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Volume 14
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Mathematics, Volume 14, Issue 6 (March-2 2026) – 162 articles

Cover Story (view full-size image): We propose a robust method for outlier detection in functional data analysis. This approach uses the robust Minimum Covariance Determinant estimator to compute the Mahalanobis distance applied to functional principal component scores. The main contribution of this research is the detection of outlier curves using the robust covariance matrix of functional principal components, in contrast to existing methods that use principal components on the discrete dataset. The proposed method is practical because it considers the entire functional form of the data, through their functional principal components, providing a comprehensive analysis that can detect anomalies across the entire functional range. A simulation study compares this approach with existing methods to evaluate their performance, followed by applications to El Niño Sea Surface Temperature data and SCImago Journal Rank data. View this paper
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24 pages, 399 KB  
Article
Branching Random Walks with Ageing
by Daniela Bertacchi, Elena Montanaro and Fabio Zucca
Mathematics 2026, 14(6), 1088; https://doi.org/10.3390/math14061088 - 23 Mar 2026
Viewed by 659
Abstract
Branching processes are stochastic models describing the evolution of populations in which individuals reproduce and die independently over time. In the classical setting, an individual’s reproductive capacity is fixed throughout its lifetime. However, in real-world situations, fertility typically rises during a juvenile phase, [...] Read more.
Branching processes are stochastic models describing the evolution of populations in which individuals reproduce and die independently over time. In the classical setting, an individual’s reproductive capacity is fixed throughout its lifetime. However, in real-world situations, fertility typically rises during a juvenile phase, peaks at maturity, and subsequently declines. In order to capture this feature, we introduce a branching random walk with ageing, as an extension of the classical branching random walk, by assigning each individual an age-dependent reproductive rate. Our model differs from classical age-dependent processes such as the Bellman–Harris model, where the remaining lifespan depends on age, while the rate of reproduction is fixed within that lifetime. As in the classical case, branching random walks with ageing are parametrised by λ>0, which tunes the reproductive speed and may be seen as a characteristic of the population. The thresholds of λ separating extinction and survival are the global and local critical parameters. We characterise the value of the local critical parameter and provide a lower bound for the global critical parameter. We identify a class of ageing branching random walks for which this lower bound coincides with the global critical parameter. We study how local modifications to the reproduction and ageing rates may change the critical parameters. This is of practical interest: in species preservation, one may want to lower the critical parameters, so that λ exceeds them, and there is a positive probability of survival. On the other hand, in epidemic control, the goal is to increase the critical parameters, since if λ is below them, then the epidemic is eventually going to disappear. We compute the expected number of individuals alive in a branching process with ageing and show that, contrary to the behaviour of classical branching processes, it may exhibit an initial growth even when the population is ultimately destined for extinction. Full article
(This article belongs to the Section D1: Probability and Statistics)
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17 pages, 436 KB  
Article
The Truncated EM Method of Jump Diffusions with Markovian Switching: A Case Study of Music Signals
by Ping Li, Ping Yu and Yuhang Zhen
Mathematics 2026, 14(6), 1087; https://doi.org/10.3390/math14061087 - 23 Mar 2026
Viewed by 456
Abstract
This paper investigates the strong convergence of jump-diffusion processes with Markovian switching using the truncated Euler–Maruyama (TEM) method. Under the assumption that the drift and diffusion coefficients satisfy a Khasminskii-type condition and the jump coefficient meets a linear growth condition, we derive the [...] Read more.
This paper investigates the strong convergence of jump-diffusion processes with Markovian switching using the truncated Euler–Maruyama (TEM) method. Under the assumption that the drift and diffusion coefficients satisfy a Khasminskii-type condition and the jump coefficient meets a linear growth condition, we derive the convergence rate. Furthermore, we demonstrate that the TEM method effectively preserves both the mean square stability and the asymptotic boundedness of the underlying jump-diffusion process. A case study involving music signals is provided to illustrate the theoretical findings. Full article
(This article belongs to the Section D1: Probability and Statistics)
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16 pages, 301 KB  
Article
Positive Solutions for Nabla Fractional Three-Point Boundary Value Problems
by Nikolay D. Dimitrov and Jagan Mohan Jonnalagadda
Mathematics 2026, 14(6), 1086; https://doi.org/10.3390/math14061086 - 23 Mar 2026
Cited by 2 | Viewed by 452
Abstract
The aim of the present work is to study a class of nabla fractional problems with two different nabla Riemann–Liouville operators and three-point parameter-dependent boundary conditions. First, we derive the expression of the Green’s function; then, we deduce a few useful inequalities with [...] Read more.
The aim of the present work is to study a class of nabla fractional problems with two different nabla Riemann–Liouville operators and three-point parameter-dependent boundary conditions. First, we derive the expression of the Green’s function; then, we deduce a few useful inequalities with it, and we establish an interval for the parameter in which the Green’s function is always positive. Using these properties, we manage to prove some non-existence, existence and multiplicity results using different fixed-point theorems. At the end, we give a few examples that verify and clarify the applications of our results. Full article
(This article belongs to the Section C1: Difference and Differential Equations)
19 pages, 932 KB  
Article
Stability-Enhanced Pseudo-Multiview Learning via Multiscale Grid Feature Extraction
by Dat Ngo
Mathematics 2026, 14(6), 1085; https://doi.org/10.3390/math14061085 - 23 Mar 2026
Viewed by 490
Abstract
Pseudo-multiview learning improves classification by integrating complementary feature representations, but its performance degrades as the number of psuedo-views increases due to model collapse and ineffective feature scaling. This paper introduces a multiscale grid architecture that extracts structured, scale-adaptive features to stabilize evidence aggregation [...] Read more.
Pseudo-multiview learning improves classification by integrating complementary feature representations, but its performance degrades as the number of psuedo-views increases due to model collapse and ineffective feature scaling. This paper introduces a multiscale grid architecture that extracts structured, scale-adaptive features to stabilize evidence aggregation in pseudo-multiview learning. The proposed design enables efficient handling of difficult classification scenarios by enforcing balanced multiscale representation and reducing redundancy across psuedo-views. Extensive experiments on challenging real-world datasets, including BreakHis (40×, 100×, 200×, 400×), Oxford-IIIT Pet, and Chest X-ray, demonstrate consistent gains in accuracy and stability over the original pseudo-multiview framework and other baseline models. The results confirm that grid-based multiscale feature extraction provides a reliable means to enhance pseudo-multiview learning, particularly in settings where prior methods struggled to generalize. Full article
(This article belongs to the Special Issue Machine Learning Applications in Image Processing and Computer Vision)
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11 pages, 235 KB  
Article
Formal Ordinal Sums of Triangular Norms on Modular Lattices
by Yang Luo
Mathematics 2026, 14(6), 1084; https://doi.org/10.3390/math14061084 - 23 Mar 2026
Viewed by 459
Abstract
The formal ordinal sums of t-norms on the bounded lattice is defined by Saminger, but the formal ordinal sum need not be a t-norm. Hence, she provides a necessary and sufficient condition such that the formal ordinal sum is a t-norm indeed. In [...] Read more.
