Mathematics

18 pages, 2692 KiB

Open AccessFeature PaperArticle

Unit Size Determination for Exploratory Brain Imaging Analysis: A Quest for a Resolution-Invariant Metric

by Jihnhee Yu, HyunAh Lee and Zohi Sternberg

Mathematics 2025, 13(7), 1195; https://doi.org/10.3390/math13071195 (registering DOI) - 4 Apr 2025

Defining an adequate unit size is often crucial in brain imaging analysis, where datasets are complex, high-dimensional, and computationally demanding. Unit size refers to the spatial resolution at which brain data is aggregated for analysis. Optimizing unit size in data aggregation requires balancing [...] Read more.

Defining an adequate unit size is often crucial in brain imaging analysis, where datasets are complex, high-dimensional, and computationally demanding. Unit size refers to the spatial resolution at which brain data is aggregated for analysis. Optimizing unit size in data aggregation requires balancing computational efficiency in handling large-scale data sets with the preservation of brain activity patterns, minimizing signal dilution. We propose using the Calinski–Harabasz index, demonstrating its invariance to sample size changes due to varying image resolutions when no distributional differences are present, while the index effectively identifies an appropriate unit size for detecting suspected regions in image comparisons. The resolution-independent metric can be used for unit size evaluation, ensuring adaptability across different imaging protocols and modalities. This study enhances the scalability and efficiency of brain imaging research by providing a robust framework for unit size optimization, ultimately strengthening analytical tools for investigating brain function and structure. Full article

(This article belongs to the Special Issue Mathematical Methods for Image Processing and Computer Vision)

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14 pages, 513 KiB

Open AccessFeature PaperArticle

Set-Valued Approximation—Revisited and Improved

by David Levin

Mathematics 2025, 13(7), 1194; https://doi.org/10.3390/math13071194 (registering DOI) - 4 Apr 2025

Abstract

We address the problem of approximating a set-valued function F, where

F : [a, b] \to K (R^{d})

given its samples

{F (a + i h)}_{i = 0}^{N}

, with [...] Read more.

We address the problem of approximating a set-valued function F, where

F : [a, b] \to K (R^{d})

given its samples

{F (a + i h)}_{i = 0}^{N}

, with

h = (b - a) / N

. We revisit an existing method that approximates set-valued functions by interpolating signed-distance functions. This method provides a high-order approximation for general topologies but loses accuracy near points where F undergoes topological changes. To address this, we introduce new techniques that enhance efficiency and maintain high-order accuracy across

[a, b]

. Building on the foundation of previous publication, we introduce new techniques to improve the method’s efficiency and extend its high-order approximation accuracy throughout the entire interval

[a, b]

. Particular focus is placed on identifying and analyzing the behavior of F near topological transition points. To address this, two algorithms are introduced. The first algorithm employs signed-distance quasi-interpolation, incorporating specialized adjustments to effectively handle singularities at points of topological change. The second algorithm leverages an implicit function representation of

G r a p h (F)

, offering an alternative and robust approach to its approximation. These enhancements improve accuracy and stability in handling set-valued functions with changing topologies. Full article

(This article belongs to the Special Issue Advances in Approximation Theory and Numerical Functional Analysis)

24 pages, 380 KiB

Open AccessArticle

Pseudorandom Function from Learning Burnside Problem

by Dhiraj K. Pandey and Antonio R. Nicolosi

Mathematics 2025, 13(7), 1193; https://doi.org/10.3390/math13071193 (registering DOI) - 4 Apr 2025

Abstract

We present three progressively refined pseudorandom function (PRF) constructions based on the learning Burnside homomorphisms with noise (

B_{n}

-LHN) assumption. A key challenge in this approach is error management, which we address by extracting errors from the secret key. Our first [...] Read more.

