Mathematics

22 pages, 292 KiB

Open AccessFeature PaperArticle

by Stefka Bouyuklieva and Mariya Dzhumalieva-Stoeva

Mathematics 2025, 13(15), 2491; https://doi.org/10.3390/math13152491 (registering DOI) - 2 Aug 2025

The hull of a linear code C is the intersection of C with its dual code. The goal is to study the dimensions of the hulls of optimal binary and ternary linear codes for a given length and dimension. The focus is on [...] Read more.

The hull of a linear code C is the intersection of C with its dual code. The goal is to study the dimensions of the hulls of optimal binary and ternary linear codes for a given length and dimension. The focus is on the lengths at which self-orthogonal (respectively, LCD) optimal codes exist at fixed dimension. Full article

(This article belongs to the Special Issue Mathematics for Algebraic Coding Theory and Cryptography)

19 pages, 4169 KiB

Open AccessFeature PaperArticle

Magnetic Coil’s Performance Optimization with Nonsmooth Search Algorithms

by Igor Reznichenko, Primož Podržaj and Aljoša Peperko

Mathematics 2025, 13(15), 2490; https://doi.org/10.3390/math13152490 (registering DOI) - 2 Aug 2025

Abstract

This research is concerned with design optimization of control systems. Our case study deals with magnetic levitation, in which an essential part is a solenoid. Its dimensions, along with controller parameters, form the optimization variables. We present a novel way of writing the [...] Read more.

This research is concerned with design optimization of control systems. Our case study deals with magnetic levitation, in which an essential part is a solenoid. Its dimensions, along with controller parameters, form the optimization variables. We present a novel way of writing the explicit expression of the solenoid’s force acting on a magnetic dipole, as well as its first derivatives. Numerical tests using non-gradient search algorithms show the difference in optimal designs provided by these methods. Since such optimization depends on output signals, a comparison of step response analysis methods is presented. Full article

(This article belongs to the Special Issue Advances in Metaheuristic Optimization Algorithms)

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17 pages, 442 KiB

Open AccessArticle

Semiparametric Transformation Models with a Change Point for Interval-Censored Failure Time Data

by Junyao Ren, Shishun Zhao, Dianliang Deng, Tianshu You and Hui Huang

Mathematics 2025, 13(15), 2489; https://doi.org/10.3390/math13152489 (registering DOI) - 2 Aug 2025

Abstract

Change point models are widely used in medical and epidemiological studies to capture the threshold effects of continuous covariates on health outcomes. These threshold effects represent critical points at which the relationship between biomarkers or risk factors and disease risk shifts, often reflecting [...] Read more.

Change point models are widely used in medical and epidemiological studies to capture the threshold effects of continuous covariates on health outcomes. These threshold effects represent critical points at which the relationship between biomarkers or risk factors and disease risk shifts, often reflecting underlying biological mechanisms or clinically relevant intervention points. While most existing methods focus on right-censored data, interval censoring is common in large-scale clinical trials and follow-up studies, where the exact event times are not observed but are known to fall within time intervals. In this paper, we propose a semiparametric transformation model with an unknown change point for interval-censored data. The model allows flexible transformation functions, including the proportional hazards and proportional odds models, and it accommodates both main effects and their interactions with the threshold variable. Model parameters are estimated via the EM algorithm, with the change point identified through a profile likelihood approach using grid search. We establish the asymptotic properties of the proposed estimators and evaluate their finite-sample performance through extensive simulations, showing good accuracy and coverage properties. The method is further illustrated through an application to the Prostate, Lung, Colorectal, and Ovarian (PLCO) Cancer Screening Trial data. Full article

(This article belongs to the Special Issue Statistics: Theories and Applications)

19 pages, 1159 KiB

Open AccessArticle

A Biased–Randomized Iterated Local Search with Round-Robin for the Periodic Vehicle Routing Problem

by Juan F. Gomez, Antonio R. Uguina, Javier Panadero and Angel A. Juan

Mathematics 2025, 13(15), 2488; https://doi.org/10.3390/math13152488 (registering DOI) - 2 Aug 2025

Abstract

The periodic vehicle routing problem (PVRP) is a well-known challenge in real-life logistics, requiring the planning of vehicle routes over multiple days while enforcing visitation frequency constraints. Although numerous metaheuristic and exact methods have tackled various PVRP extensions, real-world settings call for additional [...] Read more.

