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Axioms, Volume 14, Issue 2 (February 2025) – 44 articles

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12 pages, 254 KiB  
Article
Solving Fredholm Integral Equations Using Probabilistic F-Contractions
by Ismail Tahiri, Youssef Achtoun, Mohammed Lamarti Sefian and Stojan Radenović
Axioms 2025, 14(2), 119; https://doi.org/10.3390/axioms14020119 - 5 Feb 2025
Viewed by 235
Abstract
Fixed-point theory plays a pivotal role in addressing equations that model various real-life applications, offering robust methods to find solutions that remain stable under different conditions and dynamics. The main objective of this paper is to introduce and study the novel concept of [...] Read more.
Fixed-point theory plays a pivotal role in addressing equations that model various real-life applications, offering robust methods to find solutions that remain stable under different conditions and dynamics. The main objective of this paper is to introduce and study the novel concept of probabilistic F-contraction within the framework of Menger spaces. This innovative approach extends classical fixed-point results to probabilistic settings, leveraging the probabilistic structure of Menger spaces to handle uncertainty and variability in the modeling process. By establishing the existence and uniqueness of fixed points in this versatile class of spaces, the study highlights the broader applicability and deeper significance of the probabilistic F-contraction. We explore the intricate interrelations among these fixed points, shedding light on their implications across different contexts and presenting insights into various theorem versions that enhance our understanding of their utility. Additionally, we propose a straightforward and effective approach for solving a system of Fredholm integral equations using fixed-point techniques specifically tailored for Menger spaces, illustrating their practical utility in tackling the complex mathematical models encountered in diverse fields. Full article
(This article belongs to the Section Mathematical Analysis)
25 pages, 456 KiB  
Article
On the Global Dynamics of a Fourth-Order Riccati-Type Exponential Fuzzy Difference Equation
by Asifa Tassaddiq, Muhammad Tanveer, Muhammad Usman, Dalal Khalid Almutairi and Rabab Alharabi
Axioms 2025, 14(2), 118; https://doi.org/10.3390/axioms14020118 - 4 Feb 2025
Viewed by 244
Abstract
Fuzzy systems play a crucial role in emerging fields such as artificial intelligence, machine learning, and computer science, drawing significant research interest in fuzzy difference equations. Inspired by this, we analyze the dynamic properties of a fourth-order exponential Riccati-type fuzzy difference equation. The [...] Read more.
Fuzzy systems play a crucial role in emerging fields such as artificial intelligence, machine learning, and computer science, drawing significant research interest in fuzzy difference equations. Inspired by this, we analyze the dynamic properties of a fourth-order exponential Riccati-type fuzzy difference equation. The study is further extended to a system of fourth-order fuzzy difference equations. We investigate the boundedness, as well as the local and global stability, of positive solutions. To support the theoretical findings, numerical examples are presented along with graphical and tabular representations. Full article
13 pages, 266 KiB  
Article
Conformal Solutions of Static Plane Symmetric Cosmological Models in Cases of a Perfect Fluid and a Cosmic String Cloud
by Ragab M. Gad, Awatif Al-Jedani and Shahad T. Alsulami
Axioms 2025, 14(2), 117; https://doi.org/10.3390/axioms14020117 - 2 Feb 2025
Viewed by 363
Abstract
In this work, we obtained exact solutions of Einstein’s field equations for plane symmetric cosmological models by assuming that they admit conformal motion. The space-time geometry of these solutions is found to be nonsingular, non-vacuum and conformally flat. We have shown that in [...] Read more.