The formal ordinal sums of t-norms on the bounded lattice is defined by Saminger, but the formal ordinal sum need not be a t-norm. Hence, she provides a necessary and sufficient condition such that the formal ordinal sum is a t-norm indeed. In this paper, we first give several conditions that are equivalent to Saminger’s condition. Secondly, we prove that there is a largest sublattice containing all the pairwise non-overlapped subintervals such that the formal ordinal sum is a t-norm on this sublattice when the bounded lattice is modular. Full article
(This article belongs to the Section E1: Mathematics and Computer Science)
8 pages, 238 KB  
Article
Construction and Study of a Probabilistic Model for the Sliding Mode Along and Across the Slip Line
by Gurami Tsitsiashvili
Mathematics 2026, 14(6), 1083; https://doi.org/10.3390/math14061083 - 23 Mar 2026
Viewed by 410
Abstract
In this paper, we construct a probabilistic model of a sliding mode. This model is based on the moment a random walk with positive jumps crosses a certain critical level. It is assumed that the jump magnitude has a geometric distribution. If the [...] Read more.
In this paper, we construct a probabilistic model of a sliding mode. This model is based on the moment a random walk with positive jumps crosses a certain critical level. It is assumed that the jump magnitude has a geometric distribution. If the initial state is negative and the critical level is zero, then after crossing this level, a random walk begins in the opposite direction until it crosses zero again. As a result, motion orthogonal to the slip line is defined as a regenerative process, in which the moments of regeneration are the moments of zero crossings from right to left. An estimate of the Qi Fan metric of the maximum deviation of this random walk over a certain time interval is constructed under the assumption that the time and magnitude of the jumps are reduced by a factor of m. This estimate is found to be of the order of lnm/m as m→∞ and characterizes the deviation of a random trajectory orthogonal to the slip line. In the model of motion along a slip line, its velocity is assumed to have fixed values when the trajectory of motion orthogonal to the slip line is above or below zero. Using the central limit theorem for the integral of a regenerative process, an estimate of the non-uniformity of motion of a random trajectory along the slip line is constructed. It is found that the characteristic magnitude of this non-uniformity is of the order of 1/m as m→∞. This indicates that the accumulation of random errors during motion along the slip line is significantly faster than during motion orthogonal to the slip line. Full article
(This article belongs to the Special Issue Optimization and Control of Complex Engineering Systems: Mathematical Approaches)
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28 pages, 2584 KB  
Article
Improving Cross-Domain Generalization in Brain MRIs via Feature Space Stability Regularization
by Shawon Chakrabarty Kakon, Harishik Dev Singh Jamwal and Saurabh Singh
Mathematics 2026, 14(6), 1082; https://doi.org/10.3390/math14061082 - 23 Mar 2026
Cited by 2 | Viewed by 1590
Abstract
Deep learning models for brain tumor classification from magnetic resonance imaging (MRI) often achieve high in-dataset accuracy but exhibit substantial performance degradation when evaluated on unseen clinical data due to domain shift arising from variations in imaging protocols and intensity distributions. Existing approaches [...] Read more.
Deep learning models for brain tumor classification from magnetic resonance imaging (MRI) often achieve high in-dataset accuracy but exhibit substantial performance degradation when evaluated on unseen clinical data due to domain shift arising from variations in imaging protocols and intensity distributions. Existing approaches largely rely on architectural scaling or parameter-level regularization, which do not explicitly constrain the stability of learned feature representations. This manuscript proposes Feature Space Stability Regularization (FSSR), a lightweight and model-agnostic training framework that enforces consistency in latent feature representations under realistic, MRI-safe-intensity perturbations. FSSR introduces an auxiliary feature space loss that minimizes the ℓ2 distance between normalized embeddings extracted from the input MRI images and their intensity-perturbed counterparts, alongside standard cross-entropy supervision. This manuscript evaluated FSSR across three convolutional backbones, ResNet-18, ResNet-34, and DenseNet-121, trained exclusively on the Kaggle Brain MRI dataset. Feature space analysis demonstrates that FSSR consistently reduces mean feature deviation and variance across architectures, indicating more stable internal representations. Generalization is assessed via zero-shot evaluation on the fully unseen BRISC-2025 dataset without retraining or fine-tuning. On the source domain, the best-performing configuration achieves 97.71% accuracy and 97.55% macro-F1. Under domain shift, FSSR improves external accuracy by up to 8.20 percentage points and the macro-F1 by up to 12.50 percentage points, with DenseNet-121 achieving a 96.70% accuracy and 96.87% macro-F1 at a domain gap of only 0.94%. Confusion matrix analysis further reveals the reduced class confusion and more stable recall across challenging tumor categories, demonstrating that feature-level stability is a key factor for robust brain MRI classification under domain shift. Full article
(This article belongs to the Special Issue Recent Advances in Machine Learning Methods for Medical Imaging Analysis)
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20 pages, 578 KB  
Article
Event-Triggered Synchronization of T-S Fuzzy Neural Network with Quantized Encoding–Decoding Mechanism
by Yuanzheng Tan, Xinyu Yuan, Yang Yang, Lechao Wang and Yushun Tan
Mathematics 2026, 14(6), 1081; https://doi.org/10.3390/math14061081 - 23 Mar 2026
Viewed by 493
Abstract
This paper investigates dynamic event-triggered control (DETC) and encoding–decoding schemes to achieve the synchronization of T-S fuzzy neural networks (FNNs). DETC allows the transmission signals to be controlled aperiodically during the actual operation of the system, enabling a rapid response to practical control [...] Read more.
