Date : 2025-07-23DOI: 10.1016/j.rinam.2025.100613
Can Li , Xin Wang , Yubin Yan , Zexin Hou
In this paper, we consider a time semi-discrete scheme for a tempered subdiffusion equation with nonsmooth data. Due to the low regularity of the solution, the optimal convergence rate cannot be achieved when the L1 time-stepping scheme is directly applied to discretize the tempered fractional derivative. By introducing a correction term at the initial time step, we propose a corrected L1 scheme which recover to the optimal convergence rate. Theoretical error estimates and numerical experiments validate the improvement.
{"title":"A corrected L1 scheme for solving a tempered subdiffusion equation with nonsmooth data","authors":"Can Li , Xin Wang , Yubin Yan , Zexin Hou","doi":"10.1016/j.rinam.2025.100613","DOIUrl":"10.1016/j.rinam.2025.100613","url":null,"abstract":"<div><div>In this paper, we consider a time semi-discrete scheme for a tempered subdiffusion equation with nonsmooth data. Due to the low regularity of the solution, the optimal convergence rate cannot be achieved when the L1 time-stepping scheme is directly applied to discretize the tempered fractional derivative. By introducing a correction term at the initial time step, we propose a corrected L1 scheme which recover to the optimal convergence rate. Theoretical error estimates and numerical experiments validate the improvement.</div></div>","PeriodicalId":36918,"journal":{"name":"Results in Applied Mathematics","volume":"27 ","pages":"Article 100613"},"PeriodicalIF":1.4,"publicationDate":"2025-07-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144687563","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}
Pub Date : 2025-07-22DOI: 10.1016/j.rinam.2025.100617
Bing Tan, Yingzhe Fan
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 by employing Fourier analysis.
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 inherent in the macroscopic equation. Then the dissipation of velocity is indirectly captured by combining the macroscopic dissipation of and the linear dissipation of within the equation. Finally the uniform energy functionals of the solution can be obtained by utilizing the refined energy estimate.
本文研究了周期空间域上Vlasov-Fokker-Planck方程与不可压缩欧拉系统在规格化全局麦克斯韦方程组周围耦合的Cauchy问题的全局适定性。该系统描述了由欧拉方程控制的流体与在VFP动力学下演化的粒子分布之间的相互作用，并通过阻力进行耦合。利用傅里叶分析，建立了低正则性函数空间Lk1LT∞Lv2上小初始数据全局温和解的存在唯一性。与Navier-Stokes-Vlasov-Fokker-Planck系统（Tan and Fan, 2023）相比，Vlasov-Euler-Fokker-Planck系统由于其固有的结构差异，无法直接获得速度耗散估计。在Navier-Stokes-Vlasov-Fokker-Planck系统中，可以直接从粘性项中导出速度耗散估计。为了克服这个障碍，我们需要利用宏观方程中固有的宏观耗散b。然后结合方程中b的宏观耗散和u−b的线性耗散，间接捕捉速度耗散。最后利用精化的能量估计得到解的均匀能量泛函。
{"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}
Pub Date : 2025-07-22DOI: 10.1016/j.rinam.2025.100608
Yujie Yun, Tieqiang Gang, Lijie Chen
In this study, we employ the iterative Linear Quadratic Gaussian (ILQG) method, discretized based on the high-order exponential Runge–Kutta methods, to numerically solve stochastic optimal control problems. In the sense of weak convergence, we derive a mean-square third-order scheme with an additive noise, and provide corresponding order conditions. As the analysis of order conditions is local, the analysis is transformed into a error estimate of the discrete problem with control constraints. Finally, the global control law is approximated by computing the node control via the ILQG method. The numerical experiment further demonstrates the significant stability of ILQG in dealing with stochastic semilinear control problems. The proposed approach presents the advantages of simplicity and efficiency.