In this work, we obtained exact solutions of Einstein’s field equations for plane symmetric cosmological models by assuming that they admit conformal motion. The space-time geometry of these solutions is found to be nonsingular, non-vacuum and conformally flat. We have shown that in the case of a perfect fluid, these solutions have an energy-momentum tensor possessing dark energy with negative pressure and the energy equation of state is ρ+p=0. We have shown that a fluid has acceleration, rotation, shear-free, vanishing expansion, and rotation. In the case of a cosmic string cloud, we found that the tension density and particle density decrease as the fluid moves along the direction of the strings, then vanish at infinity. We shown that the exact conformal solution for a static plane symmetric model reduces to the well-known anti-De Sitter space-time. We obtained that the space-time under consideration admits a conformal vector field orthogonal to the 4-velocity vector and does not admits a vector parallel to the 4-velocity vector. Some physical and kinematic properties of the resulting models are also discussed. Full article
11 pages, 265 KiB  
Article
Inverse Problems of Recovering Lower-Order Coefficients from Boundary Integral Data
by Sergey Pyatkov and Oleg Soldatov
Axioms 2025, 14(2), 116; https://doi.org/10.3390/axioms14020116 - 1 Feb 2025
Viewed by 361
Abstract
We study inverse problems of identification of lower-order coefficients in a second-order parabolic equation. The coefficients are sought in the form of a finite series segment with unknown coefficients, depending on time. The linear case is also considered. Overdetermination conditions are the integrals [...] Read more.
We study inverse problems of identification of lower-order coefficients in a second-order parabolic equation. The coefficients are sought in the form of a finite series segment with unknown coefficients, depending on time. The linear case is also considered. Overdetermination conditions are the integrals over the boundary of a solution’s domain with weights. We focus on existence and uniqueness theorems and stability estimates for solutions to these inverse problems. An operator equation to which the problem is reduced is studied with the use of the contraction mapping principle. A solution belongs to some Sobolev space and has all generalized derivatives occurring into the equation summable to some power. The method of the proof is constructive, and it can be used for developing new numerical algorithms for solving the problem. Full article
10 pages, 271 KiB  
Article
Krein–Sobolev Orthogonal Polynomials II
by Alexander Jones, Lance Littlejohn and Alejandro Quintero Roba
Axioms 2025, 14(2), 115; https://doi.org/10.3390/axioms14020115 - 1 Feb 2025
Viewed by 239
Abstract
In a recent paper, Littlejohn and Quintero studied the orthogonal polynomials {Kn}n=0—which they named Krein–Sobolev polynomials—that are orthogonal in the classical Sobolev space H1[1,1] with respect to [...] Read more.
In a recent paper, Littlejohn and Quintero studied the orthogonal polynomials {Kn}n=0—which they named Krein–Sobolev polynomials—that are orthogonal in the classical Sobolev space H1[1,1] with respect to the (positive-definite) inner product (f,g)1,c:=f(1)f(1)g¯(1)g¯(1)2+11(f(x)g¯(x)+cf(x)g¯(x))dx, where c is a fixed, positive constant. These polynomials generalize the Althammer (or Legendre–Sobolev) polynomials first studied by Althammer and Schäfke. The Krein–Sobolev polynomials were found as a result of a left-definite spectral study of the self-adjoint Krein Laplacian operator Kc(c>0) in L2(1,1). Other than K0 and K1, these polynomials are not eigenfunctions of Kc. As shown by Littlejohn and Quintero, the sequence {Kn}n=0 forms a complete orthogonal set in the first left-definite space (H1[1,1],(·,·)1,c) associated with (Kc,L2(1,1)). Furthermore, they show that, for n1,Kn(x) has n distinct zeros in (1,1). In this note, we find an explicit formula for Krein–Sobolev polynomials {Kn}n=0. Full article
21 pages, 3064 KiB  
Article
Collocation Method for the Time-Fractional Generalized Kawahara Equation Using a Certain Lucas Polynomial Sequence
by Waleed Mohamed Abd-Elhameed, Abdulrahman Khalid Al-Harbi, Omar Mazen Alqubori, Mohammed H. Alharbi and Ahmed Gamal Atta
Axioms 2025, 14(2), 114; https://doi.org/10.3390/axioms14020114 - 1 Feb 2025
Viewed by 258
Abstract
This paper proposes a numerical technique to solve the time-fractional generalized Kawahara differential equation (TFGKDE). Certain shifted Lucas polynomials are utilized as basis functions. We first establish some new formulas concerned with the introduced polynomials and then tackle the equation using a suitable [...] Read more.
