Results in Applied Mathematics最新文献

{"title":"Optimization of approximate integrals of rapidly oscillating functions in the Hilbert space","authors":"Abdullo Hayotov ,&nbsp;Samandar Babaev ,&nbsp;Abdimumin Kurbonnazarov","doi":"10.1016/j.rinam.2025.100569","DOIUrl":"10.1016/j.rinam.2025.100569","url":null,"abstract":"<div><div>In this work, we construct an optimal quadrature formula in the sense of Sard based on a functional approach for numerical calculation of integrals of rapidly oscillating functions. To solve this problem, we will use Sobolev’s method.</div><div>To do this, we first solve the boundary value problem for an extremal function. To solve the boundary value problem, we use direct and inverse Fourier transforms and find the fundamental solution of the given differential operator. Using the extremal function, we find the norm of the error functional. For the given nodes, we find the minimum value of the error functional norm along the coefficients.</div><div>This quadrature formula is exact for the hyperbolic functions <span><math><mrow><mo>sinh</mo><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow><mo>,</mo><mo>cosh</mo><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow></mrow></math></span> and a constant term. In this work, we consider the case <span><math><mrow><mi>ω</mi><mi>h</mi><mo>∉</mo><mi>Z</mi></mrow></math></span> and <span><math><mrow><mi>ω</mi><mo>∈</mo><mi>R</mi></mrow></math></span> in the Hilbert space <span><math><mrow><msubsup><mrow><mtext>K</mtext></mrow><mrow><mn>2</mn></mrow><mrow><mrow><mo>(</mo><mn>3</mn><mo>)</mo></mrow></mrow></msubsup><mrow><mo>(</mo><mn>0</mn><mo>,</mo><mn>1</mn><mo>)</mo></mrow></mrow></math></span>.</div><div>We apply the constructed quadrature formula for reconstruction of a Computed Tomography image.</div></div>","PeriodicalId":36918,"journal":{"name":"Results in Applied Mathematics","volume":"26 ","pages":"Article 100569"},"PeriodicalIF":1.4,"publicationDate":"2025-04-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143776396","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"A deterministic criterion for approximate controllability of stochastic differential equations with jumps","authors":"Junfei Guo ,&nbsp;Zhiyuan Huang ,&nbsp;Rui Sun ,&nbsp;Zhao Yikai","doi":"10.1016/j.rinam.2025.100566","DOIUrl":"10.1016/j.rinam.2025.100566","url":null,"abstract":"<div><div>This paper investigates the approximate controllability and approximate null controllability of a class of linear stochastic systems driven by Gaussian random measures. The analysis focuses on controlled systems featuring both deterministic and stochastic components, where the control acts on the drift and jump terms. We establish the equivalence between approximate controllability and approximate null controllability by introducing an invariant subspace <span><math><mi>V</mi></math></span>, defined by the system’s parameters. The controllability of the system is shown to hinge on whether <span><math><mi>V</mi></math></span> reduces to the trivial space <span><math><mrow><mo>{</mo><mn>0</mn><mo>}</mo></mrow></math></span>. These findings provide a unified framework for understanding the controllability properties of stochastic systems with jump and diffusion dynamics.</div></div>","PeriodicalId":36918,"journal":{"name":"Results in Applied Mathematics","volume":"26 ","pages":"Article 100566"},"PeriodicalIF":1.4,"publicationDate":"2025-03-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143685646","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Long-time dynamics of the Kirchhoff equation with variable coefficient rotational inertia and memory","authors":"Penghui Lv ,&nbsp;Jingxin Lu ,&nbsp;Guoguang Lin","doi":"10.1016/j.rinam.2025.100565","DOIUrl":"10.1016/j.rinam.2025.100565","url":null,"abstract":"<div><div>The Kirchhoff model stems from the vibration problem of stretchable strings. This paper investigates the Kirchhoff equation incorporating variable coefficient rotational inertia and memory. By employing the Faedo–Galerkin method, the existence and uniqueness of the solution are established. Moreover, the existence of a global attractor is demonstrated through the proof of a bounded absorbing set and the asymptotic smoothness of the semigroup. The study innovatively explores the long-time dynamical behavior of the Kirchhoff model under the combined effects of variable coefficient rotational inertia, memory, and thermal interactions, thereby extending the model’s theoretical framework. These results provide a robust theoretical foundation for future applications and research endeavors.