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Volume 14
Issue 3
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Axioms, Volume 14, Issue 3 (March 2025) – 82 articles

Cover Story (view full-size image): One of the themes of this paper is recent results on large gaps between primes. The first of these results was achieved in the paper by Ford, Green, Konyagin, and Tao. The results were later improved in a joint paper between these four authors and Maynard. One of the main components of these results is previous methods introduced by Erdős and Rankin. Other factors are important breakthrough results from Goldston, Pintz, and Yildirim and their extension by Maynard on small gaps between primes. All of these previous results are discussed in brief herein. The results on the appearance of k-th powers of primes contained in those large gaps obtained by the authors in joint work with Maier are based on a combination of the results described above with the matrix method introduced by Maier. View this paper
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19 pages, 290 KiB  
Article
Fisher Information and Electromagnetic Interacting Dirac Spinors
by Asher Yahalom
Axioms 2025, 14(3), 229; https://doi.org/10.3390/axioms14030229 - 20 Mar 2025
Viewed by 161
Abstract
In earlier works, it was demonstrated that Schrödinger’s equation, which includes interactions with electromagnetic fields, can be derived from a fluid dynamic Lagrangian framework. This approach treats the system as a charged potential flow interacting with an electromagnetic field. The emergence of quantum [...] Read more.
In earlier works, it was demonstrated that Schrödinger’s equation, which includes interactions with electromagnetic fields, can be derived from a fluid dynamic Lagrangian framework. This approach treats the system as a charged potential flow interacting with an electromagnetic field. The emergence of quantum behavior was attributed to the inclusion of Fisher information terms in the classical Lagrangian. This insight suggests that quantum mechanical systems are influenced not just by electromagnetic fields but also by information, which plays a fundamental role in driving quantum dynamics. This methodology was extended to Pauli’s equations by relaxing the constraint of potential flow and employing the Clebsch formalism. Although this approach yielded significant insights, certain terms remained unexplained. Some of these unresolved terms appear to be directly related to aspects of the relativistic Dirac theory. In a recent work, the analysis was revisited within the context of relativistic flows, introducing a novel perspective for deriving the relativistic quantum theory but neglecting the interaction with electromagnetic fields for simplicity. This is rectified in the current work, which shows the implications of the field in the current context. Full article
(This article belongs to the Special Issue Recent Advances in Quantum Mechanics and Mathematical Physics)
15 pages, 694 KiB  
Article
Optimal Minimax Rate of Smoothing Parameter in Distributed Nonparametric Specification Test
by Peili Liu, Yanyan Zhao, Libai Xu and Tao Wang
Axioms 2025, 14(3), 228; https://doi.org/10.3390/axioms14030228 - 19 Mar 2025
Viewed by 109
Abstract
A model specification test is a statistical procedure used to assess whether a given statistical model accurately represents the underlying data-generating process. The smoothing-based nonparametric specification test is widely used due to its efficiency against “singular” local alternatives. However, large modern datasets create [...] Read more.
A model specification test is a statistical procedure used to assess whether a given statistical model accurately represents the underlying data-generating process. The smoothing-based nonparametric specification test is widely used due to its efficiency against “singular” local alternatives. However, large modern datasets create various computational problems when implementing the nonparametric specification test. The divide-and-conquer algorithm is highly effective for handling large datasets, as it can break down a large dataset into more manageable datasets. By applying divide-and-conquer, the nonparametric specification test can handle the computational problems induced by the massive size of the modern datasets, leading to improved scalability and efficiency and reduced processing time. However, the selection of smoothing parameters for optimal power of the distributed algorithm is an important problem. The rate of the smoothing parameter that ensures rate optimality of the test in the context of testing the specification of a nonlinear parametric regression function is studied in the literature. In this paper, we verified the uniqueness of the rate of the smoothing parameter that ensures the rate optimality of divide-and-conquer-based tests. By employing a penalty method to select the smoothing parameter, we obtain a test with an asymptotic normal null distribution and adaptiveness properties. The performance of this test is further illustrated through numerical simulations. Full article
(This article belongs to the Special Issue Advances in Statistical Simulation and Computing)
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11 pages, 501 KiB  
Article
Relativistic Scalar Particle Systems in a Spacetime with a Spiral-like Dislocation
by Ricardo L. L. Vitória
Axioms 2025, 14(3), 227; https://doi.org/10.3390/axioms14030227 - 19 Mar 2025
Viewed by 238
Abstract
We have analyzed solutions of bound states of a scalar particle in spacetime with torsion. In the first analysis, we investigate the confinement of a scalar particle in a cylindrical shell. In the second step, we investigate the Klein–Gordon oscillator. Then, we finish [...] Read more.