This paper proposes a numerical technique to solve the time-fractional generalized Kawahara differential equation (TFGKDE). Certain shifted Lucas polynomials are utilized as basis functions. We first establish some new formulas concerned with the introduced polynomials and then tackle the equation using a suitable collocation procedure. The integer and fractional derivatives of the shifted polynomials are used with the typical collocation method to convert the equation with its governing conditions into a system of algebraic equations. The convergence and error analysis of the proposed double expansion are rigorously investigated, demonstrating its accuracy and efficiency. Illustrative examples are provided to validate the effectiveness and applicability of the proposed algorithm. Full article
(This article belongs to the Special Issue Advances in Differential Equations and Its Applications)
26 pages, 580 KiB  
Article
Reliability Analysis and Numerical Simulation of the Five-Robot System with Early Warning Function
by Xing Qiao, Dan Ma and Shuang Guo
Axioms 2025, 14(2), 113; https://doi.org/10.3390/axioms14020113 - 1 Feb 2025
Viewed by 268
Abstract
The rapid advancement of robotic technologies has demonstrated the significant potential of Multi-Robot Systems (MRS) for application across various fields, particularly in automation, manufacturing, and rescue operations. However, enhancing the reliability of Multi-Robot Systems, particularly in critical applications, has emerged as a primary [...] Read more.
The rapid advancement of robotic technologies has demonstrated the significant potential of Multi-Robot Systems (MRS) for application across various fields, particularly in automation, manufacturing, and rescue operations. However, enhancing the reliability of Multi-Robot Systems, particularly in critical applications, has emerged as a primary focus of research. A mathematical model of a five-robot system, equipped with early warning capabilities, is developed using Markov process theory and the supplementary variable method in this paper. A model of an abstract Cauchy problem system is developed, employing semigroup theory to investigate the well-posedness of solutions for this five-robot system. The stability of the system is verified using analytical methods, confinal correlation theory, and modern functional analysis techniques. Several key reliability indicators are presented using the eigenvector method. Numerical simulations and comparative methods effectively demonstrate the efficacy of the proposed eigenvector method. Firstly, the innovation of this paper lies in the combination of qualitative and quantitative analyses to improve and enrich the theory and methods of repairable systems. Secondly, mathematical analysis methods and the mathematical software are employed to provide both analytical and numerical solutions for the system. Full article
24 pages, 905 KiB  
Article
The Existence and Stability of a Periodic Solution of a Nonautonomous Delayed Reaction–Diffusion Predator–Prey Model
by Lili Jia and Changyou Wang
Axioms 2025, 14(2), 112; https://doi.org/10.3390/axioms14020112 - 1 Feb 2025
Viewed by 259
Abstract
In this study, we research a nonautonomous, three-species, delayed reaction–diffusion predator–prey model (RDPPM). Firstly, we derive sufficient conditions to guarantee the existence of a strictly positive, spatially homogeneous periodic solution (SHPS) for the delayed, nonautonomous RDPPM. These conditions are obtained using the comparison [...] Read more.
In this study, we research a nonautonomous, three-species, delayed reaction–diffusion predator–prey model (RDPPM). Firstly, we derive sufficient conditions to guarantee the existence of a strictly positive, spatially homogeneous periodic solution (SHPS) for the delayed, nonautonomous RDPPM. These conditions are obtained using the comparison theorem for delayed differential equations and the fixed point theorem. Secondly, we present sufficient conditions to ensure the global asymptotic stability of the SHPS for the delayed, nonautonomous RDPPM. These conditions are established through the application of the upper and lower solution method (UALSM) for delayed parabolic partial differential equations (PDEs), along with Lyapunov stability theory. Finally, to demonstrate the practical application of our results, we numerically validate the proposed conditions using a 2-periodic, delayed, nonautonomous RDPPM. Full article
(This article belongs to the Special Issue Advances in Differential Equations and Its Applications)
18 pages, 304 KiB  
Article
Analysis of an Abstract Delayed Fractional Integro-Differential System via the α-Resolvent Operator
by Ishfaq Khan, Akbar Zada, Ioan-Lucian Popa and Afef Kallekh
Axioms 2025, 14(2), 111; https://doi.org/10.3390/axioms14020111 - 1 Feb 2025
Viewed by 268
Abstract
This paper explores the mild solutions of partial impulsive fractional integro-differential systems of order 1<α<2 in a Banach space. We derive the solution of the system under the assumption that the homogeneous part of the system admits an α [...] Read more.
