Axioms

24 pages, 393 KB

Open AccessArticle

The (n-1)-th Laplacian Immanantal Polynomials of Graphs

by Wenwei Zhang, Tingzeng Wu and Xianyue Li

Axioms 2025, 14(9), 716; https://doi.org/10.3390/axioms14090716 - 22 Sep 2025

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Let

χ_{n - 1} (σ)

denote the irreducible character of the symmetric group

S_{n}

corresponding to the partition

(n - 1, 1)

. For an

n \times n

matrix [...] Read more.

Let

χ_{n - 1} (σ)

denote the irreducible character of the symmetric group

S_{n}

corresponding to the partition

(n - 1, 1)

. For an

n \times n

matrix

M = (m_{i, j})

, we denote its

(n - 1)

-th immanant by

d_{n - 1} (M)

. Let G be a simple connected graph and let

L (G)

and

Q (G)

denote the Laplacian matrix and the signless Laplacian matrix of G, respectively. The

(n - 1)

-th Laplacian (respectively, signless Laplacian) immanantal polynomial of G is defined as

d_{n - 1} (x I - L (G))

(respectively,

d_{n - 1} (x I - Q (G))

). In this paper, we partially resolve Chan’s open problem by establishing that the broom graph minimizes

d_{n - 1} (L (T))

among all trees with given diameter. Furthermore, we give combinatorial expressions for the first five coefficients of the

(n - 1)

-th Laplacian immanantal polynomial

d_{n - 1} (x I - L (G))

. We also investigate the characterizing properties of this polynomial and present several graphs that are uniquely determined by it. Additionally, for the

(n - 1)

-th signless Laplacian immanantal polynomial

d_{n - 1} (x I - Q (G))

, we show that the multiplicity of root 1 is bounded below by the star degree of G. Full article

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30 pages, 416 KB

Open AccessArticle

Monodromy-Prescribed Polystable Bundles on Punctured Riemann Surfaces and the Geometry of Singular Control Strategies

by Álvaro Antón-Sancho

Axioms 2025, 14(9), 715; https://doi.org/10.3390/axioms14090715 - 22 Sep 2025

Viewed by 118

Abstract

This paper establishes a functorial algebraic isomorphism between the moduli space

B_{C}^{ps} (Σ, G)

of polystable principal G-bundles with prescribed monodromy on a punctured Riemann surface

Σ

of genus

g \geq 2

, for a complex reductive [...] Read more.

This paper establishes a functorial algebraic isomorphism between the moduli space

B_{C}^{ps} (Σ, G)

of polystable principal G-bundles with prescribed monodromy on a punctured Riemann surface

Σ

of genus

g \geq 2

, for a complex reductive Lie group G, and the character variety

M_{C}^{K} (Σ^{*}, G)

of representations of its fundamental group with relatively compact image. The dimension formula

dim B_{C}^{ps} (Σ, G) = 2 (g - 1) {dim}_{C} (G) + \sum_{i = 1}^{k} {dim}_{R} (C_{i})

, where

C_{1}, \dots, C_{k}

are conjugacy classes in a maximal compact subgroup

K \subset G

, is derived for complex reductive Lie groups, and singularities are characterized as polystable bundles with non-trivial automorphism groups. As applications of the above geometric results to control theory, it is proved that topologically distinct polystable robotic navigation strategies around obstacles are classified by this character variety. The geometry of singular points in families of polystable control strategies is further investigated, revealing enhanced stability properties characterized by reduced tangent space dimensions arising from non-trivial automorphism groups. Full article

(This article belongs to the Special Issue Differential Geometry and Its Application, 3rd Edition)

28 pages, 464 KB

Open AccessArticle

Analysis of a Retrial Queueing System Suitable for Modeling Operation of Ride-Hailing Platforms with the Dynamic Service Pricing

by Alexander Dudin, Sergei Dudin and Olga Dudina

Axioms 2025, 14(9), 714; https://doi.org/10.3390/axioms14090714 - 22 Sep 2025

Viewed by 140

Abstract

Effective operation of any service system requires optimal organization of the sharing of resources between the users (customers). To this end, it is necessary to elaborate on the mechanisms that allow for the mitigation of congestion, i.e., the accumulation of many users requiring [...] Read more.

Effective operation of any service system requires optimal organization of the sharing of resources between the users (customers). To this end, it is necessary to elaborate on the mechanisms that allow for the mitigation of congestion, i.e., the accumulation of many users requiring service. Due to the randomness of the user’s arrival process, congestions can occur even when an arrival rate is constant, e.g., the arrivals are described by the stationary Poisson process, which is assumed in the majority of existing papers. However, congestions can be more severe if the possibility of fluctuation of the instantaneous arrival rate exists. Such a possibility is an inherent feature of many systems and can be taken into account via the description of arrivals by the Markov arrival process (MAP). This makes the problem of congestion avoidance drastically more challenging. In many real-world systems, there exists the possibility of customer admission control via dynamic pricing. We propose a novel predictive mechanism of dynamic pricing. Decision moments coincide with the transition moments of the underlying process of the MAP. A customer may join or balk the system or postpone joining the system depending on the current cost. We illustrate the application of this mechanism in a multi-server retrial queueing model with dynamic service pricing. The behavior of the system is described by a multidimensional Markov chain with state-inhomogeneous transitions. Its stationary distribution is computed and may be used for solving the various problems of system revenue maximization via the choice of the proper pricing strategy. Full article

(This article belongs to the Special Issue Probability Theory and Stochastic Processes: Theory and Applications)

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19 pages, 1059 KB

Open AccessArticle

Performance Evaluation of Shiryaev–Roberts and Cumulative Sum Schemes for Monitoring Shape and Scale Parameters in Gamma-Distributed Data Under Type I Censoring

by He Li, Peile Chen, Ruicheng Ma and Jiujun Zhang

Axioms 2025, 14(9), 713; https://doi.org/10.3390/axioms14090713 - 22 Sep 2025

Viewed by 103

Abstract

This paper proposes two process monitoring schemes, namely the Shiryaev–Roberts (SR) procedure and the cumulative sum (CUSUM) procedure, to detect shifts in the shape and scale parameters of Type I right-censored Gamma-distributed lifetime data. The performance of the proposed schemes is compared with [...] Read more.

