Mathematics

29 pages, 3673 KB

Open AccessFeature PaperArticle

Game-Theoretic Analysis of Cooperative Advertising Decisions in Production–Retail Channels with Seasonal Demand

by Yao-Hung Hsieh, Jonas Chao-Pen Yu and Jhao-Yi Guan

Mathematics 2026, 14(4), 745; https://doi.org/10.3390/math14040745 - 23 Feb 2026

Cited by 1 | Viewed by 917

This paper investigates cooperative advertising decisions in production–retailing channels for seasonal products under demand seasonality. We develop analytical game-theoretic models to examine how advertising cooperation influences channel coordination and profit distribution between manufacturers and retailers. Two channel structures are considered: a single-manufacturer–single-retailer channel [...] Read more.

This paper investigates cooperative advertising decisions in production–retailing channels for seasonal products under demand seasonality. We develop analytical game-theoretic models to examine how advertising cooperation influences channel coordination and profit distribution between manufacturers and retailers. Two channel structures are considered: a single-manufacturer–single-retailer channel and a single-manufacturer channel with two competing retailers. For each structure, Stackelberg and Nash equilibrium settings are analyzed and compared. Our results show that cooperative advertising can serve as an effective coordination mechanism by increasing advertising intensity and improving channel efficiency. Retailers always benefit from manufacturer-supported advertising through cost sharing and higher profitability, whereas the manufacturer’s incentive to participate depends on whether demand expansion outweighs shared advertising costs. Importantly, we demonstrate that channel leadership plays a critical role: the Stackelberg equilibrium consistently dominates the Nash equilibrium in terms of total channel profit. This study contributes to the cooperative advertising literature by explicitly incorporating demand seasonality and competing retailers, and by clarifying when cooperative advertising leads to Pareto improvements in seasonal supply chains. Full article

(This article belongs to the Special Issue Modeling and Optimization in Supply Chain Management)

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26 pages, 8135 KB

Open AccessArticle

DADD-PINN: Dual Adaptive Domain Decomposition Physics-Informed Neural Networks

by Yunkang Xiong, Hongyu Wei, Zhiying Ma, Zhihong Ding and Yaxin Peng

Mathematics 2026, 14(4), 744; https://doi.org/10.3390/math14040744 - 23 Feb 2026

Viewed by 1575

Abstract

When solving partial differential equations (PDEs), traditional Physics-Informed Neural Networks (PINNs) often encounter difficulties in capturing critical physical features and addressing information bias between subdomains. To overcome these limitations, this paper proposes a Dual Adaptive Domain Decomposition Physics-Informed Neural Network (DADD-PINN). The core [...] Read more.

When solving partial differential equations (PDEs), traditional Physics-Informed Neural Networks (PINNs) often encounter difficulties in capturing critical physical features and addressing information bias between subdomains. To overcome these limitations, this paper proposes a Dual Adaptive Domain Decomposition Physics-Informed Neural Network (DADD-PINN). The core of this method lies in the construction of a dual-driven architecture that facilitates intra-subdomain feature extraction and inter-subdomain feature coordination. Within each subdomain, the solver’s precision is significantly enhanced by integrating a multi-criterion adaptive sampling strategy with a dynamic weighting mechanism. Experimental results demonstrate that DADD-PINN reduces the optimal

L^{2}

error by 1–2 orders of magnitude compared to existing baselines. The model exhibits superior generalization and robustness across various physical fields, offering a new route toward accurate and efficient solutions for complex PDEs. Full article

(This article belongs to the Special Issue Computational Intelligence and Data Analysis)

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21 pages, 437 KB

Open AccessArticle

Inverse Extremal Eigenvalue Problems for Multi-Arrowhead Pentadiagonal Matrices

by Susana Arela-Pérez, Hector Flores Callisaya, Hans Nina and Hubert Pickmann-Soto

Mathematics 2026, 14(4), 743; https://doi.org/10.3390/math14040743 - 23 Feb 2026

Viewed by 573

Abstract

We address the inverse extremal eigenvalue problem (IEEP) for multi-arrowhead pentadiagonal matrices, a structured class that combines pentadiagonal bandwidth with an alternating arrowhead structure. We identify four distinct structural classes based on the orientation and configuration of arrowhead blocks. For symmetric matrices, we [...] Read more.

We address the inverse extremal eigenvalue problem (IEEP) for multi-arrowhead pentadiagonal matrices, a structured class that combines pentadiagonal bandwidth with an alternating arrowhead structure. We identify four distinct structural classes based on the orientation and configuration of arrowhead blocks. For symmetric matrices, we establish sufficient conditions for reconstruction from extremal (smallest, largest, or both) eigenvalues of leading principal submatrices. For certain classes, we prove these conditions are also necessary, providing a complete characterization. Nonsymmetric matrices require one additional prescribed eigenvector. Our results are constructive and yield algorithmic procedures. Numerical examples illustrate our theoretical findings. This work generalizes inverse extremal eigenvalue theory for arrowhead matrices to these pentadiagonal structures. Full article

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13 pages, 332 KB

Open AccessArticle

Helfrich Functional in

H^{2} \times R

by Felix Nieto and Fredy Mesa

Mathematics 2026, 14(4), 742; https://doi.org/10.3390/math14040742 - 23 Feb 2026

Viewed by 552

Abstract

This paper presents a complete analysis of the Helfrich membrane energy functional in the product space

H^{2} \times R

. We address the analytical challenges posed by the ideal boundary of the space by developing a renormalization scheme, allowing us to formulate [...] Read more.

This paper presents a complete analysis of the Helfrich membrane energy functional in the product space

H^{2} \times R

. We address the analytical challenges posed by the ideal boundary of the space by developing a renormalization scheme, allowing us to formulate a well-posed variational problem. We derive the Euler-Lagrange equations for the renormalized functional, characterizing the equilibrium configurations through a coupled system of partial differential equations and a Neumann-type boundary condition. A central result of our work is a rigidity theorem, proven via a Killing field argument, which establishes that any admissible critical surface is necessarily axially symmetric. Finally, we connect this mathematical theory to biophysics by proposing a new variational principle for the Solvent Accessible Surface (SAS) under geometric confinement, demonstrating that our classified surfaces represent the optimal elastic energy shapes for such systems. Full article

(This article belongs to the Section B: Geometry and Topology)

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22 pages, 2414 KB

Open AccessFeature PaperArticle

The Algebra of Chebyshev Polynomials and the Transfer-Matrix Approach for the One-Dimensional Ising Model with a Defect

by Nicholay S. Tonchev and Daniel Dantchev

Mathematics 2026, 14(4), 741; https://doi.org/10.3390/math14040741 - 23 Feb 2026

Viewed by 721

Abstract

We investigate a random field of mutually dependent random variables (“spins”), indexed by a finite one-dimensional lattice, called in physical sciences the one-dimensional Ising model, in which the random variables can take only ±1 values (see the text for a precise definition). One [...] Read more.