This paper investigates dynamic event-triggered control (DETC) and encoding–decoding schemes to achieve the synchronization of T-S fuzzy neural networks (FNNs). DETC allows the transmission signals to be controlled aperiodically during the actual operation of the system, enabling a rapid response to practical control tasks. Meanwhile, during the event-triggered control process, an encoding–decoding scheme with externally injected noise is used to protect the signals. First, a dynamic event-triggered control mechanism is established, and an encoding–decoding scheme is used to optimize the transmission of controller signals. Subsequently, the Lyapunov–Krasovskii functional is constructed to derive the system’s synchronization criteria and calculate the controller gains. Finally, numerical simulation experiments are conducted to verify the effectiveness and feasibility of the proposed method. Full article
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35 pages, 585 KB  
Article
On Devising Carbon Offset Investments by Multiple-Objective Portfolio Selection and Exploring Multiple-Objective Capital Asset Pricing Models
by Yue Qi, Jianing Huang, Zhujun Qi and Yingying Li
Mathematics 2026, 14(6), 1080; https://doi.org/10.3390/math14061080 - 23 Mar 2026
Cited by 1 | Viewed by 633
Abstract
Humans face environmental deterioration. Scholars have identified carbon dioxide as one of the culprits, and they emphasize carbon offset. Researchers are investigating carbon offset investments. Some researchers have encouragingly deployed multivariate variational mode decomposition methods, but they have not fully optimized them. Some [...] Read more.
Humans face environmental deterioration. Scholars have identified carbon dioxide as one of the culprits, and they emphasize carbon offset. Researchers are investigating carbon offset investments. Some researchers have encouragingly deployed multivariate variational mode decomposition methods, but they have not fully optimized them. Some researchers have opportunely assessed capital asset pricing models, but they have not fully justified them. We devise multiple-objective portfolio selection models, fully optimize them, and dominate carbon offset indexes. We extend the classical methodology of advancing from portfolio selection to capital asset pricing models into the methodology of advancing from multiple-objective portfolio selection to multiple-objective capital asset pricing models. Specifically, we explore multiple-objective capital asset pricing models by numerically verifying many tangent lines (instead of the traditionally singular tangent line) and suggesting a tangent plane (instead of tangent lines). For multiple-objective zero-covariance capital asset pricing models, we numerically compute a set of zero-covariance portfolios (instead of the traditionally singular zero-covariance portfolio) and suggest picking an advantageous zero-covariance portfolio. We consider the second-level indicators of carbon offset and generalize three-objective portfolio selection to k-objective portfolio selection. As for contributions, first, this paper’s methodology is to logically advance from multiple-objective portfolio selection to multiple-objective capital asset pricing models, whereas the literature typically covers multiple-objective portfolio selection alone and barely covers multiple-objective capital asset pricing models. Second, this paper numerically demonstrates some difficulties and proposes hypothetical solutions in the process of obtaining multiple-objective capital asset pricing models. Full article
(This article belongs to the Special Issue Application of Multiple Criteria Decision Analysis)
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26 pages, 659 KB  
Article
Stability and Direction of Hopf Bifurcation with Optimal Control Analysis of HIV Transmission Dynamics
by Ibraheem M. Alsulami and Fahad Al Basir
Mathematics 2026, 14(6), 1079; https://doi.org/10.3390/math14061079 - 23 Mar 2026
Cited by 1 | Viewed by 695
Abstract
In this study, we examine the effectiveness of combining interleukin-2 (IL-2) with highly active antiretroviral therapy (HAART) in controlling HIV replication. A mathematical model of the immune system is developed to analyze immune recovery when IL-2 is administered alongside HAART. We investigate the [...] Read more.
In this study, we examine the effectiveness of combining interleukin-2 (IL-2) with highly active antiretroviral therapy (HAART) in controlling HIV replication. A mathematical model of the immune system is developed to analyze immune recovery when IL-2 is administered alongside HAART. We investigate the stability of the endemic equilibrium and Hopf bifurcation and determine the direction and stability of periodic solutions using center manifold theory. Numerical simulations are conducted to support the theoretical findings. The results show that the disease-free equilibrium is stable when the basic reproduction number R0<1, while the endemic equilibrium exists when R0>1. Our results also reveal the presence of a subcritical Hopf bifurcation in the system. An optimal control problem is also studied, showing that the combined therapy of IL-2 and HAART improves treatment outcomes, reduces side effects, and has a unique optimal control pair. Sensitivity analysis further highlights the importance of system parameters in influencing treatment effectiveness. Full article
(This article belongs to the Topic Modeling, Stability, and Control of Dynamic Systems and Their Applications)
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26 pages, 621 KB  
Article
Co-Evolutionary Proximal Distilled Evolutionary Reinforcement Learning with Gated Knowledge Transfer
by Ying Zhao, Yi Ding and Yinglong Dai
Mathematics 2026, 14(6), 1078; https://doi.org/10.3390/math14061078 - 23 Mar 2026
Viewed by 903
Abstract
Evolutionary reinforcement learning (ERL) offers a compelling alternative for continuous control by combining the population-level exploration of evolutionary algorithms with the gradient-based exploitation of reinforcement learning. However, applying conventional genetic operators to deep networks can be highly destructive, often inducing abrupt behavioral shifts [...] Read more.
Evolutionary reinforcement learning (ERL) offers a compelling alternative for continuous control by combining the population-level exploration of evolutionary algorithms with the gradient-based exploitation of reinforcement learning. However, applying conventional genetic operators to deep networks can be highly destructive, often inducing abrupt behavioral shifts that erase previously learned skills. Proximal distilled evolutionary reinforcement learning (PDERL) addresses this issue with phenotype-aware operators, leveraging proximal mutation and distillation crossover to produce safer and more constructive variations. Despite these advances, PDERL and many ERL frameworks still exhibit a fundamental evaluation asymmetry: an evolving actor population is guided by a single, centralized critic for fitness evaluation and action filtering. This single-critic dependence creates a bottleneck and a potential single point of failure, where bias or instability in value estimation can misdirect the evolutionary search. To overcome this limitation, we propose co-evolutionary proximal distilled evolutionary reinforcement learning (Co-PDERL), a heterogeneous dual-population framework that co-evolves both actor and critic populations. Co-PDERL extends phenotype-aware evolution to the value-function landscape via a loss-filtered distillation crossover and a Jacobian-based proximal mutation tailored for critics, and employs a condition-gated synchronization mechanism to enable robust bidirectional knowledge transfer between the evolutionary populations and the reinforcement learning agent. Experiments on MuJoCo continuous control benchmarks show that Co-PDERL outperforms competitive baselines on most tasks, including standard ERL and PDERL, improving both sample efficiency and asymptotic performance by effectively alleviating the single-critic bottleneck. Full article
(This article belongs to the Special Issue Algorithmic Advances in Reinforcement Learning: Theory and Applications)
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20 pages, 561 KB  
Article
Hybrid NN–ODE Modeling of Fossil Fuel Competition
by Dimitris Kastoris, Dimitris Papadopoulos and Kostas Giotopoulos
Mathematics 2026, 14(6), 1077; https://doi.org/10.3390/math14061077 - 22 Mar 2026
Viewed by 612
Abstract
Europe’s fossil-based electricity mix has shifted rapidly in recent years, raising a practical question: can we model competitive substitution among fuels with a framework that is both predictive and interpretable? We address this by combining a compact neural network (NN) with a three-dimensional [...] Read more.