This paper proposes two process monitoring schemes, namely the Shiryaev–Roberts (SR) procedure and the cumulative sum (CUSUM) procedure, to detect shifts in the shape and scale parameters of Type I right-censored Gamma-distributed lifetime data. The performance of the proposed schemes is compared with that of an exponentially weighted moving average (EWMA) control chart based on deep learning networks. The performance of the proposed schemes is evaluated under various censoring rates using Monte Carlo simulations, with the average run length (ARL) as the primary metric. Furthermore, the SR and CUSUM schemes are compared for both zero-state and steady-state shifts. Simulation results indicate that the SR and CUSUM procedures exhibit superior performance, with the SR scheme showing particular advantages when the actual shift is small, while the CUSUM chart proves more effective for identifying larger shifts. The shape parameter has a significant effect on the performance of the control charts such that a reduction in the shape parameter effectively improves the ability to capture early offsets. Increased censoring rates reduce detection sensitivity. To maintain

{ARL}_{0}

= 370, control limits h adapt differentially. The SR and CUSUM charts with different censoring rates need to recalibrate the parameter to mitigate performance losses under higher censoring conditions. The monitoring performance of the SR and CUSUM chart is enhanced by an increase in sample size. Finally, a practical example is provided to illustrate the application of the proposed monitoring schemes. Full article

(This article belongs to the Special Issue Mathematical and Statistical Methods and Their Applications, 2nd Edition)

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34 pages, 17998 KB

Open AccessArticle

Bayesian Stochastic Inference and Statistical Reliability Modeling of Maxwell–Boltzmann Model Under Improved Progressive Censoring for Multidisciplinary Applications

by Heba S. Mohammed, Osama E. Abo-Kasem and Ahmed Elshahhat

Axioms 2025, 14(9), 712; https://doi.org/10.3390/axioms14090712 - 21 Sep 2025

Viewed by 174

Abstract

The Maxwell–Boltzmann (MB) distribution is important because it provides the statistical foundation for connecting microscopic particle motion to macroscopic gas properties by statistically describing molecular speeds and energies, making it essential for understanding and predicting the behavior of classical ideal gases. This study [...] Read more.

The Maxwell–Boltzmann (MB) distribution is important because it provides the statistical foundation for connecting microscopic particle motion to macroscopic gas properties by statistically describing molecular speeds and energies, making it essential for understanding and predicting the behavior of classical ideal gases. This study advances the statistical modeling of lifetime distributions by developing a comprehensive reliability analysis of the MB distribution under an improved adaptive progressive censoring framework. The proposed scheme strategically enhances experimental flexibility by dynamically adjusting censoring protocols, thereby preserving more information from test samples compared to conventional designs. Maximum likelihood estimation, interval estimation, and Bayesian inference are rigorously derived for the MB parameters, with asymptotic properties established to ensure methodological soundness. To address computational challenges, Markov chain Monte Carlo algorithms are employed for efficient Bayesian implementation. A detailed exploration of reliability measures—including hazard rate, mean residual life, and stress–strength models—demonstrates the MB distribution’s suitability for complex reliability settings. Extensive Monte Carlo simulations validate the efficiency and precision of the proposed inferential procedures, highlighting significant gains over traditional censoring approaches. Finally, the utility of the methodology is showcased through real-world applications to physics and engineering datasets, where the MB distribution coupled with such censoring yields superior predictive performance. This genuine examination is conducted through two datasets (including the failure times of aircraft windshields, capturing degradation under extreme environmental and operational stress, and mechanical component failure times) that represent recurrent challenges in industrial systems. This work contributes a unified statistical framework that broadens the applicability of the Maxwell–Boltzmann model in reliability contexts and provides practitioners with a powerful tool for decision making under censored data environments. Full article

(This article belongs to the Special Issue Stochastic and Statistical Analyses in Natural Sciences, Second Edition)

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14 pages, 301 KB

Open AccessArticle

Coefficient Estimates, the Fekete–Szegö Inequality, and Hankel Determinants for Universally Prestarlike Functions Defined by Fractional Derivative in a Shell-Shaped Region

by Dina Nabil, Georgia Irina Oros, Awatef Shahin and Hanan Darwish

Axioms 2025, 14(9), 711; https://doi.org/10.3390/axioms14090711 - 21 Sep 2025

Viewed by 172

Abstract

In this paper, we introduce and investigate a new subclass

{(R_{ς}^{u})}^{g} (ϕ)

of universally prestarlike generalized functions of order

ς

, where

ς \leq 1

, associated with a shell-shaped region defined by [...] Read more.