We investigate a random field of mutually dependent random variables (“spins”), indexed by a finite one-dimensional lattice, called in physical sciences the one-dimensional Ising model, in which the random variables can take only ±1 values (see the text for a precise definition). One of the couplings, termed a “bond,” that describes the mutual influence of two adjacent random variables is altered—it does not equal the others, thereby introducing a single “defect” bond. This defect bond represents a localised perturbation within an otherwise uniform system. Utilising the recurrence relations of Chebyshev polynomials and the bijective map between the number of spins and the polynomial index, we present a new method for calculations and systematically explore, using it, the system’s properties across different chain lengths and boundary conditions. As an application, we derive analytical expressions for the dependence of the average values of the random variables on their position within the chain, which we refer to as the “local magnetisation profile”. From the findings related to the system with a defect bond, we present a novel result for this profile under free (Dirichlet) boundary conditions and re-derive the corresponding result for antiperiodic boundary conditions. Full article

(This article belongs to the Section E4: Mathematical Physics)

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23 pages, 3524 KB

Open AccessFeature PaperArticle

A Diffusion Weighted Ensemble Framework for Robust Short-Horizon Global SST Forecasting from Multivariate GODAS Data

by Gwangun Yu, GilHan Choi, Moonseung Choi, Sun-hong Min and Yonggang Kim

Mathematics 2026, 14(4), 740; https://doi.org/10.3390/math14040740 - 22 Feb 2026

Viewed by 685

Abstract

Accurate time series forecasting of sea surface temperature (SST) is essential for understanding the ocean climate system and large-scale ocean circulation, yet it remains challenging due to regime-dependent variability and correlated errors across heterogeneous prediction models. This study addresses these challenges by formulating [...] Read more.

Accurate time series forecasting of sea surface temperature (SST) is essential for understanding the ocean climate system and large-scale ocean circulation, yet it remains challenging due to regime-dependent variability and correlated errors across heterogeneous prediction models. This study addresses these challenges by formulating SST ensemble time series forecasting aggregation as a stochastic, sample-adaptive weighting problem. We propose a diffusion-conditioned ensemble framework in which heterogeneous base forecasters generate out-of-sample SST predictions that are combined through a noise-conditioned weighting network. The proposed framework produces convex, sample-specific mixture weights without requiring iterative reverse-time sampling. The approach is evaluated on short-horizon global SST forecasting using the Global Ocean Data Assimilation System (GODAS) reanalysis as a representative multivariate dataset. Under a controlled experimental protocol with fixed input windows and one-step-ahead prediction, the proposed method is compared against individual deep learning forecasters and conventional global pooling strategies, including uniform averaging and validation-optimized convex weighting. The results show that adaptive, diffusion-weighted aggregation yields consistent improvements in error metrics over the best single-model baseline and static pooling rules, with more pronounced gains in several mid- to high-latitude regimes. These findings indicate that stochastic, condition-dependent weighting provides an effective and computationally practical framework for enhancing the robustness of multivariate time series forecasting, with direct applicability to global SST prediction from large-scale geophysical reanalysis data. Full article

(This article belongs to the Special Issue Mathematical Foundations and New Advances in Deep Learning Applications)

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21 pages, 1119 KB

Open AccessFeature PaperArticle

An ALE Framework with an HLLC-2D Riemann Solver for Reactive Gas–Particle Flows

by Jianqiao Zhang, Xianggui Li and Wei Yan

Mathematics 2026, 14(4), 739; https://doi.org/10.3390/math14040739 - 22 Feb 2026

Cited by 1 | Viewed by 671

Abstract

We propose a coupled gas–particle two-phase model for particle transport in a compressible carrier gas with interphase momentum and energy exchange, and we incorporate a diffusion-based mechanism to represent gas–particle reactions. The governing equations are discretized in an Arbitrary Lagrangian–Eulerian (ALE) finite-volume framework [...] Read more.

We propose a coupled gas–particle two-phase model for particle transport in a compressible carrier gas with interphase momentum and energy exchange, and we incorporate a diffusion-based mechanism to represent gas–particle reactions. The governing equations are discretized in an Arbitrary Lagrangian–Eulerian (ALE) finite-volume framework using an HLLC-type two-dimensional Riemann solver (HLLC-2D). The solver employs a nodal-conservation construction that enforces consistency between numerical fluxes and nodal contact velocities, which helps reduce spurious oscillations near discontinuities on moving meshes. In addition, a particle-search-based Courant–Friedrichs–Lewy(CFL)-like time-step restriction is introduced to enhance robustness in coupled simulations. Numerical tests are presented to assess the method and to illustrate particle-induced modifications of wave dynamics, as well as reaction-driven variations in velocity and temperature fields. Full article

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23 pages, 649 KB

Open AccessEditor’s ChoiceArticle

Manifold Causal Conditional Deep Networks for Heterogeneous Treatment Effect Estimation and Policy Evaluation

by Jong-Min Kim

Mathematics 2026, 14(4), 738; https://doi.org/10.3390/math14040738 - 22 Feb 2026

Cited by 2 | Viewed by 809

Abstract

We present a comprehensive framework for estimating heterogeneous treatment effects and evaluating decision-making policies in high-dimensional settings. Our approach combines nonlinear manifold learning techniques—UMAP, t-SNE, and Isomap—with a Causal Conditional Deep Network (CCDN) to model complex nonlinear interactions among covariates, treatments, and outcomes. [...] Read more.

