An Eneström–Kakeya Theorem with Monotonicity Conditions on the Even- and Odd-Indexed Coefficients of a Polynomial
Approximation by Power Series of Functions
Mitigating the Drawbacks of the L₀ Norm and the Total Variation Norm
Integrability Methods for the Variable Coefficients Geophysical KdV Model
The Characterization of the Mechanical Harmonic Oscillator Extremum Envelope Shape According to Different Friction Types

Journal Description

Axioms

Axioms is an international, peer-reviewed, open access journal of mathematics, mathematical logic and mathematical physics, published monthly online by MDPI. The European Society for Fuzzy Logic and Technology (EUSFLAT), International Fuzzy Systems Association (IFSA), Union of Slovak Mathematicians and Physicists (JSMF) and Eurekas Community are affiliated with Axioms and their members receive discounts on the article processing charges.

Open Access— free for readers, with article processing charges (APC) paid by authors or their institutions.
High visibility: indexed within SCIE (Web of Science), dblp, and other databases.
Journal Rank: JCR - Q2 (Mathematics, Applied)
Rapid Publication: manuscripts are peer-reviewed and a first decision is provided to authors approximately 21.6 days after submission; acceptance to publication is undertaken in 2.8 days (median values for papers published in this journal in the first half of 2025).
Recognition of Reviewers: reviewers who provide timely, thorough peer-review reports receive vouchers entitling them to a discount on the APC of their next publication in any MDPI journal, in appreciation of the work done.
Companion journal: Logics.
Journal Cluster of Mathematics and Its Applications: AppliedMath, Axioms, Computation, Fractal and Fractional, Geometry, International Journal of Topology, Logics, Mathematics and Symmetry.

Impact Factor: 1.6 (2024); 5-Year Impact Factor: 1.5 (2024)

Imprint Information Journal Flyer Open Access ISSN: 2075-1680

Latest Articles

12 pages, 264 KB

Open AccessArticle

An Algorithm for Determining Whether the Quotient Ring Modulo, an Ideal, Has a Cyclic Basis

by Hengjia Cao and Chang Tan

Axioms 2025, 14(11), 838; https://doi.org/10.3390/axioms14110838 - 14 Nov 2025

Abstract

This paper focuses on the research of the existence of cyclic bases for the quotient ring modulo, a zero-dimensional ideal. Based on the necessary and sufficient condition for the existence of cyclic bases, it further deduces an equivalent condition for the existence of cyclic bases. In accordance with this condition, a new algorithm is proposed. The existence of a cyclic is determined by constructing a matrix and calculating its determinant in the algorithm. Compared with the original algorithm, it narrows the scope of the candidate element set and improves the computational efficiency of the algorithm. Full article

(This article belongs to the Special Issue Computational Algebra, Coding Theory and Cryptography: Theory and Applications, 2nd Edition)

11 pages, 377 KB

Open AccessArticle

Geometric Families Define Differential K-Theory

by Jae Min Lee and Byungdo Park

Axioms 2025, 14(11), 837; https://doi.org/10.3390/axioms14110837 - 14 Nov 2025

Abstract

The index-theoretic construction of differential K-theory by Bunke and Schick uses both a geometric family and a differential form as a cocycle data. We prove that geometric families alone can codify the differential K-theory. Full article

(This article belongs to the Special Issue Trends in Differential Geometry and Algebraic Topology)

23 pages, 497 KB

Open AccessArticle

Quasi-Optimal Convergence of a Family of Adaptive Nonconforming Finite Element Methods

by Xuying Zhao

Axioms 2025, 14(11), 836; https://doi.org/10.3390/axioms14110836 - 13 Nov 2025

Abstract

This study is devoted to the quasi-optimal convergence analysis of a family of adaptive nonconforming elements with high-order terms, which preserve weak continuities. In contrast with the nonconforming

P_{1}

element (Crouzeix–Raviart element) the gradient of the discrete solution considered in this paper [...] Read more.