The periodic vehicle routing problem (PVRP) is a well-known challenge in real-life logistics, requiring the planning of vehicle routes over multiple days while enforcing visitation frequency constraints. Although numerous metaheuristic and exact methods have tackled various PVRP extensions, real-world settings call for additional features such as depot configurations, tight visitation frequency constraints, and heterogeneous fleets. In this paper, we present a two-phase biased–randomized algorithm that addresses these complexities. In the first phase, a round-robin assignment quickly generates feasible and promising solutions, ensuring each customer’s frequency requirement is met across the multi-day horizon. The second phase refines these assignments via an iterative search procedure, improving route efficiency and reducing total operational costs. Extensive experimentation on standard PVRP benchmarks shows that our approach is able to generate solutions of comparable quality to established state-of-the-art algorithms in relatively low computational times and stands out in many instances, making it a practical choice for real life multi-day vehicle routing applications. Full article

(This article belongs to the Special Issue Optimization Algorithms for Operations Research and Scheduling Problems)

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14 pages, 303 KiB

Open AccessArticle

Existence Results for Nabla Fractional Problems with Anti-Periodic Boundary Conditions

by Nikolay D. Dimitrov and Jagan Mohan Jonnalagadda

Mathematics 2025, 13(15), 2487; https://doi.org/10.3390/math13152487 (registering DOI) - 2 Aug 2025

Abstract

The aim of this work is to study a class of nabla fractional difference equations with anti-periodic conditions. First, we construct the related Green’s function. After deducing some of its useful properties, we obtain an upper bound for its sum. Then, using this [...] Read more.

The aim of this work is to study a class of nabla fractional difference equations with anti-periodic conditions. First, we construct the related Green’s function. After deducing some of its useful properties, we obtain an upper bound for its sum. Then, using this bound, we are able to obtain three existence results based on the Banach contraction principle, Brouwer’s fixed point theorem, and Leray–Schauder’s nonlinear alternative, respectively. Then, we show some non-existence results for the studied problem, and existence results are also provided for a system of two equations of the considered type. Finally, we outline some particular examples in order to demonstrate the theoretical findings. Full article

(This article belongs to the Special Issue Fractional Calculus: Advances and Applications)

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30 pages, 1523 KiB

Open AccessArticle

Modeling and Simulation of Attraction–Repulsion Chemotaxis Mechanism System with Competing Signal

by Anandan P. Aswathi, Amar Debbouche, Yadhavan Karuppusamy and Lingeshwaran Shangerganesh

Mathematics 2025, 13(15), 2486; https://doi.org/10.3390/math13152486 (registering DOI) - 1 Aug 2025

Abstract

This paper addresses an attraction–repulsion chemotaxis system governed by Neumann boundary conditions within a bounded domain

Ω \subset R^{3}

that has a smooth boundary. The primary focus of the study is the chemotactic response of a species (cell population) to two competing [...] Read more.

This paper addresses an attraction–repulsion chemotaxis system governed by Neumann boundary conditions within a bounded domain

Ω \subset R^{3}

that has a smooth boundary. The primary focus of the study is the chemotactic response of a species (cell population) to two competing signals. We establish the existence and uniqueness of a weak solution to the system by analyzing the solvability of an approximate problem and utilizing the Leray–Schauder fixed-point theorem. By deriving appropriate a priori estimates, we demonstrate that the solution of the approximate problem converges to a weak solution of the original system. Additionally, we conduct computational studies of the model using the finite element method. The accuracy of our numerical implementation is evaluated through error analysis and numerical convergence, followed by various numerical simulations in a two-dimensional domain to illustrate the dynamics of the system and validate the theoretical findings. Full article

(This article belongs to the Special Issue Advances in Numerical Analysis of Partial Differential Equations)

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18 pages, 3344 KiB

Open AccessArticle

Elite Episode Replay Memory for Polyphonic Piano Fingering Estimation

by Ananda Phan Iman and Chang Wook Ahn

Mathematics 2025, 13(15), 2485; https://doi.org/10.3390/math13152485 (registering DOI) - 1 Aug 2025

Abstract

Piano fingering estimation remains a complex problem due to the combinatorial nature of hand movements and no best solution for any situation. A recent model-free reinforcement learning framework for piano fingering modeled each monophonic piece as an environment and demonstrated that value-based methods [...] Read more.