We present three progressively refined pseudorandom function (PRF) constructions based on the learning Burnside homomorphisms with noise (

B_{n}

-LHN) assumption. A key challenge in this approach is error management, which we address by extracting errors from the secret key. Our first design, a direct pseudorandom generator (PRG), leverages the lower entropy of the error set (E) compared to the Burnside group (

B_{r}

). The second, a parameterized PRG, derives its function description from public parameters and the secret key, aligning with the relaxed PRG requirements in the Goldreich–Goldwasser–Micali (GGM) PRF construction. The final indexed PRG introduces public parameters and an index to refine efficiency. To optimize computations in Burnside groups, we enhance concatenation operations and homomorphisms from

B_{n}

to

B_{r}

for

n ≫ r

. Additionally, we explore algorithmic improvements and parallel computation strategies to improve efficiency. Full article

(This article belongs to the Section E1: Mathematics and Computer Science)

27 pages, 3726 KiB

Open AccessArticle

How Can Viruses Affect the Growth of Zooplankton on Phytoplankton in a Chemostat?

by Nada A. Almuallem and Miled El Hajji

Mathematics 2025, 13(7), 1192; https://doi.org/10.3390/math13071192 (registering DOI) - 4 Apr 2025

Abstract

In this work, we investigated a simple mathematical model describing the consumption of virus-infected phytoplankton by zooplankton in a chemostat. The system was studied by calculating the basic reproduction number, the equilibrium points, and their local and global stability. A sensitivity analysis was [...] Read more.

In this work, we investigated a simple mathematical model describing the consumption of virus-infected phytoplankton by zooplankton in a chemostat. The system was studied by calculating the basic reproduction number, the equilibrium points, and their local and global stability. A sensitivity analysis was used to identify key chemostat factors that significantly affected the aquatic system. Additionally, we considered an optimal strategy based on the use of the dilution rate as an operating parameter that helps maintain the ecological balance of the aquatic food web. Full article

(This article belongs to the Section C2: Dynamical Systems)

23 pages, 2977 KiB

Open AccessArticle

Coevolutionary Algorithm with Bayes Theorem for Constrained Multiobjective Optimization

by Shaoyu Zhao, Heming Jia, Yongchao Li and Qian Shi

Mathematics 2025, 13(7), 1191; https://doi.org/10.3390/math13071191 (registering DOI) - 4 Apr 2025

Abstract

The effective resolution of constrained multi-objective optimization problems (CMOPs) requires a delicate balance between maximizing objectives and satisfying constraints. Previous studies have demonstrated that multi-swarm optimization models exhibit robust performance in CMOPs; however, their high computational resource demands can hinder convergence efficiency. This [...] Read more.

The effective resolution of constrained multi-objective optimization problems (CMOPs) requires a delicate balance between maximizing objectives and satisfying constraints. Previous studies have demonstrated that multi-swarm optimization models exhibit robust performance in CMOPs; however, their high computational resource demands can hinder convergence efficiency. This article proposes an environment selection model based on Bayes’ theorem, leveraging the advantages of dual populations. The model constructs prior knowledge using objective function values and constraint violation values, and then, it integrates this information to enhance selection processes. By dynamically adjusting the selection of the auxiliary population based on prior knowledge, the algorithm significantly improves its adaptability to various CMOPs. Additionally, a population size adjustment strategy is introduced to mitigate the computational burden of dual populations. By utilizing past prior knowledge to estimate the probability of function value changes, offspring allocation is dynamically adjusted, optimizing resource utilization. This adaptive adjustment prevents unnecessary computational waste during evolution, thereby enhancing both convergence and diversity. To validate the effectiveness of the proposed algorithm, comparative experiments were performed against seven constrained multi-objective optimization algorithms (CMOEAs) across three benchmark test sets and 12 real-world problems. The results show that the proposed algorithm outperforms the others in both convergence and diversity. Full article

26 pages, 482 KiB

Open AccessArticle

Computational Construction of Sequential Efficient Designs for the Second-Order Model

by Norah Alshammari, Stelios Georgiou and Stella Stylianou

Mathematics 2025, 13(7), 1190; https://doi.org/10.3390/math13071190 (registering DOI) - 4 Apr 2025

Abstract

Sequential experimental designs enhance data collection efficiency by reducing resource usage and accelerating experimental objectives. This paper presents a model-driven approach to sequential Latin hypercube designs (SLHDs) tailored for second-order models. Unlike traditional model-free SLHDs, our method optimizes a conditional A-criterion to improve [...] Read more.