Europe’s fossil-based electricity mix has shifted rapidly in recent years, raising a practical question: can we model competitive substitution among fuels with a framework that is both predictive and interpretable? We address this by combining a compact neural network (NN) with a three-dimensional Lotka–Volterra (LV) system to study monthly EU coal, natural gas, and oil-fired generation shares from the second semester of 2017 to 2023. After converting the series to row-wise shares that sum to one, we use the first 70% of the sample to learn smooth trajectories and data-driven derivatives with the NN and then estimate the LV interaction coefficients through a constrained nonlinear fit. We advance the calibrated LV system over the final 30% holdout with a fourth-order Runge–Kutta (RK4) scheme and evaluate forecasts using the RMSE and MAE for each fuel share series. For comparison, we report the results against both a neural network-only forecasting baseline and a classical ARIMA benchmark, both trained on the same 70% window and evaluated on the same 30% holdout. The hybrid NN–LV model achieves competitive forecast errors while yielding interpretable interaction patterns consistent with substitution pressures (for example, negative cross-effects between coal and gas). Finally, we run counterfactual shock experiments to illustrate how a change in one fuel’s share propagates through the mix under the learned LV dynamics, highlighting the usefulness of embedding a simple mechanistic structure within a data-driven estimator. Full article
(This article belongs to the Section C1: Difference and Differential Equations)
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31 pages, 629 KB  
Article
The One-Parameter Bounded p-Exponential Distribution: Properties, Inference, and Applications
by Hassan S. Bakouch, Hugo S. Salinas, Fernando A. Moala, Tassaddaq Hussain, Shaykhah Aldossari and Alanwood Al-Buainain
Mathematics 2026, 14(6), 1076; https://doi.org/10.3390/math14061076 - 22 Mar 2026
Viewed by 903
Abstract
We introduce the one-parameter bounded p-exponential distribution on (0, p+1), which includes the uniform model as a special case and converges pointwise to the exponential law as p→∞. Closed-form expressions are derived [...] Read more.
We introduce the one-parameter bounded p-exponential distribution on (0, p+1), which includes the uniform model as a special case and converges pointwise to the exponential law as p→∞. Closed-form expressions are derived for the CDF and PDF, the survival function, an explicit increasing-failure-rate hazard function, the quantile function (enabling inversion-based simulation), moments, and entropy, along with a constructive scaled beta or Kumaraswamy representation. We also establish stochastic ordering with respect to p in stop-loss and increasing convex order, formalizing how dispersion varies with the parameter while preserving the mean scale. Inference is discussed under parameter-dependent support, a non-regular setting, and we develop and compare several estimation procedures, including a likelihood-based boundary MLE, a variance-matching method-of-moments estimator, and Bayesian estimation under a gamma prior implemented via numerical quadrature or MCMC. Monte Carlo simulation studies evaluate finite-sample performance and interval behavior, and two real-world applications in survival and reliability analysis illustrate competitive goodness-of-fit relative to standard benchmark models. Full article
(This article belongs to the Special Issue New Advances in Mathematical Applications for Reliability Analysis)
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22 pages, 7851 KB  
Article
Sharp Coefficient Estimates for Analytic Functions Subordinate to the Cusp Domain: Theory and Image Processing Applications
by Mohammad El-Ityan, Adel Salim Tayyah, Mohammed Hamzah Alsalihi, Basem Aref Frasin and Alina Alb Lupaş
Mathematics 2026, 14(6), 1075; https://doi.org/10.3390/math14061075 - 22 Mar 2026
Cited by 2 | Viewed by 752
Abstract
This article proposes a new type of analytic function called Mtan and introduces a new geometric structure that blends exponential and trigonometric properties. In addition, it obtains exact bounds for all second- and third-order Hankel determinants and establishes extremal results for the [...] Read more.
This article proposes a new type of analytic function called Mtan and introduces a new geometric structure that blends exponential and trigonometric properties. In addition, it obtains exact bounds for all second- and third-order Hankel determinants and establishes extremal results for the Fekete–Szegö and Zalcman functionals. Moreover, it discusses the validity of the Krushkal inequality. Furthermore, it applies the developed methodology to improve the contrast and quality of color images and demonstrates that the proposed enhancement filters yield notable improvements in contrast and quality compared to other filters, based on the PSNR, SSIM, MSE, RMSE, PCC, and MAE metrics. This article demonstrates its dual nature, namely advances in geometric function theory and practical advantages in digital image processing. Full article
(This article belongs to the Section C4: Complex Analysis)
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23 pages, 1030 KB  
Article
Skewness and Kurtosis of mRNA Distributions in Stochastic Gene Transcription with Promoter Switching
by Shumin Tan, Wangyang Wu and Qiwen Sun
Mathematics 2026, 14(6), 1074; https://doi.org/10.3390/math14061074 - 22 Mar 2026
Cited by 1 | Viewed by 661
Abstract
Gene transcription is inherently stochastic, and promoter-switching-induced transcriptional bursting generates substantial cell-to-cell variability in mRNA abundance. Such variability is commonly characterized by the mean and variance; however, these low-order statistics fail to capture the geometric features of mRNA copy number distributions and may [...] Read more.
Gene transcription is inherently stochastic, and promoter-switching-induced transcriptional bursting generates substantial cell-to-cell variability in mRNA abundance. Such variability is commonly characterized by the mean and variance; however, these low-order statistics fail to capture the geometric features of mRNA copy number distributions and may obscure mechanistic differences in promoter dynamics. In this work, we analyze a two-state stochastic gene transcription model and derive explicit analytical expressions for higher-order moments of mRNA abundance. We show that skewness and kurtosis provide mechanistically informative signatures of transcriptional bursting, explicitly depending on promoter switching kinetics and burst size. Our results demonstrate that distinct promoter dynamics can produce identical mean expression levels and variances while exhibiting markedly different skewness and kurtosis. The explicit analytical expressions derived here reveal how higher-order moments encode mechanistically informative signatures of transcriptional bursting through distributional asymmetry and heavy-tailed behavior. These results demonstrate that higher-order moments encode mechanistic information beyond mean–variance statistics and provide a powerful framework for distinguishing between different promoter-switching mechanisms in stochastic gene transcription. Full article
(This article belongs to the Special Issue Advances in Functional Differential Equations and Their Stochastic Versions: Theory, Numerics, and Applications)
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22 pages, 3231 KB  
Article
A Unified Framework for Identification, Estimation, and Control of an Experimental Duffing–Holmes System
by Antonio Concha-Sánchez, Ulises Mondragón-Cárdenas, Suresh Thenozhi, Juan Luis Mata-Machuca and Suresh Kumar Gadi
Mathematics 2026, 14(6), 1073; https://doi.org/10.3390/math14061073 - 22 Mar 2026
Viewed by 470
Abstract
This paper presents a comprehensive framework for the identification, state estimation, and robust control of a bistable Duffing–Holmes oscillator, validated through an experimental setup. First, to address parametric uncertainty, a Recursive Least Squares Method (RLSM) with a forgetting factor is applied to a [...] Read more.