We present a comprehensive framework for estimating heterogeneous treatment effects and evaluating decision-making policies in high-dimensional settings. Our approach combines nonlinear manifold learning techniques—UMAP, t-SNE, and Isomap—with a Causal Conditional Deep Network (CCDN) to model complex nonlinear interactions among covariates, treatments, and outcomes. Within this framework, we assess five treatment assignment policies—Greedy, Thompson Sampling, Epsilon-Greedy, Random, and a novel LLM-guided Thompson policy—across simulated and real-world datasets, including Adult, Wine Quality, and Boston Housing. Empirical results reveal a fundamental trade-off: exploitative policies like Greedy minimize cumulative regret but underperform in recovering heterogeneous treatment effects, whereas exploratory policies, particularly Random and LLM-Thompson, achieve a lower Conditional Average Treatment Effect Root Mean Squared Error (CATE RMSE) by providing broader coverage of the action–covariate space. Notably, LLM-Thompson consistently delivers strong performance across noisy, real-world datasets, highlighting the advantage of uncertainty-aware exploration in capturing treatment heterogeneity. Overall, the framework demonstrates that integrating manifold-informed deep networks with principled exploration strategies enhances both policy optimization and individualized treatment effect estimation in high-dimensional, complex environments. Full article

(This article belongs to the Special Issue Statistical Data Modeling and Machine Learning with Applications, 4th Edition)

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21 pages, 2187 KB

Open AccessArticle

Reliability-Adaptive Control of Aerospace Electromechanical Actuators with Coupled Degradation via Stochastic MPC

by Le Qi

Mathematics 2026, 14(4), 737; https://doi.org/10.3390/math14040737 - 22 Feb 2026

Viewed by 795

Abstract

Electromechanical Actuators (EMAs) are critical components in More-Electric Aircraft (MEA) and Reusable Launch Vehicles (RLVs), yet they remain vulnerable to jamming and fatigue failures under high-stress flight maneuvers. Existing Health-Aware Flight Control approaches often treat failure prediction and control allocation as separate processes, [...] Read more.

Electromechanical Actuators (EMAs) are critical components in More-Electric Aircraft (MEA) and Reusable Launch Vehicles (RLVs), yet they remain vulnerable to jamming and fatigue failures under high-stress flight maneuvers. Existing Health-Aware Flight Control approaches often treat failure prediction and control allocation as separate processes, leading to suboptimal sortie generation rates. This paper presents a reliability-adaptive control framework that unifies trajectory tracking with online health management. Empowered by a hierarchical mission-to-control architecture, the system employs stochastic Model Predictive Control (SMPC) to actively modulate control surface deflection profiles in real time. A comparative case study on a coupled EMA drivetrain demonstrates that the proposed controller extends useful life by 65% compared to fixed-gain baselines, achieves 23% higher mission performance than reactive PID controllers, and it maintains zero constraint violations throughout the mission by optimally distributing the health budget across mission phases. Full article

(This article belongs to the Special Issue Mathematical Modelling and Control Theory for Aerospace Vehicles)

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23 pages, 1191 KB

Open AccessArticle

Asymptotic Expansions for Products of Weibull Random Variables

by Ričardas Kamarauskas, Aurimas Slabovas and Jonas Šiaulys

Mathematics 2026, 14(4), 736; https://doi.org/10.3390/math14040736 - 22 Feb 2026

Cited by 1 | Viewed by 650

Abstract

We derive an asymptotic expansion for the tail function of the product of

n (n \in N)

independent identically distributed Weibull random variables. The coefficients of the expansion are obtained using a recursive formula arising from the Laplace method. The resulting [...] Read more.

We derive an asymptotic expansion for the tail function of the product of

n (n \in N)

independent identically distributed Weibull random variables. The coefficients of the expansion are obtained using a recursive formula arising from the Laplace method. The resulting expansion provides explicit higher-order correction terms that significantly improve the accuracy of tail approximations for large arguments. These results are useful for both theoretical analysis and practical applications involving extreme-value behavior of products of random variables. The main result of the paper shows that multiplying Weibull distributions yields so-called Weibull-type distributions. It also shows that under multiplication, the shape parameter of the Weibull distribution decreases. This implies that the product of Weibull distributions becomes more heavily tailed. The asymptotic formula for the tail function of the product of Weibull distributions involves rather complicated coefficients. To compute these coefficients, we provide MATLAB (version 9.13.0, R2022b) code. The application of the main result is illustrated with two particular examples. Full article

(This article belongs to the Section D1: Probability and Statistics)

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18 pages, 766 KB

Open AccessFeature PaperArticle

High-Order Difference Scheme for Time-Fractional Quasilinear Parabolic Equations

by Miglena N. Koleva and Lubin G. Vulkov

Mathematics 2026, 14(4), 735; https://doi.org/10.3390/math14040735 - 22 Feb 2026

Cited by 1 | Viewed by 576

Abstract

Mathematical modeling of heat and mass transfer processes in porous media using fractional derivative equations is of great practical importance. Within the framework of such models, obtaining analytical solutions to the corresponding initial–boundary value problems is generally difficult. In this work, we numerically [...] Read more.

Mathematical modeling of heat and mass transfer processes in porous media using fractional derivative equations is of great practical importance. Within the framework of such models, obtaining analytical solutions to the corresponding initial–boundary value problems is generally difficult. In this work, we numerically investigate quasilinear parabolic problems involving Caputo time-fractional derivatives. First, the well-posedness and existence of weak solutions are discussed. Then, we construct and implement a finite-difference scheme that is fourth-order accurate in space and second-order accurate in time. Convergence in the maximum norm is proven. Numerical experiments confirm the accuracy and efficiency of the proposed approach. Full article

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12 pages, 311 KB

Open AccessArticle

Bounds on the Domination Numbers of δ-Complement Graphs

by Wipawee Tangjai, Chayapa Darayon, Panupong Vichitkunakorn, Rasimate Maungchang and Witsarut Pho-on

Mathematics 2026, 14(4), 734; https://doi.org/10.3390/math14040734 - 22 Feb 2026

Cited by 1 | Viewed by 905

Abstract

This study examines the

δ

-complements of graphs—a specific type of graph complement whose adjacency depends on the adjacency of the vertices with identical degrees in the original graph. More specifically, we study this type of complement regarding the domination number. We provide [...] Read more.

This study examines the

δ

-complements of graphs—a specific type of graph complement whose adjacency depends on the adjacency of the vertices with identical degrees in the original graph. More specifically, we study this type of complement regarding the domination number. We provide sharp Nordhaus–Gaddum-type bounds on the domination number of a graph and its

δ

-complement. We also provide sharp bounds on the domination numbers of the

δ

-complements of joined graphs and Cartesian product graphs. Full article

(This article belongs to the Special Issue Advances in Graph Theory, Combinatorics, and Applications)

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28 pages, 879 KB

Open AccessFeature PaperArticle

Elementary yet Precise Best-Case Analysis of MergeSort with an Application to the Sum of Digits Problem

by Marek A. Suchenek

Mathematics 2026, 14(4), 733; https://doi.org/10.3390/math14040733 - 21 Feb 2026

Viewed by 760

Abstract

An exact formula

B (n) = \frac{n}{2} (⌊ lg n ⌋ + 1) - \sum_{k = 0}^{⌊ lg n ⌋} 2^{k} Zigzag (\frac{n}{2^{k + 1}}),

where [...] Read more.