We have analyzed solutions of bound states of a scalar particle in spacetime with torsion. In the first analysis, we investigate the confinement of a scalar particle in a cylindrical shell. In the second step, we investigate the Klein–Gordon oscillator. Then, we finish our analysis by searching for solutions of bound states of the Klein–Gordon oscillator by interacting with a hard-wall potential. In all these systems, we determine the relativistic energy profile in the background characterized by the presence of torsion in spacetime represented by a spiral-like dislocation. Full article
(This article belongs to the Special Issue Advancements in Applied Mathematics and Computational Physics)
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8 pages, 234 KiB  
Article
Examples of Compact Simply Connected Holomorphic Symplectic Manifolds Which Are Not Formal
by Daniel Guan
Axioms 2025, 14(3), 226; https://doi.org/10.3390/axioms14030226 - 18 Mar 2025
Viewed by 164
Abstract
In this paper, we prove that the complex four dimensional compact holomorphic symplectic manifold we found earlier is not formal. This gives another strong consequence that it is not a topological Kähler manifold. We also conjecture that this is true for the higher [...] Read more.
In this paper, we prove that the complex four dimensional compact holomorphic symplectic manifold we found earlier is not formal. This gives another strong consequence that it is not a topological Kähler manifold. We also conjecture that this is true for the higher dimensional ones. Full article
7 pages, 273 KiB  
Article
Bäcklund Transformation for Solving a (3+1)-Dimensional Integrable Equation
by Binlu Feng, Linlin Gui, Yufeng Zhang and Siqi Han
Axioms 2025, 14(3), 225; https://doi.org/10.3390/axioms14030225 - 18 Mar 2025
Viewed by 130
Abstract
A new generalized (3+1)-dimensional Kadomtsev–Petviashvil (3dKP) equation is derived from the inverse scattering transform method. This equation can be reduced to the standard KP equation and the well-know (3+1)-dimensional equation. In making use of the Lax pair transformation, a Bäcklund transformation of the [...] Read more.
A new generalized (3+1)-dimensional Kadomtsev–Petviashvil (3dKP) equation is derived from the inverse scattering transform method. This equation can be reduced to the standard KP equation and the well-know (3+1)-dimensional equation. In making use of the Lax pair transformation, a Bäcklund transformation of the generalized (3+1)-dimensional KP equation is constructed and some soliton solutions are produced. Finally, a superposition formula is singled out as well by making use of the Bäcklund transformation. As far as we know, the work presented in this paper has not been studied up to now. Full article
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9 pages, 384 KiB  
Article
Linear Algebraic Approach for Delayed Patternized Time-Series Forecasting Models
by Song-Kyoo Kim
Axioms 2025, 14(3), 224; https://doi.org/10.3390/axioms14030224 - 18 Mar 2025
Viewed by 107
Abstract
This paper introduces a linear algebraic approach for forecasting time-series trends, leveraging a theoretical model that transforms historical stock data into matrices to capture temporal dynamics and market patterns. By employing an analytical approach, the model predicts future market movements through delayed patternized [...] Read more.
This paper introduces a linear algebraic approach for forecasting time-series trends, leveraging a theoretical model that transforms historical stock data into matrices to capture temporal dynamics and market patterns. By employing an analytical approach, the model predicts future market movements through delayed patternized time-series machine learning training, achieving an impressive accuracy of 83.77% across 10,539 stock data samples. The mathematical proof underlying the framework, including the use of validation matrices and NXOR operations, ensures a structured evaluation of predictive accuracy. The binary trend-based simplification further reduces computational complexity, making the model scalable for large datasets. This study highlights the potential of linear algebra in enhancing predictive models and provides a foundation for future research to refine the framework, incorporate external variables, and explore alternative machine learning algorithms for improved robustness and applicability in financial markets. The primary advantages of employing linear algebra in this research lay in its ability to systematically structure high-dimensional financial data, enhance computational efficiency, and enable rigorous validation. The results indicate not only the efficacy in trend forecasting but also its potential applicability across various financial settings, making it a valuable tool for investors seeking data-driven insights into market trends. This research paves the way for future studies aimed at refining forecasting methodologies and enhancing financial decision-making processes. Full article
(This article belongs to the Special Issue Advances in Linear Algebra with Applications, 2nd Edition)
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11 pages, 243 KiB  
Article
Conditional Exponential Convex Functions on White Noise Spaces
by Ahmed. M. Zabel, Areej A. Almoneef, Ayat Nassar and Abd-Allah Hyder
Axioms 2025, 14(3), 223; https://doi.org/10.3390/axioms14030223 - 18 Mar 2025
Viewed by 131
Abstract
This paper seeks to present the fundamental features of the category of conditional exponential convex functions (CECFs). Additionally, the study of continuous CECFs contributes to the characterization of convolution semigroups. In this context, we expand our focus to include a much broader class [...] Read more.
This paper seeks to present the fundamental features of the category of conditional exponential convex functions (CECFs). Additionally, the study of continuous CECFs contributes to the characterization of convolution semigroups. In this context, we expand our focus to include a much broader class of Gaussian processes, where we define the generalized Fourier transform in a more straightforward manner. This approach is closely connected to the method by which we derived the Gaussian process, utilizing the framework of a Gelfand triple and the theorem of Bochner–Minlos. A part of this work involves constructing the reproducing kernel Hilbert spaces (RKHS) directly from CECFs. Full article
(This article belongs to the Special Issue Research on Stochastic Analysis and Applied Statistics)
30 pages, 456 KiB  
Article
Classification of the Second Minimal Orbits in the Sharkovski Ordering
by Ugur G. Abdulla, Naveed H. Iqbal, Muhammad U. Abdulla and Rashad U. Abdulla
Axioms 2025, 14(3), 222; https://doi.org/10.3390/axioms14030222 - 17 Mar 2025
Viewed by 110
Abstract
We prove a conjecture on the second minimal odd periodic orbits with respect to Sharkovski ordering for the continuous endomorphisms on the real line. A (2k+1)-periodic orbit [...] Read more.