Piano fingering estimation remains a complex problem due to the combinatorial nature of hand movements and no best solution for any situation. A recent model-free reinforcement learning framework for piano fingering modeled each monophonic piece as an environment and demonstrated that value-based methods outperform probability-based approaches. Building on their finding, this paper addresses the more complex polyphonic fingering problem by formulating it as an online model-free reinforcement learning task with a novel training strategy. Thus, we introduce a novel Elite Episode Replay (EER) method to improve learning efficiency by prioritizing high-quality episodes during training. This strategy accelerates early reward acquisition and improves convergence without sacrificing fingering quality. The proposed architecture produces multiple-action outputs for polyphonic settings and is trained using both elite-guided and uniform sampling. Experimental results show that the EER strategy reduces training time per step by 21% and speeds up convergence by 18% while preserving the difficulty level and result of the generated fingerings. An empirical study of elite memory size further highlights its impact on training performance in solving piano fingering estimation. Full article

(This article belongs to the Special Issue New Advances in Data Analytics and Mining)

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13 pages, 251 KiB

Open AccessArticle

On Solution Set Associated with a Class of Multiple Objective Control Models

by Savin Treanţă and Omar Mutab Alsalami

Mathematics 2025, 13(15), 2484; https://doi.org/10.3390/math13152484 (registering DOI) - 1 Aug 2025

Abstract

In this paper, necessary and sufficient efficiency conditions in new multi-cost variational models are formulated and proved. To this end, we introduce a new notion of [...] Read more.

In this paper, necessary and sufficient efficiency conditions in new multi-cost variational models are formulated and proved. To this end, we introduce a new notion of

(ϑ_{0}, ϑ_{1}) - (σ_{0}, σ_{1}) - t y p e - I

functionals determined by multiple integrals. To better emphasize the significance of the suggested

(ϑ_{0}, ϑ_{1}) - (σ_{0}, σ_{1}) - t y p e - I

functionals and how they add to previous studies, we mention that the

(ϑ_{0}, ϑ_{1}) - (σ_{0}, σ_{1}) - t y p e - I

and generalized

(ϑ_{0}, ϑ_{1}) - (σ_{0}, σ_{1}) - t y p e - I - t y p e I

assumptions associated with the involved multiple integral functionals cover broader and more general classes of problems, where the convexity of the functionals is not fulfilled or the functionals considered are not of simple integral type. In addition, innovative proofs are provided for the main results. Full article

(This article belongs to the Special Issue Applied Functional Analysis and Applications: 2nd Edition)

27 pages, 4163 KiB

Open AccessArticle

Rainfall Forecasting Using a BiLSTM Model Optimized by an Improved Whale Migration Algorithm and Variational Mode Decomposition

by Yueqiao Yang, Shichuang Li, Ting Zhou, Liang Zhao, Xiao Shi and Boni Du

Mathematics 2025, 13(15), 2483; https://doi.org/10.3390/math13152483 (registering DOI) - 1 Aug 2025

Abstract

The highly stochastic nature of rainfall presents significant challenges for the accurate prediction of its time series. To enhance the prediction performance of non-stationary rainfall time series, this study proposes a hybrid deep learning forecasting framework—VMD-IWMA-BiLSTM—that integrates Variational Mode Decomposition (VMD), Improved Whale [...] Read more.

The highly stochastic nature of rainfall presents significant challenges for the accurate prediction of its time series. To enhance the prediction performance of non-stationary rainfall time series, this study proposes a hybrid deep learning forecasting framework—VMD-IWMA-BiLSTM—that integrates Variational Mode Decomposition (VMD), Improved Whale Migration Algorithm (IWMA), and Bidirectional Long Short-Term Memory network (BiLSTM). Firstly, VMD is employed to decompose the original rainfall series into multiple modes, extracting Intrinsic Mode Functions (IMFs) with more stable frequency characteristics. Secondly, IWMA is utilized to globally optimize multiple hyperparameters of the BiLSTM model, enhancing its ability to capture complex nonlinear relationships and long-term dependencies. Finally, experimental validation is conducted using daily rainfall data from 2020 to 2024 at the Xinzheng National Meteorological Observatory. The results demonstrate that the proposed framework outperforms traditional models such as LSTM, ARIMA, SVM, and LSSVM in terms of prediction accuracy. This research provides new insights and effective technical pathways for improving rainfall time series prediction accuracy and addressing the challenges posed by high randomness. Full article