In this paper, we introduce and investigate a new subclass

{(R_{ς}^{u})}^{g} (ϕ)

of universally prestarlike generalized functions of order

ς

, where

ς \leq 1

, associated with a shell-shaped region defined by

Λ = C ∖ [1, \infty)

for the present investigation, by utilizing the Srivastava–Owa fractional derivative of order

δ

. Coefficient inequalities for

| a_{2} |

and

| a_{3} |

for functions belonging to the newly introduced class are obtained. Additionally, the Fekete–Szegö inequality is investigated for this class of functions. In order to enhance the coefficient studies for this class, the second Hankel determinant is also evaluated. Full article

(This article belongs to the Special Issue New Developments in Geometric Function Theory, 4th Edition)

14 pages, 685 KB

Open AccessArticle

Input-to-Output Stability for Stochastic Complex Networked Control Systems

by Xuexin Li and Shang Gao

Axioms 2025, 14(9), 710; https://doi.org/10.3390/axioms14090710 - 20 Sep 2025

Viewed by 126

Abstract

In this article, input-to-output stability (IOS) for stochastic complex networked control systems (SCNCS) is investigated. By applying Kirchhoff’s matrix tree theorem in graph theory, an appropriate Lyapunov function is established which is related to topological structure and the Lyapunov function of each node [...] Read more.

In this article, input-to-output stability (IOS) for stochastic complex networked control systems (SCNCS) is investigated. By applying Kirchhoff’s matrix tree theorem in graph theory, an appropriate Lyapunov function is established which is related to topological structure and the Lyapunov function of each node system of SCNCS. Combining Lyapunov method and stochastic analysis skills, some sufficient criteria are provided to ensure SCNCS to satisfy IOS. In order to further analyze and verify the validity of our theoretical results, the results are applied to a class of stochastic Lurie coupled control systems on networks (SLCCSN) and the numerical test is performed. Full article

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15 pages, 246 KB

Open AccessArticle

Decompositions for Based Algebras with Bilinear Forms: A Graph Theory Connection

by Antonio J. Calderón Martín and Diouf Mame Cheikh

Axioms 2025, 14(9), 709; https://doi.org/10.3390/axioms14090709 - 20 Sep 2025

Viewed by 128

Abstract

We consider the category of based algebras with bilinear forms and show that any object in this category decomposes as a direct sum of irreducible orthogonal ideals. By associating an adequate graph with a based algebra with a bilinear form, this decomposition can [...] Read more.

We consider the category of based algebras with bilinear forms and show that any object in this category decomposes as a direct sum of irreducible orthogonal ideals. By associating an adequate graph with a based algebra with a bilinear form, this decomposition can be recovered from a graph theory viewpoint. Full article

(This article belongs to the Special Issue Advances in Linear Algebra with Applications, 2nd Edition)

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18 pages, 394 KB

Open AccessArticle

Existence and Uniqueness in Fractional Boundary Value Problems: A Refined Criterion

by Saleh S. Almuthaybiri and Abdelhamid Zaidi

Axioms 2025, 14(9), 708; https://doi.org/10.3390/axioms14090708 - 19 Sep 2025

Viewed by 203

Abstract

This paper is devoted to the study of the existence and uniqueness of solutions for a class of differential problems previously investigated by Laadjal. Our main contribution lies in deriving sharper estimates for the associated Green’s functions and employing Rus’s fixed-point theorem within [...] Read more.

This paper is devoted to the study of the existence and uniqueness of solutions for a class of differential problems previously investigated by Laadjal. Our main contribution lies in deriving sharper estimates for the associated Green’s functions and employing Rus’s fixed-point theorem within a suitably defined metric framework. Notably, the conditions under which our results hold are less restrictive, thereby encompassing a wider class of problems for which the existence and uniqueness of solutions can be rigorously guaranteed. This theoretical advancement is supported by numerical evidence presented in the final stage of our analysis. A key strength of the proposed approach is that it does not rely on stringent contraction conditions, which enhances its potential applicability to more general classes of fractional differential systems. Full article

(This article belongs to the Special Issue Advances in Nonlinear Analysis and Boundary Value Problems)

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24 pages, 795 KB

Open AccessArticle

Extended Expressive Intonation: An Application of the Convergents and Semiconvergents in Pythagorean Tuning

by Rafael Cubarsi

Axioms 2025, 14(9), 707; https://doi.org/10.3390/axioms14090707 - 19 Sep 2025

Viewed by 246

Abstract

Cyclic scales are associated with convergents and semiconvergents of the continued fraction expansions of the generator tone. After each convergent, a scale lineage ends and another begins. Along a lineage, a constant number of generic accidentals are successively added to its first scale, [...] Read more.

Cyclic scales are associated with convergents and semiconvergents of the continued fraction expansions of the generator tone. After each convergent, a scale lineage ends and another begins. Along a lineage, a constant number of generic accidentals are successively added to its first scale, becoming regularly interspersed. In this way, it is easier to know where each note is to go. This process, applied to the lineage of the 7-, 12-, and 17-tone scales, is related to expressive intonation. Such a concept is extended to larger scales with added microtones and it is described how they can be chosen in terms of the starting index of the scale. An automorphism in terms of the step and co-step indices associated with the two elementary intervals provides a two-dimensional representation that shares some common features with the musical staff. Full article

(This article belongs to the Special Issue Applied Mathematics and Mathematical Modeling)

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22 pages, 521 KB

Open AccessArticle

A Novel Exponentiated Generalized Weibull Exponential Distribution: Properties, Estimation, and Regression Model

by Hadeel S. Klakattawi

Axioms 2025, 14(9), 706; https://doi.org/10.3390/axioms14090706 - 19 Sep 2025

Viewed by 154

Abstract

The exponential distribution is one of the most popular models for fitting lifetime data. This study proposes a novel generalization of the exponential distribution, referred to as the exponentiated generalized Weibull exponential, for the modeling of lifetime data. This new distribution is a [...] Read more.

