Results in Applied Mathematics最新文献_第3页

Resolving implicit nonconvex state-dependent sweeping processes in Banach spaces 求解Banach空间中隐式非凸状态相关清扫过程

IF 1.5

Results in Applied Mathematics Pub Date : 2026-08-01 Epub Date: 2026-08-22 DOI: 10.1016/j.rinam.2026.100756

Bushra R. Al-Sinan

引用次数: 0

A potential exploring of a multi-dimensional coupled Burgers–Fisher–Huxley equation using finite volume and element methods (FVM/FEM) 基于有限体积单元法（FVM/FEM）的多维耦合Burgers-Fisher-Huxley方程的潜在探索

IF 1.5

Results in Applied Mathematics Pub Date : 2026-08-01 Epub Date: 2026-08-21 DOI: 10.1016/j.rinam.2026.100753

Tarik Chakkour

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引用次数: 0

On Gabor frame networks 在Gabor框架网络上

IF 1.5

Results in Applied Mathematics Pub Date : 2026-08-01 Epub Date: 2026-08-03 DOI: 10.1016/j.rinam.2026.100746

Jamkhongam Touthang

引用次数: 0

Pathwise approximations to solving the filtering problem for the stochastic chemostat 求解随机恒化器滤波问题的路径逼近

IF 1.5

Results in Applied Mathematics Pub Date : 2026-08-01 Epub Date: 2026-09-04 DOI: 10.1016/j.rinam.2026.100757

José Augusto Fontenele Magalhães, Muhammad Fuady Emzir, Francesco Corona

{"title":"Pathwise approximations to solving the filtering problem for the stochastic chemostat","authors":"José Augusto Fontenele Magalhães, Muhammad Fuady Emzir, Francesco Corona","doi":"10.1016/j.rinam.2026.100757","DOIUrl":"10.1016/j.rinam.2026.100757","url":null,"abstract":"<div><div>This paper concerns the inverse problem of characterising the state of a bioreactor from observations. In laboratory settings, the bioreactor is represented by a device called a chemostat. We consider a differential description of the evolution of the state of the chemostat under environmental fluctuations. We model the state evolution as a stochastic process driven by Brownian motion. Under this model, the state is described by its probability distribution in time, given the distribution of the initial state. The corresponding probability density function solves a deterministic partial differential equation (PDE), the Kolmogorov forward equation. This description is refined by incorporating observations. More formally, we seek the conditional distribution of the state given an observation process as the solution to a filtering problem, with the corresponding conditional probability density function solving a non-linear stochastic PDE, the Kushner–Stratonovich equation. In numerical studies of bioreactors, the well-posedness of these differential equations is frequently assumed rather than verified. Consequently, it remains unclear whether unique solutions exist and whether numerical approximations preserve key qualitative properties, such as positivity (e.g. non-negative chemical concentrations). This paper establishes the existence and uniqueness of solutions, ensuring well-posedness before presenting numerical approximations. Furthermore, we approximate the pathwise solution to the filtering problem by three approaches: a PDE-based approximation combining finite difference and splitting methods, a classical sequential Monte Carlo method, and a linearisation method. Our results show that the first two provide a richer probabilistic description of the state than the linearisation method, making them suitable for bioreactor control architectures.</div></div>","PeriodicalId":36918,"journal":{"name":"Results in Applied Mathematics","volume":"31 ","pages":"Article 100757"},"PeriodicalIF":1.5,"publicationDate":"2026-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148934371","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}

引用次数: 0

A higher-order L1-2-3 tension spline scheme for nonlinear two-dimensional time-fractional reaction–diffusion equation 非线性二维时间-分数反应-扩散方程的高阶L1-2-3张力样条格式

IF 1.5

Results in Applied Mathematics Pub Date : 2026-08-01 Epub Date: 2026-08-17 DOI: 10.1016/j.rinam.2026.100749

Alemu Senbeta Bekela, Lemi Guta Enyadene, Mesfin Mekuria Woldaregay, Zerihun Kinfe Birhanu