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28 pages, 15616 KiB

Open AccessArticle

Binary Secretary Bird Optimization Algorithm for the Set Covering Problem

by Broderick Crawford, Felipe Cisternas-Caneo, Ricardo Soto, Claudio Patricio Toledo Mac-lean, José Lara Arce, Fabián Solís-Piñones, Gino Astorga and Giovanni Giachetti

Mathematics 2025, 13(15), 2482; https://doi.org/10.3390/math13152482 (registering DOI) - 1 Aug 2025

Abstract

The Set Coverage Problem (SCP) is an important combinatorial optimization problem known to be NP-complete. The use of metaheuristics to solve the SCP includes different algorithms. In particular, binarization techniques have been explored to adapt metaheuristics designed for continuous optimization problems to the [...] Read more.

The Set Coverage Problem (SCP) is an important combinatorial optimization problem known to be NP-complete. The use of metaheuristics to solve the SCP includes different algorithms. In particular, binarization techniques have been explored to adapt metaheuristics designed for continuous optimization problems to the binary domain of the SCP. In this work, we present a new approach to solve the SCP based on the Secretary Bird Optimization Algorithm (SBOA). This algorithm is inspired by the natural behavior of the secretary bird, known for its ability to hunt prey and evade predators in its environment. Since the SBOA was originally designed for optimization problems in continuous space and the SCP is a binary problem, this paper proposes the implementation of several binarization techniques to adapt the algorithm to the discrete domain. These techniques include eight transfer functions and five different discretization methods. Taken together, these combinations create multiple SBOA adaptations that effectively balance exploration and exploitation, promoting an adequate distribution in the search space. Experimental results applied to the SCP together with its variant Unicost SCP and compared to Grey Wolf Optimizer and Particle Swarm Optimization suggest that the binary version of SBOA is a robust algorithm capable of producing high quality solutions with low computational cost. Given the promising results obtained, it is proposed as future work to focus on complex and large-scale problems as well as to optimize their performance in terms of time and accuracy. Full article

(This article belongs to the Special Issue Recent Advances in Swarm Intelligence Algorithms: Optimization and Application)

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42 pages, 2867 KiB

Open AccessArticle

A Heuristic Approach to Competitive Facility Location via Multi-View K-Means Clustering with Co-Regularization and Customer Behavior

by Thanathorn Phoka, Praeploy Poonprapan and Pornpimon Boriwan

Mathematics 2025, 13(15), 2481; https://doi.org/10.3390/math13152481 (registering DOI) - 1 Aug 2025

Abstract

Solving competitive facility location problems can optimize market share or operational efficiency in environments where multiple firms compete for customer attention. In such contexts, facility attractiveness is shaped not only by geographic proximity but also by customer preference characteristics. This study presents a [...] Read more.

Solving competitive facility location problems can optimize market share or operational efficiency in environments where multiple firms compete for customer attention. In such contexts, facility attractiveness is shaped not only by geographic proximity but also by customer preference characteristics. This study presents a novel heuristic framework that integrates multi-view K-means clustering with customer behavior modeling reinforced by a co-regularization mechanism to align clustering results across heterogeneous data views. By jointly exploiting spatial and behavioral information, the framework clusters customers and facilities into meaningful market segments. Within each segment, a bilevel optimization model is applied to represent the sequential decision-making of competing entities—where a leader first selects facility locations, followed by a reactive follower. An empirical evaluation on a real-world dataset from San Francisco demonstrates that the proposed approach, using optimal co-regularization parameters, achieves a total runtime of approximately 4.00 s—representing a 99.34% reduction compared to the full CFLBP-CB model (608.58 s) and a 99.32% reduction compared to a genetic algorithm (585.20 s). Concurrently, it yields an overall profit of 16,104.17, which is an approximate 0.72% increase over the Direct CFLBP-CB profit of 15,988.27 and is only 0.21% lower than the genetic algorithm’s highest profit of 16,137.75. Moreover, comparative analysis reveals that the proposed multi-view clustering with co-regularization outperforms all single-view baselines, including K-means, spectral, and hierarchical methods. This superiority is evidenced by an approximate 5.21% increase in overall profit and a simultaneous reduction in optimization time, thereby demonstrating its effectiveness in capturing complementary spatial and behavioral structures for competitive facility location. Notably, the proposed two-stage approach achieves high-quality solutions with significantly shorter computation times, making it suitable for large-scale or time-sensitive competitive facility planning tasks. Full article