The exponential distribution is one of the most popular models for fitting lifetime data. This study proposes a novel generalization of the exponential distribution, referred to as the exponentiated generalized Weibull exponential, for the modeling of lifetime data. This new distribution is a member of a family that combines two well-known distribution families: the exponentiated generalized family and the T-X family. It has five parameters, allowing it to fit data that exhibit increasing, decreasing, bathtub, upside-down bathtub, S-shaped, J-shaped and reversed-J hazard rates. Some mathematical and statistical properties of the newly suggested distribution are derived and the estimation of its parameters is studied using the method of maximum likelihood. Different simulation studies have been applied to evaluate the parameter estimation. Four lifetime datasets are analyzed to investigate the superiority of the proposed exponentiated generalized Weibull exponential distribution. A regression model based on the proposed distribution is then developed for both complete and censored samples, and its performance is assessed on two real datasets. The new distribution and its associated regression model are empirically demonstrated to be practically useful. Full article

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16 pages, 3147 KB

Open AccessArticle

A Note on Multi-Index Mittag-Leffler Functions and Parametric Laguerre-Type Exponentials

by Hari Mohan Srivastava, Diego Caratelli and Paolo Emilio Ricci

Axioms 2025, 14(9), 705; https://doi.org/10.3390/axioms14090705 - 18 Sep 2025

Viewed by 239

Abstract

This paper explores the eigenfunctions of specific Laguerre-type parametric operators to develop multi-parametric models, which are associated with a class of the generalized Mittag-Leffler type functions, for dynamical systems and population dynamics. By leveraging these multi-parametric approaches, we introduce new concepts in number [...] Read more.

This paper explores the eigenfunctions of specific Laguerre-type parametric operators to develop multi-parametric models, which are associated with a class of the generalized Mittag-Leffler type functions, for dynamical systems and population dynamics. By leveraging these multi-parametric approaches, we introduce new concepts in number theory, specifically those involving multi-parametric Bernoulli and Euler numbers, along with other related polynomials. Several numerical examples, which are generated by using the computer algebra program Mathematica© (Version 14.3), demonstrate the effectiveness of the models that we have presented and analyzed in this paper. Full article

(This article belongs to the Special Issue Special Functions and Related Topics, 2nd Edition)

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11 pages, 254 KB

Open AccessArticle

Distortion Theory of Biunivalent Holomorphic Functions

by Samuel L. Krushkal

Axioms 2025, 14(9), 704; https://doi.org/10.3390/axioms14090704 - 18 Sep 2025

Viewed by 228

Abstract

Biunivalent holomorphic functions form an interesting class in geometric function theory and are associated with special functions and solutions of complex differential equations. This paper provides a complete distortion theory for such functions, in particular, the sharp coefficient estimates. Another interesting feature is [...] Read more.

Biunivalent holomorphic functions form an interesting class in geometric function theory and are associated with special functions and solutions of complex differential equations. This paper provides a complete distortion theory for such functions, in particular, the sharp coefficient estimates. Another interesting feature is that (in contrast to general collections of univalent functions) one obtains in the same fashion the sharp bounds for coefficients of biunivalent functions with k-quasiconformal extension for any

k < 1

. Full article

(This article belongs to the Special Issue Mathematical Analysis and Applications IV)

26 pages, 1253 KB

Open AccessArticle

Integrated Production, EWMA Scheme, and Maintenance Policy for Imperfect Manufacturing Systems of Bolt-On Vibroseis Equipment Considering Quality and Inventory Constraints

by Nuan Xia, Zilin Lu, Yuting Zhang and Jundong Fu

Axioms 2025, 14(9), 703; https://doi.org/10.3390/axioms14090703 - 17 Sep 2025

Viewed by 178

Abstract

In recent years, the synergistic effect among production, maintenance, and quality control within manufacturing systems has garnered increasing attention in academic and industrial circles. In high-quality production settings, the real-time identification of minute process deviations holds significant importance for ensuring product quality. Traditional [...] Read more.

In recent years, the synergistic effect among production, maintenance, and quality control within manufacturing systems has garnered increasing attention in academic and industrial circles. In high-quality production settings, the real-time identification of minute process deviations holds significant importance for ensuring product quality. Traditional approaches, such as routine quality inspections or Shewhart control charts, exhibit limitations in sensitivity and response speed, rendering them inadequate for meeting the stringent requirements of high-precision quality control. To address this issue, this paper presents an integrated framework that seamlessly integrates stochastic process modeling, dynamic optimization, and quality monitoring. In the realm of quality monitoring, an exponentially weighted moving average (EWMA) control chart is employed to monitor the production process. The statistic derived from this chart forms a Markov process, enabling it to more acutely detect minor shifts in the process mean. Regarding maintenance strategies, a state-dependent preventive maintenance (PM) and corrective maintenance (CM) mechanism is introduced. Specifically, preventive maintenance is initiated when the system is in a statistically controlled state and the inventory level falls below a predefined threshold. Conversely, corrective maintenance is triggered when the EWMA control chart generates an out-of-control (OOC) signal. To facilitate continuous production during maintenance activities, an inventory buffer mechanism is incorporated into the model. Building upon this foundation, a joint optimization model is formulated, with system states, including equipment degradation state, inventory level, and quality state, serving as decision variables and the minimization of the expected total cost (ETC) per unit time as the objective. This problem is formalized as a constrained dynamic optimization problem and is solved using the genetic algorithm (GA). Finally, through a case study of the production process of vibroseis equipment, the superiority of the proposed model in terms of cost savings and system performance enhancement is empirically verified. Full article

(This article belongs to the Special Issue Mathematical and Statistical Methods and Their Applications, 2nd Edition)

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29 pages, 19296 KB

Open AccessArticle

Inference for the Chris–Jerry Lifetime Distribution Under Improved Adaptive Progressive Type-II Censoring for Physics and Engineering Data Modelling

by Heba S. Mohammed, Osama E. Abo-Kasem and Ahmed Elshahhat

Axioms 2025, 14(9), 702; https://doi.org/10.3390/axioms14090702 - 17 Sep 2025

Viewed by 172

Abstract

This paper presents a comprehensive reliability analysis framework for the Chris–Jerry (CJ) lifetime distribution under an improved adaptive progressive Type-II censoring plan. The CJ model, recently introduced to capture skewed lifetime behaviors, is studied under a modified censoring structure designed to provide greater [...] Read more.