We prove a conjecture on the second minimal odd periodic orbits with respect to Sharkovski ordering for the continuous endomorphisms on the real line. A (2k+1)-periodic orbit {β1<β2<⋯<β2k+1}, (k≥3) is called second minimal for the map f, if 2k−1 is a minimal period of f|[β1,β2k+1] in the Sharkovski ordering. Full classification of second minimal orbits is presented in terms of cyclic permutations and directed graphs of transitions. It is proved that second minimal odd orbits either have a Stefan-type structure like minimal odd orbits or one of the 4k−3 types, each characterized with unique cyclic permutations and directed graphs of transitions with an accuracy up to the inverses. The new concept of second minimal orbits and its classification have an important application towards an understanding of the universal structure of the distribution of the periodic windows in the bifurcation diagram generated by the chaotic dynamics of nonlinear maps on the interval. Full article
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25 pages, 510 KiB  
Article
The Waiting Time Distribution of Competing Patterns in Markov-Dependent Bernoulli Trials
by Itzhak Moshkovitz and Yonit Barron
Axioms 2025, 14(3), 221; https://doi.org/10.3390/axioms14030221 - 17 Mar 2025
Viewed by 111
Abstract
Competing patterns are compound patterns that compete to be the first to occur a pattern-specific number of times, known as a stopping rule. In this paper, we study a higher-order Markovian dependent Bernoulli trials model with competing patterns. The waiting time distribution refers [...] Read more.
Competing patterns are compound patterns that compete to be the first to occur a pattern-specific number of times, known as a stopping rule. In this paper, we study a higher-order Markovian dependent Bernoulli trials model with competing patterns. The waiting time distribution refers to the distribution of the number of trials required until the stopping rule is met. Based on a finite Markov chain, a hierarchical algorithm is proposed to derive the conditional probability generating function (pgf) of the waiting time of the competing patterns model. By applying the law of total expectation, the final pgf is then obtained. Using examples, we further demonstrate that the proposed algorithm is an effective and easy-to-implement tool. Full article
(This article belongs to the Special Issue Computational and Mathematical Methods in Science and Engineering, 2nd Edition)
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18 pages, 275 KiB  
Article
Calculation of Coefficients of the Optimal Quadrature Formulas in W2(7,0) Space
by Ying Yang and Xuehua Li
Axioms 2025, 14(3), 220; https://doi.org/10.3390/axioms14030220 - 17 Mar 2025
Viewed by 126
Abstract
In this paper, we construct an optimal quadrature formula in the sense of Sard by Sobolev’s method in the W2(7,0) space. We give explicit expressions for the corresponding optimal coefficients. This formula is exact for exponentional–trigonometric functions. Full article
30 pages, 1867 KiB  
Article
A New Hybrid Class of Distributions: Model Characteristics and Stress–Strength Reliability Studies
by Mustapha Muhammad, Jinsen Xiao, Badamasi Abba, Isyaku Muhammad and Refka Ghodhbani
Axioms 2025, 14(3), 219; https://doi.org/10.3390/axioms14030219 - 16 Mar 2025
Viewed by 221
Abstract
This study proposes a generalized family of distributions to enhance flexibility in modeling complex engineering and biomedical data. The framework unifies existing models and improves reliability analysis in both engineering and biomedical applications by capturing diverse system behaviors. We introduce a novel hybrid [...] Read more.