(This article belongs to the Section E: Applied Mathematics)

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14 pages, 387 KiB

Open AccessFeature PaperArticle

Recovery of Implied Volatility in a Spatial-Fractional Black–Scholes Equation Under a Finite Moment Log Stable Model

by Xiaoying Jiang, Chunmei Shi and Yujie Wei

Mathematics 2025, 13(15), 2480; https://doi.org/10.3390/math13152480 (registering DOI) - 1 Aug 2025

Abstract

In this paper, we study direct and inverse problems for a spatial-fractional Black–Scholes equation with space-dependent volatility. For the direct problem, we provide CN-WSGD (Crank–Nicholson and the weighted and shifted Grünwald difference) scheme to solve the initial boundary value problem. The latter aims [...] Read more.

In this paper, we study direct and inverse problems for a spatial-fractional Black–Scholes equation with space-dependent volatility. For the direct problem, we provide CN-WSGD (Crank–Nicholson and the weighted and shifted Grünwald difference) scheme to solve the initial boundary value problem. The latter aims to recover the implied volatility via observable option prices. Using a linearization technique, we rigorously derive a mathematical formulation of the inverse problem in terms of a Fredholm integral equation of the first kind. Based on an integral equation, an efficient numerical reconstruction algorithm is proposed to recover the coefficient. Numerical results for both problems are provided to illustrate the validity and effectiveness of proposed methods. Full article

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30 pages, 599 KiB

Open AccessReview

A Survey of Approximation Algorithms for the Power Cover Problem

by Jiaming Zhang, Zhikang Zhang and Weidong Li

Mathematics 2025, 13(15), 2479; https://doi.org/10.3390/math13152479 (registering DOI) - 1 Aug 2025

Abstract

Wireless sensor networks (WSNs) have attracted significant attention due to their widespread applications in various fields such as environmental monitoring, agriculture, intelligent transportation, and healthcare. In these networks, the power cost of a sensor node is closely related to the radius of its [...] Read more.

Wireless sensor networks (WSNs) have attracted significant attention due to their widespread applications in various fields such as environmental monitoring, agriculture, intelligent transportation, and healthcare. In these networks, the power cost of a sensor node is closely related to the radius of its coverage area, following a nonlinear relationship where power increases as the coverage radius grows according to an attenuation factor. This means that increasing the coverage radius of a sensor leads to a corresponding increase in its power cost. Consequently, minimizing the total power cost of the network while all clients are served has become a crucial research topic. The power cover problem focuses on adjusting the power levels of sensors to serve all clients while minimizing the total power cost. This survey focuses on the power cover problem and its related variants in WSNs. Specifically, it introduces nonlinear integer programming formulations for the power cover problem and its related variants, all within the specified sensor setting. It also provides a comprehensive overview of the power cover problem and its variants under both specified and unspecified sensor settings, summarizes existing results and approximation algorithms, and outlines potential directions for future research. Full article

(This article belongs to the Special Issue Data-Driven or AI-Driven Optimization Algorithms and Their Applications)

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21 pages, 670 KiB

Open AccessArticle

I-fp Convergence in Fuzzy Paranormed Spaces and Its Application to Robust Base-Stock Policies with Triangular Fuzzy Demand

by Muhammed Recai Türkmen and Hasan Öğünmez

Mathematics 2025, 13(15), 2478; https://doi.org/10.3390/math13152478 - 1 Aug 2025

Abstract

We introduce I-fp convergence (ideal convergence in fuzzy paranormed spaces) and develop its core theory, including stability results and an equivalence to

I^{*}

-fp convergence under the AP Property. Building on this foundation, we design an adaptive base-stock policy for a single-echelon [...] Read more.

We introduce I-fp convergence (ideal convergence in fuzzy paranormed spaces) and develop its core theory, including stability results and an equivalence to

I^{*}

-fp convergence under the AP Property. Building on this foundation, we design an adaptive base-stock policy for a single-echelon inventory system in which weekly demand is expressed as triangular fuzzy numbers while holiday or promotion weeks are treated as ideal-small anomalies. The policy is updated by a simple learning rule that can be implemented in any spreadsheet, requires no optimisation software, and remains insensitive to tuning choices. Extensive simulation confirms that the method simultaneously lowers cost, reduces average inventory and raises service level relative to a crisp benchmark, all while filtering sparse demand spikes in a principled way. These findings position I-fp convergence as a lightweight yet rigorous tool for blending linguistic uncertainty with anomaly-aware decision making in supply-chain analytics. Full article