This paper presents a comprehensive reliability analysis framework for the Chris–Jerry (CJ) lifetime distribution under an improved adaptive progressive Type-II censoring plan. The CJ model, recently introduced to capture skewed lifetime behaviors, is studied under a modified censoring structure designed to provide greater flexibility in terminating life-testing experiments. We derive maximum likelihood estimators for the CJ parameters and key reliability measures, including the reliability and hazard rate functions, and construct approximate confidence intervals using the observed Fisher information matrix and the delta method. To address the intractability of the likelihood function, Bayesian estimators are obtained under independent gamma priors and a squared-error loss function. Because the posterior distributions are not available in closed form, we apply the Metropolis–Hastings algorithm to generate Bayesian estimates and two types of credible intervals. A comprehensive simulation study evaluates the performance of the proposed estimation techniques under various censoring scenarios. The framework is further validated through two real-world datasets: one involving rainfall measurements and another concerning mechanical failure times. In both cases, the CJ model combined with the proposed censoring strategy demonstrates superior fit and reliability inference compared to competing models. These findings highlight the value of the CJ distribution, together with advanced censoring methods, for modeling lifetime data in physics and engineering applications. Full article

(This article belongs to the Special Issue Reliability and Risk of Complex Systems: Modelling, Analysis and Optimization, 2nd Edition)

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15 pages, 341 KB

Open AccessArticle

Robust Adaptive Lasso via Robust Sample Autocorrelation Coefficient for the Autoregressive Models

by Yunlu Jiang, Fudong Chen and Xiao Yan

Axioms 2025, 14(9), 701; https://doi.org/10.3390/axioms14090701 - 17 Sep 2025

Viewed by 222

Abstract

For the autoregressive models, classical estimation methods, including the least squares estimator or the maximum likelihood estimator are not robust to heavy-tailed distributions or outliers in the dataset, and lack sparsity, leading to potentially inaccurate estimation and poor generalization capability. Meanwhile, the existing [...] Read more.

For the autoregressive models, classical estimation methods, including the least squares estimator or the maximum likelihood estimator are not robust to heavy-tailed distributions or outliers in the dataset, and lack sparsity, leading to potentially inaccurate estimation and poor generalization capability. Meanwhile, the existing variable selection methods can not handle the case where the influence of explanatory variables on the dependent variable gradually weakens as the lag order increases. To address these issues, we propose a novel robust adaptive lasso method for the autoregressive models. The proposed method is constructed by using partial autocorrelation coefficients as adaptive penalty weights to promote sparsity in parameter estimation, and by employing a robust autocorrelation estimator based on the

F Q_{n}

statistic to enhance resistance to outliers. Numerical simulations and two real data analyses illustrate the promising performance of our proposed approach. The results indicate that our proposed approach exhibits good robustness and sparsity in the presence of outliers in the dataset. Full article

(This article belongs to the Special Issue Advances in Statistical Simulation and Computing)

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13 pages, 295 KB

Open AccessArticle

On Corresponding Cauchy–Riemann Equations Applied to Laplace-Type Operators over Generalized Quaternions, with an Application

by Ji Eun Kim

Axioms 2025, 14(9), 700; https://doi.org/10.3390/axioms14090700 - 16 Sep 2025

Viewed by 222

Abstract

In this paper, we develop a concise differential–potential framework for the functions of a generalized quaternionic variable in the two-parameter algebra

H_{α, β}

, with

α, β \in R ∖ {0}

. Starting from left/right difference quotients, we [...] Read more.

In this paper, we develop a concise differential–potential framework for the functions of a generalized quaternionic variable in the two-parameter algebra

H_{α, β}

, with

α, β \in R ∖ {0}

. Starting from left/right difference quotients, we derive complete Cauchy–Riemann (CR) systems and prove that, away from the null cone where the reduced norm N vanishes, these first-order systems are necessary and, under

C^{1}

regularity, sufficient for left/right differentiability, thereby linking classical one-dimensional calculus to a genuinely four-dimensional setting. On the potential theoretic side, the Dirac factorization

Δ_{α, β} = \bar{D} D = D \bar{D}

shows that each real component of a differentiable mapping is

Δ_{α, β}

-harmonic, yielding a clean second-order theory that separates the elliptic (Hamiltonian) and split (coquaternionic) regimes via the principal symbol. In the classical case

(α, β) = (- 1, - 1)

, we present a Poisson-type representation solving a model Dirichlet problem on the unit ball

B \subset R^{4}

, recovering mean-value and maximum principles. For computation and symbolic verification, real

4 \times 4

matrix models for left/right multiplication linearize the CR systems. Examples (polynomials, affine CR families, and split-signature contrasts) illustrate the theory, and the outlook highlights boundary integral formulations, Green kernel constructions, and discretization strategies for quaternionic PDEs. Full article

(This article belongs to the Special Issue New Perspectives in Operator Theory and Functional Analysis)

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22 pages, 703 KB

Open AccessArticle

Modified C_p and C_pk Indices Based on Left-Truncated Data

by Yimin Yin, Bin Yan and Pengfei Liu

Axioms 2025, 14(9), 699; https://doi.org/10.3390/axioms14090699 - 16 Sep 2025

Viewed by 196

Abstract

The process capability indices

C_{p}

and

C_{p k}

are commonly used in industry to evaluate process capability, but they usually require that quality data follow a normal distribution. However, in the actual supply–demand relationship, some suppliers artificially eliminate products that do [...] Read more.

