Results in Applied Mathematics最新文献

{"title":"Remarks on numerical approximation of Volterra integral equations by Walsh–Hadamard transform","authors":"Farrukh Mukhamedov ,&nbsp;Ushangi Goginava ,&nbsp;Akaki Goginava ,&nbsp;James Wheeldon","doi":"10.1016/j.rinam.2025.100648","DOIUrl":"10.1016/j.rinam.2025.100648","url":null,"abstract":"<div><div>Walsh functions form a piecewise-constant orthonormal basis that is particularly well-suited for digital computation and signal approximation. Nevertheless, the direct evaluation of Walsh transforms for discrete functions becomes computationally prohibitive as the resolution increases. To overcome this difficulty, we develop an efficient numerical scheme based on the <em>Fast Walsh–Hadamard–Fourier Transform</em> (FWHFT) for the approximation of solutions to Volterra integral equations. The proposed method reduces the computational complexity from <span><math><mrow><mi>O</mi><mrow><mo>(</mo><msup><mrow><mn>2</mn></mrow><mrow><mn>2</mn><mi>n</mi></mrow></msup><mo>)</mo></mrow></mrow></math></span> to <span><math><mrow><mi>O</mi><mrow><mo>(</mo><mi>n</mi><msup><mrow><mn>2</mn></mrow><mrow><mi>n</mi></mrow></msup><mo>)</mo></mrow><mo>,</mo></mrow></math></span> thereby rendering the approach scalable to high-resolution problems. We present a complete algorithmic framework that exploits this fast transform and analyze its performance on a variety of examples. In particular, we illustrate several examples for the broad applicability of the method. These examples highlight the principal advantages of the FWHFT approach, as well as certain limitations inherent in the transform structure. As a further application, we implement the method in a financial setting by addressing the problem of pricing European options under the Bachelier model. This example demonstrates not only the accuracy of the proposed algorithm but also its practical relevance to computational finance, especially in scenarios involving structured payoff functions. Numerical experiments confirm the expected convergence behavior and the substantial computational savings afforded by the method. Finally, we discuss possible extensions of the approach to fractional-order models, which are naturally linked to Volterra-type integral equations and arise frequently in applications.</div></div>","PeriodicalId":36918,"journal":{"name":"Results in Applied Mathematics","volume":"28 ","pages":"Article 100648"},"PeriodicalIF":1.3,"publicationDate":"2025-10-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145222750","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":"The effect of inventory on asset prices","authors":"Jiaqi Hou ,&nbsp;Jing Wang ,&nbsp;Zhi Yang","doi":"10.1016/j.rinam.2025.100650","DOIUrl":"10.1016/j.rinam.2025.100650","url":null,"abstract":"<div><div>In this paper, we extend the existing asset pricing model of the market maker mechanism to consider the market maker clearing the market price through inventory. Using the stability and branching theory of discrete dynamical systems, we discuss the existence of the steady state and the influence of the change with the adjustment rate of the market maker’s inventory on the stability region of the model. Through numerical simulation, we obtain the result that the faster or slower the adjustment of the market maker’s inventory, the more unstable the market price is. We establish a linear regression model and analyze it by empirical tests using the stock data of Lanqi Technology, which shows that there is a positive correlation between the market maker’s inventory and price; the increase of the market maker’s inventory will cause the price to increase. By analyzing the theoretical model data through the TVP-VAR model, it can also be obtained that there is a positive correlation between the price and the market maker’s inventory.</div></div>","PeriodicalId":36918,"journal":{"name":"Results in Applied Mathematics","volume":"28 ","pages":"Article 100650"},"PeriodicalIF":1.3,"publicationDate":"2025-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145222754","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":"The existence of ground state normalized solution for mass supercritical modified Kirchhoff equation","authors":"Zhongxiang Wang ,&nbsp;Cai Chang","doi":"10.1016/j.rinam.2025.100649","DOIUrl":"10.1016/j.rinam.2025.100649","url":null,"abstract":"<div><div>In this paper, we focus on the existence of ground state solution with prescribed <span><math><msup><mrow><mi>L</mi></mrow><mrow><mn>2</mn></mrow></msup></math></span>-norm for the following modified Kirchhoff problem: <span><span><span><math><mrow><mo>−</mo><mfenced><mrow><mi>a</mi><mo>+</mo><mi>b</mi><msub><mrow><mo>∫</mo></mrow><mrow><msup><mrow><mi>R</mi></mrow><mrow><mi>N</mi></mrow></msup></mrow></msub><msup><mrow><mrow><mo>|</mo><mo>∇</mo><mi>u</mi><mo>|</mo></mrow></mrow><mrow><mn>2</mn></mrow></msup><mi>d</mi><mi>x</mi></mrow></mfenced><mi>Δ</mi><mi>u</mi><mo>−</mo><mi>u</mi><mi>Δ</mi><mrow><mo>(</mo><msup><mrow><mi>u</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>)</mo></mrow><mo>−</mo><mi>λ</mi><mi>u</mi><mo>=</mo><msup><mrow><mrow><mo>|</mo><mi>u</mi><mo>|</mo></mrow></mrow><mrow><mi>p</mi><mo>−</mo><mn>2</mn></mrow></msup><mi>u</mi><mo>,</mo><mspace></mspace><mspace></mspace><mspace></mspace><mi>x</mi><mo>∈</mo><msup><mrow><mi>R</mi></mrow><mrow><mi>N</mi></mrow></msup><mo>,</mo></mrow></math></span></span></span>where <span><math><mrow><mi>N</mi><mo>=</mo><mn>2</mn><mo>,</mo><mn>3</mn></mrow></math></span>, <span><math><mrow><mi>a</mi><mo>,</mo><mi>b</mi><mo>&gt;</mo><mn>0</mn></mrow></math></span> are constants, <span><math><mrow><mi>p</mi><mo>∈</mo><mfenced><mrow><mn>4</mn><mo>+</mo><mfrac><mrow><mn>4</mn></mrow><mrow><mi>N</mi></mrow></mfrac><mo>,</mo><msup><mrow><mn>2</mn></mrow><mrow><mo>∗</mo></mrow></msup></mrow></mfenced></mrow></math></span>, <span><math><mrow><msup><mrow><mn>2</mn></mrow><mrow><mo>∗</mo></mrow></msup><mo>=</mo><mn>6</mn></mrow></math></span> if <span><math><mrow><mi>N</mi><mo>=</mo><mn>3</mn></mrow></math></span>, and <span><math><mrow><msup><mrow><mn>2</mn></mrow><mrow><mo>∗</mo></mrow></msup><mo>=</mo><mo>+</mo><mi>∞</mi></mrow></math></span> if <span><math><mrow><mi>N</mi><mo>=</mo><mn>2</mn></mrow></math></span>. By employing a novel scaling method, we establish the existence of ground state normalized solutions for the above problem. Our result is new for the mass supercritical case <span><math><mrow><mn>4</mn><mo>+</mo><mfrac><mrow><mn>4</mn></mrow><mrow><mi>N</mi></mrow></mfrac><mo>&lt;</mo><mi>p</mi><mo>≤</mo><msup><mrow><mn>2</mn></mrow><mrow><mo>∗</mo></mrow></msup></mrow></math></span>, notably for the case <span><math><mrow><mi>p</mi><mo>=</mo><msup><mrow><mn>2</mn></mrow><mrow><mo>∗</mo></mrow></msup></mrow></math></span>.</div></div>","PeriodicalId":36918,"journal":{"name":"Results in Applied Mathematics","volume":"28 ","pages":"Article 100649"},"PeriodicalIF":1.3,"publicationDate":"2025-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145222756","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":"Pullback D−attractors for the fractional non-autonomous beam equation with fractional rotational inertia and structural damping or strong damping","authors":"Penghui Lv ,&nbsp;Jingxin Lu ,&nbsp;Guoguang Lin","doi":"10.1016/j.rinam.2025.100640","DOIUrl":"10.1016/j.rinam.2025.100640","url":null,"abstract":"<div><div>This paper investigates the well-posedness and long-time dynamics of a class of fractional non-autonomous beam equations with fractional rotational inertia and structural damping or strong damping. We prove that if <span><math><mrow><mn>1</mn><mo>≤</mo><mi>p</mi><mo>&lt;</mo><msup><mrow><mi>p</mi></mrow><mrow><msub><mrow><mi>θ</mi></mrow><mrow><mn>2</mn></mrow></msub></mrow></msup><mo>≡</mo><mfrac><mrow><mi>N</mi><mo>+</mo><mn>4</mn><msub><mrow><mi>θ</mi></mrow><mrow><mn>2</mn></mrow></msub></mrow><mrow><msup><mrow><mrow><mo>(</mo><mi>N</mi><mo>−</mo><mn>4</mn><msub><mrow><mi>θ</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>)</mo></mrow></mrow><mrow><mo>+</mo></mrow></msup></mrow></mfrac></mrow></math></span> <span><math><mrow><mo>(</mo><mfrac><mrow><mn>1</mn></mrow><mrow><mn>2</mn></mrow></mfrac><mo>≤</mo><msub><mrow><mi>θ</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>≤</mo><mn>1</mn><mo>)</mo></mrow></math></span>, then: (i) The initial–boundary value problem (IBVP) of the equations admits a unique solution in <span><math><msubsup><mrow><mi>X</mi></mrow><mrow><msub><mrow><mi>θ</mi></mrow><mrow><mn>2</mn></mrow></msub></mrow><mrow><msub><mrow><mi>θ</mi></mrow><mrow><mn>1</mn></mrow></msub></mrow></msubsup></math></span>; (ii) there exists a pullback <span><math><mrow><mi>D</mi><mo>−</mo></mrow></math></span>attractor for the non-autonomous dynamical system <span><math><mrow><mo>(</mo><mi>ϕ</mi><mo>,</mo><mi>θ</mi><mo>)</mo></mrow></math></span>. We provide a systematic proof of pullback <span><math><mrow><mi>D</mi><mo>−</mo></mrow></math></span>attractors and extend the existing results on non-autonomous beam models. The findings establish a theoretical foundation for future practical applications.