This study proposes a generalized family of distributions to enhance flexibility in modeling complex engineering and biomedical data. The framework unifies existing models and improves reliability analysis in both engineering and biomedical applications by capturing diverse system behaviors. We introduce a novel hybrid family of distributions that incorporates a flexible set of hybrid functions, enabling the extension of various existing distributions. Specifically, we present a three-parameter special member called the hybrid-Weibull–exponential (HWE) distribution. We derive several fundamental mathematical properties of this new family, including moments, random data generation processes, mean residual life (MRL) and its relationship with the failure rate function, and its related asymptotic behavior. Furthermore, we compute advanced information measures, such as extropy and cumulative residual entropy, and derive order statistics along with their asymptotic behaviors. Model identifiability is demonstrated numerically using the Kullback–Leibler divergence. Additionally, we perform a stress–strength (SS) reliability analysis of the HWE under two common scale parameters, supported by illustrative numerical evaluations. For parameter estimation, we adopt the maximum likelihood estimation (MLE) method in both density estimation and SS-parameter studies. The simulation results indicated that the MLE demonstrates consistency in both density and SS-parameter estimations, with the mean squared error of the MLEs decreasing as the sample size increases. Moreover, the average length of the confidence interval for the percentile and Student’s t-bootstrap for the SS-parameter becomes smaller with larger sample sizes, and the coverage probability progressively aligns with the nominal confidence level of 95%. To demonstrate the practical effectiveness of the hybrid family, we provide three real-world data applications in which the HWE distribution outperforms many existing Weibull-based models, as measured by AIC, BIC, CAIC, KS, Anderson–Darling, and Cramer–von Mises criteria. Furthermore, the HLW exhibits strong performance in SS-parameter analysis. Consequently, this hybrid family holds immense potential for modeling lifetime data and advancing reliability and survival analysis. Full article
(This article belongs to the Special Issue Mathematical and Statistical Methods and Their Applications, 2nd Edition)
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46 pages, 521 KiB  
Article
On Finite Exceptional Orthogonal Polynomial Sequences Composed of Rational Darboux Transforms of Romanovski-Jacobi Polynomials
by Gregory Natanson
Axioms 2025, 14(3), 218; https://doi.org/10.3390/axioms14030218 - 16 Mar 2025
Viewed by 156
Abstract
The paper presents the united analysis of the finite exceptional orthogonal polynomial (EOP) sequences composed of rational Darboux transforms of Romanovski-Jacobi polynomials. It is shown that there are four distinguished exceptional differential polynomial systems (X-Jacobi DPSs) of series J1, J2, J3, and W. [...] Read more.
The paper presents the united analysis of the finite exceptional orthogonal polynomial (EOP) sequences composed of rational Darboux transforms of Romanovski-Jacobi polynomials. It is shown that there are four distinguished exceptional differential polynomial systems (X-Jacobi DPSs) of series J1, J2, J3, and W. The first three X-DPSs formed by pseudo-Wronskians of two Jacobi polynomials contain both exceptional orthogonal polynomial systems (X-Jacobi OPSs) on the interval (−1, +1) and the finite EOP sequences on the positive interval (1, ∞). On the contrary, the X-DPS of series W formed by Wronskians of two Jacobi polynomials contains only (infinitely many) finite EOP sequences on the interval (1, ∞). In addition, the paper rigorously examines the three isospectral families of the associated Liouville potentials (rationally extended hyperbolic Pöschl-Teller potentials of types a, b, and a′) exactly quantized by the EOPs in question. Full article
(This article belongs to the Special Issue Orthogonal Polynomials, Special Functions and Applications: 2nd Edition)
24 pages, 755 KiB  
Article
Inference for Dependent Competing Risks with Partially Observed Causes from Bivariate Inverted Exponentiated Pareto Distribution Under Generalized Progressive Hybrid Censoring
by Rani Kumari, Yogesh Mani Tripathi, Rajesh Kumar Sinha and Liang Wang
Axioms 2025, 14(3), 217; https://doi.org/10.3390/axioms14030217 - 16 Mar 2025
Viewed by 254
Abstract
In this paper, inference under dependent competing risk data is considered with multiple causes of failure. We discuss both classical and Bayesian methods for estimating model parameters under the assumption that data are observed under generalized progressive hybrid censoring. The maximum likelihood estimators [...] Read more.
In this paper, inference under dependent competing risk data is considered with multiple causes of failure. We discuss both classical and Bayesian methods for estimating model parameters under the assumption that data are observed under generalized progressive hybrid censoring. The maximum likelihood estimators of model parameters are obtained when occurrences of latent failure follow a bivariate inverted exponentiated Pareto distribution. The associated existence and uniqueness properties of these estimators are established. The asymptotic interval estimators are also constructed. Further, Bayes estimates and highest posterior density intervals are derived using flexible priors. A Monte Carlo sampling algorithm is proposed for posterior computations. The performance of all proposed methods is evaluated through extensive simulations. Moreover, a real-life example is also presented to illustrate the practical applications of our inferential procedures. Full article
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18 pages, 307 KiB  
Article
Entire Functions of Several Variables: Analogs of Wiman’s Theorem
by Oleh Skaskiv, Andriy Bandura, Tetyana Salo and Sviatoslav Dubei
Axioms 2025, 14(3), 216; https://doi.org/10.3390/axioms14030216 - 15 Mar 2025
Viewed by 204
Abstract
This article considers a class of entire functions of several complex variables that are bounded in the Cartesian product of some half-planes. Each such hyperplane is defined on the condition that the real part of the corresponding variable is less than some r [...] Read more.
