CSIAM Transactions on Applied Mathematics
type: channel
description: The CSIAM Transactions on Applied Mathematics (CSIAM-AM) is the flagship journal of the Chinese Society for Industrial and Applied Mathematics. It publishes original research articles of high quality on a topic in applied mathematics or computational mathematics or scientific computing. Papers should address mathematically and computationally interesting and challenging problems. Manuscripts applying known methods to previously solved problems will not be accepted.
publisher: Global Science Press
language: en
publication name: CSIAM Transactions on Applied Mathematics
issn: 2708-0560
items: An Optimization Process for p-Curves in Surface-to-Surface Intersection to Improve Accuracy and Reduce Redundancy
items: Reconstructing Dynamic Scenes with Topologically-Varying Neural Implicit Fields
items: Structure-Aware Indoor RGB-D SLAM via Manhattan-Constrained 2D Gaussian Splatting
items: Linear Maximum Bound Principle Preserving Finite Difference Schemes for the Convective Allen-Cahn Equation
items: Generalized Product-Type Variants of RBiCG for Solving Families of Linear Systems
items: A Mathematical Perspective on Corruption’s Effect on Productivity and Service Efficiency with Cost-Effective Control Strategies
items: An Accelerated Spectral Perry-Type Conjugate Gradient Projection Method for Unconstrained Nonlinear Equations with Applications
items: Biharmonic Distance Driven Voronoi Diagrams Restricted on Curved Surfaces
items: A Neural Network Framework for High-Dimensional Dynamic Unbalanced Optimal Transport
items: Smooth Bijective Projection of Polygonal Meshes via a Cubic B-Spline Shell
items: Multistability of Bi-Reaction Networks
items: Data- and Mechanism-Driven Hybrid Computing: A New Paradigm for Scientific and Engineering Computation
items: Tackling Challenge of Masked and Unmasked Face for Facial Recognition Through Dimensionality Reduction and Deep Learning
items: Optimizing Interdisciplinarity in Data Analysis with the Adapted Alpha-Power Transformation of the Nadarajah-Haghighi Distribution
items: Transport of Contaminant Release by Three Different Sources: A Medium with Complex Geometry
items: The Poisson-Garima Distribution: Additional Key Features and Its Significance on Statistical Process Control in Agriculture
items: Thermodynamics of Freshwater Production via CuS-Infused Porous Membrane Solar Absorber in Seawater Desalination
items: Superconvergence Points of Several Polynomial and Nonpolynomial Hermite Spectral Interpolations
items: An Efficient Iterative Convolution-Thresholding Method for Image Inpainting
items: Double-Domain Driven Unet for Selective Segmentation of Medical Image
items: Assessment and Evaluation of Surface Water Quality and Human Health Risk in the Inkomati River Catchment Basin, South Africa
items: Bifurcation and Crossover Processes in the Dynamics of a Marburg Haemorrhagic Fever Model
items: Interface Laplace Learning: Learnable Interface Term Helps Semi-Supervised Learning
items: Error Estimates of Operator Splitting Spectral Method for Semiclassical Sub-Diffusive Gross-Pitaevskii Equation
items: pETNNs: Partial Evolutionary Tensor Neural Networks for Solving Time-Dependent Partial Differential Equations
items: A Mathematical Analysis for the Dynamics of Multiple Languages
items: Global Solvability in a Two-Species Keller-Segel-Navier-Stokes System with Sub-Logistic Source
items: An Efficient Iteration Based on Reduced Basis Method for Time-Dependent Problems with Random Inputs
items: A Sharp Uniform-in-Time Error Estimate for Stochastic Gradient Langevin Dynamics
items: Two Methods Addressing Variable-Exponent Fractional Initial and Boundary Value Problems and Abel Integral Equation

An Optimization Process for p-Curves in Surface-to-Surface Intersection to Improve Accuracy and Reduce Redundancy
type: item
description: The problem of surface-to-surface intersection (SSI) is among the most fundamental challenges encountered in computer-aided geometric design. In industrial applications, the execution of an SSI operation usually demands a high degree of precision while maintaining a concise representation of the intersection curve. We present a post-processing scheme for refining the intersection curve in the parameter domain (p-curves), achieving an improvement in accuracy without additional control points inserted. Moreover, by adjusting the parameterization, a one-to-one correspondence is created between a pair of p-curves. The proposed methodology is grounded on the minimization of an objective function that describes both accuracy and parameterization. The effectiveness of our method is illustrated through examples in comparison with the open-source NURBS library SISL and commercial software ACIS.
subject: Articles
  topic: section
subject: CAGD
  topic: keywords
subject: surface intersections
  topic: keywords
subject: watertigh
  topic: keywords
subject: parameterization
  topic: keywords
subject: optimization
  topic: keywords
creator: Xiaohan Wang
creator: Jieqing Feng
rights: Copyright (c) 2025 CSIAM Transactions on Applied Mathematics
date: 2026-03-02
publication date: 2026-03-02
doi: 10.4208/csiam-am.SO-2025-0065

Reconstructing Dynamic Scenes with Topologically-Varying Neural Implicit Fields
type: item
description: This paper addresses the challenge of reconstructing dynamic scenes from monocular videos with dynamic neural implicit fields. Previous methods combine a single canonical template with a per-frame deformation field or optimize a hyper-space of templates to cover the variance of the scenes with a large amount of templates. However, single-template based methods cannot recover scenes with topology changes, while hyperspace template approaches may fail to be optimized under large-scale topology changes or motions without any constraints over the high-dimensional space. To address these issues, we propose a topologically-varying neural implicit fields by deforming the sum of multiple canonical templates and recovering large-scale motion and topology changes with a video segmentation strategy. Specifically, multiple templates are defined in canonical space, i.e. a primary template and sparse auxiliary templates. The primary template represents parts that do not change significantly during movement, while the auxiliary templates are combined linearly to represent topological changes. To reconstruct large-scale topologically-varying scenes, a dynamic segmentation strategy is adopted to divide the entire video into multiple segments, and each segment is modeled with its own templates. Compared to existing reconstruction methods for topologically changing objects, our method uses sparse auxiliary templates to form a continuous hyperspace, which is easier to optimize even under large topology changes and motions. Experimental results on various datasets demonstrate that our method outperforms previous works in both geometric reconstruction and novel-view synthesis.
subject: Articles
  topic: section
subject: Dynamic reconstruction
  topic: keywords
subject: topologically-varying neural implicit fields
  topic: keywords
subject: monocular videos
  topic: keywords
creator: Kangkan Wang
creator: Miao Zhao
creator: Shao-Yuan Li
rights: Copyright (c) 2025 CSIAM Transactions on Applied Mathematics
date: 2026-03-02
publication date: 2026-03-02
doi: 10.4208/csiam-am.SO-2025-0064