This paper explores the mild solutions of partial impulsive fractional integro-differential systems of order 1<α<2 in a Banach space. We derive the solution of the system under the assumption that the homogeneous part of the system admits an α-resolvent operator. Krasnoselskii’s fixed point theorem is used for the existence of solution, while uniqueness is ensured using Banach’s fixed point theorem. The stability of the system is analyzed through the framework of Hyers–Ulam stability using Lipschitz conditions. Finally, examples are presented to illustrate the applicability of the theoretical results. Full article
19 pages, 293 KiB  
Article
Super Quasi-Einstein Warped Products Manifolds with Respect to Affine Connections
by Mohd Vasiulla, Mohabbat Ali, Meraj Ali Khan and Ibrahim Aldayel
Axioms 2025, 14(2), 110; https://doi.org/10.3390/axioms14020110 - 31 Jan 2025
Viewed by 316
Abstract
In this paper, we investigate warped products on super quasi-Einstein manifolds under affine connections. We explore their fundamental properties, establish conditions for their existence, and prove that these manifolds can also be nearly quasi-Einstein and pseudo quasi-Einstein. To illustrate, we provide examples in [...] Read more.
In this paper, we investigate warped products on super quasi-Einstein manifolds under affine connections. We explore their fundamental properties, establish conditions for their existence, and prove that these manifolds can also be nearly quasi-Einstein and pseudo quasi-Einstein. To illustrate, we provide examples in both Riemannian and Lorentzian geometries, confirming their existence. Finally, we construct and analyze an explicit example of a warped product on a super quasi-Einstein manifold with respect to affine connections. Full article
(This article belongs to the Special Issue Differential Geometry and Its Application, 3rd Edition)
15 pages, 231 KiB  
Article
A Brief Study on the k-Dimensional Repunit Sequence
by Eudes A. Costa, Paula M. M. C. Catarino, Paulo J. M. Vasco and Francisco R. V. Alves
Axioms 2025, 14(2), 109; https://doi.org/10.3390/axioms14020109 - 31 Jan 2025
Viewed by 253
Abstract
In this paper, we aim to introduce and investigate the bidimensional, tridimensional and k-dimensional extension of Repunit numbers, with a particular focus on their recurrence relations, key properties, and various sum identities. Full article
(This article belongs to the Section Algebra and Number Theory)
27 pages, 498 KiB  
Article
Spherical Fuzzy Credibility Dombi Aggregation Operators and Their Application in Artificial Intelligence
by Neelam Khan, Muhammad Qiyas, Darjan Karabasevic, Muhammad Ramzan, Mubashir Ali, Igor Dugonjic and Dragisa Stanujkic
Axioms 2025, 14(2), 108; https://doi.org/10.3390/axioms14020108 - 31 Jan 2025
Viewed by 267
Abstract
It was recently proposed to extend the spherical fuzzy set to spherical fuzzy credibility sets (SFCSs). In this paper, we define the concept of SFCSs. We then define new operational laws for SFCSs using Dombi operational laws. Various spherical fuzzy credibility aggregation operators [...] Read more.