An exact formula

B (n) = \frac{n}{2} (⌊ lg n ⌋ + 1) - \sum_{k = 0}^{⌊ lg n ⌋} 2^{k} Zigzag (\frac{n}{2^{k + 1}}),

where

Zigzag (x) = min (x - ⌊ x ⌋, ⌈ x ⌉ - x),

for the minimum number

B (n)

of comparisons of keys performed by

MergeSort

on an n-element array is derived and analyzed. The said formula is less complex than any other known formula for the same and can be evaluated in

O ({log}^{c})

time, where c is a constant. It is shown that there is no closed-form formula for the above. Other variants for

B (n)

are described as well. Since the recurrence relation for the minimum number of comparisons of keys for

MergeSort

is identical with a recurrence relation for the number of 1s in binary expansions of all integers between 0 and n (exclusively), the above results extend to the sum of binary digits problem. Full article

(This article belongs to the Special Issue Computational Approaches in Computer Science: Methods, Algorithms, and Applications)

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23 pages, 1799 KB

Open AccessArticle

Slow Translation of a Soft Sphere in an Unbounded Micropolar Fluid with Interfacial Stress Jump

by Shreen El-Sapa

Mathematics 2026, 14(4), 732; https://doi.org/10.3390/math14040732 - 21 Feb 2026

Cited by 2 | Viewed by 502

Abstract

This study presents a theoretical analysis of the slow translation of a soft sphere through an unbounded micropolar fluid under steady, low Reynolds number conditions, accounting for the influence of interfacial stress jump. The soft sphere is modeled as a rigid solid core [...] Read more.

This study presents a theoretical analysis of the slow translation of a soft sphere through an unbounded micropolar fluid under steady, low Reynolds number conditions, accounting for the influence of interfacial stress jump. The soft sphere is modeled as a rigid solid core surrounded by a permeable porous gel layer, allowing fluid penetration and momentum exchange across the interface. This core–shell configuration captures the essential structural characteristics of coated or gel-like particles encountered in biological and engineering systems. Closed-form expressions for the velocity components, microrotation, stresses, and couple stresses are derived both within the porous micropolar gel layer surrounding the particle and in the exterior micropolar fluid. The flow inside the permeable coating is described using the general Brinkman solution in spherical coordinates, while the governing micropolar fluid equations are applied in the outer region. Appropriate boundary conditions are imposed at the solid core surface and at the permeable soft-sphere interface to ensure continuity of velocity and microrotation, together with the prescribed stress jump. The normalized drag force acting on the particle is obtained as a function of the particle-to-core radius ratio, permeability, stress-jump parameter, and micropolarity parameter. The results indicate that the hydrodynamic drag decreases as the porous layer becomes thicker and remains finite, approaching unity even when the soft sphere behaves as a solid particle or as a porous sphere translating through an infinite micropolar medium, with other parameters held fixed. Overall, the analysis elucidates the coupled roles of micropolar effects, interfacial stress jump, and porous-layer structure in governing the hydrodynamic resistance experienced by soft particles. Full article

(This article belongs to the Special Issue Mathematical Methods in Computational Fluid Dynamics: Theory and Applications)

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20 pages, 1939 KB

Open AccessArticle

Optimal Extraction Under Endogenous Degradation Risk

by Luca Grosset, Maddalena Muttoni and Elena Sartori

Mathematics 2026, 14(4), 731; https://doi.org/10.3390/math14040731 - 21 Feb 2026

Viewed by 554

Abstract

We study the optimal extraction of a non-renewable resource under an endogenous risk of irreversible degradation. The extractor faces a stochastic switching time at which extraction costs permanently increase, with the hazard rate of this transition depending on the current extraction intensity. As [...] Read more.

We study the optimal extraction of a non-renewable resource under an endogenous risk of irreversible degradation. The extractor faces a stochastic switching time at which extraction costs permanently increase, with the hazard rate of this transition depending on the current extraction intensity. As a result, faster extraction not only accelerates depletion but also raises the probability of entering a high-cost regime. We formulate the problem as an optimal control model with a control-dependent hazard process and derive a deterministic equivalent representation. Although extraction before and after degradation is individually trivial, their coupling through the endogenous hazard generates a nonlinear control problem. We provide an explicit characterization of the optimal extraction policy and show that degradation risk fundamentally alters the optimal depletion path. In contrast to the deterministic benchmark, optimal extraction becomes smoother over time, as the decision maker trades off immediate profits against the expected increase in future costs. The analysis highlights how endogenous operational risk can discipline extraction incentives and offers new insights into the sustainable management of exhaustible resources under technological fragility. Full article

(This article belongs to the Special Issue Mathematical Programming, Optimization and Operations Research, 2nd Edition)

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28 pages, 582 KB

Open AccessArticle

On Expectation Measures for Failure Processes in Multiple Populations: Mathematical Theory and Applications on Two Lines

by Rashad M. EL-Sagheer, Mohamed F. Abouelenein, Mohamed H. El-Menshawy and Mahmoud M. Ramadan

Mathematics 2026, 14(4), 730; https://doi.org/10.3390/math14040730 - 20 Feb 2026

Cited by 1 | Viewed by 610

Abstract

This paper develops classical and Bayesian inferential procedures for Weibull exponential lifetime models under joint progressive Type-II censoring, motivated by comparative reliability analysis of products manufactured across multiple production lines. The theoretical framework is formulated for a general setting involving k independentWeibull exponential [...] Read more.