This article considers a class of entire functions of several complex variables that are bounded in the Cartesian product of some half-planes. Each such hyperplane is defined on the condition that the real part of the corresponding variable is less than some r. For this class of functions, there are established analogs of the Wiman theorems. The first result describes the behavior of an entire function from the given class at the neighborhood of the point of the supremum of its modulus. The second result shows asymptotic equality for supremums of the modulus of the function and its real part outside some exceptional set. In addition, the analogs of Wiman’s theorem are obtained for entire multiple Dirichlet series with arbitrary non-negative exponents. These results are obtained as consequences of a new statement describing the behavior of an entire function F(z) of several complex variables z=(z1,…,zp) at the neighborhood of a point w, where the value F(w) is close to the supremum of its modulus on the boundary of polylinear domains. The paper has two moments of novelty: the results use a more general geometric exhaustion of p-dimensional complex space by polylinear domains than previously known; another aspect of novelty concerns the results obtained for entire multiple Dirichlet series. There is no restriction that every component of exponents is strictly increasing. These statements are valid for any non-negative exponents. Full article
20 pages, 503 KiB  
Article
Local Equivalence of the Black–Scholes and Merton–Garman Equations
by Ivan Arraut
Axioms 2025, 14(3), 215; https://doi.org/10.3390/axioms14030215 - 15 Mar 2025
Viewed by 152
Abstract
It has been previously demonstrated that stochastic volatility emerges as the gauge field necessary to restore local symmetry under changes in stock prices in the Black–Scholes (BS) equation. When this occurs, a Merton–Garman-like equation emerges. From the perspective of manifolds, this means that [...] Read more.
It has been previously demonstrated that stochastic volatility emerges as the gauge field necessary to restore local symmetry under changes in stock prices in the Black–Scholes (BS) equation. When this occurs, a Merton–Garman-like equation emerges. From the perspective of manifolds, this means that the Black–Scholes and Merton–Garman (MG) equations can be considered locally equivalent. In this scenario, the MG Hamiltonian is a special case of a more general Hamiltonian, here referred to as the gauge Hamiltonian. We then show that the gauge character of volatility implies a specific functional relationship between stock prices and volatility. The connection between stock prices and volatility is a powerful tool for improving volatility estimations in the stock market, which is a key ingredient for investors to make good decisions. Finally, we define an extended version of the martingale condition, defined for the gauge Hamiltonian. Full article
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17 pages, 307 KiB  
Article
Hammerstein Nonlinear Integral Equations and Iterative Methods for the Computation of Common Fixed Points
by María A. Navascués
Axioms 2025, 14(3), 214; https://doi.org/10.3390/axioms14030214 - 15 Mar 2025
Viewed by 247
Abstract
In the first part of this article, a special type of Hammerstein nonlinear integral equation is studied. A theorem of the existence of solutions is given in the framework of L2-spaces. Afterwards, an iterative method for the resolution of this kind [...] Read more.
In the first part of this article, a special type of Hammerstein nonlinear integral equation is studied. A theorem of the existence of solutions is given in the framework of L2-spaces. Afterwards, an iterative method for the resolution of this kind of equations is considered, and the convergence of this algorithm towards a solution of the equation is proved. The rest of the paper considers two modifications of the algorithm. The first one is devoted to the sought of common fixed points of a family of nearly asymptotically nonexpansive mappings. The second variant focuses on the search of common fixed points of a finite number of nonexpansive operators. The characteristics of convergence of these methods are studied in the context of uniformly convex Banach spaces. The iterative scheme is applied to approach the common solution of three nonlinear integral equations of Hammerstein type. Full article
(This article belongs to the Special Issue New Perspectives in Operator Theory and Functional Analysis)
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15 pages, 268 KiB  
Article
An Optimal Inequality for Warped Product Pointwise Semi-Slant Submanifolds in Complex Space Forms
by Md Aquib
Axioms 2025, 14(3), 213; https://doi.org/10.3390/axioms14030213 - 14 Mar 2025
Viewed by 125
Abstract
In this paper, we utilize advanced optimization techniques on Riemannian submanifolds to establish two distinct inequalities concerning the generalized normalized δ-Casorati curvatures of warped product pointwise semi-slant (WPPSS) submanifolds within complex space forms. We further identify the precise conditions under which these [...] Read more.
In this paper, we utilize advanced optimization techniques on Riemannian submanifolds to establish two distinct inequalities concerning the generalized normalized δ-Casorati curvatures of warped product pointwise semi-slant (WPPSS) submanifolds within complex space forms. We further identify the precise conditions under which these inequalities attain equality, providing valuable insights into their geometric and structural significance. Additionally, we also present results involving harmonic and Hessian functions, revealing a broader connection between curvature properties and analytic functions. Full article
(This article belongs to the Special Issue Advances in Geometry and Its Applications)
14 pages, 241 KiB  
Article
New Approach to Neutrosophic Numbers and Neutrosophic Complex Numbers
by Abdullah Dertli and Ceremnur Tetik
Axioms 2025, 14(3), 212; https://doi.org/10.3390/axioms14030212 - 14 Mar 2025
Viewed by 105
Abstract
In this study, we introduced non-Newtonian neutrosophic numbers and non-Newtonian neutrosophic complex numbers by combining two recently popular approaches and examined some of their properties. Furthermore, we presented the non-Newtonian neutrosophic triangle inequality and some properties of the non-Newtonian neutrosophic norm, which can [...] Read more.