Structure-Aware Indoor RGB-D SLAM via Manhattan-Constrained 2D Gaussian Splatting
type: item
description: Accurate and layout-consistent reconstruction remains a key challenge in indoor simultaneous localization and mapping (SLAM) due to the prevalence of planar and axis-aligned structures. Traditional visual and RGB-D SLAM methods often suffer from incomplete geometry and weak structural reasoning, while NeRF-based SLAM improves fidelity but is computationally expensive and unsuitable for real-time use. 3D Gaussian splatting offers improved efficiency but lacks structural priors, often resulting in distortions in structured scenes. To address these issues, we propose a structure-aware SLAM framework based on 2D Gaussian splatting, which provides efficient, view-consistent mapping. We introduce a lightweight regularization scheme under the Manhattan-world assumption to align Gaussian orientations and positions with dominant axes, improving layout consistency and geometric fidelity. Extensive experiments on Replica and TUM-RGBD datasets demonstrate that our method consistently outperforms existing SLAM baselines in terms of geometric accuracy and edge preservation across multiple indoor scenes.
subject: Articles
  topic: section
subject: SLAM
  topic: keywords
subject: 2DGS
  topic: keywords
subject: Manhattan-regularized
  topic: keywords
creator: Wenwu Guo
creator: Xia Yuan
creator: Yanli Liu
creator: Xiangyu Wu
creator: Wenyi Ge
creator: Guanyu Xing
creator: Jing Hu
creator: Xi Wu
rights: Copyright (c) 2025 CSIAM Transactions on Applied Mathematics
date: 2026-01-30
publication date: 2026-01-30
doi: 10.4208/csiam-am.SO-2025-0070

Linear Maximum Bound Principle Preserving Finite Difference Schemes for the Convective Allen-Cahn Equation
type: item
description: The convective Allen-Cahn equation generalizes the classical Allen-Cahn equation by introducing an additional convective term associated with a solenoidal velocity field while maintaining the maximum bound principle (MBP). However, developing high-order numerical schemes that are accurate in both time and space and preserve the MBP unconditionally has remained a significant challenge. In this paper, we address this by first defining new auxiliary variables to reformulate the interaction of the velocity field with the phase field. We then transform the convective Allen-Cahn equation into a generalized Fokker-Planck form using an exponential transformation, enabling the development of MBP-preserving linear numerical schemes. Subsequently, we propose first- and second-order in time numerical schemes for the reformulated equations with a second-order quasi-symmetric finite difference discretization in space. In this approach, the auxiliary variables are replaced with known functions related to the velocity field, simplifying the numerical implementation. For the first-order in time scheme, we derive its optimal error estimate and prove its unconditional MBP-preservation. For the second-order in time scheme, we show its MBP-preservation under mild constraints on the mesh and time step sizes. Some numerical experiments in two and three dimensions are also presented to validate the theoretical findings and illustrate the accuracy and efficiency of our proposed schemes.
subject: Articles
  topic: section
subject: Convective Allen-Cahn equation
  topic: keywords
subject: maximum bound principle
  topic: keywords
subject: exponential transformation
  topic: keywords
subject: quasi-symmetric finite difference
  topic: keywords
subject: error estimation
  topic: keywords
creator: Jingwei Li
creator: Kun Wang
creator: Lili Ju
rights: Copyright (c) 2025 CSIAM Transactions on Applied Mathematics
date: 2026-01-28
publication date: 2026-01-28
doi: 10.4208/csiam-am.SO-2024-0067

Generalized Product-Type Variants of RBiCG for Solving Families of Linear Systems
type: item
description: Families of slowly changing nonsingular large sparse linear systems arise frequently in many simulation problems in science and engineering. We consider iterative solution with recycling techniques for a general case where both left-hand sides and right-hand sides of the systems change from one family to the next. We firstly develop a generalized product-type method in the framework of recycling biconjugate gradient method (RBiCG), referred to as RGPBiCG, which can also be considered as a recycling variant of GPBiCG. However, as the same situation in RBiCG stabilized method (RBiCGSTAB), the construction of recycling spaces in RGPBiCG requires expensive computational costs due to invoking other algorithms (like RBiCG) to compute approximate eigenspaces. In order to further reduce such computational costs, we alternatively form the recycling spaces in RGPBiCG with difference vectors of approximate solutions, as employed for loose GMRES (LGMRES), resulting in a more promising algorithm termed as LR-GPBiCG. Numerical experiments on both a set of academic problems and engineering simulation problems demonstrate the efficiency of our proposed algorithms.
subject: Articles
  topic: section
subject: Sequences of linear systems
  topic: keywords
subject: subspace recycling
  topic: keywords
subject: RBiCG
  topic: keywords
subject: GPBiCG
  topic: keywords
subject: difference vectors of approximate solutions
  topic: keywords
creator: Yuhao Zhong
creator: Yanfei Jing
creator: Li Xu
creator: Hao Wang
rights: Copyright (c) 2025 CSIAM Transactions on Applied Mathematics
date: 2026-01-21
publication date: 2026-01-21
doi: 10.4208/csiam-am.SO-2024-0053