This paper develops classical and Bayesian inferential procedures for Weibull exponential lifetime models under joint progressive Type-II censoring, motivated by comparative reliability analysis of products manufactured across multiple production lines. The theoretical framework is formulated for a general setting involving k independentWeibull exponential populations, allowing for flexible modeling of heterogeneous lifetime behaviors under a common censoring scheme. Maximum likelihood estimators and their asymptotic confidence intervals are derived, and Bayesian estimation is conducted using Markov chain Monte Carlo methods under both squared-error and LINEX loss functions. For numerical illustration and practical interpretability, the primary emphasis of the simulation study, expected-failure analysis, and real-data applications is placed on the two-population case (k = 2), which commonly arises in comparative life-testing scenarios such as the evaluation of two production lines or systems. Explicit expressions for the expected number of failures are presented for two populations, and their performance is examined through Monte Carlo simulations under various censoring schemes. The proposed methods are further illustrated using real datasets, demonstrating their applicability and effectiveness in reliability assessment. Overall, the results show that the proposed inferential procedures perform well under joint progressive censoring and provide a useful statistical framework for comparative reliability analysis, with methodology that naturally extends to general k-population settings. Full article

(This article belongs to the Section D1: Probability and Statistics)

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24 pages, 316 KB

Open AccessFeature PaperArticle

Optimal Control of Impulsive Systems Under State, Control, and Terminal Constraints

by Hugo Leiva and Mozhgan N. Entekhabi

Mathematics 2026, 14(4), 729; https://doi.org/10.3390/math14040729 - 20 Feb 2026

Cited by 1 | Viewed by 628

Abstract

We establish a version of Pontryagin’s maximum principle for optimal control problems with impulses and phase constraints. Using the Dubovitskii–Milyutin theory, we construct a conic variational framework that handles impulsive dynamics and general state constraints. The main difficulty lies in working with piecewise [...] Read more.

We establish a version of Pontryagin’s maximum principle for optimal control problems with impulses and phase constraints. Using the Dubovitskii–Milyutin theory, we construct a conic variational framework that handles impulsive dynamics and general state constraints. The main difficulty lies in working with piecewise continuous functions, required by the impulsive nature of the system. This setting also demands an extension of the classical result on the existence of non-negative Borel measures, which leads to an adjoint equation formulated as a Stieltjes integral. Theoretical results are illustrated with examples, and key results by I. Girsanov are extended to the impulsive context. Full article

(This article belongs to the Special Issue Numerical Methods for Linear PDEs and Applications)

18 pages, 636 KB

Open AccessFeature PaperEditor’s ChoiceArticle

Directional Quaternion Step Differentiation and a Bicomplex Double-Step Calculus for Cancellation-Free First and Second Derivatives

by Ji Eun Kim

Mathematics 2026, 14(4), 728; https://doi.org/10.3390/math14040728 - 20 Feb 2026

Viewed by 590

Abstract

Accurate derivative information is central to sensitivity analysis and optimization, yet standard finite differences can lose many digits when the step size is small because of subtractive cancellation. Complex-step differentiation largely resolves this issue for first derivatives, but robust second derivatives and mixed [...] Read more.

Accurate derivative information is central to sensitivity analysis and optimization, yet standard finite differences can lose many digits when the step size is small because of subtractive cancellation. Complex-step differentiation largely resolves this issue for first derivatives, but robust second derivatives and mixed partials remain delicate: several practical complex-step variants for

f^{″}

still subtract nearly equal quantities, and quaternion-step rules are often presented as separate constructions. We develop a unified slice-based framework that extracts first and second derivatives from a single evaluation by projecting algebraic coefficients in commutative subalgebras of the complexified quaternions. First, we formulate a directional quaternion-steprule parameterized by an arbitrary unit pure quaternion u and provide an explicit projection operator that makes the underlying complex slice

C_{u} ≃ C

transparent; the resulting first-derivative formula is rotation invariant and recovers classical j-step and planar

(j, k)

-step rules as special cases. Second, we construct a bicomplex double-step calculus in the commuting imaginary units

i

and u and show that one evaluation at

z + (i + u) h

separates derivative information into distinct coefficients, with the

i u

-component equal to

h^{2} f^{″} (z) + O (h^{4})

, giving a subtraction-free

O (h^{2})

approximation of

f^{″}

. For bivariate analytic functions we additionally derive one-shot identities for

f_{x}

,

f_{y}

, and

f_{x y}

from

f (x + u h, y + i h)

and supply practical extraction identities, step-size guidance for

h^{2}

-scaled coefficients, and branch-consistency diagnostics for non-entire functions. The “cancellation-free” property here refers to avoiding the subtraction of nearly equal real quantities at the level of the differentiation formula; in floating-point arithmetic, coefficient extraction and the

1 / h^{2}

scaling for second-order quantities still interact with roundoff, and we quantify the resulting stable regimes numerically. Full article

(This article belongs to the Special Issue New Advances in Complex Analysis and Functional Analysis)

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21 pages, 809 KB

Open AccessArticle

Hypothesis Tests for Comparing Point Processes

by Yue Mu and Wei Wu

Mathematics 2026, 14(4), 727; https://doi.org/10.3390/math14040727 - 19 Feb 2026

Viewed by 753

Abstract

This paper presents a comprehensive study of statistical tests for comparing temporal point processes in general, with a particular focus on Poisson processes. We explore three key approaches: (1) an intensity-based test specifically for Poisson processes, (2) general parametric tests using the notion [...] Read more.

This paper presents a comprehensive study of statistical tests for comparing temporal point processes in general, with a particular focus on Poisson processes. We explore three key approaches: (1) an intensity-based test specifically for Poisson processes, (2) general parametric tests using the notion of maximum likelihood estimation, and (3) a general nonparametric test using the Isometric Log-Ratio (ILR) transformation. The first approach adopts a three-step procedure for comparing inhomogeneous Poisson processes by testing total and normalized intensities separately and then combining the corresponding p-values using Fisher’s method. The second method proposes a likelihood-based parametric test to examine the conditional intensity functions in point processes, emphasizing the application to Hawkes processes. Lastly, the third approach introduces a nonparametric test for general point processes, by transforming inter-event times into a Euclidean space via the ILR transformation, followed by conventional depth-based methods on multivariate data. We then conduct thorough studies on simulations as well as real-world data to illustrate these testing procedures and demonstrate their effectiveness. Full article

(This article belongs to the Section D1: Probability and Statistics)

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21 pages, 475 KB

Open AccessFeature PaperArticle

Synchronization of Delay Switched Fractional Cohen–Grossberg Neural Network Models

by Donal O’Regan and Snezhana Hristova

Mathematics 2026, 14(4), 726; https://doi.org/10.3390/math14040726 - 19 Feb 2026

Cited by 1 | Viewed by 606

Abstract

The Cohen–Grossberg neural network is studied in the case when the dynamics of the neurons are modeled by generalized Caputo fractional derivatives with respect to another function (GCFDF). We consider a time-dependent delay and a switching rule in the model, which specifies when [...] Read more.