The process capability indices

C_{p}

and

C_{p k}

are commonly used in industry to evaluate process capability, but they usually require that quality data follow a normal distribution. However, in the actual supply–demand relationship, some suppliers artificially eliminate products that do not meet the inspection requirements in order to make buyers accept their products, and these truncated sample data have a more significant impact on process capability evaluation. Based on the left-truncated sample, two modified process capability indices,

C_{p}^{T}

and

C_{p k}^{T}

, are proposed, and bootstrap confidence interval estimation methods are established for each of them. Extensive simulation experiments are conducted on the modified indices by varying the sample size and truncation location parameters, and the results are compared with those of traditional methods. The comparison reveals that the new methods outperform the traditional ones across a range of sample sizes and truncation locations. Finally, a real example is used to validate the usefulness of the new method in guiding production management. Full article

(This article belongs to the Section Mathematical Analysis)

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15 pages, 364 KB

Open AccessArticle

Graph-Theoretic Perspectives on Fixed Points in Double-Composed Metric Spaces

by Nizar Souayah

Axioms 2025, 14(9), 698; https://doi.org/10.3390/axioms14090698 - 16 Sep 2025

Viewed by 228

Abstract

This study explores the development of fixed-point results in the setting of the recently proposed double-composed metric spaces. We establish conditions ensuring both existence and uniqueness of fixed points for several types of contractive mappings defined on such spaces. To enrich the analysis, [...] Read more.

This study explores the development of fixed-point results in the setting of the recently proposed double-composed metric spaces. We establish conditions ensuring both existence and uniqueness of fixed points for several types of contractive mappings defined on such spaces. To enrich the analysis, the space is further equipped with a graph structure through the use of concepts from graph theory, leading to the formulation of two novel fixed-point theorems. An illustrative example is also provided to highlight the applicability and relevance of the obtained results. Full article

(This article belongs to the Special Issue Research in Fixed Point Theory and Its Applications)

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18 pages, 316 KB

Open AccessArticle

On the Laplace-Type Transform and Its Applications

by Slobodan B. Tričković and Miomir S. Stanković

Axioms 2025, 14(9), 697; https://doi.org/10.3390/axioms14090697 - 15 Sep 2025

Viewed by 202

Abstract

Using the Laplace transform and the Gamma function, we obtain the Laplace-type transform, with the property of mapping a function to a functional sequence, which cannot be realized by the Laplace transform. In addition, we construct a backward difference as a generalization of [...] Read more.

Using the Laplace transform and the Gamma function, we obtain the Laplace-type transform, with the property of mapping a function to a functional sequence, which cannot be realized by the Laplace transform. In addition, we construct a backward difference as a generalization of the backward difference operator ∇. By connecting it to the Laplace-type transform, we deduce a method for solving difference equations and, relying on classical orthogonal polynomials, for obtaining combinatorial identities. A table of some elementary functions and their images is at the end of the text. Full article

(This article belongs to the Special Issue Special Functions and Related Topics, 2nd Edition)

14 pages, 354 KB

Open AccessArticle

Geometric Characteristics of Specific Classes Associated with q-Janowski Functions

by Fuad Alsarari, Abdulbasit Darem, Amel Touati and Alaa Awad Alzulaibani

Axioms 2025, 14(9), 696; https://doi.org/10.3390/axioms14090696 - 15 Sep 2025

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Abstract

In this paper, we integrate the concepts of spiral-like functions and Janowski-type functions within the framework of q-calculus to define new subclasses in the open unit disk. Our primary focus is on analyzing convolution conditions that form the foundation for further theoretical [...] Read more.

In this paper, we integrate the concepts of spiral-like functions and Janowski-type functions within the framework of q-calculus to define new subclasses in the open unit disk. Our primary focus is on analyzing convolution conditions that form the foundation for further theoretical developments. The main contributions include establishing sufficient conditions and applying Robertson’s theorem. Furthermore, motivated by a recent definition, we propose analogous neighborhood concepts for the above-mentioned classes, and we explore the corresponding neighborhood results. Full article

(This article belongs to the Special Issue Advances in Geometric Function Theory and Related Topics)

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21 pages, 285 KB

Open AccessArticle

Generalized Cross-Curvature Solitons of 3D Lorentzian Lie Groups

by Mehdi Jafari

Axioms 2025, 14(9), 695; https://doi.org/10.3390/axioms14090695 - 12 Sep 2025

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Abstract

We investigate left-invariant generalized cross-curvature solitons on simply connected three-dimensional Lorentzian Lie groups. Working with the assumption that the contravariant tensor

P_{i j}

(defined from the Ricci tensor and scalar curvature) is invertible, we derive the algebraic soliton equations for left-invariant metrics [...] Read more.