A Mathematical Perspective on Corruption’s Effect on Productivity and Service Efficiency with Cost-Effective Control Strategies
type: item
description: Corruption remains a major barrier to development in Africa, undermining public trust, weakening service delivery, and hindering economic growth. Defined as the abuse of public power for personal gain, it appears in forms such as bribery, embezzlement, nepotism, and cronyism, affecting both public and private sectors. Despite various anti-corruption efforts, the problem persists. This study presents a non-linear system of differential equations to evaluate the impact of corruption on productivity and service delivery, incorporating both constant and time-dependent control strategies. The basic reproduction number ($R_0$) is calculated using the next-generation matrix method. Model behaviour is further analysed through sensitivity analysis and stability assessments using the Routh-Hurwitz criterion and Lyapunov functions. An optimal control framework, based on Pontryagin’s maximum principle, assesses the effectiveness and cost-efficiency of preventative and punitive interventions. Numerical simulations, using the fourth-order Runge-Kutta method, indicate that strong enforcement of punitive measures is the most effective and cost-efficient strategy to combat corruption. These measures significantly improve productivity and public service delivery. The key policy recommendation is that governments and institutions should prioritize robust punitive controls as the primary approach to reducing corruption and promoting sustainable development.
subject: Articles
  topic: section
subject: Corruption dynamics
  topic: keywords
subject: productivity and service delivery
  topic: keywords
subject: basic reproductive number
  topic: keywords
subject: sensitivity analysis
  topic: keywords
subject: optimal control analysis
  topic: keywords
subject: cost-effectiveness analysis
  topic: keywords
subject: numerical simulation
  topic: keywords
creator: N. S. Tibane
creator: O. D. Makinde
creator: R. L. Monaledi
rights: Copyright (c) 2025 CSIAM Transactions on Applied Mathematics
date: 2026-01-21
publication date: 2026-01-21
starting page: 433
ending page: 460
doi: 10.4208/csiam-am.SO-2025-0015

An Accelerated Spectral Perry-Type Conjugate Gradient Projection Method for Unconstrained Nonlinear Equations with Applications
type: item
description: In this paper, we propose an accelerated spectral Perry-type conjugate gradient projection method for solving systems of unconstrained nonlinear equations. The spectral parameter is generated using an accelerated gradient-descent method, which ensures that the proposed search direction always satisfies the sufficient descent condition. By incorporating a self-adaptive strategy into the optimal Perry conjugate parameter, the proposed search direction possesses the trust region property independent of any line search. Additionally, the proposed method incorporates an inertial extrapolation step to enhance computational performance. The global convergence of the proposed method is theoretically established without requiring monotonicity or pseudo-monotonicity of the underlying mapping. Numerical experiments on systems of unconstrained nonlinear equations and image de-blurring problems demonstrate the effectiveness of the proposed method.
subject: Articles
  topic: section
subject: Unconstrained nonlinear equations
  topic: keywords
subject: derivative-free projection method
  topic: keywords
subject: convergence analysis
  topic: keywords
creator: Pengjie Liu
creator: Xiaoyu Wu
creator: Hu Shao
creator: Ting Wu
rights: Copyright (c) 2025 CSIAM Transactions on Applied Mathematics
date: 2026-01-05
publication date: 2026-01-05
doi: 10.4208/csiam-am.SO-2023-0039

Biharmonic Distance Driven Voronoi Diagrams Restricted on Curved Surfaces
type: item
description: Computing surface-based Voronoi diagrams is a fundamental operation in geometry processing, typically relying on either geodesic or straight-line distances as solvers. However, when the input is a 3D model containing thin-plate structures, geodesic distances incur significant computational overhead,whereas straight-line distances can result in ownerless regions. To address this issue, we propose integrating biharmonic embedding distances into the SurfaceVoronoi framework. Specifically, mesh vertices can be embedded into a high-dimensional spectral space, ensuring that the embedding distance closely approximates the straight-line distance between sufficiently close points. In contrast, when points reside on opposite sides of a thin plate, the embedding distance significantly exceeds the straight-line distance, effectively preventing dominance from penetrating through to the opposite side. Our proposed framework offers several advantages: 1) It operates efficiently, as the embedding distance can be rapidly evaluated as a straight-line distance in high-dimensional space. 2) It guarantees the “one site, one region” property, even for models consisting of thinplate structures. 3) It enables high-quality triangulation through iterative repositioning of each site to the centroid of its dominant region. Extensive experiments conducted on benchmark meshes demonstrate these benefits.
subject: Articles
  topic: section
subject: Surface Voronoi diagram
  topic: keywords
subject: biharmonic embedding
  topic: keywords
subject: intrinsic distance
  topic: keywords
subject: spectral geometry processing
  topic: keywords
creator: Xuetong Zhao
creator: Pengfei Wang
creator: Yining Xu
creator: Shuangmin Chen
rights: Copyright (c) 2025 CSIAM Transactions on Applied Mathematics
date: 2026-01-05
publication date: 2026-01-05
doi: 10.4208/csiam-am.SO-2025-0066

A Neural Network Framework for High-Dimensional Dynamic Unbalanced Optimal Transport
type: item
description: In this paper, we introduce a neural network-based method to address the high-dimensional dynamic unbalanced optimal transport (UOT) problem. Dynamic UOT focuses on the optimal transportation between two densities with unequal total mass, however, it introduces additional complexities compared to the traditional dynamic optimal transport problem. To efficiently solve the dynamic UOT problem in high-dimensional space, we first relax the original problem by using the generalized Kullback-Leibler divergence to constrain the terminal density. Next, we adopt the Lagrangian discretization to address the unbalanced continuity equation and apply the Monte Carlo method to approximate the high-dimensional spatial integrals. Moreover, a carefully designed neural network is introduced for modeling the velocity field and source function. Numerous experiments demonstrate that the proposed framework performs excellently in high-dimensional cases. Additionally, this method can be easily extended to more general applications, such as crowd motion problem.
subject: Articles
  topic: section
subject: Unbalanced optimal transport
  topic: keywords
subject: neural network
  topic: keywords
subject: Lagrangian discretization
  topic: keywords
subject: crowd motion
  topic: keywords
creator: Wei Wan
creator: Jiangong Pan
creator: Yuejin Zhang
creator: Chenglong Bao
creator: Zuoqiang Shi
rights: Copyright (c) 2025 CSIAM Transactions on Applied Mathematics
date: 2026-01-05
publication date: 2026-01-05
doi: 10.4208/csiam-am.SO-2025-0009

