Results in Applied Mathematics最新文献

{"title":"Analysis of variational inequalities with fractional curvilinear integral functionals","authors":"Octavian Postavaru ,&nbsp;Antonela Toma ,&nbsp;Savin Treanţă","doi":"10.1016/j.rinam.2025.100572","DOIUrl":"10.1016/j.rinam.2025.100572","url":null,"abstract":"<div><div>This study examines weak sharp solutions for a category of variational inequalities incorporating functionals based on fractional curvilinear integrals, expanding the conventional approach with concepts from fractional calculus. Furthermore, by using the sufficiency property of the minimum principle, the paper establishes and proves results on the weak sharpness characteristic of the solution collection for this type of inequality constraints. An application is provided to illustrate the main theoretical findings.</div></div>","PeriodicalId":36918,"journal":{"name":"Results in Applied Mathematics","volume":"26 ","pages":"Article 100572"},"PeriodicalIF":1.4,"publicationDate":"2025-04-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143828743","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":"Higher-order differential operators having bivariate orthogonal polynomials as eigenfunctions","authors":"Misael E. Marriaga","doi":"10.1016/j.rinam.2025.100571","DOIUrl":"10.1016/j.rinam.2025.100571","url":null,"abstract":"<div><div>We introduce a systematic method for constructing higher-order partial differential equations for which bivariate orthogonal polynomials are eigenfunctions. Using the framework of moment functionals, the approach is independent of the orthogonality domain’s geometry, enabling broad applicability across different polynomial families. Applications to classical weight functions on the unit disk and triangle modified by measures defined on lower-dimensional manifolds are presented.</div></div>","PeriodicalId":36918,"journal":{"name":"Results in Applied Mathematics","volume":"26 ","pages":"Article 100571"},"PeriodicalIF":1.4,"publicationDate":"2025-04-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143828188","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":"Three sixth-order explicit symplectic Runge–Kutta-Nystrom methods with exact parameters","authors":"Mengjiao Pan ,&nbsp;Jingjing Zhang ,&nbsp;Shangyou Zhang","doi":"10.1016/j.rinam.2025.100568","DOIUrl":"10.1016/j.rinam.2025.100568","url":null,"abstract":"<div><div>For separable Hamiltonian systems, we construct first ever three symplectic explicit Runge–Kutta-Nyström methods of six orders with exact parameters. We numerically and theoretically compare these three new exact methods with the only existing exact 6-th order symplectic explicit partitioned Runge–Kutta method and two approximate 6-th order symplectic explicit Runge–Kutta-Nyström methods. These new methods are more accurate and stable.</div></div>","PeriodicalId":36918,"journal":{"name":"Results in Applied Mathematics","volume":"26 ","pages":"Article 100568"},"PeriodicalIF":1.4,"publicationDate":"2025-04-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143800553","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":"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}