It was recently proposed to extend the spherical fuzzy set to spherical fuzzy credibility sets (SFCSs). In this paper, we define the concept of SFCSs. We then define new operational laws for SFCSs using Dombi operational laws. Various spherical fuzzy credibility aggregation operators such as spherical fuzzy credibility Dombi weighted averaging (SFCDWA), spherical fuzzy credibility Dombi ordered weighted averaging (SFCDOWA), spherical fuzzy credibility Dombi weighted geometric (SFCDWG), and spherical fuzzy credibility Dombi ordered weighted geometric (SFCDOWG) are defined. We also show the boundedness, monotonicity, and idempotency aspects of the suggested operators. We proposed the spherical fuzzy credibility entropy to find the unknown weight information of the attributes. Symmetry analysis is a useful and important tool in artificial intelligence that may be used in a variety of fields. To calculate the significant factor, we determine the multi-attribute decision-making (MADM) method using the suggested operators for SFCSs to increase the value of the assessed operators. To demonstrate the effectiveness and superiority of the suggested approach, we compare our findings to those of many other approaches. Full article
(This article belongs to the Special Issue New Perspectives in Fuzzy Sets and Their Applications, 2nd Edition)
16 pages, 293 KiB  
Article
On Ulam Stability of the Davison Functional Equation in m-Banach Spaces
by El-sayed El-hady and Janusz Brzdęk
Axioms 2025, 14(2), 107; https://doi.org/10.3390/axioms14020107 - 30 Jan 2025
Viewed by 351
Abstract
We prove new Ulam stability results for the Davison functional equation, h(sv)+h(s+v)=h(sv+s)+h(v), in the class of mappings h [...] Read more.
We prove new Ulam stability results for the Davison functional equation, h(sv)+h(s+v)=h(sv+s)+h(v), in the class of mappings h from a ring F into an m-Banach space. In this way, we complement several earlier outcomes, by extending them to the case of m-normed spaces. Our proofs are based on an earlier Ulam stability result obtained for some functional equation in a single variable. Full article
(This article belongs to the Special Issue Difference, Functional, and Related Equations)
48 pages, 1898 KiB  
Essay
The Code Underneath
by Julio Rives
Axioms 2025, 14(2), 106; https://doi.org/10.3390/axioms14020106 - 30 Jan 2025
Viewed by 249
Abstract
An inverse-square probability mass function (PMF) is at the Newcomb–Benford law (NBL)’s root and ultimately at the origin of positional notation and conformality. PrZ=2Z2, where ZZ+. Under its tail, we find information [...] Read more.
An inverse-square probability mass function (PMF) is at the Newcomb–Benford law (NBL)’s root and ultimately at the origin of positional notation and conformality. PrZ=2Z2, where ZZ+. Under its tail, we find information as harmonic likelihood Ls,t=Ht1Hs1, where Hn is the nth harmonic number. The global Q-NBL is Prb,q=Lq,q+1L1,b=qHb11, where b is the base and q is a quantum (1q<b). Under its tail, we find information as logarithmic likelihood i,j=lnji. The fiducial R-NBL is Prr,d=d,d+11,r=logr1+1d, where rb is the radix of a local complex system. The global Bayesian rule multiplies the correlation between two numbers, s and t, by a likelihood ratio that is the NBL probability of bucket s,t relative to b’s support. To encode the odds of quantum j against i locally, we multiply the prior odds Prb,jPrb,i by a likelihood ratio, which is the NBL probability of bin i,j relative to r’s support; the local Bayesian coding rule is o˜j:i|r=ijlogrji. The Bayesian rule to recode local data is o˜j:i|r=o˜j:i|rlnrlnr. Global and local Bayesian data are elements of the algebraic field of “gap ratios”, ABCD. The cross-ratio, the central tool in conformal geometry, is a subclass of gap ratio. A one-dimensional coding source reflects the global Bayesian data of the harmonic external world, the annulus xQ|1x<b, into the local Bayesian data of its logarithmic coding space, the ball xQ|x<11b. The source’s conformal encoding function is y=logr2x1, where x is the observed Euclidean distance to an object’s position. The conformal decoding function is x=121+ry. Both functions, unique under basic requirements, enable information- and granularity-invariant recursion to model the multiscale reality. Full article
(This article belongs to the Special Issue Mathematical Modelling of Complex Systems)
23 pages, 3187 KiB  
Article
Numerical Solution of Mathematical Model of Heat Conduction in Multi-Layered Nanoscale Solids
by Aníbal Coronel, Ian Hess, Fernando Huancas and José Chiroque
Axioms 2025, 14(2), 105; https://doi.org/10.3390/axioms14020105 - 30 Jan 2025
Viewed by 283
Abstract
In this article, we are interested in studying and analyzing the heat conduction phenomenon in a multi-layered solid. We consider the physical assumptions that the dual-phase-lag model governs the heat flow on each solid layer. We introduce a one-dimensional mathematical model given by [...] Read more.