Smooth Bijective Projection of Polygonal Meshes via a Cubic B-Spline Shell
type: item
description: Polygonal meshes are a fundamental surface representation, yet their resolution can vary significantly. Establishing a smooth, bijective projection between meshes of different resolutions is crucial for consistent attribute transfer but becomes challenging when handling sharp bends and complex geometric features. This paper presents a novel approach to address this challenge by implicitly representing the shell enclosing two polygonal meshes using a cubic trivariate B-spline function, where the inner and outer bounding surfaces are formulated as level sets of a single cubic B-spline function. Our method enforces the bijective projection requirements on the cubic B-spline function, ensuring that the resulting gradient field naturally defines a robust bijective projection. Leveraging the favorable properties of cubic B-spline functions – namely, 1) sufficient smoothness while maintaining expressive representation, and 2) computational efficiency and ease of implementation, our approach efficiently computes a smooth and bijective projection even for challenging cases. Compared to existing shell-based bijective projection methods, our method consistently produces valid bijective projections, even in complex scenarios, outperforming state-of-the-art techniques. We further demonstrate its effectiveness in robust attribute transfer and precision-controlled shape manipulation.
subject: Articles
  topic: section
subject: Cubic B-spline shell
  topic: keywords
subject: attribute transfer
  topic: keywords
subject: smooth bijective projection
  topic: keywords
creator: Guilong He
creator: Huibiao Wen
creator: Shuangmin Chen
creator: Lin Lu
creator: Shiqing Xin
creator: Changhe Tu
rights: Copyright (c) 2025 CSIAM Transactions on Applied Mathematics
date: 2025-12-28
publication date: 2025-12-28
doi: 10.4208/csiam-am.SO-2025-0071

Multistability of Bi-Reaction Networks
type: item
description: We provide a sufficient and necessary condition in terms of the stoichiometric coefficients for a bi-reaction network to admit multistability. Also, this result completely characterizes the bi-reaction networks according to if they admit multistability.
subject: Articles
  topic: section
subject: Reaction networks
  topic: keywords
subject: mass-action kinetics
  topic: keywords
subject: multistationarity
  topic: keywords
subject: multistability
  topic: keywords
creator: Yixuan Liang
creator: Xiaoxian Tang
creator: Qian Zhang
rights: Copyright (c) 2025 CSIAM Transactions on Applied Mathematics
date: 2025-12-27
publication date: 2025-12-27
doi: 10.4208/csiam-am.SO-2024-0035

Data- and Mechanism-Driven Hybrid Computing: A New Paradigm for Scientific and Engineering Computation
type: item
description: Data- and mechanism-driven hybrid computing refers to the integration of traditional mechanism-based computing with data-driven methods. In this article, we present three typical patterns of this emerging paradigm: (1) mechanism-driven model optimization via data-driven refinement, (2) data-driven model construction with physical constraints, and (3) alternating optimization of mechanism-driven and data-driven models. We present several concrete examples to illustrate how hybrid computing improves accuracy, efficiency, and robustness across a variety of computational tasks.
subject: Articles
  topic: section
subject: Data-driven methods
  topic: keywords
subject: mechanism-driven models
  topic: keywords
subject: hybrid computing
  topic: keywords
creator: Jerry Zhijian Yang
creator: Pingwen Zhang
rights: Copyright (c) 2025 CSIAM Transactions on Applied Mathematics
date: 2026-01-25
publication date: 2026-01-25
starting page: 1
ending page: 28
doi: 10.4208/csiam-am.SO-2025-0074

Tackling Challenge of Masked and Unmasked Face for Facial Recognition Through Dimensionality Reduction and Deep Learning
type: item
description: Facial recognition systems face considerable performance degradation in the presence of occlusions, particularly face masks, which are increasingly common in public setting. This research examines the impact of such occlusions by employing dimensionality reduction techniques: principal component analysis (PCA) and auto-encoders, combined with convolutional neural networks for classification. Through experiments on custom-built dataset comprising masked, unmasked, and mixed facial images, we observe that PCA consistently outperforms auto-encoders across all evaluation metrics, including accuracy, precision, recall and F1-score. However, PCA is more sensitive to occlusion variability, while auto-encoders exhibit more stable, though generally lower performance. Notably, performance declines significantly when models are evaluated on mixed datasets, emphasizing the complexity of realworld scenarios. Data augmentation yields only marginal improvement, underscoring the limitation of current approaches in handling diverse occlusions. The study also explores the potential of advanced mathematical tools such as higher-order tensor decomposition and fractional differentiation to enhance feature representation and model robustness. Overall, this research directions involving diverse training sets, sophisticated feature extraction and hybrid architectures to enhance model generalization in dynamic environments. Hence, contributing to the development of more reliable biometric systems.
subject: Articles
  topic: section
subject: Faces recognition
  topic: keywords
subject: face occlusion
  topic: keywords
subject: masked face
  topic: keywords
subject: PCA
  topic: keywords
subject: auto-encoder
  topic: keywords
subject: CNN
  topic: keywords
subject: machine learning
  topic: keywords
creator: Guy Mathias Gouaya
creator: Emil Franc Doungmo Goufo
creator: Amos Kubeka
rights: Copyright (c) 2025 CSIAM Transactions on Applied Mathematics
date: 2025-12-20
publication date: 2025-12-20
starting page: 296
ending page: 328
doi: 10.4208/csiam-am.SO-2024-0065

Optimizing Interdisciplinarity in Data Analysis with the Adapted Alpha-Power Transformation of the Nadarajah-Haghighi Distribution
type: item
description: The practice of incorporating extra parameters into standard models is a common technique in statistical analysis. Adding an extra parameter enables the formation of a new model by applying the modified alpha-power transformation, employing the Nadarajah-Haghighi model as the baseline. Numerous characteristics of the said model are acquired, like the mode, quantiles, entropies, stochastic orders, mean residual life function, and order statistics. The maximum likelihood estimation method has been employed to estimate the parameters of the suggested model. To show how well the suggested distributions will function in a real-world setting, a simulation study has also been carried out and data has been examined. It is attained that the proposed model outperforms several other cutting-edge, current models as well as the baseline.
subject: Articles
  topic: section
subject: Modified alpha-power transformation
  topic: keywords
subject: Nadarajah-Haghighi
  topic: keywords
subject: characteristic function
  topic: keywords
subject: simulation study
  topic: keywords
subject: real data sets
  topic: keywords
creator: Tabassum Naz Sindhu
creator: Anum Shafiq
creator: Amirah Saeed Alharthi
creator: Tahani A. Abushal
creator: Alia A. Alkhathami
rights: Copyright (c) 2025 CSIAM Transactions on Applied Mathematics
date: 2025-12-17
publication date: 2025-12-17
starting page: 267
ending page: 295
doi: 10.4208/csiam-am.SO-2024-0057