Sequential experimental designs enhance data collection efficiency by reducing resource usage and accelerating experimental objectives. This paper presents a model-driven approach to sequential Latin hypercube designs (SLHDs) tailored for second-order models. Unlike traditional model-free SLHDs, our method optimizes a conditional A-criterion to improve efficiency, particularly in higher dimensions. By relaxing the restriction of non-replicated points within equally spaced intervals, our approach maintains space-filling properties while allowing greater flexibility for model-specific optimization. Using Sobol sequences, the algorithm iteratively selects good points, enhancing conditional A-efficiency compared to distance minimization methods. Additional criteria, such as D-efficiency, further validate the generated design matrices, ensuring robust performance. The proposed approach demonstrates superior results, with detailed tables and graphs illustrating its advantages across applications in engineering, pharmacology, and manufacturing. Full article

(This article belongs to the Special Issue Advances in Computational Statistics, Design of Experiments, and Its Applications)

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17 pages, 5491 KiB

Open AccessArticle

Dynamics of the Diphtheria Epidemic in Nigeria: Insights from the Kano State Outbreak Data

by Sani Musa, Salisu Usaini, Idris Ahmed, Chanakarn Kiataramkul and Jessada Tariboon

Mathematics 2025, 13(7), 1189; https://doi.org/10.3390/math13071189 - 4 Apr 2025

Abstract

Diphtheria is a severely infectious and deadly bacterial disease with Corynebacterium diphtheriae as the causative agent. Since the COVID-19 pandemic, contagious diseases such as diphtheria have re-emerged due to disruptions in routine childhood immunization programs worldwide. Nigeria is witnessing a significant increase in [...] Read more.

Diphtheria is a severely infectious and deadly bacterial disease with Corynebacterium diphtheriae as the causative agent. Since the COVID-19 pandemic, contagious diseases such as diphtheria have re-emerged due to disruptions in routine childhood immunization programs worldwide. Nigeria is witnessing a significant increase in diphtheria outbreaks likely due to an inadequate health care system and insufficient public enlightenment campaign. This paper presents a mathematical epidemic diphtheria model in Nigeria, which includes a public enlightenment campaign to assess its positive impact on the prevalence of the disease. The mathematical analysis of the model reveals two equilibrium points: the diphtheria infection-free equilibrium and the endemic equilibrium. These equilibrium points are shown to be stable globally asymptotically if

R_{c} < 1

and

R_{c} > 1

, respectively. The model was fit using the confirmed diphtheria cases data of Kano State from January to December 2023. Sensitivity analysis indicates that the transmission rate and recovery rate of asymptomatic peopleare crucial parameters to be considered in developing effective strategies for diphtheria control and prevention. This analysis also reveals that the implementation of a high-level public enlightenment campaign and its high efficacy effectively reduce the prevalence of diphtheria. Finally, numerical simulations show that combining the public enlightenment campaign and isolating infected individuals is the best strategy to contain the spread of diphtheria. Full article

(This article belongs to the Special Issue Mathematical Modeling of Disease Dynamics)

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16 pages, 7032 KiB

Open AccessArticle

I-NeRV: A Single-Network Implicit Neural Representation for Efficient Video Inpainting

by Jie Ji, Shuxuan Fu and Jiaju Man

Mathematics 2025, 13(7), 1188; https://doi.org/10.3390/math13071188 - 4 Apr 2025

Abstract

Deep learning methods based on implicit neural representations offer an efficient and automated solution for video inpainting by leveraging the inherent characteristics of video data. However, the limited size of the video embedding (e.g.,

16 \times 2 \times 4

) generated by the [...] Read more.