P_{1}

element (Crouzeix–Raviart element) the gradient of the discrete solution considered in this paper is not a piecewise constant vector. New quasi-orthogonality and a new discrete upper bound are established for the first time, based on which the convergence of the adaptive algorithm with a standard Dörfler collective marking strategy and quasi-optimality results are eventually established. Some other properties are also investigated, for example, the discrete Helmholtz decomposition for this family of nonconforming elements. Numerical experiments confirm the theoretical results. Full article

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7 pages, 234 KB

Open AccessArticle

Polyadic Encryption

by Steven Duplij and Qiang Guo

Axioms 2025, 14(11), 835; https://doi.org/10.3390/axioms14110835 - 13 Nov 2025

Abstract

A novel original procedure of encryption/decryption based on the polyadic algebraic structures and on signal processing methods is proposed. First, we use signals with integer amplitudes to send information. Then, we use polyadic techniques to transfer the plaintext into series of special integers. [...] Read more.

(This article belongs to the Special Issue Computational Algebra, Coding Theory and Cryptography: Theory and Applications, 2nd Edition)

50 pages, 413 KB

Open AccessArticle

Asymptotic Behavior of the Time-Dependent Solution of the M^[X]/G/1 Queuing Model with Feedback and Optional Server Vacations Based on a Single Vacation Policy

by Nuraya Nurahmat and Geni Gupur

Axioms 2025, 14(11), 834; https://doi.org/10.3390/axioms14110834 - 12 Nov 2025

Abstract

By using the

C_{0}

-semigroup theory, we study the asymptotic behavior of the time-dependent solution and the time-dependent indices of the

M^{[X]} / G / 1

queuing model with feedback and optional server vacations based on a single vacation [...] Read more.

By using the

C_{0}

-semigroup theory, we study the asymptotic behavior of the time-dependent solution and the time-dependent indices of the

M^{[X]} / G / 1

queuing model with feedback and optional server vacations based on a single vacation policy. This queuing model is described by infinitely many partial differential equations with integral boundary conditions in an unbounded interval. Under certain conditions, by studying spectrum of the underlying operator of this queuing model on the imaginary axis, we prove that the time-dependent solution of this queuing model strongly converges to its steady-state solution. Next, we prove that the time-dependent queuing length of this queuing system converges to its steady-state queuing length and the time-dependent waiting time of this queuing system converges to its steady-state waiting time as time tends to infinity. Our results extend the steady-state results of this queuing system. Full article

(This article belongs to the Special Issue Numerical and Analytical Methods for Partial Differential Equations with Integral Boundary Conditions)

14 pages, 267 KB

Open AccessArticle

A Quasi-Boundary Value Method for Solving a Backward Problem of the Fractional Rayleigh–Stokes Equation

by Xiaomin Wang and Aimin Yang

Axioms 2025, 14(11), 833; https://doi.org/10.3390/axioms14110833 - 12 Nov 2025

Abstract

In this paper, we study a backward problem for a fractional Rayleigh–Stokes equation by using a quasi-boundary value method. This problem is ill-posed; i.e., the solution (if it exists) does not depend continuously on the data. To overcome its instability, a regularization method is employed, and convergence rate estimates are derived under both a priori and a posteriori criteria for selecting the regularization parameter. The theoretical results demonstrate the effectiveness of the proposed method in deriving stable and accurate solutions. Full article

(This article belongs to the Special Issue Differential Equations and Inverse Problems, 2nd Edition)

23 pages, 7293 KB

Open AccessArticle

The Influence of Generalist Predator and Michaelis–Menten Harvesting in a Holling–Tanner Model

by Tanglei Huang, Huiling Wu and Zhong Li

Axioms 2025, 14(11), 832; https://doi.org/10.3390/axioms14110832 - 12 Nov 2025

Abstract

In this paper, a Holling–Tanner predator–prey model with generalist predators and Michaelis–Menten-type prey harvesting is investigated. We analyze the existence and stability of equilibria and find the system has at most three positive equilibria. The double positive equilibrium belongs to the cusp type, with its codimension being at least 5. We then prove that the triple positive equilibrium is either a nilpotent focus (or elliptic point) of codimension 3, or a nilpotent elliptic equilibrium with codimension no less than 4. Additionally, the system undergoes two types of bifurcations: a cusp-type degenerate Bogdanov–Takens bifurcation (codimension 3) and a Hopf bifurcation. Using numerical simulations, the system has two limit cycles, which indicates that Michaelis–Menten-type prey harvesting makes the system’s dynamics more complex. Full article