{"title":"A higher-order L1-2-3 tension spline scheme for nonlinear two-dimensional time-fractional reaction–diffusion equation","authors":"Alemu Senbeta Bekela, Lemi Guta Enyadene, Mesfin Mekuria Woldaregay, Zerihun Kinfe Birhanu","doi":"10.1016/j.rinam.2026.100749","DOIUrl":"10.1016/j.rinam.2026.100749","url":null,"abstract":"<div><div>The paper presents the design and analysis of a high-order numerical scheme for nonlinear two-dimensional time-fractional reaction–diffusion equations. The Caputo time-fractional derivative is approximated using the L1-2-3 scheme, while the spatial derivatives are discretized by means of tension spline difference scheme. The existence, uniqueness, and regularity of the solution are established to support the theoretical analysis. The truncation error, stability, and convergence of the proposed method are rigorously investigated. Two test problems are considered to validate the accuracy and efficiency of the method. For sufficiently smooth solutions, the proposed method is shown to be unconditionally stable and to achieve fourth-order spatial accuracy and <span><math><mrow><mo>(</mo><mn>4</mn><mo>−</mo><mi>α</mi><mo>)</mo></mrow></math></span>-order temporal accuracy. The numerical results confirm the theoretical convergence rates and demonstrates that the proposed method provides higher accuracy, improved convergence behavior, and competitive computational efficiency compared with existing numerical methods. These results indicate that the proposed method is an effective and reliable approach for solving nonlinear two-dimensional time-fractional reaction–diffusion equations with sufficiently smooth solutions arising in models with memory and hereditary effects.</div></div>","PeriodicalId":36918,"journal":{"name":"Results in Applied Mathematics","volume":"31 ","pages":"Article 100749"},"PeriodicalIF":1.5,"publicationDate":"2026-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148776383","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}

引用次数: 0

A novel RKHS method for solving space–time FDEs 求解时空fde的RKHS新方法

IF 1.3

Results in Applied Mathematics Pub Date : 2026-05-01 Epub Date: 2026-05-14 DOI: 10.1016/j.rinam.2026.100708

Sizhe Wang, Yibo Yang, Wenyan Wang

引用次数: 0

Stability of purely convective steady-states of fractional Boussinesq equations in an exterior domain 分数阶Boussinesq方程外域纯对流稳态的稳定性

IF 1.3

Results in Applied Mathematics Pub Date : 2026-05-01 Epub Date: 2026-05-13 DOI: 10.1016/j.rinam.2026.100712

Zhi-Min Chen

引用次数: 0

Accelerated iterative simultaneous hard thresholding algorithm for joint sparse optimization 联合稀疏优化的加速迭代同步硬阈值算法

IF 1.3

Results in Applied Mathematics Pub Date : 2026-05-01 Epub Date: 2026-05-22 DOI: 10.1016/j.rinam.2026.100711

Heran Huang , Zihe Zheng , Xinlin Hu , Yifan Ye

引用次数: 0

Corrigendum to “Analytical strength-duration curve for the spiking response of the LIF neuron to an alpha-function-shaped excitatory current pulse” [Results Appl. Math. 25 (2025) 100548] “LIF神经元对α函数型兴奋电流脉冲的尖峰响应的分析强度-持续时间曲线”的勘误[结果应用程序]。数学。25 (2025)100548 [j]

IF 1.5

Results in Applied Mathematics Pub Date : 2026-05-01 Epub Date: 2026-05-29 DOI: 10.1016/j.rinam.2026.100713

Alexander Paraskevov

引用次数: 0

Fungi as functors: A category-theoretic approach to mycelial organisation 作为功能因子的真菌：菌丝组织的范畴论方法

IF 1.3

Results in Applied Mathematics Pub Date : 2026-05-01 Epub Date: 2026-05-27 DOI: 10.1016/j.rinam.2026.100715

Andrew Adamatzky

{"title":"Fungi as functors: A category-theoretic approach to mycelial organisation","authors":"Andrew Adamatzky","doi":"10.1016/j.rinam.2026.100715","DOIUrl":"10.1016/j.rinam.2026.100715","url":null,"abstract":"<div><div>We develop a category-theoretic foundation for fungal organisation. A fungal organism is formalised as a functor from a category <span><math><mi>Env</mi></math></span> of structured environmental states and admissible transformations to a category <span><math><mi>Myc</mi></math></span> of mycelial network states and biologically meaningful morphisms. An operational program category <span><math><mi>Prog</mi></math></span> models time-ordered exposure protocols, and a semantics functor <span><math><mrow><msub><mrow><mi>F</mi></mrow><mrow><mi>prog</mi></mrow></msub><mo>:</mo><mi>Prog</mi><mo>→</mo><mi>Myc</mi></mrow></math></span> maps experimental perturbations to induced network transformations. Species and strain variability are expressed as natural transformations between fungal functors, and ecological feedback is captured via an adjunction between sensing and environment modification. Network fusion is identified with pushouts in <span><math><mi>Myc</mi></math></span>, and order effects in exposure sequences are quantified by a local Lie structure and a Baker–Campbell–Hausdorff expansion near the identity program. A minimal example demonstrates how non-commutativity yields experimentally testable quadratic scaling of order asymmetry. The framework provides a structurally explicit and falsifiable basis for analysing compositional perturbations, mixture coupling, robustness limits, and cross-species comparability in fungal systems.</div></div>","PeriodicalId":36918,"journal":{"name":"Results in Applied Mathematics","volume":"30 ","pages":"Article 100715"},"PeriodicalIF":1.3,"publicationDate":"2026-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148184754","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}

引用次数: 0