This paper presents a comprehensive framework for the identification, state estimation, and robust control of a bistable Duffing–Holmes oscillator, validated through an experimental setup. First, to address parametric uncertainty, a Recursive Least Squares Method (RLSM) with a forgetting factor is applied to a filtered model representation, enabling accurate parameter convergence from noisy measurements. Subsequently, a Nonlinear Integral Extended State Observer (NIESO) is designed to reconstruct unmeasured states and estimate total disturbances. A key theoretical contribution is the derivation of explicit gain conditions that guarantee the observer’s stability, overcoming limitations of previous designs. For trajectory tracking, an observer-based backstepping controller is synthesized. Crucially, to bridge the gap between theory and practice, a drift-free integration scheme is implemented to generate feasible position commands for the shake table, preventing actuator saturation. Experimental results confirm the framework’s effectiveness, achieving a 3.7-fold reduction in RMS tracking error compared to open-loop operation, with the tracking error rapidly converging to a small neighborhood within approximately 0.2 s. Furthermore, the closed-loop system demonstrates superior energy efficiency, requiring significantly lower actuator voltage to sustain stable interwell oscillations. Full article
(This article belongs to the Special Issue Nonlinear Dynamics and Control Theory)
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37 pages, 2886 KB  
Article
A Zero-Touch Vulnerability Remediation Framework Based on OpenVAS, Threat Intelligence, and RAG-Enhanced Large Language Models
by Cheng-Hui Hsieh, Chen-Yi Cheng and Yung-Chung Wang
Mathematics 2026, 14(6), 1072; https://doi.org/10.3390/math14061072 - 22 Mar 2026
Viewed by 2647
Abstract
Vulnerability disclosures are outpacing manual remediation capacity. We present a Zero-Touch Vulnerability Remediation Framework combining OpenVAS scanning, multi-source threat intelligence, and Large Language Models (LLMs) enhanced through Retrieval-Augmented Generation (RAG). The Scanning Layer normalizes findings into structured JSON; the AI Decision Layer applies [...] Read more.
Vulnerability disclosures are outpacing manual remediation capacity. We present a Zero-Touch Vulnerability Remediation Framework combining OpenVAS scanning, multi-source threat intelligence, and Large Language Models (LLMs) enhanced through Retrieval-Augmented Generation (RAG). The Scanning Layer normalizes findings into structured JSON; the AI Decision Layer applies hybrid FAISS + BM25 retrieval, dual-LLM verification (a primary generator checked by a gpt-4o auxiliary verifier), and confidence-based routing; the Orchestration Layer executes validated patches via CI/CD pipelines with automated rollback. On 350 real-world vulnerability cases across five GPT-family models, the full Prompt + RAG pipeline raised accuracy from 52.0% to 76.7–82.6% (all p < 0.001, Cohen’s h = 0.51–0.68) and reduced hallucination from 23.4% to 7.8%. Confidence routing routed 34.9% of cases to the high-confidence auto-execution tier, yielding a 4.1% rollback rate and zero service outages. The framework addresses the most relevant categories of the OWASP LLM Top 10 and lays groundwork for enterprise-scale, Zero-Touch vulnerability management. Full article
(This article belongs to the Section E1: Mathematics and Computer Science)
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34 pages, 852 KB  
Article
Equivalence of Doubly Periodic Tangles
by Ioannis Diamantis, Sofia Lambropoulou and Sonia Mahmoudi
Mathematics 2026, 14(6), 1071; https://doi.org/10.3390/math14061071 - 22 Mar 2026
Cited by 2 | Viewed by 716
Abstract
Doubly periodic tangles, or DP tangles, are embeddings of curves in the thickened plane that are periodically repeated in two directions. They are defined as universal covers of their generating cells, the flat motifs, which represent knots and links in the [...] Read more.
Doubly periodic tangles, or DP tangles, are embeddings of curves in the thickened plane that are periodically repeated in two directions. They are defined as universal covers of their generating cells, the flat motifs, which represent knots and links in the thickened torus, and which can be chosen in infinitely many ways. DP tangles are used in modeling materials and physical systems of entangled filaments. In this paper, we establish the complete mathematical framework of the topological theory of DP tangles. We present an exhaustive analysis of DP tangle isotopies. These are distinguished in local isotopies and global isotopies. Our analysis yields the characterization of DP isotopy as an equivalence relation on the level of their (flat) motifs, called DP tangle equivalence. Along the way, we also discuss motif minimality. We further generalize our results to other diagrammatic categories, namely framed, virtual, welded, singular, pseudo, tied and bonded DP tangles, which could be used in novel applications. Full article
(This article belongs to the Special Issue Mathematical Modeling of Complex Entangled Structures)
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12 pages, 257 KB  
Article
Efficient Solution of DC-Type Vector Optimization via Abstract Convex Analysis
by Ruimin Gao and Chaoli Yao
Mathematics 2026, 14(6), 1070; https://doi.org/10.3390/math14061070 - 22 Mar 2026
Viewed by 438
Abstract
The concept of vector topical functions, which take values in a partially ordered Banach space endowed with a complete lattice structure, was introduced in our preceding study. This structure enabled the development of an abstract convexity theory for vector topical functions, utilizing the [...] Read more.
The concept of vector topical functions, which take values in a partially ordered Banach space endowed with a complete lattice structure, was introduced in our preceding study. This structure enabled the development of an abstract convexity theory for vector topical functions, utilizing the notion of vector support. In this paper, applying these abstract convex theories, a DC-type vector optimization is investigated. Using the idea of a slack, the support set of a vector-valued map can be fully characterized by the subdifferential in abstract convex sense. Then, with the aid of this result, a sufficient condition to detect the efficient solutions for the DC-type vector optimization is obtained. In addition, a dual problem for the DC optimization is proposed, for which some strong dual results are established. Full article
(This article belongs to the Special Issue Nonlinear Functional Analysis: Theory, Methods, and Applications)
16 pages, 1318 KB  
Article
A Wright-Based Generalization of the Euler Beta Function with Statistical Applications
by Layth T. Khudhuir, Hiba F. Al-Janaby, Firas Ghanim and Alina Alb Lupaș
Mathematics 2026, 14(6), 1069; https://doi.org/10.3390/math14061069 - 21 Mar 2026
Viewed by 589
Abstract
In recent years, special function theory has played an increasingly important role in the development of advanced mathematical models and statistical distributions. In this paper, a new extension of the Euler Beta function is introduced by employing the Wright function as a kernel, [...] Read more.