In this study, we introduced non-Newtonian neutrosophic numbers and non-Newtonian neutrosophic complex numbers by combining two recently popular approaches and examined some of their properties. Furthermore, we presented the non-Newtonian neutrosophic triangle inequality and some properties of the non-Newtonian neutrosophic norm, which can be frequently used in analysis and geometry. Thus, compared to existing studies, we provided a broader perspective for fields such as artificial intelligence, quantum mechanics, medicine, analysis, and geometry. Full article
(This article belongs to the Section Algebra and Number Theory)
13 pages, 3104 KiB  
Article
Interaction of a Four-Level Atom with a Deformed Quantum Field: Mathematical Model and Quantum Resources
by Mariam Algarni, Sayed Abdel-Khalek and Kamal Berrada
Axioms 2025, 14(3), 211; https://doi.org/10.3390/axioms14030211 - 13 Mar 2025
Viewed by 205
Abstract
We introduce a framework presenting the interaction between a four-level atom (F-LA) and a field mode that begins in a coherent state within the para-Bose field (P-BF). The F-LA is considered in a cascade configuration and initially prepared in the upper level. We [...] Read more.
We introduce a framework presenting the interaction between a four-level atom (F-LA) and a field mode that begins in a coherent state within the para-Bose field (P-BF). The F-LA is considered in a cascade configuration and initially prepared in the upper level. We display the system dynamics by solving the motion equation. We discuss various dynamical behaviors of fundamental quantum resources used in quantum optics and information tasks, including atomic population inversion, quantum entanglement (QE), and the statistical properties of the P-BF based on the parameters of the quantum model. In this context, we demonstrate the impact of various system parameters on these quantum resources. Finally, we illustrate the dynamic relationships among the quantum resources within the model. Full article
(This article belongs to the Special Issue Advancements in Applied Mathematics and Computational Physics)
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13 pages, 257 KiB  
Article
Trivial Homology Groups of Warped Product Semi-Slant Submanifolds in Kenmotsu Space Forms
by Noura M. Alhouiti, Ali H. Alkhaldi, Akram Ali, Fatemah Mofarreh and Piscoran Laurian-Ioan
Axioms 2025, 14(3), 210; https://doi.org/10.3390/axioms14030210 - 13 Mar 2025
Viewed by 208
Abstract
This paper investigates the relationship between homology groups and warped product semi-slant submanifolds in Kenmotsu space forms. Some rigidity theorems for vanishing homology groups on warped product semi-slant submanifolds are obtained using the moving-frame method and the second fundamental form inequality. Our results [...] Read more.
This paper investigates the relationship between homology groups and warped product semi-slant submanifolds in Kenmotsu space forms. Some rigidity theorems for vanishing homology groups on warped product semi-slant submanifolds are obtained using the moving-frame method and the second fundamental form inequality. Our results are an extension of previous studies in this direction. Full article
(This article belongs to the Special Issue Advances in Differential Geometry and Singularity Theory, 2nd Edition)
22 pages, 5079 KiB  
Article
A New Flexible Model for Three-Stage Phenomena: The Fragmented Kumar-Trapez Distribution
by Salma Omar Bleed, Aisha A. Ben Taher and Taha Radwan
Axioms 2025, 14(3), 209; https://doi.org/10.3390/axioms14030209 - 13 Mar 2025
Viewed by 218
Abstract
This article proposes a solution to the problem of limiting the representation of three-stage phenomena to linear forms and addresses the stability of the second stage by introducing a novel distribution, the Fragmented Kumar-Trapez (FKT) distribution, which includes two additional parameters beyond the [...] Read more.
This article proposes a solution to the problem of limiting the representation of three-stage phenomena to linear forms and addresses the stability of the second stage by introducing a novel distribution, the Fragmented Kumar-Trapez (FKT) distribution, which includes two additional parameters beyond the parameters used for an existing standard model. These parameters provide flexibility to the density function, enabling it to model a wide range of shapes. This work contributes to the understanding of distributions whose probability density functions are divided into three parts, addressing key questions such as: How to handle such distributions? How to estimate the range parameters of the trapezoidal and proposed distributions using the maximum likelihood method? How to estimate the unknown parameters of the proposed distribution using both maximum likelihood and Bayesian methods? In addition, the article explores some of the mathematical properties of the proposed distribution. Finally, a simulation study on generated data and an illustrated example are conducted to demonstrate the practical importance of the FKT distribution. WinBUGS 1.4 program is used to illustrate the application of MCMC simulation. Full article
(This article belongs to the Special Issue Computational Statistics and Its Applications)
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18 pages, 575 KiB  
Article
Some Bounds for the Fragmentation Coefficient of Random Graphs
by Katerina Adler, Reuven Cohen and Simi Haber
Axioms 2025, 14(3), 208; https://doi.org/10.3390/axioms14030208 - 12 Mar 2025
Viewed by 189
Abstract
Graph fragmentation aims to find the smallest vertex subset whose removal breaks a graph into components of bounded size. While this problem has applications in network dismantling and combinatorics, theoretical bounds on optimal solutions remain limited. We derive rigorous bounds for several graph [...] Read more.