Transport of Contaminant Release by Three Different Sources: A Medium with Complex Geometry
type: item
description: This study develops a mathematical model for contaminant transport from two industrial sources and one natural source through a heterogeneous aquifer featuring fracture networks with variable apertures, faults of heterogeneous width, and a complex rock matrix. Key innovations include: (1) A nonlinear Darcy’s law with concentration-dependent conductivity; (2) Three coupled advection-dispersion equations with nonlinear dispersion and reaction terms for multispecies interactions; (3) Seasonal recharge dynamics integrated into flow-transport coupling. Non-dimensional analysis reveals advection-dominated regimes governed by Péclet and Damköhler numbers. Bifurcation analysis identifies stability thresholds for ternary chemical reactions. Numerical solutions via the Crank-Nicolson scheme demonstrate fracture-controlled contaminant pathways and recharge-modulated plume evolution. The framework provides critical insights for pollution management in geologically complex aquifers.
subject: Articles
  topic: section
subject: Nonlinear groundwater flow
  topic: keywords
subject: nonlinear transport equation
  topic: keywords
subject: faults and fractures
  topic: keywords
subject: three species
  topic: keywords
creator: Abdon Atangana
rights: Copyright (c) 2025 CSIAM Transactions on Applied Mathematics
date: 2025-12-10
publication date: 2025-12-10
starting page: 329
ending page: 351
doi: 10.4208/csiam-am.SO-2025-0001

The Poisson-Garima Distribution: Additional Key Features and Its Significance on Statistical Process Control in Agriculture
type: item
description: This study primarily advances the theoretical development of the Poisson-Garima (PSNG) distribution by establishing several novel properties not previously addressed in existing literature. These theoretical enrichments enhance the model’s statistical foundation and extend its applicability to overdispersed count data commonly observed in fields such as agriculture, biology, and medicine. As a secondary contribution, the improved PSNG model is applied to statistical process control through the development of PSNG-based control charts for monitoring count data. The proposed charts are evaluated via simulation studies and validated with an empirical agricultural dataset, where their performance is benchmarked against eight competing models. Additionally, comparisons between PSNG- and Poisson-based control charts demonstrate the superiority of the proposed approach in detecting process shifts under overdispersion. This integrated approach reinforces the PSNG distribution’s theoretical depth while demonstrating its practical relevance in quality monitoring contexts.
subject: Articles
  topic: section
subject: Poisson-Garima distribution
  topic: keywords
subject: numerical result
  topic: keywords
subject: lifetime model
  topic: keywords
subject: simulation study
  topic: keywords
subject: statistical process control
  topic: keywords
subject: real data study
  topic: keywords
creator: Tabassum Naz Sindhu
creator: Anum Shafiq
creator: Tahani A. Abushal
creator: Alia A. Alkhathami
rights: Copyright (c) 2025 CSIAM Transactions on Applied Mathematics
date: 2025-12-10
publication date: 2025-12-10
starting page: 352
ending page: 382
doi: 10.4208/csiam-am.SO-2025-0010

Thermodynamics of Freshwater Production via CuS-Infused Porous Membrane Solar Absorber in Seawater Desalination
type: item
description: In our advanced modern world, ensuring the availability and access to freshwater resources remains a significant global challenge. Seawater desalination is viewed as one of the most promising solutions to address the increasing human demand for freshwater. This study theoretically examines the thermodynamics of a novel desalination system that integrates a copper sulfide (CuS) nanomaterial-porous membrane solar absorber for freshwater production. The governing partial differential equations for energy and mass balance in the model were derived from conservation laws and solved numerically using the method of lines. The impact of various parameters on steam temperature and freshwater production rate was analyzed in two scenarios: (i) under constant solar radiation flux in a controlled laboratory setting, and (ii) as a time-dependent function under typical daily solar radiation conditions. The pertinent results were presented graphically and discussed. It was found that the Nusselt number at the surface of the porous membrane solar absorber increases with the infusion of CuS nanomaterial. The desalination system reached a steady state with steam temperature, and the rate of freshwater production improved as the volume fraction of CuS nanomaterial in the porous membrane solar absorber increased. Additionally, an increase in steam generation and condensation Biot numbers further boosted the freshwater production rate.
subject: Articles
  topic: section
subject: Seawater desalination
  topic: keywords
subject: freshwater production
  topic: keywords
subject: selective porous solar absorber
  topic: keywords
subject: copper sulfide nanomaterial
  topic: keywords
subject: thermodynamics analysis
  topic: keywords
creator: A. E. Makinde
creator: O. D. Makinde
creator: M. Maaza
creator: T. Mokrani
rights: Copyright (c) 2025 CSIAM Transactions on Applied Mathematics
date: 2025-12-08
publication date: 2025-12-08
starting page: 383
ending page: 405
doi: 10.4208/csiam-am.SO-2025-0011

Superconvergence Points of Several Polynomial and Nonpolynomial Hermite Spectral Interpolations
type: item
description: In this paper, we analyze the superconvergence properties for spectral interpolations by Hermite polynomials and mapped Hermite functions. At the superconvergence points, the $(N−k)$-th term in the Hermite spectral interpolation remainder for the $(k+1)$-th derivatives vanish. To solve multi-point weakly singular nonlocal problems, we previously introduced mapped Hermite functions (MHFs), which are constructed by applying a mapping to the Hermite polynomials. We prove that the superconvergence points of the spectral interpolations based on MHFs for the $(k+1)$-th derivatives are the zero points of the $(N−k)$-th term. Additionally, due to the rapid growth of the logarithmic function at the endpoints 0 and 1, we further propose generalized mapped Hermite functions (GMHFs). We develop basic approximation theory for these new orthogonal functions and prove the projection error and interpolation error in the $L^2$-weighted space using the pseudo-derivative. We demonstrate that the superconvergence points of the spectral interpolations based on both MHFs and GMHFs for the $(k+1)$-th derivative are the zero points of the $(N−k)$-th term. Numerical experiments confirm our theoretical results.
subject: Articles
  topic: section
subject: Superconvergence points
  topic: keywords
subject: interpolation
  topic: keywords
subject: Hermite polynomials
  topic: keywords
subject: mapped Hermite functions
  topic: keywords
subject: generalized mapped Hermite functions
  topic: keywords
creator: Min Wang
creator: Zhimin Zhang
rights: Copyright (c) 2025 CSIAM Transactions on Applied Mathematics
date: 2026-01-25
publication date: 2026-01-25
starting page: 146
ending page: 177
doi: 10.4208/csiam-am.SO-2024-0046