In recent years, special function theory has played an increasingly important role in the development of advanced mathematical models and statistical distributions. In this paper, a new extension of the Euler Beta function is introduced by employing the Wright function as a kernel, leading to the formulation of the Beta–Wright function. Several fundamental properties of the proposed function are systematically investigated, including summation formulas, functional relations, Mellin transforms, integral representations, and derivative formulas. Furthermore, extended forms of Gauss and confluent hypergeometric functions are constructed within this framework. In addition to its theoretical significance, the proposed function is applied to statistical modeling, and the associated distributions are analyzed using graphical and analytical techniques. The obtained results demonstrate that the Beta–Wright function provides a flexible and effective tool for both analytical investigations and statistical applications. Full article
(This article belongs to the Special Issue Current Topics in Geometric Function Theory, 2nd Edition)
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19 pages, 13660 KB  
Article
CA-GFNet: A Cross-Modal Adaptive Gated Fusion Network for Facial Emotion Recognition
by Sitara Afzal and Jong-Ha Lee
Mathematics 2026, 14(6), 1068; https://doi.org/10.3390/math14061068 - 21 Mar 2026
Viewed by 769
Abstract
Facial emotion recognition (FER) plays an important role in healthcare, human–computer interaction, and intelligent security systems. However, despite recent advances, many state-of-the-art FER methods depend on computationally intensive CNN or transformer backbones and large-scale annotated datasets while suffering noticeable performance degradation under cross-dataset [...] Read more.
Facial emotion recognition (FER) plays an important role in healthcare, human–computer interaction, and intelligent security systems. However, despite recent advances, many state-of-the-art FER methods depend on computationally intensive CNN or transformer backbones and large-scale annotated datasets while suffering noticeable performance degradation under cross-dataset evaluation because of domain shift. These limitations hinder practical usage in resource-constrained and real-world environments. To address this issue, we propose Cross-Adaptive Gated Fusion Network (CA-GFNet), a lightweight dual-stream FER framework that explicitly combines shallow structural features with deep semantic representations. The proposed architecture integrates domain-robust gradient-based descriptors with compact deep features extracted from a VGG-based backbone. After face detection and normalization, the structural stream captures fine-grained local appearance cues, whereas the semantic stream encodes high-level facial configurations. The two feature streams are projected into a shared latent space and adaptively fused using a gated fusion mechanism that learns sample-specific weights, allowing the model to prioritize the more reliable feature source under dataset shift. Extensive experiments on KDEF along with zero-shot cross-dataset evaluation on CK+ using a strict train-on-KDEF/test-on-CK+ protocol with subject-independent splits demonstrate the effectiveness of the proposed method. CA-GFNet achieves 99.30% accuracy on KDEF and 98.98% on CK+ while requiring significantly fewer parameters than conventional deep FER models. These results confirm that adaptive gated fusion of shallow and deep features can deliver both high recognition accuracy and strong cross-dataset robustness. Full article
(This article belongs to the Special Issue Advanced Algorithms in Multimodal Affective Computing)
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29 pages, 1953 KB  
Article
JDC-DA: An Unsupervised Target Domain Algorithm for Alzheimer’s Disease Diagnosis with Structural MRI Using Joint Domain and Category Dual Adaptation
by Yuan Sui, Yujie Zhang, Ying Wei and Gang Yang
Mathematics 2026, 14(6), 1067; https://doi.org/10.3390/math14061067 - 21 Mar 2026
Viewed by 505
Abstract
Domain shift in multi-source MRI imaging data significantly degrades the performance of Alzheimer’s disease diagnostic models. This study aims to develop an effective unsupervised domain adaptation method to enhance diagnostic accuracy across different clinical datasets. We propose a Joint Domain and Category Dual [...] Read more.
Domain shift in multi-source MRI imaging data significantly degrades the performance of Alzheimer’s disease diagnostic models. This study aims to develop an effective unsupervised domain adaptation method to enhance diagnostic accuracy across different clinical datasets. We propose a Joint Domain and Category Dual Adaptation framework (JDC-DA) that integrates metric learning and adversarial learning. The method employs multi-scale feature aggregation to capture diverse lesion characteristics, generates dynamic prototype features through category clustering, and implements a novel metric learning approach that simultaneously aligns both domain-level and category-level feature distributions. Additionally, we introduce a classification certainty maximization strategy that establishes a dual adversarial mechanism between domain discriminator and classification discrepancy discriminator. The framework was evaluated on four public datasets (ADNI-1, ADNI-2, ADNI-3, AIBL) containing 1230 baseline sMRI scans for four classification tasks: AD vs. NC, MCI vs. NC, AD vs. MCI, and AD vs. MCI vs. NC. The proposed JDC-DA method achieved superior performance with accuracies of 92.16%, 83.56%, 81.96%, and 79.12% for the four classification tasks respectively, significantly outperforming existing state-of-the-art domain adaptation methods across all evaluation metrics. The JDC-DA framework effectively addresses domain shift challenges in Alzheimer’s disease diagnosis through its integrated approach to feature alignment and adversarial learning. The method demonstrates strong potential for clinical application in automated diagnosis systems, particularly for handling multi-center neuroimaging data with distribution discrepancies. Full article
(This article belongs to the Special Issue Recent Advances in Machine Learning Methods for Medical Imaging Analysis)
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12 pages, 370 KB  
Article
Surfaces of Revolution with Constant Mean Curvature in Galilean 3-Space
by İsmet Gölgeleyen, Yusuf Yaylı and Elif Yaren Bulgan
Mathematics 2026, 14(6), 1066; https://doi.org/10.3390/math14061066 - 21 Mar 2026
Cited by 1 | Viewed by 498
Abstract
Revolution surfaces with zero mean curvature in the Galilean 3-space have been extensively studied in the literature. However, revolution surfaces with non-zero constant mean curvature in this geometric setting have not yet been investigated in a systematic way. In this paper, we address [...] Read more.