The Cohen–Grossberg neural network is studied in the case when the dynamics of the neurons are modeled by generalized Caputo fractional derivatives with respect to another function (GCFDF). We consider a time-dependent delay and a switching rule in the model, which specifies when to switch the system at the initially given times. The switching rule is a piecewise constant function, and its points of discontinuity are the lower limits of the applied GCFDF on the corresponding intervals. We develop theoretical tools for GCFDF, starting with an important inequality for estimating that derivative on quadratic functions. We define the global Mittag–Leffler synchronization and obtain sufficient conditions based on the Lyapunov method, using a Razumikhin condition and quadratic functions. Full article

(This article belongs to the Special Issue Fractional Differential Equations, Inclusions and Inequalities with Applications: 3rd Edition)

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18 pages, 355 KB

Open AccessArticle

FDC-LGL: Fast Discrete Clustering with Local Graph Learning for Large-Scale Datasets

by Shenfei Pei, Ruiyu Huang and Zengwei Zheng

Mathematics 2026, 14(4), 725; https://doi.org/10.3390/math14040725 - 19 Feb 2026

Viewed by 588

Abstract

Graph-based clustering is a fundamental task in unsupervised machine learning and has been extensively applied to complex data mining scenarios, such as pattern recognition and data classification. However, most existing graph clustering algorithms still face significant challenges, including low graph learning efficiency, poor [...] Read more.

Graph-based clustering is a fundamental task in unsupervised machine learning and has been extensively applied to complex data mining scenarios, such as pattern recognition and data classification. However, most existing graph clustering algorithms still face significant challenges, including low graph learning efficiency, poor adaptability to datasets with large numbers of samples and clusters, and inevitable accuracy loss caused by post-processing steps. To effectively tackle these critical challenges and enhance clustering performance, we propose a novel Fast Discrete Clustering algorithm integrated with Local Graph Learning, namely FDC-LGL. Based on the classical normalized cut criterion, the proposed algorithm innovatively integrates a Local Graph Learning module into the clustering objective function, efficiently and reliably learning graph structures by introducing second-order neighbor constraints. It directly outputs accurate clustering results through a discrete indicator matrix, thereby eliminating the need for additional post-processing. Extensive comparative experiments conducted on synthetic datasets, medium-scale real-world datasets, and large-scale real-world datasets demonstrate that FDC-LGL is significantly superior to other state-of-the-art graph clustering algorithms in terms of key evaluation metrics, including clustering accuracy (ACC), normalized mutual information (NMI), and the adjusted rand index (ARI), as well as computational efficiency. Full article

(This article belongs to the Special Issue Advanced Neural Network and Machine Learning Algorithms, Models and Architectures in Data Mining)

20 pages, 4635 KB

Open AccessArticle

Intelligent Inversion of Deep In Situ Stress Fields Based on the ABC-SVR Algorithm

by Weipeng Gong, Keping Zhou, Xin Xiong, Jun Wei, Feng Gao and Zhuquan Li

Mathematics 2026, 14(4), 724; https://doi.org/10.3390/math14040724 - 19 Feb 2026

Cited by 1 | Viewed by 645

Abstract

Accurate inversion of the deep initial in situ stress field is a fundamental prerequisite for stability analysis of surrounding rock in underground engineering, roadway support design, and prevention and control of dynamic disasters. To address the problems of scarce in situ stress measurements [...] Read more.

Accurate inversion of the deep initial in situ stress field is a fundamental prerequisite for stability analysis of surrounding rock in underground engineering, roadway support design, and prevention and control of dynamic disasters. To address the problems of scarce in situ stress measurements in deep mining areas, the inability of conventional regression methods to capture the nonlinear characteristics of complex tectonic stress fields, and the tendency of traditional inversion algorithms to fall into local optima and overfitting, this paper proposes an intelligent inversion method based on support vector regression optimized by the artificial bee colony algorithm (ABC-SVR). The artificial bee colony algorithm is employed to adaptively optimize the core parameters of the SVR model, thereby enabling high-precision inversion of complex deep stress fields. Comparing the results with acoustic emission tests demonstrated that the ABC-SVR model significantly outperforms conventional SVR and backpropagation neural networks across various performance metrics. The inversion results show high consistency with the measured data, achieving a root mean square error (RMSE) of 1.25, a mean absolute percentage error (MAPE) of 4.16%, and a coefficient of determination (R²) of 0.908. This method can rapidly reconstruct high-precision initial in situ stress fields in deep unmined regions, providing highly reliable boundary conditions for numerical simulations and demonstrating significant engineering application potential. Full article

(This article belongs to the Special Issue Advances in Numerical Computation and Mathematical Modelling for Mechanics and Dynamics in Geotechnical Engineering)

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48 pages, 3619 KB

Open AccessArticle

Comparative Assessment of the Reliability of Non-Recoverable Subsystems of Mining Electronic Equipment Using Various Computational Methods

by Nikita V. Martyushev, Boris V. Malozyomov, Anton Y. Demin, Alexander V. Pogrebnoy, Georgy E. Kurdyumov, Viktor V. Kondratiev and Antonina I. Karlina

Mathematics 2026, 14(4), 723; https://doi.org/10.3390/math14040723 - 19 Feb 2026

Cited by 18 | Viewed by 847

Abstract

The assessment of reliability in non-repairable subsystems of mining electronic equipment represents a computationally challenging problem, particularly for complex and highly connected structures. This study presents a systematic comparative analysis of several deterministic approaches for reliability estimation, focusing on their computational efficiency, accuracy, [...] Read more.

The assessment of reliability in non-repairable subsystems of mining electronic equipment represents a computationally challenging problem, particularly for complex and highly connected structures. This study presents a systematic comparative analysis of several deterministic approaches for reliability estimation, focusing on their computational efficiency, accuracy, and applicability. The investigated methods include classical boundary techniques (minimal paths and cuts), analytical decomposition based on the Bayes theorem, the logic–probabilistic method (LPM) employing triangle–star transformations, and the algorithmic Structure Convolution Method (SCM), which is based on matrix reduction of the system’s connectivity graph. The reliability problem is formally represented using graph theory, where each element is modeled as a binary variable with independent failures, which is a standard and practically justified assumption for power electronic subsystems operating without common-cause coupling. Numerical experiments were carried out on canonical benchmark topologies—bridge, tree, grid, and random connected graphs—representing different levels of structural complexity. The results demonstrate that the SCM achieves exact reliability values with up to six orders of magnitude acceleration compared to the LPM for systems containing more than 20 elements, while maintaining polynomial computational complexity. Qualitatively, the compared approaches differ in the nature of the output and practical applicability: boundary methods provide fast interval estimates suitable for preliminary screening, whereas decomposition may exhibit a systematic bias for highly connected (non-series–parallel) topologies. In contrast, the SCM consistently preserves exactness while remaining computationally tractable for medium and large sparse-to-moderately dense graphs, making it preferable for repeated recalculations in design and optimization workflows. The methods were implemented in Python 3.7 using NumPy and NetworkX, ensuring transparency and reproducibility. The findings confirm that the SCM is an efficient, scalable, and mathematically rigorous tool for reliability assessment and structural optimization of large-scale non-repairable systems. The presented methodology provides practical guidelines for selecting appropriate reliability evaluation techniques based on system complexity and computational resource constraints. Full article