We investigate left-invariant generalized cross-curvature solitons on simply connected three-dimensional Lorentzian Lie groups. Working with the assumption that the contravariant tensor

P_{i j}

(defined from the Ricci tensor and scalar curvature) is invertible, we derive the algebraic soliton equations for left-invariant metrics and classify all left-invariant generalized cross-curvature solitons (for the generalized equation

L_{X} g + λ g = 2 h + 2 ρ R g

) on the standard 3D Lorentzian Lie algebra types (unimodular Types Ia, Ib, II, and III and non-unimodular Types IV.1, IV.2, and IV.3). For each Lie algebra type, we state the necessary and sufficient algebraic conditions on the structure constants, provide explicit formulas for the soliton vector fields X (when they exist), and compute the soliton parameter

λ

in terms of the structure constants and the parameter

ρ

. Our results include several existence families, explicit nonexistence results (notably for Type Ib and Type IV.3), and consequences linking the existence of left-invariant solitons with local conformal flatness in certain cases. The classification yields new explicit homogeneous generalized cross-curvature solitons in the Lorentzian setting and clarifies how the parameter

ρ

modifies the algebraic constraints. Examples and brief geometric remarks are provided. Full article

(This article belongs to the Special Issue Advances in Differential Geometry and Singularity Theory, 2nd Edition)

14 pages, 2087 KB

Open AccessArticle

The Second Approximation of the Averaging Method in the Dynamics of Controlled Motions of Vibration Systems with Dry Friction

by Igor Zeidis, Nikolay Bolotnik and Klaus Zimmermann

Axioms 2025, 14(9), 694; https://doi.org/10.3390/axioms14090694 - 12 Sep 2025

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Abstract

The second approximation of the averaging method is constructed in the problem of motion along a horizontal rough plane of a vibration-driven mechanical system consisting of a carrying body (robot housing) in contact with the plane and two internal masses oscillating vertically and [...] Read more.

The second approximation of the averaging method is constructed in the problem of motion along a horizontal rough plane of a vibration-driven mechanical system consisting of a carrying body (robot housing) in contact with the plane and two internal masses oscillating vertically and horizontally according to a harmonic law with the same frequency. In the absence of a phase shift in the first approximation, the directed motion of the system as a single whole (locomotion) cannot be detected. In the second approximation, an expression for the average velocity of motion is obtained. The values of velocity calculated using the obtained formula are in good agreement with the results of numerical calculations. The described technique for constructing the second approximation can be used to solve other problems with dry friction. Full article

(This article belongs to the Special Issue Trends in Dynamical Systems and Applied Mathematics)

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18 pages, 1808 KB

Open AccessArticle

Non-Parametric Hypothesis Testing for Used Better than Aged in Laplace Transform (UBAL) Life Distributions: A Moment Inequalities Approach with Medical Applications

by Mahmoud E. Bakr, Oluwafemi Samson Balogun, Arwa M. Alsahangiti and Asmaa A. El-Toony

Axioms 2025, 14(9), 693; https://doi.org/10.3390/axioms14090693 - 12 Sep 2025

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Abstract

Life distribution comparison is important in reliability and survival analysis to model system aging and longevity. The article develops a non-parametric hypothesis test procedure for testing exponentiality against the Used Better than Aged in Laplace transform (UBAL) family of life distributions. The test [...] Read more.

Life distribution comparison is important in reliability and survival analysis to model system aging and longevity. The article develops a non-parametric hypothesis test procedure for testing exponentiality against the Used Better than Aged in Laplace transform (UBAL) family of life distributions. The test in this case is developed based on moment inequalities in the Laplace transform, which yields a computationally straightforward and theoretically sound methodology. We establish the asymptotic behavior of the test statistic and evaluate its performance through Monte Carlo simulations, showing acceptable power against common alternatives such as the Weibull, linear failure rate, and Makeham distributions. Critical values are also provided for practical use under complete and right-censored data. The usefulness of the procedure is also illustrated on real medical data sets, including leukemia, liver cancer, and lung cancer patient survival times, and COVID-19 deaths data. The results indicate the applicability and success of the proposed method in detecting deviations from exponentiality. Overall, this research contributes a handy statistical method for reliability, risk analysis, and medical survival analysis, where system aging is of the utmost importance. Full article

(This article belongs to the Section Mathematical Analysis)

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3 pages, 143 KB

Open AccessEditorial

Axioms and Methods for Handling Differential Equations and Inverse Problems

by Zoltán Vizvári, Mihály Klincsik, Róbert Kersner, Péter Odry, Zoltán Sári and Vladimir Tadić

Axioms 2025, 14(9), 692; https://doi.org/10.3390/axioms14090692 - 12 Sep 2025

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Abstract

Modeling real-life problems requires a variety of differential equations that often cause significant challenges for researchers [...] Full article

(This article belongs to the Special Issue Axioms and Methods for Handling Differential Equations and Inverse Problems)

19 pages, 647 KB

Open AccessArticle

Max+Sum Spanning Tree Interdiction and Improvement Problems Under Weighted l_∞ Norm

by Qiao Zhang, Junhua Jia and Xiao Li

Axioms 2025, 14(9), 691; https://doi.org/10.3390/axioms14090691 - 11 Sep 2025

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Abstract

The Max+Sum Spanning Tree (MSST) problem, with applications in secure communication systems, seeks a spanning tree T minimizing

{max}_{e \in T} w (e) + \sum_{e \in T} c (e)

on a given edge-weighted undirected network [...] Read more.

The Max+Sum Spanning Tree (MSST) problem, with applications in secure communication systems, seeks a spanning tree T minimizing

{max}_{e \in T} w (e) + \sum_{e \in T} c (e)

on a given edge-weighted undirected network

G (V, E, c, w)

, where the sets V and E are the sets of vertices and edges, respectively. The functions c and w are defined on the edge set, representing transmission cost and verification delay in secure communication systems, respectively. This problem can be solved within

O (| E | log | V |)

time. We investigate its interdiction (MSSTID) and improvement (MSSTIP) problems under the weighted

l_{\infty}

norm. MSSTID seeks minimal edge weight adjustments (to either c or w) to degrade network performance by ensuring the optimal MSST’s weight is at least K, while MSSTIP similarly aims to enhance performance by making the optimal MSST’s weight at most K through minimal weight modifications. These problems naturally arise in adversarial and proactive performance enhancement scenarios, respectively, where network robustness or efficiency must be guaranteed through constrained resource allocation. We first establish their mathematical models. Subsequently, we analyze the properties of the optimal value to determine the relationship between the magnitude of a given number and the optimal value. Then, utilizing binary search methods and greedy techniques, we design four algorithms with time complexity