Revolution surfaces with zero mean curvature in the Galilean 3-space have been extensively studied in the literature. However, revolution surfaces with non-zero constant mean curvature in this geometric setting have not yet been investigated in a systematic way. In this paper, we address this gap by studying surfaces of revolution in the Galilean 3-space with constant mean curvature. We derive the necessary and sufficient differential conditions for such surfaces and obtain explicit parametrizations of the corresponding families. The results extend the theory beyond the minimal case and reveal geometric features that arise from the degenerate nature of the Galilean metric. Several examples are presented to illustrate the obtained surfaces and to emphasize the qualitative differences between minimal and non-minimal constant mean curvature configurations. Full article
(This article belongs to the Special Issue New Trends in Differential Geometry and Geometric Analysis)
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18 pages, 7856 KB  
Article
An Investigation of Variable Segmental Inertial Parameters in Manual Load Lifting: A Genetic Algorithm-Based Inverse Dynamics Approach
by Muhammed Çil, Bilal Usanmaz and Ömer Gündoğdu
Mathematics 2026, 14(6), 1065; https://doi.org/10.3390/math14061065 - 21 Mar 2026
Cited by 1 | Viewed by 596
Abstract
This study investigates the common assumption that segmental inertial parameters remain constant during manual lifting using a model-based experimental approach. The primary objective was to evaluate the variability in these parameters and the subsequent effects on biomechanical calculations. The research was conducted with [...] Read more.
This study investigates the common assumption that segmental inertial parameters remain constant during manual lifting using a model-based experimental approach. The primary objective was to evaluate the variability in these parameters and the subsequent effects on biomechanical calculations. The research was conducted with 20 participants (10 females and 10 males) who performed lifting tasks in the two-dimensional sagittal plane under three distinct load conditions: 2.5 kg, 5.0 kg, and 7.5 kg. Angular variations of the hand, arm, and leg joints were recorded using video-based image processing techniques. These kinematic data, integrated with anthropometric measurements, were incorporated into Newton–Euler-based equations of motion to determine joint reaction forces and net joint moments. During the initial forward dynamics stage, the solvability of the problem was tested using constant mass ratios from the established literature. In the following inverse dynamics stage, genetic algorithms were utilized to overcome solution diversity and identify the variable inertial parameters responsible for the observed motion. The results indicate that changes in segment moments of inertia reached 18–37%, leading to variations of 0–19% in net joint moments. These findings highlight the critical necessity of incorporating dynamic inertial parameters into accurate biomechanical moment calculations for manual materials handling. Full article
(This article belongs to the Special Issue Mathematical Modelling of Nonlinear Dynamical Systems)
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43 pages, 10109 KB  
Article
Stabilizer Variables for Measurement Invariance–Induced Heterogeneity: Identification Theory and Testing in Multi-Group Models
by Salim Yilmaz and Erhan Cene
Mathematics 2026, 14(6), 1064; https://doi.org/10.3390/math14061064 - 21 Mar 2026
Cited by 6 | Viewed by 969
Abstract
When measurement invariance (MI) is violated in multi-group structural equation models, group-specific measurement artifacts inflate the between-group variance of structural parameters beyond their true values. Existing remedies—partial invariance, group-specific estimation, or moderation analysis—address the consequences of inflation but not its mechanism. This article [...] Read more.
When measurement invariance (MI) is violated in multi-group structural equation models, group-specific measurement artifacts inflate the between-group variance of structural parameters beyond their true values. Existing remedies—partial invariance, group-specific estimation, or moderation analysis—address the consequences of inflation but not its mechanism. This article introduces the stabilizer variable, a covariate that absorbs measurement-induced parameter heterogeneity while maintaining structural independence from the focal relationship. Two theoretical results are established: a variance decomposition theorem showing that MI violations inflate dispersion through an identifiable artifactual component, and a purification theorem proving that a stabilizer reduces this dispersion via Frisch–Waugh–Lovell projection. Two stabilization mechanisms are identified: variance purification (Type A) and directional alignment (Type B). We then develop the stabilizer variable test, a dual-criterion procedure combining nonparametric bootstrap testing for stabilization magnitude with binomial testing for directional consistency, incorporating adaptive MI severity scoring with calibrated fit-index weights. Simulations comprising 949,100 replications across varying group counts, sample sizes, and MI severity levels demonstrate 80–99% power with false-positive rates below 2%. Practical guidelines recommend K≥10 groups and n≥100 per group for conservative applications. The framework generalizes to any multi-group regression context where systematic measurement error induces spurious parameter heterogeneity. Full article
(This article belongs to the Special Issue Advances in Statistical Approaches with Applications for Multivariate Data Analysis)
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19 pages, 575 KB  
Article
Approximating Eigenvalues of a Class of Perturbed Tridiagonal Systems
by Christos Chorianopoulos and Ioannis Th. Famelis
Mathematics 2026, 14(6), 1063; https://doi.org/10.3390/math14061063 - 21 Mar 2026
Viewed by 397
Abstract
We study a class of perturbed tridiagonal problems in the form of a rank-one update of a symmetric tridiagonal Toeplitz matrix. We derive computable formulas for up to eighth-order polynomial approximations or closed formulas for quartic approximation. Moreover, we study some symmetries that [...] Read more.
We study a class of perturbed tridiagonal problems in the form of a rank-one update of a symmetric tridiagonal Toeplitz matrix. We derive computable formulas for up to eighth-order polynomial approximations or closed formulas for quartic approximation. Moreover, we study some symmetries that characterise the coefficients of these polynomials. Numerical testing suggested that the error is close to machine accuracy in the former case and surprising low in the latter, whereas for big matrices the computational time is clearly lower compared to the MATLAB’s eig function. Full article
(This article belongs to the Section E: Applied Mathematics)
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28 pages, 3863 KB  
Article
DeepSORT-OCR: Design and Application Research of a Maritime Ship Target Tracking Algorithm Incorporating Hull Number Features
by Jing Ma, Xihang Su, Kehui Xu, Hongliang Yin, Zhihong Xiao, Jiale Wang and Peng Liu
Mathematics 2026, 14(6), 1062; https://doi.org/10.3390/math14061062 - 20 Mar 2026
Viewed by 664
Abstract
Maritime ship target tracking plays an important role in applications such as maritime patrol and maritime surveillance. However, complex sea conditions, similar target appearances, and long-distance imaging often lead to target identity confusion and unstable trajectories. To address these issues, in this paper, [...] Read more.