Graph fragmentation aims to find the smallest vertex subset whose removal breaks a graph into components of bounded size. While this problem has applications in network dismantling and combinatorics, theoretical bounds on optimal solutions remain limited. We derive rigorous bounds for several graph classes, characterize hard instances, and illuminate the relationship between graph structure and optimal fragmentation strategies. Specifically, we show that for random d-regular graphs with n vertices, the minimal size of the fragmenting subset of nodes is asymptotically almost surely |S|≥d−22d−2n−o(n), and that asymptotically almost surely, n−2α(G)−o(n)≤|S|≤n−α(G)+o(n), where α(G) is the independence number of G. For d≫1, we prove that asymptotically almost surely, |S|/n≈1−logd/d. However, we show that the line graphs of random regular graphs are considerably harder to fragment, with |S|/n≥1−c/d for some constant c. Full article
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24 pages, 457 KiB  
Article
A Taxonomy of the Greimas Square
by Michael Fowler
Axioms 2025, 14(3), 207; https://doi.org/10.3390/axioms14030207 - 12 Mar 2025
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Abstract
In this article I introduce the semiotic square by A.J. Greimas and the notions of negation and opposition that were central to the Paris School of structural semiotics. I trace the connection of the square to both Aristotle’s square of opposition and the [...] Read more.
In this article I introduce the semiotic square by A.J. Greimas and the notions of negation and opposition that were central to the Paris School of structural semiotics. I trace the connection of the square to both Aristotle’s square of opposition and the Klein four-group as well as propose a formalization of the square. This is first achieved through identifying R-relations on meta-term/seme pairs of the square, then applying lattice theory and formal concept analysis in order to visualize an extended structure. The main result is a protoconcept algebra that generalizes the Greimas square through Boolean operations and provides an ordering of all possible formal concepts, thereby acting as a taxonomy. Full article
(This article belongs to the Special Issue Applied Mathematics and Mathematical Modeling)
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16 pages, 299 KiB  
Article
Banach Limit and Fixed Point Approach in the Ulam Stability of the Quadratic Functional Equation
by El-sayed El-hady and Janusz Brzdęk
Axioms 2025, 14(3), 206; https://doi.org/10.3390/axioms14030206 - 12 Mar 2025
Viewed by 271
Abstract
We show how to obtain new results on the Ulam stability of the quadratic equation q(a+b)+q(a−b)=2q(a)+2q(b) using the Banach [...] Read more.
We show how to obtain new results on the Ulam stability of the quadratic equation q(a+b)+q(a−b)=2q(a)+2q(b) using the Banach limit and the fixed point theorem obtained quite recently for some function spaces. The equation is modeled on the parallelogram identity used by Jordan and von Neumann to characterize the inner product spaces. Our main results state that the maps, from the Abelian groups into the set of reals, that satisfy the equation approximately (in a certain sense) are close to its solutions. In this way, we generalize several previous similar outcomes, by giving much finer estimations of the distances between such solutions to the equation. We also present a simplified survey of the earlier related outcomes. Full article
(This article belongs to the Special Issue Advances in Fixed Point Theory with Applications)
24 pages, 591 KiB  
Article
Fractional Evolution Equation with Nonlocal Multi-Point Condition: Application to Fractional Ginzburg–Landau Equation
by Ahmed Salem and Rania Al-Maalwi
Axioms 2025, 14(3), 205; https://doi.org/10.3390/axioms14030205 - 11 Mar 2025
Viewed by 182
Abstract
This paper is devoted to studying the existence and uniqueness of mild solutions for semilinear fractional evolution equations with the Hilfer–Katugampola fractional derivative and under the nonlocal multi-point condition. The analysis is based on analytic semigroup theory, the Krasnoselskii fixed-point theorem, and the [...] Read more.
This paper is devoted to studying the existence and uniqueness of mild solutions for semilinear fractional evolution equations with the Hilfer–Katugampola fractional derivative and under the nonlocal multi-point condition. The analysis is based on analytic semigroup theory, the Krasnoselskii fixed-point theorem, and the Banach fixed-point theorem. An application to a time-fractional real Ginzburg–Landau equation is also given to illustrate the applicability of our results. Furthermore, we determine some conditions to make the control (Bifurcation) parameter in the Ginzburg–Landau equation sufficiently small. Full article
(This article belongs to the Special Issue Advances in Differential Equations and Its Applications)
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59 pages, 1333 KiB  
Review
Category-Theoretical and Topos-Theoretical Frameworks in Machine Learning: A Survey
by Yiyang Jia, Guohong Peng, Zheng Yang and Tianhao Chen
Axioms 2025, 14(3), 204; https://doi.org/10.3390/axioms14030204 - 10 Mar 2025
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Abstract
In this survey, we provide an overview of category theory-derived machine learning from four mainstream perspectives: gradient-based learning, probability-based learning, invariance and equivalence-based learning, and topos-based learning. For the first three topics, we primarily review research in the past five years, updating and [...] Read more.