Deep learning methods based on implicit neural representations offer an efficient and automated solution for video inpainting by leveraging the inherent characteristics of video data. However, the limited size of the video embedding (e.g.,

16 \times 2 \times 4

) generated by the encoder restricts the available feature information for the decoder, which, in turn, constrains the model’s representational capacity and degrades inpainting performance. While implicit neural representations have shown promise for video inpainting, most of the existing research still revolves around image inpainting and does not fully account for the spatiotemporal continuity and relationships present in videos. This gap highlights the need for more advanced techniques capable of capturing and exploiting the spatiotemporal dynamics of video data to further improve inpainting results. To address this issue, we introduce I-NeRV, the first implicit neural-representation-based design specifically tailored for video inpainting. By embedding spatial features and modeling the spatiotemporal continuity between frames, I-NeRV significantly enhances inpainting performance, especially for videos with missing regions. To further boost the quality of inpainting, we propose an adaptive embedding size design and a weighted loss function. We also explore strategies for balancing model size and computational efficiency, such as fine-tuning the embedding size and customizing convolution kernels to accommodate various resource constraints. Extensive experiments on benchmark datasets demonstrate that our approach substantially outperforms state-of-the-art methods in video inpainting, achieving an average of 3.47 PSNR improvement in quality metrics. Full article

(This article belongs to the Special Issue New Trends in Computer Vision, Deep Learning and Artificial Intelligence)

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19 pages, 910 KiB

Open AccessFeature PaperArticle

The Inverse Scattering of Three-Dimensional Inhomogeneous Steady-State Sound Field Models

by Zhaoxi Sun, Wenbin Zhang and Meiling Zhao

Mathematics 2025, 13(7), 1187; https://doi.org/10.3390/math13071187 - 3 Apr 2025

Abstract

We propose a U-Net regression network model for sliced data to reconstruct a three-dimensional irregular steady-state sound field filling inhomogeneous anisotropic media. Through an innovative sliced data processing strategy, the 3D reconstruction problem is decomposed into a combination of 2D problems, thereby significantly [...] Read more.

We propose a U-Net regression network model for sliced data to reconstruct a three-dimensional irregular steady-state sound field filling inhomogeneous anisotropic media. Through an innovative sliced data processing strategy, the 3D reconstruction problem is decomposed into a combination of 2D problems, thereby significantly reducing the computational cost. The designed multi-channel U-Net fully utilizes the strengths of both the encoder and decoder, exhibiting strong feature extraction and spatial detail recovery capabilities. Numerical experiments show that the model can not only effectively reconstruct the complex sound field structure containing non-convex regions, but it can also synchronously restore the spatial distribution of the media and their parameter matrix, successfully achieving the dual reconstruction of the shape and physical parameters of the steady-state sound field. Full article

22 pages, 503 KiB

Open AccessFeature PaperArticle

A Novel Group Decision-Making Method with Adjustment Willingness in a Distributed Hesitant Fuzzy Linguistic Environment

by Xiao Liang, Xiaoxia Xu and Francisco Javier Cabrerizo

Mathematics 2025, 13(7), 1186; https://doi.org/10.3390/math13071186 - 3 Apr 2025

Abstract

This research aims to construct a group decision-making (GDM) method that considers decision makers’ (DMs’) willingness to adjust in a distributed hesitant fuzzy linguistic (DHFL) environment. First, to address the practical scenario where DMs may express preferences using multiple linguistic values with explicit [...] Read more.