(This article belongs to the Special Issue Mathematical Models and Methods for Supply Chain and Operations Research)

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22 pages, 7609 KiB

Open AccessArticle

Bidirectional Conservative–Dissipative Transitions in a Five-Dimensional Fractional Chaotic System

by Yiming Wang, Fengjiao Gao and Mingqing Zhu

Mathematics 2025, 13(15), 2477; https://doi.org/10.3390/math13152477 - 1 Aug 2025

Abstract

This study investigates a modified five-dimensional chaotic system by incorporating structural term adjustments and Caputo fractional-order differential operators. The modified system exhibits significantly enriched dynamic behaviors, including offset boosting, phase trajectory rotation, phase trajectory reversal, and contraction phenomena. Additionally, the system exhibits bidirectional [...] Read more.

This study investigates a modified five-dimensional chaotic system by incorporating structural term adjustments and Caputo fractional-order differential operators. The modified system exhibits significantly enriched dynamic behaviors, including offset boosting, phase trajectory rotation, phase trajectory reversal, and contraction phenomena. Additionally, the system exhibits bidirectional transitions—conservative-to-dissipative transitions governed by initial conditions and dissipative-to-conservative transitions controlled by fractional order variations—along with a unique chaotic-to-quasiperiodic transition observed exclusively at low fractional orders. To validate the system’s physical realizability, a signal processing platform based on Digital Signal Processing (DSP) is implemented. Experimental measurements closely align with numerical simulations, confirming the system’s feasibility for practical applications. Full article

(This article belongs to the Special Issue Nonlinear Dynamics and Chaos Theory, 2nd Edition)

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23 pages, 930 KiB

Open AccessFeature PaperArticle

One-Dimensional Shallow Water Equations Ill-Posedness

by Tew-Fik Mahdi

Mathematics 2025, 13(15), 2476; https://doi.org/10.3390/math13152476 - 1 Aug 2025

Abstract

In 2071, the Hydraulic community will commemorate the second centenary of the Baré de Saint-Venant equations, also known as the Shallow Water Equations (SWE). These equations are fundamental to the study of open-channel flow. As non-linear partial differential equations, their solutions were largely [...] Read more.

In 2071, the Hydraulic community will commemorate the second centenary of the Baré de Saint-Venant equations, also known as the Shallow Water Equations (SWE). These equations are fundamental to the study of open-channel flow. As non-linear partial differential equations, their solutions were largely unattainable until the development of computers and numerical methods. Following 1960, various numerical schemes emerged, with Preissmann’s scheme becoming the most widely employed in many software applications. In the 1990s, some researchers identified a significant limitation in existing software and codes: the inability to simulate transcritical flow. At that time, Preissmann’s scheme was the dominant method employed in hydraulics tools, leading the research community to conclude that this scheme could not handle transcritical flow due to suspected instability. In response to this concern, several researchers suggested modifications to Preissmann’s scheme to enable the simulation of transcritical flow. This paper will demonstrate that these accusations against the Preissmann scheme are unfounded and that the proposed improvements are unnecessary. The observed instability is not due to the numerical method itself, but rather a mathematical instability inherent to the SWE, which can lead to ill-posed conditions if a specific derived condition is not met. In the context of a friction slope formula based on Manning or Chézy types, the condition for ill-posedness of the 1D shallow water equations simplifies to the Vedernikov number condition, which is necessary for roll waves to develop in uniform flow. This derived condition is also relevant for the formation of roll waves in unsteady flow when the 1D shallow water equations become ill-posed. Full article

(This article belongs to the Special Issue Computational Fluid Dynamics, 3rd Edition)

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9 pages, 1015 KiB

Open AccessArticle

Extremal Values of Second Zagreb Index of Unicyclic Graphs Having Maximum Cycle Length: Two New Algorithms

by Hacer Ozden Ayna

Mathematics 2025, 13(15), 2475; https://doi.org/10.3390/math13152475 - 31 Jul 2025

Abstract

It is well-known that the necessary and sufficient condition for a connected graph to be unicyclic is that its omega invariant, a recently introduced graph invariant useful in combinatorial and topological calculations, is zero. This condition could be stated as the condition that [...] Read more.