In this survey, we provide an overview of category theory-derived machine learning from four mainstream perspectives: gradient-based learning, probability-based learning, invariance and equivalence-based learning, and topos-based learning. For the first three topics, we primarily review research in the past five years, updating and expanding on the previous survey by Shiebler et al. The fourth topic, which delves into higher category theory, particularly topos theory, is surveyed for the first time in this paper. In certain machine learning methods, the compositionality of functors plays a vital role, prompting the development of specific categorical frameworks. However, when considering how the global properties of a network reflect in local structures and how geometric properties and semantics are expressed with logic, the topos structure becomes particularly significant and profound. Full article
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13 pages, 249 KiB  
Article
On Gersenne Sequence: A Study of One Family in the Horadam-Type Sequence
by Douglas Catulio Santos, Eudes Antonio Costa and Paula M. M. C. Catarino
Axioms 2025, 14(3), 203; https://doi.org/10.3390/axioms14030203 - 10 Mar 2025
Viewed by 185
Abstract
This study introduces an innovative approach to Mersenne-type numbers. This paper introduces a new class of numbers, which we call Gersenne numbers. The aim of this paper is to define the Gersenne sequence and to investigate some of their properties, such as the [...] Read more.
This study introduces an innovative approach to Mersenne-type numbers. This paper introduces a new class of numbers, which we call Gersenne numbers. The aim of this paper is to define the Gersenne sequence and to investigate some of their properties, such as the recurrence relation, the summation formula, and the generating function. Moreover, the classical identities are derived, such as the Tagiuri–Vajda, Catalan, Cassini, and d’Ocagne identities for Gersenne numbers. Full article
(This article belongs to the Section Algebra and Number Theory)
12 pages, 286 KiB  
Article
On the Abscissa of Convergence of Laplace–Stieltjes Integrals in the Euclidean Real Vector Space Rp
by Andriy Bandura, Oleh Skaskiv and Olha Zadorozhna
Axioms 2025, 14(3), 202; https://doi.org/10.3390/axioms14030202 - 10 Mar 2025
Viewed by 199
Abstract
New estimates for the convergence abscissas of the multiple Laplace–Stieltjes integral are obtained. There is described the relationship between the integrand function, the Lebesgue–Stieltjes measure, and the abscissa of convergence of the multiple Laplace–Stieltjes integral. Since the multiple Laplace–Stieltjes integral is a direct [...] Read more.
New estimates for the convergence abscissas of the multiple Laplace–Stieltjes integral are obtained. There is described the relationship between the integrand function, the Lebesgue–Stieltjes measure, and the abscissa of convergence of the multiple Laplace–Stieltjes integral. Since the multiple Laplace–Stieltjes integral is a direct generalization of the Laplace integral and multiple Dirichlet series, known results about convergence domains for the multiple Dirichlet series are obtained as corollaries of the presented more general statements for the multiple Laplace–Stieltjes integral. Full article
(This article belongs to the Special Issue Recent Advances in Special Functions and Applications, 2nd Edition)
14 pages, 320 KiB  
Article
Odd Cycles in Conditionally Faulty Enhanced Hypercube Networks
by Min Liu
Axioms 2025, 14(3), 201; https://doi.org/10.3390/axioms14030201 - 10 Mar 2025
Viewed by 208
Abstract
The n-dimensional enhanced hypercube Qn,k(1≤k≤n−1) is a well-known variation of hypercube networks. Its structure can be obtained from the hypercube by adding 2n−1 complementary edges. We denote [...] Read more.
The n-dimensional enhanced hypercube Qn,k(1≤k≤n−1) is a well-known variation of hypercube networks. Its structure can be obtained from the hypercube by adding 2n−1 complementary edges. We denote a network G to be a conditionally faulty model if every fault-free vertex of G connects at least two fault-free edges. Let Fv and Fe be the set of faulty vertices and faulty edges in Qn,k(1≤k≤n−1), respectively. In this paper, for the conditionally faulty Qn,k with |Fv|+|Fe|≤2n−5, where n(≥3) and k have different parity, I prove that Qn,k−Fv−Fe contains a fault-free cycle with every odd length l, where n−k+4≤l≤2n−2|Fv|−1. Full article
(This article belongs to the Special Issue Graph Theory and Combinatorics: Theory and Applications)
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14 pages, 240 KiB  
Article
Analysis of Screen Generic Lightlike Submanifolds in an Indefinite Kaehler Statistical Manifold Endowed with a Quarter-Symmetric Non-Metric Connection
by Vandana Gupta, Jasleen Kaur, Oğuzhan Bahadır and Meraj Ali Khan
Axioms 2025, 14(3), 200; https://doi.org/10.3390/axioms14030200 - 8 Mar 2025
Viewed by 300
Abstract
This paper introduces the notion of screen generic lightlike submanifolds (SGLSs) of an indefinite Kaehler statistical manifold equipped with a quarter-symmetric non-metric (QSNM) connection, supported by suitable illustrations. Assertions for induced connection on the lightlike submanifold and integrability of the distributions are proved. [...] Read more.
This paper introduces the notion of screen generic lightlike submanifolds (SGLSs) of an indefinite Kaehler statistical manifold equipped with a quarter-symmetric non-metric (QSNM) connection, supported by suitable illustrations. Assertions for induced connection on the lightlike submanifold and integrability of the distributions are proved. The characterization theorems on parallelism and geodesicity of the SGLSs are presented. Results for the totally umbilic screen generic lightlike submanifold with a QSNM connection are also established. Full article
(This article belongs to the Special Issue Differential Geometry and Its Application, 3rd Edition)
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