O (| E |^{2} log | V |)

to solve the above problems by modifying w or c. Finally, numerical experiments are conducted to demonstrate the effectiveness of the algorithms. Full article

(This article belongs to the Special Issue Graph Theory and Combinatorics: Theory and Applications)

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21 pages, 1502 KB

Open AccessArticle

Max–Min Transitive Closure of Randomly Generated Fuzzy Matrix: Bernoulli and Classical Probabilistic Models

by Nan Li, Xianfeng Yu and Wuniu Liu

Axioms 2025, 14(9), 690; https://doi.org/10.3390/axioms14090690 - 11 Sep 2025

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Abstract

A randomly generated fuzzy matrix refers to a fuzzy matrix in which the values of elements belong to the sample space of a [0,1]-random variable that follows a certain probability distribution. This paper studies the max–min transitive closure of two-type randomly generated fuzzy [...] Read more.

A randomly generated fuzzy matrix refers to a fuzzy matrix in which the values of elements belong to the sample space of a [0,1]-random variable that follows a certain probability distribution. This paper studies the max–min transitive closure of two-type randomly generated fuzzy matrices: Bernoulli and classical probabilistic models. By introducing the concept of superposed fuzzy matrices, we investigate the probability distribution of the transitive closure of randomly generated fuzzy matrices for two probabilistic models. First, we presented the arithmetic operation rules for the superposed fuzzy relations. The expected value of the randomly generated Bernoulli fuzzy matrix transition closure was studied. A direct calculation method for the randomly generated fuzzy matrix transitive closure of the classical probability model was provided. Finally, the errors between the direct calculation method and the traditional transitive closure calculation method were compared. Full article

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18 pages, 796 KB

Open AccessArticle

Hybrid Beamforming via Fourth-Order Tucker Decomposition for Multiuser Millimeter-Wave Massive MIMO Systems

by Haiyang Dong and Zheng Dou

Axioms 2025, 14(9), 689; https://doi.org/10.3390/axioms14090689 - 9 Sep 2025

Viewed by 627

Abstract

To enhance the spectral efficiency of hybrid beamforming in millimeter-wave massive MIMO systems, the problem is formulated as a high-dimensional non-convex optimization under constant modulus constraints. A novel algorithm based on fourth-order tensor Tucker decomposition is proposed. Specifically, the frequency-domain channel matrices are [...] Read more.

To enhance the spectral efficiency of hybrid beamforming in millimeter-wave massive MIMO systems, the problem is formulated as a high-dimensional non-convex optimization under constant modulus constraints. A novel algorithm based on fourth-order tensor Tucker decomposition is proposed. Specifically, the frequency-domain channel matrices are structured into a fourth-order tensor to explicitly capture the couplings across the spatial, frequency, and user domains. To tackle the non-convexity induced by constant modulus constraints, the analog precoder and combiner are derived by solving a truncated-rank Tucker decomposition problem through the Alternating Direction Method of Multipliers and Alternating Least Squares schemes. Subsequently, in the digital domain, the Regularized Block Diagonalization algorithm is integrated with the subcarrier and user factor matrices—obtained from the tensor decomposition—along with the water-filling strategy to design the digital precoder and combiner, thereby achieving a balance between multi-user interference suppression and noise enhancement. The proposed tensor-based algorithm is demonstrated through simulations to outperform existing state-of-the-art schemes. This work provides an efficient and mathematically sound solution for hybrid beamforming in dense multi-user scenarios envisioned for sixth-generation mobile communications. Full article

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19 pages, 1123 KB

Open AccessArticle

Partitioning AG(2,q), q≡7 Mod 12, into MöbiusKantor Configurations and One Point

by Stefano Innamorati

Axioms 2025, 14(9), 688; https://doi.org/10.3390/axioms14090688 - 9 Sep 2025

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Abstract

By the cyclic structure of the affine plane AG(2,q), q≡7 mod 12, a mixed partition into a set of Möbius–Kantor configurations and a one-point set is provided. This generalizes a 2006 result of L. Berardi and T. Masini, who partitioned [...] Read more.

By the cyclic structure of the affine plane AG(2,q), q≡7 mod 12, a mixed partition into a set of Möbius–Kantor configurations and a one-point set is provided. This generalizes a 2006 result of L. Berardi and T. Masini, who partitioned the affine plane of order 7 into a set of Möbius–Kantor configurations and a one-point set. Full article

(This article belongs to the Section Geometry and Topology)

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21 pages, 347 KB

Open AccessArticle

Fixed-Point Theorems in Sequential G-Metric Spaces and Their Application to the Solvability of a System of Integral Equations

by Robab Abdi, Hasan Hosseinzadeh, Vahid Parvaneh, Monica Bota and Jamal Rezaei Roshan

Axioms 2025, 14(9), 687; https://doi.org/10.3390/axioms14090687 - 8 Sep 2025

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Abstract

The goal of this work is to demonstrate some fixed-point theorems for

J S

-contractions over sequential G-metric spaces that are not necessarily continuous in any variable and do not enjoy the triangle inequality. This new space is a generalization of standard [...] Read more.

The goal of this work is to demonstrate some fixed-point theorems for

J S

-contractions over sequential G-metric spaces that are not necessarily continuous in any variable and do not enjoy the triangle inequality. This new space is a generalization of standard G-metric spaces and

G_{b}

-metric spaces. Additionally, a related application and an illustrated example are included to verify the accuracy of the findings. Full article

(This article belongs to the Section Mathematical Analysis)

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Axioms, Volume 14, Issue 9 (September 2025) – 68 articles

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