It is well-known that the necessary and sufficient condition for a connected graph to be unicyclic is that its omega invariant, a recently introduced graph invariant useful in combinatorial and topological calculations, is zero. This condition could be stated as the condition that the order and the size of the graph are equal. Using a recent result saying that the length of the unique cycle could be any integer between 1 and n − a₁ where a₁ is the number of pendant vertices in the graph, two explicit labeling algorithms are provided that attain these extremal values of the first and second Zagreb indices by means of an application of the well-known rearrangement inequality. When the cycle has the maximum length, we obtain the situation where all the pendant vertices are adjacent to the support vertices, the neighbors of the pendant vertices, which are placed only on the unique cycle. This makes it easy to calculate the second Zagreb index, as the contribution of the pendant edges to such indices is fixed, implying that we can only calculate these indices for the edges on the cycle. Full article

(This article belongs to the Special Issue Graph Theory and Applications, 3rd Edition)

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22 pages, 1642 KiB

Open AccessArticle

Spatiotemporal Dynamics of a Predator–Prey Model with Harvest and Disease in Prey

by Jingen Yang, Zhong Zhao, Yingying Kong and Jing Xu

Mathematics 2025, 13(15), 2474; https://doi.org/10.3390/math13152474 - 31 Jul 2025

Abstract

In this paper, we propose a diffusion-type predator–prey interaction model with harvest and disease in prey, and conduct stability analysis and pattern formation analysis on the model. For the temporal model, the asymptotic stability of each equilibrium is analyzed using the linear stability [...] Read more.

In this paper, we propose a diffusion-type predator–prey interaction model with harvest and disease in prey, and conduct stability analysis and pattern formation analysis on the model. For the temporal model, the asymptotic stability of each equilibrium is analyzed using the linear stability method, and the conditions for Hopf bifurcation to occur near the positive equilibrium are investigated. The simulation results indicate that an increase in infection force might disrupt the stability of the model, while an increase in harvesting intensity would make the model stable. For the spatiotemporal model, a priori estimate for the positive steady state is obtained for the non-existence of the non-constant positive solution using maximum principle and Harnack inequality. The Leray–Schauder degree theory is used to study the sufficient conditions for the existence of non-constant positive steady states of the model, and pattern formation are achieved through numerical simulations. This indicates that the movement of prey and predators plays an important role in pattern formation, and different diffusions of these species may play essentially different effects. Full article

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40 pages, 6841 KiB

Open AccessArticle

Distributionally Robust Multivariate Stochastic Cone Order Portfolio Optimization: Theory and Evidence from Borsa Istanbul

by Larissa Margerata Batrancea, Mehmet Ali Balcı, Ömer Akgüller and Lucian Gaban

Mathematics 2025, 13(15), 2473; https://doi.org/10.3390/math13152473 - 31 Jul 2025

Abstract

We introduce a novel portfolio optimization framework—Distributionally Robust Multivariate Stochastic Cone Order (DR-MSCO)—which integrates partial orders on random vectors with Wasserstein-metric ambiguity sets and adaptive cone structures to model multivariate investor preferences under distributional uncertainty. Grounded in measure theory and convex analysis, DR-MSCO [...] Read more.

We introduce a novel portfolio optimization framework—Distributionally Robust Multivariate Stochastic Cone Order (DR-MSCO)—which integrates partial orders on random vectors with Wasserstein-metric ambiguity sets and adaptive cone structures to model multivariate investor preferences under distributional uncertainty. Grounded in measure theory and convex analysis, DR-MSCO employs data-driven cone selection calibrated to market regimes, along with coherent tail-risk operators that generalize Conditional Value-at-Risk to the multivariate setting. We derive a tractable second-order cone programming reformulation and demonstrate statistical consistency under empirical ambiguity sets. Empirically, we apply DR-MSCO to 23 Borsa Istanbul equities from 2021–2024, using a rolling estimation window and realistic transaction costs. Compared to classical mean–variance and standard distributionally robust benchmarks, DR-MSCO achieves higher overall and crisis-period Sharpe ratios (2.18 vs. 2.09 full sample; 0.95 vs. 0.69 during crises), reduces maximum drawdown by 10%, and yields endogenous diversification without exogenous constraints. Our results underscore the practical benefits of combining multivariate preference modeling with distributional robustness, offering institutional investors a tractable tool for resilient portfolio construction in volatile emerging markets. Full article

(This article belongs to the Special Issue Modern Trends in Mathematics, Probability and Statistics for Finance)

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