This research aims to construct a group decision-making (GDM) method that considers decision makers’ (DMs’) willingness to adjust in a distributed hesitant fuzzy linguistic (DHFL) environment. First, to address the practical scenario where DMs may express preferences using multiple linguistic values with explicit preference strengths, this paper extends the distributed hesitant fuzzy linguistic preference relation (DHFLPR) and supplements missing probabilities. Second, we integrate multiplicative consistency and consensus within a DHFL environment to construct two preference optimization models, whose objective functions are to minimize the overall adjustment based on DMs’ willingness to adjust, thus making the decision more consistent with actual environments. Finally, the viability and effectiveness of the new method are validated by numerical examples. The results show that our new method allows individual preferences to quickly meet the consistency requirement while maximally preserving their original preferences. Additionally, the DHFLPRs maintain the fuzziness and hesitancy in the new preferences, and effectively address the issue of unequal importance among distinct linguistic preference values. Full article

14 pages, 269 KiB

Open AccessArticle

Weak Solutions to Leray–Lions-Type Degenerate Quasilinear Elliptic Equations with Nonlocal Effects, Double Hardy Terms, and Variable Exponents

by Khaled Kefi and Mohammed M. Al-Shomrani

Mathematics 2025, 13(7), 1185; https://doi.org/10.3390/math13071185 - 3 Apr 2025

Abstract

This study investigates the existence and multiplicity of weak solutions for a class of degenerate weighted quasilinear elliptic equations that incorporate nonlocal nonlinearities, a double Hardy term, and variable exponents. The problem encompasses a degenerate nonlinear operator characterized by variable exponent growth, along [...] Read more.

This study investigates the existence and multiplicity of weak solutions for a class of degenerate weighted quasilinear elliptic equations that incorporate nonlocal nonlinearities, a double Hardy term, and variable exponents. The problem encompasses a degenerate nonlinear operator characterized by variable exponent growth, along with a nonlocal interaction term and specific constraints on the nonlinearity. By employing critical point theory, we establish the existence of at least three weak solutions under sufficiently general assumptions. Full article

23 pages, 307 KiB

Open AccessFeature PaperArticle

SO(3): The Principal Bundle Structure

by Ján Brajerčík and Demeter Krupka

Mathematics 2025, 13(7), 1184; https://doi.org/10.3390/math13071184 - 3 Apr 2025

Abstract

In this article, the special orthogonal group SO(3) is considered as a topological group. We show that SO(3) has the structure of a principal SO(2)-bundle over the sphere

S^{2}

. As a consequence, we prove that every orbit of an SO(3)-action on [...] Read more.

In this article, the special orthogonal group SO(3) is considered as a topological group. We show that SO(3) has the structure of a principal SO(2)-bundle over the sphere

S^{2}

. As a consequence, we prove that every orbit of an SO(3)-action on a topological space is either trivial or homeomorphic to

S^{2}

. We also introduce a topological atlas on SO(3), by means of its principal bundle structure, and prove that this atlas is smooth. Full article

(This article belongs to the Special Issue Mathematical Structures and Their Applications)

30 pages, 2328 KiB

Open AccessFeature PaperArticle

Multi-Satellite Task Parallelism via Priority-Aware Decomposition and Dynamic Resource Mapping

by Shangpeng Wang, Chenyuan Zhang, Zihan Su, Limin Liu and Jun Long

Mathematics 2025, 13(7), 1183; https://doi.org/10.3390/math13071183 - 3 Apr 2025

Abstract

Multi-satellite collaborative computing has achieved task decomposition and collaborative execution through inter-satellite links (ISLs), which has significantly improved the efficiency of task execution and system responsiveness. However, existing methods focus on single-task execution and lack multi-task parallel processing capability. Most methods ignore task [...] Read more.