An Efficient Iterative Convolution-Thresholding Method for Image Inpainting
type: item
description: Variational methods have been developed for image inpainting, which involve minimizing an objective functional consisting of the regularization term and the fidelity term. The fidelity term controls the consistency of the restored region with the original image, while the regularization term smooths the boundary of the region. In this paper, we develop an efficient iterative convolution-thresholding method to solve variational approach-based image inpainting problems. In the proposed method, the region is represented by its indicator function, and the regularization term is approximated by the heat kernel convolution with the indicator function. Based on this approximation, we derive an efficient iterative method to update the indicator function only within the damaged region by alternating the convolution and thresholding steps, relying on a relaxation and linearization procedure. Extensive numerical experiments demonstrate the simplicity and efficiency of the proposed method.
subject: Articles
  topic: section
subject: Iterative convolution-thresholding method
  topic: keywords
subject: heat kernel
  topic: keywords
subject: image inpainting
  topic: keywords
creator: Caixia Nan
creator: Zhonghua Qiao
creator: Dong Wang
rights: Copyright (c) 2025 CSIAM Transactions on Applied Mathematics
date: 2025-12-04
publication date: 2025-12-04
doi: 10.4208/csiam-am.SO-2024-0044

Double-Domain Driven Unet for Selective Segmentation of Medical Image
type: item
description: Selective segmentation has been a notable increase in interest in the use of interactive deep learning-based methods. However, developing an efficient and accurate segmentation method for medical applications remains a formidable challenge, primarily due to the inherent complexity and diversity of medical image structures. To address these challenges, we introduce a novel deep learning approach, termed the double-domain driven Unet method (DDUM), designed for the selective segmentation of medical images. Our approach utilizes a threshold geodesic distance in conjunction with the original images as input to construct a parallel Unet architecture that captures information from both the image domain and the geodesic distance domain. To further enhance the accuracy and efficacy of the segmentation process, we employ soft threshold dynamics as a replacement for the sigmoid activation function in the final layer. The efficacy of our proposed DDUM is substantiated through extensive experiments conducted on multiple medical image datasets. In particular, the DDUM method exhibits exceptional performance in terms of both segmentation accuracy and robustness.
subject: Articles
  topic: section
subject: Image segmentation
  topic: keywords
subject: regions of interest
  topic: keywords
subject: threshold geodesic distance
  topic: keywords
subject: double-domain driven Unet method
  topic: keywords
subject: soft threshold dynamics
  topic: keywords
creator: Zhi-Feng Pang
creator: Lin Yang
creator: Mingxiang Wu
creator: Ziyu Niu
creator: Raymond Chan
creator: Xue-Cheng Tai
rights: Copyright (c) 2025 CSIAM Transactions on Applied Mathematics
date: 2026-01-25
publication date: 2026-01-25
starting page: 178
ending page: 206
doi: 10.4208/csiam-am.SO-2024-0043

Assessment and Evaluation of Surface Water Quality and Human Health Risk in the Inkomati River Catchment Basin, South Africa
type: item
description: Multivariate statistical methods, dimensionality reduction, clustering techniques, water quality indices (WQIs) of the Canadian Council of Ministers of the Environment (CCME), comprehensive pollution index (CPI), and human health risk assessment indices for carcinogenic risk of heavy metals, using the hazard index (HI), are utilized in this work to assess the surface water quality of the Inkomati catchment. Six physicochemical parameters – ${\rm EC},$ ${\rm pH},$ ${\rm SO_4},$ ${\rm Fe},$ ${\rm Mn},$ and ${\rm Cu}$ were measured monthly from January 2015 to June 2019 from two sites Crocodile and Sabie rivers. The outcomes were compared to standard regulatory guidelines values. Recommended parameter values from US-EPA and peer-reviewed literature were used for the HI. The findings indicated that the river water was turbid and suffered from EC, specifically distressed due to trace metals. The US-WQI range (103.15-431.38) showed that the water quality level of the catchment was in the poor category but excellent during the winter. Water quality improved from marginal to good, according to the CCME-WQI scores, whereas the CPI scores (2.359-8.459) showed that the catchment’s water quality was in a very poor condition. The US-WQI suggested that the overall quality of the basin has declined in both the upper and lower portions. The hazard quotient through ingestion exposure did not exceed the threshold limit of 1 for children. This implies there is no potential carcinogenic health risk from trace elements via ingestion of drinking water for children. However, cancer risk for children was computed in relation to ${\rm Cu},$ ${\rm Fe},$ ${\rm Mn},$ and levels. It did not exceed the carcinogenic threshold limit of $10^{-4}$ for both sites.
subject: Articles
  topic: section
subject: Inkomati catchment
  topic: keywords
subject: river water quality
  topic: keywords
subject: water quality indices
  topic: keywords
subject: robust statistical techniques
  topic: keywords
subject: health risk assessment
  topic: keywords
creator: Ernestine Atangana
creator: Rodrigue G. Batogna
rights: Copyright (c) 2025 CSIAM Transactions on Applied Mathematics
date: 2025-12-04
publication date: 2025-12-04
starting page: 207
ending page: 235
doi: 10.4208/csiam-am.SO-2024-0060

Bifurcation and Crossover Processes in the Dynamics of a Marburg Haemorrhagic Fever Model
type: item
description: Just like Ebola disease, the Marburg virus disease (MVD) remains a constant threat to people’s live, not only in Africa, but also in the other parts of the globe. Recorded past outbreaks occurred in Europe, America and of course Africa, especially in places where inhabitants come into contact with wild animal products or live along-side wild animals such as apes, monkeys and fruit bats on a daily basis. Therefore, studying the dynamics of the Marburg virus and making some epidemiological assessments remain relevant and important in preventing future outbreaks. In this paper, we analyze a Marburg epidemic model in which the transmission is nonlinear. The well-posedness result is established as well as conditions for boundedness and dissipativity results. Then, we intensively analyze the stability of the Marburg model’s equilibria. The bifurcation dynamics indicate the existence of both transcritical (exchange of stability between the endemic equilibrium (EE) point and the disease free equilibrium (DFE)) and backward bifurcation where the classical epidemiological condition for the MVD to die out $(\mathcal{R}_0<1)$ is not sufficient anymore, but remains necessary. Lastly, some numerical simulations show convergence of the trajectories to both the EE and the DFE. Some adequate preventive measures are provided.
subject: Articles
  topic: section
subject: Marburg hemorrhagic fever model
  topic: keywords
subject: numerical solvability
  topic: keywords
subject: filovirus
  topic: keywords
subject: nonlinear incidence
  topic: keywords
subject: bifurcation
  topic: keywords
subject: crossover
  topic: keywords
subject: stability
  topic: keywords
creator: EF. Doungmo Goufo
creator: I. Tchangou Toudjeu
rights: Copyright (c) 2025 CSIAM Transactions on Applied Mathematics
date: 2025-12-01
publication date: 2025-12-01
starting page: 406
ending page: 432
doi: 10.4208/csiam-am.SO-2025-0014