</div></div>","PeriodicalId":36918,"journal":{"name":"Results in Applied Mathematics","volume":"28 ","pages":"Article 100640"},"PeriodicalIF":1.3,"publicationDate":"2025-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145222755","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":"Enabling dendrite-free lithium metal batteries through a constrained phase-field model","authors":"Ben Mansour Dia ,&nbsp;Guy Olivier Ngongang Ndjawa","doi":"10.1016/j.rinam.2025.100632","DOIUrl":"10.1016/j.rinam.2025.100632","url":null,"abstract":"<div><div>High-capacity batteries that employ lithium-metal anodes experience filamentary dendrite growth at the anode/electrolyte interface, which significantly impacts battery performance and safety. In this study, we introduce a constrained phase-field approach to model dendrite-free electro-deposition by incorporating an optimal control mechanism into the phase-field evolution. Specifically, dendrite formation is mitigated by introducing an energy functional that penalizes the formation of interfaces with high-curvature protrusions. We develop a coupled multiphysics model comprising a nonconserved Allen–Cahn equation for the metal electrode interface, a reaction–diffusion (Cahn–Hilliard-type) equation for ionic transport, and electrostatic charge conservation with Butler–Volmer boundary kinetics. The model is solved under a variational framework, yielding modified phase-field evolution equations that steers deposition away from dendritic pathways. Our findings suggest a novel paradigm for designing charging protocols and interface modifications that could enable safer dendrite-free lithium-metal batteries.</div></div>","PeriodicalId":36918,"journal":{"name":"Results in Applied Mathematics","volume":"28 ","pages":"Article 100632"},"PeriodicalIF":1.3,"publicationDate":"2025-09-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145222751","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":"Fractional logistic growth with memory effects: A tool for industry-oriented modeling","authors":"M.O. Aibinu ,&nbsp;A. Shoukat ,&nbsp;F.M. Mahomed","doi":"10.1016/j.rinam.2025.100647","DOIUrl":"10.1016/j.rinam.2025.100647","url":null,"abstract":"<div><div>The logistic growth model is a classical framework for describing constrained growth phenomena, widely applied in areas such as population dynamics, epidemiology, and resource management. This study presents a generalized extension using Atangana–Baleanu in Caputo sense (ABC)-type fractional derivatives. Proportional time delay is also included, allowing the model to capture memory-dependent and nonlocal dynamics not addressed in classical formulations. Free parameters provide flexibility for modeling complex growth in industrial, medical, and social systems. The Hybrid Sumudu Variational (HSV) method is employed to efficiently obtain semi-analytical solutions. Results highlight the combined effects of fractional order and delay on system behavior. This approach demonstrates the novelty of integrating ABC-type derivatives, proportional delay, and HSV-based solutions for real-world applications.</div></div>","PeriodicalId":36918,"journal":{"name":"Results in Applied Mathematics","volume":"28 ","pages":"Article 100647"},"PeriodicalIF":1.3,"publicationDate":"2025-09-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145222753","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":"Bayesian estimation of discretely observed diffusion processes using Wiener chaos expansion","authors":"Fernando Baltazar-Larios ,&nbsp;Gabriel Adrián Salcedo-Varela ,&nbsp;Francisco Delgado-Vences","doi":"10.1016/j.rinam.2025.100644","DOIUrl":"10.1016/j.rinam.2025.100644","url":null,"abstract":"<div><div>We employ a Bayesian inference technique for discretely observed diffusion processes that arise as solutions of stochastic differential equations. Our aim is to estimate the parameters of the stochastic differential equation. To achieve this, we frame the estimation procedure as a missing data problem. In this framework, the complete dataset includes the theoretically continuous-time path between observed points. We propose augmenting the dataset and using a Gibbs sampler to derive Bayesian estimators for the parameters in cases where the diffusion process is observed discretely. The Gibbs sampler is integrated with a diffusion bridge simulation technique based on the Wiener chaos expansion. The methodology and its implementation are demonstrated through examples and simulation studies. We also present an application to actual data.