Multi-satellite collaborative computing has achieved task decomposition and collaborative execution through inter-satellite links (ISLs), which has significantly improved the efficiency of task execution and system responsiveness. However, existing methods focus on single-task execution and lack multi-task parallel processing capability. Most methods ignore task priorities and dependencies, leading to excessive waiting times and poor scheduling results. To address these problems, this paper proposes a task decomposition and resource mapping method based on task priorities and resource constraints. First, we introduce a graph theoretic model to represent the task dependency and priority relationships explicitly, combined with a novel algorithm for task decomposition. Meanwhile, we construct a resource allocation model based on game theory and combine it with deep reinforcement learning to achieve resource mapping in a dynamic environment. Finally, we adopt the theory of temporal logic to formalize the execution order and time constraints of tasks and solve the dynamic scheduling problem through mixed-integer nonlinear programming to ensure the optimality and real-time updating of the scheduling scheme. The experimental results demonstrate that the proposed method improves resource utilization by up to about 24% and reduces overall execution time by up to about 42.6% in large-scale scenarios. Full article

(This article belongs to the Special Issue New Advances in Network and Edge Computing)

28 pages, 2969 KiB

Open AccessArticle

Hesitant Fuzzy Consensus Reaching Process for Large-Scale Group Decision-Making Methods

by Wei Liang, Álvaro Labella, Meng-Jun Meng, Ying-Ming Wang and Rosa M. Rodríguez

Mathematics 2025, 13(7), 1182; https://doi.org/10.3390/math13071182 - 3 Apr 2025

Abstract

The emergence and popularity of social media have made large-scale group decision-making (LSGDM) problems increasingly common, resulting in significant research interest in this field. LSGDM involves numerous evaluators, which can lead to disagreements and hesitancy among them. Hesitant fuzzy sets (HFSs) become crucial [...] Read more.

The emergence and popularity of social media have made large-scale group decision-making (LSGDM) problems increasingly common, resulting in significant research interest in this field. LSGDM involves numerous evaluators, which can lead to disagreements and hesitancy among them. Hesitant fuzzy sets (HFSs) become crucial in this context as they capture the uncertainty and hesitancy among evaluators. On the other hand, research on the Consensus Reaching Process (CRP) becomes particularly important in dealing with the inevitable differences among the great number of evaluators. Ways to mitigate these differences to reach an agreement are a crucial area of study. For this reason, this paper presents a new CRP model to deal with LSGDM problems in hesitant fuzzy environments. First, HFSs and Normal-type Hesitant Fuzzy Sets (N-HFSs) are introduced to integrate evaluators’ subgroup and collective opinions, aiming to preserve as much decision information as possible while reducing computational complexity. Subsequently, a CRP with a detailed feedback suggestion generation mechanism is developed, which considers the willingness of evaluators to modify their opinions, thereby improving the effectiveness of reaching an agreement. Finally, a LSGDM framework that does not require any normalization process is proposed, and its feasibility and robustness are demonstrated through a numerical example. Full article

(This article belongs to the Special Issue Multi-criteria Decision Making under Uncertainty)

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26 pages, 1624 KiB

Open AccessFeature PaperArticle

Openness, Unionized Labor Markets, and Monetary Policy

by Xakousti Chrysanthopoulou, Evangelos Ioannidis and Moïse Sidiropoulos

Mathematics 2025, 13(7), 1181; https://doi.org/10.3390/math13071181 - 3 Apr 2025

Abstract

This paper extends the micro-founded DSGE open economy model by incorporating unionized labor markets. Unlike the standard framework with atomistic unions, large labor unions consider broader economic conditions and internalize the impact of their wage settlements on the aggregate economy. By emphasizing the [...] Read more.