Interface Laplace Learning: Learnable Interface Term Helps Semi-Supervised Learning
type: item
description: We introduce a novel framework, called Interface Laplace Learning, for graph-based semi-supervised learning. Motivated by the observation that an interface should exist between different classes where the function value is non-smooth, we propose a Laplace learning model that incorporates an interface term. This model challenges the long-standing assumption that functions are smooth at all unlabeled points. In the proposed approach, we add an interface term to the Laplace learning model at the interface positions. We provide a practical algorithm to approximate the interface positions using k-hop neighborhood indices, and to learn the interface term from labeled data without artificial design. Our method is efficient and effective, and we present extensive experiments demonstrating that Interface Laplace Learning achieves better performance than other recent semi-supervised learning approaches at extremely low label rates on the MNIST, FashionMNIST, and CIFAR-10 datasets.
subject: Articles
  topic: section
subject: Graph-based semi-supervised learning
  topic: keywords
subject: Laplace learning
  topic: keywords
subject: interface
  topic: keywords
subject: nonlocal model
  topic: keywords
creator: Tangjun Wang
creator: Chenglong Bao
creator: Zuoqiang Shi
rights: Copyright (c) 2025 CSIAM Transactions on Applied Mathematics
date: 2025-12-01
publication date: 2025-12-01
doi: 10.4208/csiam-am.SO-2024-0064

Error Estimates of Operator Splitting Spectral Method for Semiclassical Sub-Diffusive Gross-Pitaevskii Equation
type: item
description: Nonlinear Gross-Pitaevskii-type models are frequently seen in the fields of Bose-Einstein condensation and quantum mechanics. We derive error estimates for the Lie-Trotter operator splitting spectral method for semiclassical sub-diffusive Gross-Pitaevskii equation in the unbounded domain or with the periodic boundary condition. After establishing a priori estimates for the analytic solution in fractional Sobolev space, the local error estimates for the Lie-Trotter splitting operator method are derived. The related estimates for the Lie commutator of nonlocal linear operator and nonlinear operator play key roles in deriving the local error estimates. We then obtain the global error bounds for the fully discrete scheme based on the space approximation with mapped Chebyshev spectral-Galerkin methods in the case of the unbounded domain and with Fourier spectral methods in the case of the periodic boundary condition. Especially, their convergence orders with respect to the small (scaled) Planck constant $ε$ are obtained for the first time under the framework of Wentzel-Kramers-Brillouin analysis. Numerical experiments verify and complement our theoretical results.
subject: Articles
  topic: section
subject: Lie-Trotter operator splitting
  topic: keywords
subject: sub-diffusive Gross-Pitaevskii equation
  topic: keywords
subject: semiclassical regime
  topic: keywords
subject: error estimates
  topic: keywords
subject: mapped Chebyshev spectral-Galerkin methods
  topic: keywords
subject: Fourier spectral methods
  topic: keywords
creator: Wansheng Wang
creator: Yi Huang
creator: Yanming Zhang
rights: Copyright (c) 2025 CSIAM Transactions on Applied Mathematics
date: 2025-11-25
publication date: 2025-11-25
doi: 10.4208/csiam-am.SO-2024-0047

pETNNs: Partial Evolutionary Tensor Neural Networks for Solving Time-Dependent Partial Differential Equations
type: item
description: We present partial evolutionary tensor neural networks (pETNNs), a novel approach for solving time-dependent partial differential equations with high accuracy and capable of handling high-dimensional problems. Our architecture incorporates tensor neural networks and evolutionary parametric approximation. A posteriori error bound is proposed to support the extrapolation capabilities. In numerical implementations, we adopt a partial update strategy to achieve a significant reduction in computational cost while maintaining precision and robustness. Notably, as a low-rank approximation method of complex dynamical systems, pETNNs enhance the accuracy of evolutionary deep neural networks and empower computational abilities to address high-dimensional problems. Numerical experiments demonstrate the superior performance of the pETNNs in solving complex time-dependent equations, including the incompressible Navier-Stokes equations, high-dimensional heat equations, high-dimensional transport equations, and dispersive equations of higher-order derivatives.
subject: Articles
  topic: section
subject: Time-dependent partial differential equations
  topic: keywords
subject: tensor neural networks
  topic: keywords
subject: evolutionary deep neural networks
  topic: keywords
subject: high-dimensional problems.
  topic: keywords
subject: 65M99
  topic: subjects
subject: 65L05
  topic: subjects
subject: 68T07
  topic: subjects
creator: Tunan Kao
creator: He Zhang
creator: Lei Zhang
creator: Jin Zhao
rights: Copyright (c) 2025 COPYRIGHT: © Global Science Press
date: 2025-09-30
publication date: 2025-09-30
starting page: 862
ending page: 891
doi: 10.4208/csiam-am.SO-2024-0048

A Mathematical Analysis for the Dynamics of Multiple Languages
type: item
description: In many regions of the world, languages coexist in daily life, but often one tongue increases its use at the expense of another. In the present paper, we build a large compartmental system of differential equations that meets the situation of two “prestigious” tongues and many local languages, whose use is reduced by social interaction. The focus is on the preferred language in social relationships for communicating, rather than mere knowledge. We aim at stating and proving theorems on the qualitative behavior of the system. Numerical simulations illustrate the results, giving rise to distinct dynamics.
subject: Articles
  topic: section
subject: Language competition
  topic: keywords
subject: mathematical model
  topic: keywords
subject: dynamical system
  topic: keywords
subject: simulation.
  topic: keywords
subject: 34A34
  topic: subjects
subject: 37M05
  topic: subjects
subject: 91D10
  topic: subjects
creator: Iván Area
creator: Marc Jornet
rights: Copyright (c) 2025 COPYRIGHT: © Global Science Press
date: 2025-09-30
publication date: 2025-09-30
starting page: 842
ending page: 861
doi: 10.4208/csiam-am.SO-2024-0056