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20 pages, 36430 KB

Open AccessArticle

A Brief Review of Wormhole Cosmic Censorship

by Leonel Bixano, I. A. Sarmiento-Alvarado and Tonatiuh Matos

Axioms 2025, 14(11), 831; https://doi.org/10.3390/axioms14110831 - 11 Nov 2025

Abstract

Spacetime singularities, in the sense that curvature invariants are infinite at some point or region, are thought to be impossible to observe, and must be hidden within an event horizon. This conjecture is called Cosmic Censorship (CC), and was formulated by Penrose. Here we review another type of CC where spacetime singularities are causally disconnected from the universe, because the throat of a wormhole “sucks in” the geodesics and prevents them from making contact with the singularity. In this work, we present a series of exact solutions to the Einstein–Maxwell–Dilaton equations that feature a ring singularity; that is, the curvature invariants are singular in this ring, but the ring is causally disconnected from the universe so that no geodesics can touch it. This extension of CC is called Wormhole Cosmic Censorship. Full article

(This article belongs to the Special Issue Mathematical Aspects of Black Holes in General Relativity and Beyond)

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21 pages, 395 KB

Open AccessArticle

An Efficient Iteration Method for Fixed-Point Approximation and Its Application to Fractional Volterra–Fredholm Integro–Differential Equations

by Ekta Sharma, Shubham Kumar Mittal, Sunil Panday and Lorentz Jäntschi

Axioms 2025, 14(11), 830; https://doi.org/10.3390/axioms14110830 - 11 Nov 2025

Abstract

This paper proposes an efficient iteration method for fixed-point approximation in Banach spaces. The method accelerates convergence by incorporating a squared operator term within the iteration process. Analytical proofs verify its convergence and stability. Comparative numerical tests show that it converges faster and more reliably than established Picard-type methods. Its application to fractional models involving the Gamma function highlights the method’s efficiency and potential for broader use in nonlinear and fractional systems. Full article

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

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23 pages, 356 KB

Open AccessArticle

Foundations of the Preisach Operator in Real Options Problems with Subscription Cost and Heterogeneous Population of Consumers

by Dmitrii Rachinskii, Lev Rachinskiy and Alejandro Rivera

Axioms 2025, 14(11), 829; https://doi.org/10.3390/axioms14110829 - 10 Nov 2025

Abstract

This paper considers the pricing of a subscription service in a heterogeneous market with consumers having different discount rates. We show that in the case of a non-zero enrollment/cancellation cost, solutions of the Hamilton–Jacobi–Bellman equation naturally contain an equivalent of the well-known Preisach operator, a fundamental model of hysteresis in engineering applications. Singular perturbation expansions are used to approximate the optimal solution, assuming that enrollment/cancellation costs are small, relative to the total subscription cost. As a case study, we consider and compare markets with one and two consumers. Full article

18 pages, 807 KB

Open AccessArticle

Comparative Study of Dragonfly and Cuckoo Search Algorithms Applying Type-2 Fuzzy Logic Parameter Adaptation

by Hector M. Guajardo, Fevrier Valdez, Patricia Melin, Oscar Castillo and Prometeo Cortes-Antonio

Axioms 2025, 14(11), 828; https://doi.org/10.3390/axioms14110828 - 8 Nov 2025

Abstract

This study presents a comparative analysis of two bio-inspired optimization techniques: the Dragonfly Algorithm (DA) and Cuckoo Search (CS). The DA models the collective behavior of dragonflies, replicating dynamic processes such as foraging, evasion, and synchronized movement to effectively explore and exploit the solution space. In contrast, the CS algorithm draws inspiration from the brood parasitism strategy observed in certain Cuckoo species, where eggs are laid in the nests of other birds, thereby leveraging randomization and selection mechanisms for optimization. To enhance the performance of both algorithms, Type-2 fuzzy logic systems were integrated into their structures. Specifically, the DA was fine-tuned through the adjustment of its inertia weight (W) and attraction coefficient (Beta), while the CS algorithm was optimized by calibrating the Lévy flight distribution parameter. A comprehensive set of benchmark functions, F1 through F10, was employed to evaluate and compare the effectiveness and convergence behavior of each method under fuzzy-enhanced configurations. Results indicate that the fuzzy-based adaptations consistently improved convergence stability and accuracy, demonstrating the advantage of integrating Type-2 fuzzy parameter control into swarm-based optimization frameworks. Full article