This paper extends the micro-founded DSGE open economy model by incorporating unionized labor markets. Unlike the standard framework with atomistic unions, large labor unions consider broader economic conditions and internalize the impact of their wage settlements on the aggregate economy. By emphasizing the interplay between internal and external sources of economic distortions and monetary policy regimes, we demonstrate that the economy’s openness, the degree of wage-setting centralization, and different monetary policy regimes influence unions’ wage-setting behavior and macroeconomic outcomes. The analysis identifies three key effects—the monetary policy effect, the intertemporal substitution effect, and the open economy effect—that large unions internalize when adjusting their wage demands in response to policy actions and external conditions. This novel wage-based mechanism alters the New Keynesian Phillips curve, with implications for the conduct of monetary policy, particularly in shaping the economy’s response to shocks and equilibrium determinacy. The real effects of monetary policy shocks under different policy settings depend on large unions’ internalization effect. In a unionized labor market, the impact of monetary shocks on the real economy is amplified compared to the standard case with atomistic unions. Additionally, interactions among large unions, openness, and monetary policy regimes affect determinacy properties of equilibrium (i.e., uniqueness of the solution path) under various forms and timing of monetary policy rules. This paper offers new insights into how union coordination interacts with monetary policy regimes and trade openness to shape macroeconomic stability (uniqueness of rational expectations equilibrium) and the dynamic response of the economy to shocks. These findings enhance our understanding of monetary policy design in economies with strong large labor institutions and external trade exposure—an area that remains underexplored in the existing DSGE literature. Full article

(This article belongs to the Special Issue Latest Advances in Mathematical Economics)

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23 pages, 5532 KiB

Open AccessArticle

A Collaborative Design Method for the Cylindrical Gear Paired with Skived Face Gears Driven by Contact Performances

by Zhenyu Zhou, Yuanyuan Zhang, Mou Li, Yuansheng Zhou, Zhongwei Tang, Jinyuan Tang and Liang Zhou

Mathematics 2025, 13(7), 1180; https://doi.org/10.3390/math13071180 - 3 Apr 2025

Abstract

Skiving is an efficient method for manufacturing face gears, but theoretical machining errors may occur when face gears designed for shaping or grinding are processed by skiving. This study presents a face gear directly designed for the skiving process, eliminating theoretical machining errors. [...] Read more.

Skiving is an efficient method for manufacturing face gears, but theoretical machining errors may occur when face gears designed for shaping or grinding are processed by skiving. This study presents a face gear directly designed for the skiving process, eliminating theoretical machining errors. Additionally, a new design approach for the cylindrical gear is proposed to pair with this face gear. The tooth surface models of both the cylindrical pinion and face gear are established. For the pinion, surface modifications are applied in both profile and longitudinal directions, while the face gear’s tooth surface model is tailored for the skiving process to avoid theoretical machining errors. The contact performance, including transmission error, contact stress, and contact pattern, is evaluated through Tooth Contact Analysis (TCA). An optimization model is developed to identify the optimal cylindrical gear tooth surface parameters, targeting improved contact performance. The proposed method is validated by a case study, which shows that the optimized face gear transmission results in lower maximum contact stress and reduced transmission error amplitude. Full article

(This article belongs to the Special Issue Advanced Applications of Mathematical Modeling and Optimization in Logistics and Manufacturing)

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19 pages, 286 KiB

Open AccessArticle

On Log-Definite Tempered Combinatorial Sequences

by Tomislav Došlić and Biserka Kolarec

Mathematics 2025, 13(7), 1179; https://doi.org/10.3390/math13071179 - 3 Apr 2025

Abstract

This article is concerned with qualitative and quantitative refinements of the concepts of the log-convexity and log-concavity of positive sequences. A new class of tempered sequences is introduced, its basic properties are established and several interesting examples are provided. The new class extends [...] Read more.

This article is concerned with qualitative and quantitative refinements of the concepts of the log-convexity and log-concavity of positive sequences. A new class of tempered sequences is introduced, its basic properties are established and several interesting examples are provided. The new class extends the class of log-balanced sequences by including the sequences of similar growth rates, but of the opposite log-behavior. Special attention is paid to the sequences defined by two- and three-term linear recurrences with constant coefficients. For the special cases of generalized Fibonacci and Lucas sequences, we graphically illustrate the domains of their log-convexity and log-concavity. For an application, we establish the concyclicity of the points

(\frac{a_{2 n}}{a_{2 n + 1}}, \frac{1}{a_{2 n + 1}})

for some classes of Horadam sequences

(a_{n})

with positive terms. Full article

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30 pages, 4365 KiB

Open AccessArticle

Optimal Service Operation Strategy in Battery Swapping Supply Chain

by Chao Li and Kaifu Yuan

Mathematics 2025, 13(7), 1178; https://doi.org/10.3390/math13071178 - 2 Apr 2025

Abstract

To explore the operation strategy of battery leasing and battery swapping services (the two services), this paper constructs a battery swapping supply chain consisting of the battery manufacturer and the vehicle company. Taking the battery manufacturer as a core enterprise, this paper examines [...] Read more.