(This article belongs to the Special Issue Mathematical Foundations of Reliability Theory with Applications in Engineering and Applied Statistics)

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32 pages, 8198 KB

Open AccessArticle

Study of Jeffrey Fluid Motion Through Irregular Porous Circular Microchannel Under the Implications of Electromagnetohydrodynamic and Surface Charge-Dependent Slip

by Serdi Dio Ranandrasana, Lijun Zhang, Muhammad Mubashir Bhatti and Marin Marin

Mathematics 2026, 14(4), 722; https://doi.org/10.3390/math14040722 - 19 Feb 2026

Cited by 5 | Viewed by 753

Abstract

This work analyzes the non-Newtonian electromagnetohydrodynamic (EMHD) flow in an irregular circular porous microchannel while incorporating the consequences of surface charge-dependent slip boundary conditions. The Jeffrey fluid is employed to examine the non-Newtonian behavior, such as elasticity. The boundary walls of the channel [...] Read more.

This work analyzes the non-Newtonian electromagnetohydrodynamic (EMHD) flow in an irregular circular porous microchannel while incorporating the consequences of surface charge-dependent slip boundary conditions. The Jeffrey fluid is employed to examine the non-Newtonian behavior, such as elasticity. The boundary walls of the channel are considered in the form of periodic sinusoidal wave function. The mathematical formulation is developed using the momentum equation, modified Darcy’s law, the continuity equation, and Ohm’s law. The perturbation method is used to derive the solutions up to second-order approximation. The analytical expression for the velocity field and volumetric flow rate are explicitly presented. At the zeroth-order, a nonhomogeneous partial differential equation is solved, and the solutions are presented in terms of Bessel functions. The first-order problem defined by a homogeneous partial differential equation is solved using the method of separation of variables. At the second-order, a homogeneous partial differential equation is obtained, and the solution form is prescribed by the boundary conditions, consisting of a radially varying mean component and a second-harmonic angular contribution. Two- and three-dimensional plots are used to analyze and discuss the impacts of key parameters, namely the Reynolds, Darcy, and Hartmann numbers, channel corrugation amplitude and wave number, surface charge density, and the relaxation and retardation times on the velocity field and flow rate. It is found that elastic memory causes a proportional growth between the flow rate and the relaxation time, emphasizing the consequences of surface charge application in conjunction with corrugations. Conversely, maintaining a short retardation time mitigates changes in wave amplitude and surface charge. While prolonging it lessens the flow rate and diminishes corrugations and surface charge effects. The Darcy number dampens the velocity and the flow rate, while its enhancement reduces the impact of surface charge density and corrugations amplitude. For high Reynolds number, a ring phenomenon emerges which is attenuated by increased Darcy number, preventing the formation of trapped boluses close to the border. Ignoring surface charge amplifies the flow rate while its consideration diminishes the latter with reinforced impacts of surface charge and wall corrugations at higher Reynolds number. Full article

(This article belongs to the Special Issue Research on Applied Partial Differential Equations)

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14 pages, 395 KB

Open AccessArticle

Geodesic Boundary of Parabolic Surfaces and Existence of H-Fillable Curves in

H^{2} \times R

by Felix Nieto and Fredy Mesa

Mathematics 2026, 14(4), 721; https://doi.org/10.3390/math14040721 - 19 Feb 2026

Viewed by 547

Abstract

This article provides a geometric characterization of the geodesic boundary for surfaces invariant under parabolic isometries in

H^{2} \times R

. We present an alternative, constructive proof for the existence of minimal surfaces with rectangular asymptotic boundaries by utilizing a specific family [...] Read more.

This article provides a geometric characterization of the geodesic boundary for surfaces invariant under parabolic isometries in

H^{2} \times R

. We present an alternative, constructive proof for the existence of minimal surfaces with rectangular asymptotic boundaries by utilizing a specific family of invariant surfaces. Furthermore, we generalize these existence results to surfaces with constant mean curvature

H \in (0, 1 / 2)

. By analyzing the variation in the relative asymptotic height, we establish the existence of properly embedded H-surfaces whose geodesic boundary is a rectangle of arbitrary height, provided it exceeds a specific lower bound determined by the parabolic solution. Full article

(This article belongs to the Section B: Geometry and Topology)

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31 pages, 3003 KB

Open AccessArticle

A Two-Phase Nonlocal Integral Continuum Model Combined with Machine Learning for Flexural Wave Propagation in Small-Scale Breast Ducts

by Ali Farajpour and Wendy V. Ingman

Mathematics 2026, 14(4), 720; https://doi.org/10.3390/math14040720 - 19 Feb 2026

Viewed by 904

Abstract

The majority of breast malignancies arise from breast ducts at the small-scale level. Understanding the wave characteristics of breast ducts may assist in developing new technologies to detect very early changes that precede breast cancer. In this study, a two-phase nonlocal integral model [...] Read more.

The majority of breast malignancies arise from breast ducts at the small-scale level. Understanding the wave characteristics of breast ducts may assist in developing new technologies to detect very early changes that precede breast cancer. In this study, a two-phase nonlocal integral model is developed to analyse the biomechanical behavior of breast ducts under flexural wave propagation. The influence of surface stiffness, surface residual stress, stress nonlocality, and stromal matrix is taken into consideration. The breast duct consists of different biological layers, including the basement membrane, myoepithelial cells, and luminal epithelial cells. Surface properties are calculated for the outer basement membrane and inner luminal epithelial cell layer. The results of the two-phase nonlocal integral model are validated using available molecular dynamics simulations. In addition, various machine learning algorithms, such as a neural network model, gradient boosting, random forest, logistic regression, and Ridge regression, are developed and integrated with the two-phase nonlocal model to better understand the flexural wave characteristics of breast ducts. Incorporation of two-phase nonlocal integral stress effects, surface energy, and residual stress reduces the root mean square error from 4.16 to 0.24 when compared against molecular dynamics simulation data. Full article

(This article belongs to the Special Issue Advanced Mathematical Methods for Machine Learning in Biomedical Applications)

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27 pages, 842 KB

Open AccessArticle

An Automated Synthesis Framework for Benchmarking Quantum Resource Costs of Symmetric-Key Cryptography

by Chanho Choi, Jinseob Oh, SangMan Lee, Geumhwan Cho and Dooho Choi

Mathematics 2026, 14(4), 719; https://doi.org/10.3390/math14040719 - 19 Feb 2026

Viewed by 787

Abstract

Modern information security relies heavily on symmetric-key cryptography such as AES. As quantum computing advances, these classical schemes face increasing pressure from quantum key-search attacks, most notably Grover’s algorithm. To evaluate and compare quantum security quantitatively, the core components of symmetric-key algorithms must [...] Read more.