Maritime ship target tracking plays an important role in applications such as maritime patrol and maritime surveillance. However, complex sea conditions, similar target appearances, and long-distance imaging often lead to target identity confusion and unstable trajectories. To address these issues, in this paper, a ship multi-object tracking algorithm, DeepSORT-OCR, that integrates hull number semantic features is proposed. Based on the YOLO detection framework and the DeepSORT tracking architecture, a CBAM-ResNet network is introduced to enhance the representation of ship appearance features. An Inner-SIoU metric is adopted to improve the geometric matching of slender ship targets, while an LSTM-Adaptive Kalman Filter is employed to model the nonlinear motion patterns of ships and improve trajectory prediction stability. In addition, a Hull Number Feature Extraction module is designed in order to recognize ship hull numbers using OCR and match them with a hull number database. The extracted hull number semantic features are dynamically fused with visual appearance features to strengthen identity constraints during target association. The experimental results show that the proposed method achieves an MOTA of 66.53% on the MOT16 dataset, representing an improvement of 5.13% over DeepSORT. On the self-constructed maritime ship dataset, the method achieves an MOTA of 70.89% and an MOTP of 80.84%. Furthermore, on the hull-number subset, the MOTA further increases to 77.18%, an improvement of 7.31% compared with DeepSORT, while the number of ID switches is significantly reduced. In addition, experiments conducted on pure real data, pure synthetic data, and cross-domain evaluation settings demonstrate the stability and strong generalization capability of the proposed algorithm under different data distributions. The proposed method effectively improves the stability and identity consistency of ship multi-object tracking in complex maritime environments. Full article
(This article belongs to the Special Issue Control Theory for Multi-Agent Systems: Recent Advances and Applications)
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19 pages, 2331 KB  
Article
Dynamic Behavior and Isolation Performance of a Constant-Force Vibration Isolation System
by Thanh Danh Le
Mathematics 2026, 14(6), 1061; https://doi.org/10.3390/math14061061 - 20 Mar 2026
Viewed by 542
Abstract
This paper will present a constant-force vibration isolator (CFVI), in which the isolated load is supported by two pulley-roller mechanisms, while the dynamic stiffness is modified by a cam mechanism with the piecewise profile redefined by the user. As a result, this model [...] Read more.
This paper will present a constant-force vibration isolator (CFVI), in which the isolated load is supported by two pulley-roller mechanisms, while the dynamic stiffness is modified by a cam mechanism with the piecewise profile redefined by the user. As a result, this model can generate the constant force-displacement response within the working region, thereby obtaining quasi-zero stiffness in this range. Because of the piecewise configuration of the cam, the system motion governed by the piecewise dynamic equation under base motion excitation will be analyzed and established. The approximate solution of the piecewise dynamic equation is derived by using the average method, from which the relative amplitude–frequency relation and the absolute amplitude transmissibility of the CFVI will be obtained. The effects of the key working parameters involving the damping coefficient, critical position, and excited amplitude on the dynamic behavior and isolation effectiveness of the CFVI are considered through numerical simulations. The simulation result reveals that the dynamic response of the CFVI offers two branches: resonance and isolation. The former is significantly affected by the working parameters, whereas the latter is weakly influenced. Furthermore, the isolation effectiveness of the CFVI will be compared with that of its linear counterpart and the quasi-zero stiffness vibration isolation model using a semicircle cam (QZSI). The results demonstrate that the CFVI outperforms the other models for base motion excitations. Full article
(This article belongs to the Section C2: Dynamical Systems)
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26 pages, 2035 KB  
Article
Stability Dependence on Inertia in the Driven Damped Pendulum: A Master Control Parameter Analysis
by Alexander N. Pisarchik
Mathematics 2026, 14(6), 1060; https://doi.org/10.3390/math14061060 - 20 Mar 2026
Viewed by 983
Abstract
The driven damped pendulum is a foundational model in nonlinear dynamics, with applications ranging from Josephson junctions to MEMS oscillators. Conventional dimensionless treatments obscure the common physical origin of damping and driving in the inertia coefficient. Here we restore this dependence and establish [...] Read more.
The driven damped pendulum is a foundational model in nonlinear dynamics, with applications ranging from Josephson junctions to MEMS oscillators. Conventional dimensionless treatments obscure the common physical origin of damping and driving in the inertia coefficient. Here we restore this dependence and establish inertia as a master control parameter governing stability, resonance, and bifurcations. Through linear analysis and perturbation theory, we derive universal scaling laws revealing a fundamental dichotomy: quantities at resonance—peak amplitude and nonlinear frequency shift—are independent of inertia due to exact algebraic cancellation between the inertia dependence of the effective driving amplitude and effective damping coefficient. Off resonance, however, amplitude scales inversely with inertia, bandwidth narrows proportionally, and the bistability threshold exhibits an even steeper dependence. A critical inertia separates underdamped from overdamped regimes, yielding non-monotonic relaxation times that maximize attractor memory at extreme inertia values. These scaling laws provide design guidelines: low inertia promotes broadband response for energy harvesting; high inertia suppresses off-resonant vibrations for precision timing and quantum applications. By establishing inertia as a physically realizable path through parameter space, this work unifies disparate phenomena and provides a framework for understanding stability in inertial-driven systems. Full article
(This article belongs to the Special Issue Mathematical Modelling of Nonlinear Dynamical Systems)
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39 pages, 4563 KB  
Article
A DSGE Framework with Green and Fossil Energy for Kazakhstan
by Akbobek Akhmedyarova, Bauyrzhan Temirbayev, Andrea Tick and Askar Sarygulov
Mathematics 2026, 14(6), 1059; https://doi.org/10.3390/math14061059 - 20 Mar 2026
Cited by 1 | Viewed by 1016
Abstract
This paper constructs and estimates a novel two-sector Dynamic Stochastic General Equilibrium (DSGE) model to analyze the macroeconomics of Kazakhstan’s dual-energy structure, where a large fossil fuel sector coexists with an emerging renewable segment. The model’s key innovation is its integration of an [...] Read more.
This paper constructs and estimates a novel two-sector Dynamic Stochastic General Equilibrium (DSGE) model to analyze the macroeconomics of Kazakhstan’s dual-energy structure, where a large fossil fuel sector coexists with an emerging renewable segment. The model’s key innovation is its integration of an endogenous, depletable oil stock and a dual-inflation Taylor-type rule, which together capture the specific transmission channels between hydrocarbon dependence and green investment. By differentiating between oil-driven and core inflation, the framework quantifies how oil price volatility transmits monetary conditions to the renewable sector. Bayesian estimation, using sectoral data from national accounts, reveals a pronounced asymmetry: oil stock/discovery dynamics and oil revenue fluctuations dominate macroeconomic volatility, while the renewable sector exhibits stable output but remains vulnerable to oil-driven monetary tightening transmitted mainly through indirect channels. The results indicate that Kazakhstan’s ongoing energy transition offers a stabilizing diversification benefit in principle but remains structurally constrained by macroeconomic dynamics and fiscal patterns anchored to hydrocarbon conditions. These findings provide a quantitative basis for designing transition policies that mitigate cross-sector spillovers and support effective diversification in resource-dependent economies. Full article
(This article belongs to the Special Issue Mathematical Modeling of Energy Transition, Climate Finance, and Sustainable Economic Systems)
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