To explore the operation strategy of battery leasing and battery swapping services (the two services), this paper constructs a battery swapping supply chain consisting of the battery manufacturer and the vehicle company. Taking the battery manufacturer as a core enterprise, this paper examines four service operation strategies: two self-operated services, self-operated battery swapping services, self-operated battery leasing services and two outsourcing services. Through comparative analysis, the findings indicate that the optimal strategy for the battery manufacturers depends on the vehicle body price. Specifically, when the vehicle body price is low, self-operating both services maximizes profitability and effectively stimulates demand for battery-swapping vehicles. Conversely, when the price is high, a complete outsourcing strategy is preferable, as it is the most effective way to stimulate battery-swapping vehicle demand. Similarly, the optimal strategy for the vehicle company is influenced by the vehicle body price. The vehicle company should provide the two services only when the vehicle body price is low; otherwise, they should focus on producing battery-swapping vehicles. Moreover, to stimulate demand for battery-swapping services, the determination of the optimal strategy is contingent upon several key variables, including the vehicle body price, the battery-swapping service price sensitivity, and the battery-swapping operating cost-sharing ratio. Full article

(This article belongs to the Section D2: Operations Research and Fuzzy Decision Making)

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24 pages, 9271 KiB

Open AccessArticle

Performance Evaluation of Beluga Whale Optimization–Long Short-Term Memory–Random Forest Networks for Trajectory Control and Energy Optimization in Excavator Systems

by Van Hien Nguyen and Kyoung Kwan Ahn

Mathematics 2025, 13(7), 1177; https://doi.org/10.3390/math13071177 - 2 Apr 2025

Abstract

Over the past few years, reducing energy consumption in hydraulic excavators has gained increasing attention, driving significant research in this field. One effective strategy involves integrating hydrostatic transmission (HST) and hydraulic pump/motor (HPM) systems into hydraulic excavators. However, challenges like disturbances, throttling-induced pressure [...] Read more.

Over the past few years, reducing energy consumption in hydraulic excavators has gained increasing attention, driving significant research in this field. One effective strategy involves integrating hydrostatic transmission (HST) and hydraulic pump/motor (HPM) systems into hydraulic excavators. However, challenges like disturbances, throttling-induced pressure drops, and fluid leakage often hinder both positional accuracy and energy efficiency. To tackle these issues, our study proposes a sophisticated dynamic forecasting model for positional control, integrating beluga whale optimization (BWO), long short-term memory (LSTM), and random forest (RF) techniques. The approach begins with dynamic data evaluation using Pearson’s correlation analysis to identify tuning parameters that have moderate to strong correlations with control variables, which are then used as inputs for predictive modeling. Initially, a standalone LSTM framework is developed to estimate the system’s positional output, with BWO optimizing four key tuning parameters. Subsequently, a hybrid BWO-enhanced LSTM-RF system is deployed to capture complex nonlinear patterns, improving the accuracy of motion trajectory predictions. Simulations and experiments confirm that our approach achieves a positional error below 3 mm, ensuring precise tracking and providing reliable data for operators. Compared to conventional proportional–integral–derivative (PID) controllers, standalone LSTM-RF, and a hybrid controller combining particle swarm optimization (PSO), LSTM, a gated recurrent unit (GRU), and PID (PSO-LSTM-GRU-PID), our method achieves superior tracking precision and energy savings of 12.46%, 8.98%, and 3.97%, respectively. Full article

(This article belongs to the Section E2: Control Theory and Mechanics)

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