(This article belongs to the Special Issue Advances in Mathematical Optimization Algorithms and Its Applications)

20 pages, 328 KB

Open AccessArticle

Resource Allocation and Minmax Scheduling Under Group Technology and Different Due-Window Assignments

by Li-Han Zhang and Ji-Bo Wang

Axioms 2025, 14(11), 827; https://doi.org/10.3390/axioms14110827 - 7 Nov 2025

Abstract

This article investigates single-machine group scheduling integrated with resource allocation under different due-window (

D I F D W

) assignment. Three distinct scenarios are examined: one with constant processing times, one with a linear resource consumption function, and one with a convex [...] Read more.

This article investigates single-machine group scheduling integrated with resource allocation under different due-window (

D I F D W

) assignment. Three distinct scenarios are examined: one with constant processing times, one with a linear resource consumption function, and one with a convex resource consumption function. The objective is to minimize the total cost comprising the maximum earliness/tardiness penalties, the due-window starting time cost, the due-window size cost, and the resource consumption cost. For each problem variant, we analyze the structural properties of optimal solutions and develop corresponding solution algorithms: a polynomial-time optimal algorithm for the case with constant processing times, heuristic algorithms for problems involving linear and convex resource allocation, and the branch-and-bound algorithm for obtaining exact solutions. Numerical experiments are conducted to evaluate the performance of the proposed algorithms. Full article

(This article belongs to the Special Issue Advances in Mathematical Optimization Algorithms and Its Applications)

13 pages, 300 KB

Open AccessArticle

Equivalence of Common Metrics on Trapezoidal Fuzzy Numbers

by Qingsong Mao and Huan Huang

Axioms 2025, 14(11), 826; https://doi.org/10.3390/axioms14110826 - 7 Nov 2025

Abstract

From both theoretical and applied perspectives, the trapezoidal fuzzy numbers are widely relevant fuzzy sets. In this paper, we show that the four kinds of common metrics—the supremum metric, the

L_{p}

-type

d_{p}

metrics, the sendograph metric, and the endograph metric—are [...] Read more.

From both theoretical and applied perspectives, the trapezoidal fuzzy numbers are widely relevant fuzzy sets. In this paper, we show that the four kinds of common metrics—the supremum metric, the

L_{p}

-type

d_{p}

metrics, the sendograph metric, and the endograph metric—are equivalent on the trapezoidal fuzzy numbers. In fact, we obtain a stronger result: the convergence induced by these four kinds of metrics on the trapezoidal fuzzy numbers is equivalent to the convergence of the corresponding representation quadruples of the trapezoidal fuzzy numbers in

R^{4}

. The latter convergence is very easy to verify. Our results give a fundamental understanding of these four kinds of common metrics on the trapezoidal fuzzy numbers and provide a quick judgment condition for the convergence induced by them. Full article

(This article belongs to the Special Issue Recent Advances in Fuzzy Sets and Related Topics, 2nd Edition)

17 pages, 295 KB

Open AccessArticle

On Distance Laplacian Energy of Unicyclic and Bicyclic Graphs

by Dan Li and Shiqi Zhou

Axioms 2025, 14(11), 825; https://doi.org/10.3390/axioms14110825 - 7 Nov 2025

Abstract

For a connected graph G, let

D^{L} (G)

be its distance Laplacian matrix and [...] Read more.