</div></div>","PeriodicalId":36918,"journal":{"name":"Results in Applied Mathematics","volume":"28 ","pages":"Article 100644"},"PeriodicalIF":1.3,"publicationDate":"2025-09-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145159101","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":"Efficient computation for the eigenvalues and eigenfunctions of two-dimensional non-separable linear canonical transform","authors":"Yuru Tian,&nbsp;Feng Zhang","doi":"10.1016/j.rinam.2025.100645","DOIUrl":"10.1016/j.rinam.2025.100645","url":null,"abstract":"<div><div>The parameter matrix of the two-dimensional non-separable linear canonical transform (2D-NSLCT) determines its specific form and properties. Certain forms of the 2D-NSLCT are consistent with well-known transforms, such as two-dimensional non-separable fractional Fourier transform (2D-NSFrFT), Fresnel transform, and other related transforms. Based on the analysis of the eigenvalues and eigenfunctions of these special transforms, this paper proposes an efficient method for computing the eigenvalues and eigenfunctions of the 2D-NSLCT. Specifically, based on the properties of similar matrices, if the parameter matrix of the 2D-NSLCT is similar to that of a special transform (e.g., 2D-NSFrFT or other transforms), then the eigenvalues of the 2D-NSLCT are identical to those of the special transform. Moreover, the eigenfunctions of the 2D-NSLCT can be computed using the known eigenfunctions of this special transform based on the additivity of the 2D-NSLCT. The detailed derivation is presented in this paper, and some applications of the 2D-NSLCT’s eigenfunction are also discussed.</div></div>","PeriodicalId":36918,"journal":{"name":"Results in Applied Mathematics","volume":"28 ","pages":"Article 100645"},"PeriodicalIF":1.3,"publicationDate":"2025-09-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145222752","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":"Isogeometric boundary element method for solving 2D multi-media heat conduction problems","authors":"Kunpeng Li ,&nbsp;Wei Jiang ,&nbsp;Haozhi Li","doi":"10.1016/j.rinam.2025.100639","DOIUrl":"10.1016/j.rinam.2025.100639","url":null,"abstract":"<div><div>In this work, we employ the isogeometric boundary element approach to investigate heat transfer mechanisms in various media. We derive and construct integral equations for the interface of different media to address heat transfer issues. Our proposed modeling technique for two-dimensional problems can be dynamically constructed by incorporating control points and weight factors. In comparison to other numerical software, this approach offers high customizability, improves model accuracy, mitigates mesh errors, and seamlessly integrates the advantages of Computer-Aided Design (CAD) and Computer-Aided Engineering (CAE) through the isogeometric method. The boundary element approach boasts several advantages, with numerical stability and excellent precision being paramount. The amalgamation of the isogeometric approach with the boundary element method holds promise for future applications in practical engineering. Simultaneously, we address the domain integral using the radial integration approach. The algorithmic results reveal that the isogeometric boundary element method, in contrast to the traditional boundary element method, expands the applicability of the latter while maintaining good stability and robustness. This provides substantial support for further software integration.</div></div>","PeriodicalId":36918,"journal":{"name":"Results in Applied Mathematics","volume":"28 ","pages":"Article 100639"},"PeriodicalIF":1.3,"publicationDate":"2025-09-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145119769","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 analysis of shallow water wave and the generalized Hirota-Satsuma-Ito models: Soliton solutions and their interactions","authors":"M. Belal Hossen ,&nbsp;Md. Towhiduzzaman ,&nbsp;Harun-Or-Roshid ,&nbsp;K. M. Abdul A. Woadud","doi":"10.1016/j.rinam.2025.100641","DOIUrl":"10.1016/j.rinam.2025.100641","url":null,"abstract":"<div><div>This study investigates the mathematical properties and soliton dynamics of the (2+1)-dimensional extended Shallow Water Wave (eSWW) and the generalized Hirota-Satsuma-Ito (gHSI) models by Hirota bilinear scheme. A comprehensive mathematical analysis is conducted to derive multi-soliton solutions, including 2-soliton and 3-soliton solutions, while breather, rogue and lump solutions derive from 2-soliton. Investigation focuses on soliton interactions under various conditions, with particular attention to special cases like rogue and lump type solutions, highlighting their distinct characteristics and physical significance. Additionally, the analysis extends to the gHSI equation, where long wave limit scheme is applied to attain rogue and lump wave solutions. We analyzed the planar dynamics of the system to assess its sensitivity. These findings enhance our knowledge of nonlinear wave processes, with potential applications in oceanography, fluid mechanics, and related scientific fields.</div></div>","PeriodicalId":36918,"journal":{"name":"Results in Applied Mathematics","volume":"28 ","pages":"Article 100641"},"PeriodicalIF":1.3,"publicationDate":"2025-09-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145098083","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}