{"title":"Discrete ILQG method based on high-order exponential Runge–Kutta discretization","authors":"Yujie Yun, Tieqiang Gang, Lijie Chen","doi":"10.1016/j.rinam.2025.100608","DOIUrl":"10.1016/j.rinam.2025.100608","url":null,"abstract":"<div><div>In this study, we employ the iterative Linear Quadratic Gaussian (ILQG) method, discretized based on the high-order exponential Runge–Kutta methods, to numerically solve stochastic optimal control problems. In the sense of weak convergence, we derive a mean-square third-order scheme with an additive noise, and provide corresponding order conditions. As the analysis of order conditions is local, the analysis is transformed into a <span><math><msup><mrow><mi>L</mi></mrow><mrow><mi>∞</mi></mrow></msup></math></span> error estimate of the discrete problem with control constraints. Finally, the global control law is approximated by computing the node control via the ILQG method. The numerical experiment further demonstrates the significant stability of ILQG in dealing with stochastic semilinear control problems. The proposed approach presents the advantages of simplicity and efficiency.</div></div>","PeriodicalId":36918,"journal":{"name":"Results in Applied Mathematics","volume":"27 ","pages":"Article 100608"},"PeriodicalIF":1.4,"publicationDate":"2025-07-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144679589","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}
Pub Date : 2025-07-18DOI: 10.1016/j.rinam.2025.100615
Xiaofeng Li
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— ratio, , and —govern wave reflection coefficients (). Key discoveries reveal that the ratio controls resonance peak frequencies (inducing 12% shifts per 0.1 change), the radius parameter triggers complete reflection () at a critical value of 0.5, and optimal 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.
{"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}
This work deals with the offset fractional Fourier transform (OFrFT), which is a more general version of the fractional Fourier transform (FrFT). We demonstrate the basic properties such as translation, modulation and parity. The results are generalization of the FrFT properties. We study a relation of the OFrFT with the FrFT and the Fourier transform. Based on the relation, the key properties such as Parseval’s identity and inversion formula are derived. Applying the properties and the relation allow us to establish several versions of the uncertainty inequalities for the OFrFT. In addition, we discuss the comparison of the OFrFT with the FrFT in terms of properties and uncertainty principles. Finally, we perform an illustrative example to demonstrate that the value of Heisenberg uncertainty inequality for the OFrFT is bigger than that of Heisenberg uncertainty inequality for the FrFT and effect of the offset parameter in minimizing the Heisenberg uncertainty principle associated with the OFrFT.
{"title":"A comparative study on properties and uncertainty principles of fractional Fourier transform and offset fractional Fourier transform","authors":"Mawardi Bahri , Airien Nabilla B.A. , Nasrullah Bachtiar , Muhammad Zakir","doi":"10.1016/j.rinam.2025.100616","DOIUrl":"10.1016/j.rinam.2025.100616","url":null,"abstract":"<div><div>This work deals with the offset fractional Fourier transform (OFrFT), which is a more general version of the fractional Fourier transform (FrFT). We demonstrate the basic properties such as translation, modulation and parity. The results are generalization of the FrFT properties. We study a relation of the OFrFT with the FrFT and the Fourier transform. Based on the relation, the key properties such as Parseval’s identity and inversion formula are derived. Applying the properties and the relation allow us to establish several versions of the uncertainty inequalities for the OFrFT. In addition, we discuss the comparison of the OFrFT with the FrFT in terms of properties and uncertainty principles. Finally, we perform an illustrative example to demonstrate that the value of Heisenberg uncertainty inequality for the OFrFT is bigger than that of Heisenberg uncertainty inequality for the FrFT and effect of the offset parameter in minimizing the Heisenberg uncertainty principle associated with the OFrFT.</div></div>","PeriodicalId":36918,"journal":{"name":"Results in Applied Mathematics","volume":"27 ","pages":"Article 100616"},"PeriodicalIF":1.4,"publicationDate":"2025-07-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144654181","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}
扫码关注我们
求助内容：
应助结果提醒方式：
京公网安备 11010802042870号