For a connected graph G, let

D^{L} (G)

be its distance Laplacian matrix and

λ_{1} (G) \geq λ_{2} (G) \geq \dots \geq λ_{n - 1} (G) > λ_{n} (G) = 0

be its

D^{L}

eigenvalues. The

D^{L}

energy of G is defined as

D L E (G) = \sum_{i = 1}^{n} |λ_{i} (G) - \frac{2 W (G)}{n}|

, where

W (G)

is the Wiener index of G. An important problem in graph energy studies is to determine exact formulations of the energy for specific graph classes and their complements. This paper gives the precise

D^{L}

energy formulations of a class of bicyclic graphs

C_{2} (p, q)

, a class of unicyclic graphs

C_{1} (p, q)

, and their complements. Moreover, we order the graphs

C_{2} (p, q)

on the basic of

λ_{1}

λ_{n - 1}

, and consider the same problems for their complements. And the ordering of the graphs

C_{1} (p, q)

on the basic of

λ_{n - 1}

and the ordering of their complements on the basics of

λ_{1}

λ_{n - 1}

and the

D^{L}

energy are obtained. Full article

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12 pages, 245 KB

Open AccessArticle

Weak Resolution Dimensions of Subcategories

by Juxiang Sun, Xinpeng Liu and Weimin Liu

Axioms 2025, 14(11), 824; https://doi.org/10.3390/axioms14110824 - 7 Nov 2025

Abstract

We investigate the relationships between the weak resolution dimensions of subcategories of module categories of Artinian algebras in the present paper. Let

Λ

be an Artinian algebra, and

A

B

and

X

subcategories of

Λ

-modules, such that each object X in [...] Read more.

We investigate the relationships between the weak resolution dimensions of subcategories of module categories of Artinian algebras in the present paper. Let

Λ

be an Artinian algebra, and

A

B

and

X

subcategories of

Λ

-modules, such that each object X in

X

is given by an exact sequence

0 \to A \to B \to X \to 0

with

A \in O b A

and

B \in O b B

. We prove that the weak resolution dimension of

X

is bounded above by the sum of the corresponding dimensions for

A

and

B

plus 1. As applications, we study weak resolution dimensions of Artinian algebras under left idealized extensions and conditions on special ideals. Full article

15 pages, 337 KB

Open AccessArticle

Fractional Error Bounds for Lobatto Quadrature: A Convexity Approach via Riemann–Liouville Integrals

by Li Liao, Abdelghani Lakhdari, Muhammad Uzair Awan, Hongyan Xu and Badreddine Meftah

Axioms 2025, 14(11), 823; https://doi.org/10.3390/axioms14110823 - 7 Nov 2025

Abstract

In this paper, we establish a new fractional integral identity linked to the 4-point Lobatto quadrature rule within the Riemann–Liouville fractional calculus framework. Building on this identity, we derive several Lobatto-type inequalities under convexity assumptions, yielding error bounds that involve only first-order derivatives, thereby improving practical applicability. A numerical example with graphical illustration confirms the theoretical findings and demonstrates their accuracy. We also present applications to special means, highlighting the utility of the obtained inequalities. The integration of fractional analysis, quadrature theory, and numerical validation provides a robust methodology for refining and analyzing high-order integration rules. Full article

(This article belongs to the Special Issue Theory and Application of Integral Inequalities, 2nd Edition)

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29 pages, 10424 KB

Open AccessArticle

Fuzzy Edge Chromatic Number of the Join of Fuzzy Graphs and Its Applications

by Jing Qu, Qian Wang and Angmo Deji

Axioms 2025, 14(11), 822; https://doi.org/10.3390/axioms14110822 - 6 Nov 2025

Abstract

Fuzzy edge coloring has proven to be a powerful tool for modeling and optimizing complex network systems, owing to its ability to effectively represent and manage the uncertainty in relational strengths and conflicts. It focuses on defining the fuzzy edge chromatic number, optimizing its computation, and exploring practical applications. For join graphs derived from fuzzy graphs, we propose an efficient fuzzy edge coloring algorithm and analyze the associated properties. Building on this, fuzzy edge coloring offers effective strategies for software promotion and traffic signal optimization. This work addresses fundamental theoretical challenges related to algorithm design, complexity analysis, and structural properties in fuzzy graph edge coloring, while also demonstrating its practical utility in complex scenarios such as software promotion and traffic signal optimization. Full article