Global Solvability in a Two-Species Keller-Segel-Navier-Stokes System with Sub-Logistic Source
type: item
description: This paper is concerned with a two-species Keller-Segel-Navier-Stokes model with sub-logistic source in a bounded domain with smooth boundary under noflux/no-flux/no-flux/Dirichlet boundary conditions. For a large class of cell kinetics including sub-logistic degradation, it is shown that under an explicit condition involving the chemotactic strength and initial mass of cells, the two-dimensional Keller-Segel-Navier-Stokes problem possesses a global and bounded classical solution. In the case with arbitrary superlinear logistic degradation, it is proved that for all suitably regular initial data, the two-dimensional Keller-Segel-Navier-Stokes problem has at least one globally defined solution in an appropriate generalized sense. These results improves and extends the previously known ones.
subject: Articles
  topic: section
subject: Keller-Segel-Navier-Stokes
  topic: keywords
subject: sub-logistic source
  topic: keywords
subject: boundedness
  topic: keywords
subject: generalized solution.
  topic: keywords
subject: 35A09
  topic: subjects
subject: 35D30
  topic: subjects
subject: 35Q35
  topic: subjects
subject: 92C17
  topic: subjects
creator: Chao Liu
creator: Bin Liu
rights: Copyright (c) 2025 COPYRIGHT: © Global Science Press
date: 2025-09-30
publication date: 2025-09-30
starting page: 799
ending page: 841
doi: 10.4208/csiam-am.SO-2024-0016

An Efficient Iteration Based on Reduced Basis Method for Time-Dependent Problems with Random Inputs
type: item
description: In this paper, we propose an efficient iterative method called RB-iteration, based on reduced basis (RB) techniques, for addressing time-dependent problems with random input parameters. This method reformulates the original model such that the left-hand side is parameter-independent, while the right-hand side remains parameterdependent, facilitating the application of fixed-point iteration for solving the system. High-fidelity simulations for time-dependent problems often demand considerable computational resources, rendering them impractical for many applications. RB-iteration enhances computational efficiency by executing iterations in a reduced order space. This approach results in significant reductions in computational costs. We conduct a rigorous convergence analysis and present detailed numerical experiments for the RB-iteration method. Our results clearly demonstrate that RB-iteration achieves superior efficiency compared to the direct fixed-point iteration method and provides enhanced accuracy relative to the classical proper orthogonal decomposition (POD) greedy method.
subject: Articles
  topic: section
subject: Reduced order model
  topic: keywords
subject: time-dependent problems
  topic: keywords
subject: random inputs
  topic: keywords
subject: reduced basis
  topic: keywords
subject: iteration method.
  topic: keywords
subject: 35B30
  topic: subjects
subject: 65M12
  topic: subjects
subject: 65M50
  topic: subjects
subject: 65R20
  topic: subjects
subject: 76R99
  topic: subjects
subject: 78M34
  topic: subjects
creator: Dou Dai
creator: Qiuqi Li
creator: Huailing Song
rights: Copyright (c) 2025 COPYRIGHT: © Global Science Press
date: 2025-09-30
publication date: 2025-09-30
starting page: 760
ending page: 798
doi: 10.4208/csiam-am.SO-2024-0045

A Sharp Uniform-in-Time Error Estimate for Stochastic Gradient Langevin Dynamics
type: item
description: Abstract. We establish a sharp uniform-in-time error estimate for the stochastic gradient Langevin dynamics (SGLD), which is a widely-used sampling algorithm. Under mild assumptions, we obtain a uniform-in-time $\mathcal{O}(η^2)$ bound for the Kullback-Leibler divergence between the SGLD iteration and the Langevin diffusion, where $η$ is the step size (or learning rate). Our analysis is also valid for varying step sizes. Consequently, we are able to derive an $\mathcal{O}(\eta)$ bound for the distance between the invariant measures of the SGLD iteration and the Langevin diffusion, in terms of Wasserstein or total variation distances. Our result can be viewed as a significant improvement compared with existing analysis for SGLD in related literature.
subject: Articles
  topic: section
subject: Random batch
  topic: keywords
subject: Euler-Maruyama scheme
  topic: keywords
subject: Fokker-Planck equation
  topic: keywords
subject: log-Sobolev inequality.
  topic: keywords
subject: 65C20
  topic: subjects
subject: 68Q25
  topic: subjects
subject: 60H30
  topic: subjects
creator: Lei Li
creator: Yuliang Wang
rights: Copyright (c) 2025 COPYRIGHT: © Global Science Press
date: 2025-09-30
publication date: 2025-09-30
starting page: 711
ending page: 759
doi: 10.4208/csiam-am.SO-2024-0039

Two Methods Addressing Variable-Exponent Fractional Initial and Boundary Value Problems and Abel Integral Equation
type: item
description: Variable-exponent fractional models attract increasing attentions in various applications, while rigorous mathematical and numerical analysis for typical models remains largely untreated. This work provides general tools to address these models. Specifically, we first develop a convolution method to study the well-posedness, regularity, an inverse problem and numerical approximation for the subdiffusion of variable exponent. For models such as the variable-exponent two-sided space-fractional boundary value problem (including the variable-exponent fractional Laplacian equation as a special case) and the distributed variable-exponent model, for which the convolution method does not apply, we develop a perturbation method to prove their well-posedness. The relations between the convolution method and the perturbation method are discussed, and we further apply the latter to prove the well-posedness of the variable-exponent Abel integral equation and discuss the constraint on the data under different initial values of variable exponent.
subject: Articles
  topic: section
subject: Variable exponent
  topic: keywords
subject: fractional differential equation
  topic: keywords
subject: integral equation
  topic: keywords
subject: mathematical analysis
  topic: keywords
subject: numerical analysis.
  topic: keywords
subject: 35R11
  topic: subjects
subject: 45D05
  topic: subjects
subject: 65M12
  topic: subjects
creator: Xiangcheng Zheng
rights: Copyright (c) 2025 COPYRIGHT: © Global Science Press
date: 2025-09-30
publication date: 2025-09-30
starting page: 666
ending page: 710
doi: 10.4208/csiam-am.SO-2024-0052