Modern information security relies heavily on symmetric-key cryptography such as AES. As quantum computing advances, these classical schemes face increasing pressure from quantum key-search attacks, most notably Grover’s algorithm. To evaluate and compare quantum security quantitatively, the core components of symmetric-key algorithms must be implemented and optimized as quantum circuits. Among them, the S-box is a key source of nonlinearity and often dominates the circuit cost. In this paper, we introduce ADOQ (Automatic Depth Optimizer for Quantum circuits), a modular Python (version 3.13.3) framework that automatically synthesizes reversible quantum circuits from S-box specifications and applies a sequence of depth optimization techniques to produce optimized QASM circuits. Our experiments show that ADOQ achieves circuit depths comparable to prior work on 4-qubit S-boxes, and it also supports synthesis for larger S-boxes. Full article

(This article belongs to the Special Issue Recent Advances in Quantum Optimization)

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17 pages, 354 KB

Open AccessArticle

Exploring Bi-Univalent Classes via q-Derivatives and Bivariate Fibonacci Polynomials

by Aruna Mogarala Guruvaya, Basem Aref Frasin, Ibtisam Aldawish and Sondekola Rudra Swamy

Mathematics 2026, 14(4), 718; https://doi.org/10.3390/math14040718 - 19 Feb 2026

Viewed by 586

Abstract

The q-calculus framework has emerged as a powerful tool in geometric function theory, enabling refined analysis of analytic and bi-univalent functions. Inspired by the versatility of the q-derivative operator, this paper introduces a new generalized subclass of bi-univalent functions defined via [...] Read more.

The q-calculus framework has emerged as a powerful tool in geometric function theory, enabling refined analysis of analytic and bi-univalent functions. Inspired by the versatility of the q-derivative operator, this paper introduces a new generalized subclass of bi-univalent functions defined via the q-derivative in combination with generalized bivariate Fibonacci polynomials, which have recently gained significant attention in mathematical research. For functions in this class, we establish bounds on the initial coefficients and provide estimates for the corresponding Fekete–Szegö functional. By appropriate specialization of parameters, our results recover several known findings and, importantly, produce bounds for new subclasses of bi-univalent functions not previously studied. This framework unifies earlier developments while extending the theory to novel, analytically meaningful classes. Full article

(This article belongs to the Special Issue Advanced Research in Complex Analysis Operators and Special Classes of Analytic Functions, 2nd Edition)

18 pages, 345 KB

Open AccessFeature PaperArticle

Dual Ternary Hyperholomorphicity: Cauchy–Pompeiu Formulas, Teodorescu Transforms, and Boundary Limits

by Ji Eun Kim

Mathematics 2026, 14(4), 717; https://doi.org/10.3390/math14040717 - 19 Feb 2026

Viewed by 678

Abstract

We develop a function theory on a three-dimensional reduced quaternionic model endowed with a projected (and, therefore, non-associative) product, together with its natural dual extension generated by a nilpotent infinitesimal unit. After introducing the associated first-order Dirac-type system, we construct explicit Cauchy kernels [...] Read more.

We develop a function theory on a three-dimensional reduced quaternionic model endowed with a projected (and, therefore, non-associative) product, together with its natural dual extension generated by a nilpotent infinitesimal unit. After introducing the associated first-order Dirac-type system, we construct explicit Cauchy kernels and prove a Cauchy–Pompeiu representation for sufficiently smooth functions with values in the dual algebra. We derive a Teodorescu-type right inverse, Liouville- and uniqueness-type principles, and residue formulas for isolated singularities. For smooth hypersurfaces, we establish Plemelj–Sokhotski boundary limits for the Cauchy transform and its dual lift. Worked examples illustrate how the reduced product interacts with boundary geometry and provide a practical route to computation. Full article

(This article belongs to the Special Issue Advances in Nonlinear Differential Equations with Applications)

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43 pages, 8869 KB

Open AccessArticle

Mathematical Modeling of Operational Reliability of Mine Lifting Equipment Based on Censored Data

by Denis A. Zadkov, Nikita V. Martyushev, Boris V. Malozyomov, Anton Y. Demin, Alexander V. Pogrebnoy, Elezaveta E. Kuleshova and Denis V. Valuev

Mathematics 2026, 14(4), 716; https://doi.org/10.3390/math14040716 - 18 Feb 2026

Cited by 19 | Viewed by 1262

Abstract

In this study, a comprehensive mathematical method for modeling the operational reliability of mine hoisting equipment under conditions of incomplete and heavily censored data is developed. The analyzed dataset includes 259 observations collected over a five-year period for six critical components, with the [...] Read more.

In this study, a comprehensive mathematical method for modeling the operational reliability of mine hoisting equipment under conditions of incomplete and heavily censored data is developed. The analyzed dataset includes 259 observations collected over a five-year period for six critical components, with the overall level of censoring reaching 62% and exceeding 70% for long life mechanical subsystems. Considering right, left, and interval censoring, the paper proposes a unified statistical procedure that combines empirical estimation of failure rates with parametric identification using Weibull, exponential, normal, and lognormal distributions. Model parameters are estimated using censored data–aware fitting procedures, while model selection is performed based on likelihood-based criteria, supplemented by correlation analysis to assess agreement between empirical and fitted reliability curves. The methodology is implemented computationally in the Mathcad Prime environment and is supplemented with mathematical tools for reconstructing survival curves, analyzing parameter sensitivity, and evaluating robustness at different censoring levels. In addition, an economic optimization model is formulated to determine cost-effective maintenance intervals by minimizing an integral functional that accounts for preventive maintenance, repair, and downtime costs. The results demonstrate that the proposed approach provides stable reliability estimates and reliable forecast intervals, enabling the construction of generalized life cycle curves for individual subsystems. The study establishes a rigorous mathematical basis for the transition from fixed-interval maintenance to adaptive, reliability-oriented maintenance strategies in industrial mine hoisting systems. Full article

(This article belongs to the Special Issue Reliability Analysis and Statistical Computing)

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