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24 pages, 1707 KB

Open AccessArticle

Differential Game Analysis of Green Technology Investment in the Food Industry Under a Governmental Coordination Mechanism

by Enquan Luo, Shuwen Xiang and Yanlong Yang

Axioms 2025, 14(11), 821; https://doi.org/10.3390/axioms14110821 - 6 Nov 2025

Abstract

This study constructs a Stackelberg differential game model for green technology invest-ment in the food industry under a governmental coordination mechanism. The optimal dynamic strategies for local governments and enterprises are derived using Pontryagin’s maximum principle. The backward differential equation method is employed in this study. It is used to analyze the impact of shadow prices on the optimal decisions of both parties. Furthermore, the study examines how social welfare benefits influence the food quality levels within the jurisdiction of local governments. Based on these findings, optimal strategy pathways are proposed to achieve social welfare and enterprise profit maximization in the green transition process of both government and enterprises. The results indicate that a local government’s investment in food quality improvement significantly enhances the food quality levels within their jurisdictions—greater government investment leads to higher food quality. At the same time, food quality levels are positively correlated with the enterprises’ green technology capital investment. Additionally, consumer price sensitivity and sensitivity to price differences have a notable impact on product pricing. As consumers become more price-sensitive, product prices decrease accordingly, which, in turn, helps increase the market share of the enterprises’ products. Full article

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18 pages, 1005 KB

Open AccessArticle

An Online Generalized Multiscale Method for Embedded Discrete Fracture Model

by Zhengkang He and Bangmin Wu

Axioms 2025, 14(11), 820; https://doi.org/10.3390/axioms14110820 - 5 Nov 2025

Abstract

This study concerns an online generalized multiscale method for flow in fractured porous media that is based on an embedded discrete fracture model. We first convert a two-point flux-approximation scheme into an equivalent discrete weak formulation that results in the same linear algebraic system for the unknown pressure. Then, by the use of a suitable local snapshot space and a well-designed spectral decomposition, we compute offline basis functions to capture local heterogeneity information on account of the presence of various fractures in each coarse cell. After that, we compute residual-based online basis functions that contain global multiscale information to enrich the multiscale space and thus achieve higher accuracy of the multiscale solution. Meanwhile, theoretical analyses are conducted to show the convergence behavior, and a number of numerical tests with different fracture configurations are performed to investigate the performance of online enrichment. Full article

(This article belongs to the Section Mathematical Analysis)

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11 pages, 237 KB

Open AccessArticle

A Grammatical Interpretation of Horadam Sequences

by Jun-Ying Liu, Hai-Ling Li and Zhi-Hong Zhang

Axioms 2025, 14(11), 819; https://doi.org/10.3390/axioms14110819 - 3 Nov 2025

Abstract

The Horadam sequence

{H_{n} (a, b; p, q)}_{n ⩾ 0}

has been widely studied in combinatorics and number theory. In this paper, we find that the context-free grammar [...] Read more.

The Horadam sequence

{H_{n} (a, b; p, q)}_{n ⩾ 0}

has been widely studied in combinatorics and number theory. In this paper, we find that the context-free grammar

G = {x \to p x + y, y \to q x}

can be used to generate Horadam sequences. Using this grammar, we deduce several identities, including Cassini-like identities. Moreover, we investigate the relationship between two distinct Horadam sequences

H_{n} (a, b; p, q)

and

H_{n} (c, d; p, q)

with

(a, b) \neq (c, d)

and provide an approach to derive identities, which can be illustrated by the Fibonacci and Lucas sequences as well as the two kinds of Chebyshev polynomials. Full article

(This article belongs to the Section Algebra and Number Theory)

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Fixed Point Theory and Measure Theory Topic Editors: Safeer Hussain Khan, Lateef Olakunle Jolaoso, Olaniyi S. Iyiola
Deadline: 30 November 2025

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Special Issue in Axioms

Mathematical Physics and Integrable Systems Guest Editors: Chuanzhong Li, Haifeng Wang
Deadline: 20 November 2025

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Deadline: 20 November 2025

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