</div></div>","PeriodicalId":36918,"journal":{"name":"Results in Applied Mathematics","volume":"26 ","pages":"Article 100565"},"PeriodicalIF":1.4,"publicationDate":"2025-03-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143685647","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Optimal harvest under a Gilpin–Ayala model driven by the Hawkes process","authors":"Nyassoke Titi Gaston Clément ,&nbsp;Sadefo Kamdem Jules ,&nbsp;Fono Louis Aimé","doi":"10.1016/j.rinam.2025.100564","DOIUrl":"10.1016/j.rinam.2025.100564","url":null,"abstract":"<div><div>This paper analyzes the optimal effort for a risk-averse fisherman where the biomass process follows a Hawkes jump–diffusion process with Gilpin–Ayala drift. The main feature of the Hawkes process is to capture the phenomenon of clustering. The price process is of the mean-reverting type. We prove a sufficient maximum principle for the optimal control of a stochastic system consisting of an SDE driven by the Hawkes process and, by the concavity of the Hamiltonian, we obtain the optimal effort of the fisherman for a risk-averse investor.</div></div>","PeriodicalId":36918,"journal":{"name":"Results in Applied Mathematics","volume":"26 ","pages":"Article 100564"},"PeriodicalIF":1.4,"publicationDate":"2025-03-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143643158","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Asymptotic analysis of solutions of delay difference equations","authors":"Qin Diao ,&nbsp;Yong-Guo Shi ,&nbsp;Hari Mohan Srivastava ,&nbsp;Babak Shiri ,&nbsp;Kelin Li","doi":"10.1016/j.rinam.2025.100562","DOIUrl":"10.1016/j.rinam.2025.100562","url":null,"abstract":"<div><div>The asymptotic behavior of solutions for the delay difference equation <span><math><mrow><msub><mrow><mi>x</mi></mrow><mrow><mi>n</mi><mo>+</mo><mn>1</mn></mrow></msub><mo>=</mo><msub><mrow><mi>x</mi></mrow><mrow><mi>n</mi></mrow></msub><mi>f</mi><mrow><mo>(</mo><msub><mrow><mi>x</mi></mrow><mrow><mi>n</mi><mo>−</mo><mi>k</mi></mrow></msub><mo>)</mo></mrow><mo>,</mo><mspace></mspace><mspace></mspace><mi>n</mi><mo>&gt;</mo><mi>k</mi><mo>,</mo><mspace></mspace><mspace></mspace><mtext>for some</mtext><mspace></mspace><mspace></mspace><mi>k</mi><mo>∈</mo><mi>N</mi><mo>,</mo></mrow></math></span> is investigated, where <span><math><mi>f</mi></math></span> has an asymptotic power series. These equations have been studied for some special cases. This paper analyzes other cases and presents asymptotic expansions of solutions for such higher-order difference equations. Several examples are provided.</div></div>","PeriodicalId":36918,"journal":{"name":"Results in Applied Mathematics","volume":"26 ","pages":"Article 100562"},"PeriodicalIF":1.4,"publicationDate":"2025-03-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143629415","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"An integral representation of the local time of the Brownian motion via the Clark–Ocone formula","authors":"Allaoui Omar ,&nbsp;Hadiri Sokaina ,&nbsp;Sghir Aissa","doi":"10.1016/j.rinam.2025.100563","DOIUrl":"10.1016/j.rinam.2025.100563","url":null,"abstract":"<div><div>Let <span><math><mrow><mo>(</mo><mrow><msup><mrow><mi>L</mi></mrow><mrow><mi>B</mi></mrow></msup><mrow><mo>(</mo><mi>t</mi><mo>,</mo><mi>x</mi><mo>)</mo></mrow><mo>,</mo><mspace></mspace><mi>t</mi><mo>≥</mo><mn>0</mn><mo>,</mo><mspace></mspace><mi>x</mi><mo>∈</mo><mi>R</mi></mrow><mo>)</mo></mrow></math></span> be the local time of <span><math><mrow><mrow><mo>(</mo><mrow><msub><mrow><mi>B</mi></mrow><mrow><mi>t</mi></mrow></msub><mo>,</mo><mspace></mspace><mi>t</mi><mo>≥</mo><mn>0</mn></mrow><mo>)</mo></mrow><mo>,</mo></mrow></math></span> the real-valued one-dimensional Brownian motion. In this paper, in case of <span><math><mrow><mi>g</mi><mo>,</mo></mrow></math></span> a strictly increasing and bijective function, we propose some integral representations of <span><math><mrow><msup><mrow><mi>L</mi></mrow><mrow><mi>g</mi><mrow><mo>(</mo><mi>B</mi><mo>)</mo></mrow></mrow></msup><mrow><mo>(</mo><mi>t</mi><mo>,</mo><mi>x</mi><mo>)</mo></mrow><mo>,</mo></mrow></math></span> of the form: <span><math><mrow><mi>R</mi><mrow><mo>(</mo><mi>t</mi><mo>,</mo><mi>x</mi><mo>)</mo></mrow><mo>+</mo><msubsup><mrow><mo>∫</mo></mrow><mrow><mn>0</mn></mrow><mrow><mi>t</mi></mrow></msubsup><mi>K</mi><mrow><mo>(</mo><mi>t</mi><mo>,</mo><mi>x</mi><mo>,</mo><msub><mrow><mi>B</mi></mrow><mrow><mi>s</mi></mrow></msub><mo>)</mo></mrow><mi>d</mi><msub><mrow><mi>B</mi></mrow><mrow><mi>s</mi></mrow></msub><mo>,</mo></mrow></math></span> where <span><math><mrow><mi>R</mi><mrow><mo>(</mo><mi>t</mi><mo>,</mo><mi>x</mi><mo>)</mo></mrow></mrow></math></span> is a deterministic function and <span><math><mrow><mi>K</mi><mrow><mo>(</mo><mi>t</mi><mo>,</mo><mi>x</mi><mo>,</mo><msub><mrow><mi>B</mi></mrow><mrow><mi>s</mi></mrow></msub><mo>)</mo></mrow></mrow></math></span> is a random function depending on <span><math><mi>t</mi></math></span> and <span><math><mrow><mi>F</mi><mo>,</mo></mrow></math></span> the cumulative distribution function of the standard normal distribution <span><math><mrow><mi>N</mi><mrow><mo>(</mo><mn>0</mn><mo>,</mo><mn>1</mn><mo>)</mo></mrow></mrow></math></span> and some Brownian functionals with no Malliavin derivative. Our study is based on the case <span><math><mrow><msup><mrow><mi>L</mi></mrow><mrow><mi>B</mi></mrow></msup><mrow><mo>(</mo><mi>t</mi><mo>,</mo><mi>x</mi><mo>)</mo></mrow><mo>.</mo></mrow></math></span> An exact formula of the expectation <span><math><mrow><mi>E</mi><mrow><mo>[</mo><mrow><msup><mrow><mi>L</mi></mrow><mrow><mi>B</mi></mrow></msup><mrow><mo>(</mo><mi>t</mi><mo>,</mo><mi>x</mi><mo>)</mo></mrow></mrow><mo>]</mo></mrow></mrow></math></span> is given in this paper.</div></div>","PeriodicalId":36918,"journal":{"name":"Results in Applied Mathematics","volume":"26 ","pages":"Article 100563"},"PeriodicalIF":1.4,"publicationDate":"2025-03-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143629414","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Shared-endpoint correlations and hierarchy in random flows on graphs","authors":"Joshua Richland ,&nbsp;Alexander Strang","doi":"10.1016/j.rinam.2025.100549","DOIUrl":"10.1016/j.rinam.2025.100549","url":null,"abstract":"<div><div>We analyze the correlation between randomly chosen edge weights on neighboring edges in a directed graph. This shared-endpoint correlation controls the expected organization of randomly drawn edge flows, assuming each edge’s flow is conditionally independent of others given its endpoints. We model different relationships between endpoint attributes and flow by varying the kernel associated with a Gaussian process evaluated on every vertex. We then relate the expected flow structure to the smoothness of functions generated by the Gaussian process. We investigate the shared-endpoint correlation for the squared exponential, mixture, and Matèrn kernels while exploring asymptotics in smooth and rough limits.</div></div>","PeriodicalId":36918,"journal":{"name":"Results in Applied Mathematics","volume":"26 ","pages":"Article 100549"},"PeriodicalIF":1.4,"publicationDate":"2025-03-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143611525","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Singular bifurcations in a slow-fast modified Leslie-Gower model","authors":"Roberto Albarran-García ,&nbsp;Martha Alvarez-Ramírez ,&nbsp;Hildeberto Jardón-Kojakhmetov","doi":"10.1016/j.rinam.2025.100558","DOIUrl":"10.1016/j.rinam.2025.100558","url":null,"abstract":"<div><div>We study a predator–prey system with a generalist Leslie–Gower predator, a functional Holling type II response, and a weak Allee effect on the prey. The prey’s population often grows much faster than its predator, allowing us to introduce a small time scale parameter <span><math><mi>ɛ</mi></math></span> that relates the growth rates of both species, giving rise to a slow-fast system. Zhu and Liu (2022) show that, in the case of the weak Allee effect, Hopf singular bifurcation, slow-fast canard cycles, relaxation oscillations, etc. Our main contribution lies in the rigorous analysis of a degenerate scenario organized by a (degenerate) transcritical bifurcation. The key tool employed is the blow-up method that desingularizes the degenerate singularity. In addition, we determine the criticality of the singular Hopf bifurcation using recent intrinsic techniques that do not require a local normal form. The theoretical analysis is complemented by a numerical bifurcation analysis, in which we numerically identify and analytically confirm the existence of a nearby Takens–Bogdanov point.</div></div>","PeriodicalId":36918,"journal":{"name":"Results in Applied Mathematics","volume":"26 ","pages":"Article 100558"},"PeriodicalIF":1.4,"publicationDate":"2025-03-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143611588","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"An accurate collocation method for distributed order time fractional nonlinear diffusion wave equation with error analysis","authors":"M. Taghipour ,&nbsp;H. Aminikhah","doi":"10.1016/j.rinam.2025.100556","DOIUrl":"10.1016/j.rinam.2025.100556","url":null,"abstract":"<div><div>The distributed-order fractional nonlinear diffusion-wave problem is a mathematical model that combines the concepts of fractional calculus and nonlinear diffusion-wave equations. It involves the use of distributed-order fractional operators, which generalize the traditional constant-order fractional operators by allowing the order of the derivative to vary over a range of values. This method works especially well for modeling complex systems whose behavior is affected by memory and nonlocal effects that happen across several scales. The objective of this article is to offer an appropriate numerical method for treating this problem. In order to achieve this, we dealt with the integral terms in the main equation using the Newton–Cotes quadrature rule. The problem reduces to a nonlinear system of equations through the computation of operational matrices. With the Levenberg–Marquardt algorithm as an option, the resulting system had been solved using Matlab’s fsolve tool. The analysis of the scheme and the function approximation have been thoroughly covered. Some test problem provided to compare the method with existing one. Additionally, the effect of collocation points on the numerical solution’s accuracy has been investigated.</div></div>","PeriodicalId":36918,"journal":{"name":"Results in Applied Mathematics","volume":"26 ","pages":"Article 100556"},"PeriodicalIF":1.4,"publicationDate":"2025-03-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143592757","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"On the numerical solution of a parabolic Fredholm integro-differential equation by the RBF method","authors":"Ihor Borachok,&nbsp;Roman Chapko,&nbsp;Oksana Palianytsia","doi":"10.1016/j.rinam.2025.100559","DOIUrl":"10.1016/j.rinam.2025.100559","url":null,"abstract":"<div><div>This paper presents the numerical solution of an initial boundary value problem for a parabolic Fredholm integro-differential equation (FIDE) in bounded 2D and 3D spatial domains. To reduce the dimensionality of the problem, we employ the Laguerre transformation and Rothe’s method, with both first- and second-order time discretization approximations. As a result, the time-dependent problem is transformed into a recurrent sequence of boundary value problems for elliptic FIDEs. The radial basis function (RBF) method is then applied, where each stationary solution is approximated as a linear combination of radial basis functions centered at specific points, along with polynomial basis functions. The placement of these center points is outlined for both two-dimensional and three-dimensional regions. Collocation at center points generates a sequence of linear systems with integral coefficients. To compute these coefficients numerically, parameterization is performed, and Gauss–Legendre and trapezoidal quadratures are used. The shape parameter of the RBFs is optimized through a real-coded genetic algorithm. Numerical results in both two-dimensional and three-dimensional domains confirm the effectiveness and applicability of the proposed approaches.</div></div>","PeriodicalId":36918,"journal":{"name":"Results in Applied Mathematics","volume":"26 ","pages":"Article 100559"},"PeriodicalIF":1.4,"publicationDate":"2025-03-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143592759","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}