In this article, we are interested in studying and analyzing the heat conduction phenomenon in a multi-layered solid. We consider the physical assumptions that the dual-phase-lag model governs the heat flow on each solid layer. We introduce a one-dimensional mathematical model given by an initial interface-boundary value problem, where the unknown is the solid temperature. More precisely, the mathematical model is described by the following four features: the model equation is given by a dual-phase-lag equation at the inside each layer, an initial condition for temperature and the temporal derivative of the temperature, heat flux boundary conditions, and the interfacial condition for the temperature and heat flux conditions between the layers. We discretize the mathematical model by a finite difference scheme. The numerical approach has similar features to the continuous model: it is considered to be the accuracy of the dual-phase-lag model on the inside each layer, the initial conditions are discretized by the average of the temperature on each discrete interval, the inside of each layer approximation is extended to the interfaces by using the behavior of the continuous interface conditions, and the inside each layer approximation on the boundary layers is extended to state the numerical boundary conditions. We prove that the finite difference scheme is unconditionally stable and unconditionally convergent. In addition, we provide some numerical examples. Full article
(This article belongs to the Special Issue Mathematical Methods in the Applied Sciences, 2nd Edition)
21 pages, 10512 KiB  
Article
Parallel Primal-Dual Method with Linearization for Structured Convex Optimization
by Xiayang Zhang, Weiye Tang, Jiayue Wang, Shiyu Zhang and Kangqun Zhang
Axioms 2025, 14(2), 104; https://doi.org/10.3390/axioms14020104 - 29 Jan 2025
Viewed by 333
Abstract
This paper presents the Parallel Primal-Dual (PPD3) algorithm, an innovative approach to solving optimization problems characterized by the minimization of the sum of three convex functions, including a Lipschitz continuous term. The proposed algorithm operates in a parallel framework, simultaneously updating primal and [...] Read more.
This paper presents the Parallel Primal-Dual (PPD3) algorithm, an innovative approach to solving optimization problems characterized by the minimization of the sum of three convex functions, including a Lipschitz continuous term. The proposed algorithm operates in a parallel framework, simultaneously updating primal and dual variables, and offers potential computational advantages. This parallelization can greatly accelerate computation, particularly when run on parallel computing platforms. By departing from traditional primal-dual methods that necessitate strict parameter constraints, the PPD3 algorithm removes reliance on the spectral norm of the linear operator, significantly reducing the computational burden associated with its evaluation. As the problem size grows, calculating the spectral norm, which is essential for many primal-dual methods, becomes progressively more expensive. In addition, adaptive step sizes are computed to accelerate the convergence process. In contrast to most primal-dual approaches that employ a fixed step size constrained by a global upper limit throughout all iterations, the adaptive step size is typically greater and may result in faster convergence. An O(1/k) ergodic convergence rate is proved theoretically. Applications in Fused LASSO and image inpainting demonstrate the method’s efficiency in computation time and convergence rate compared to state-of-the-art algorithms. Full article
15 pages, 244 KiB  
Article
On Polynomials Associated with Finite Topologies
by Moussa Benoumhani and Brahim Chaourar
Axioms 2025, 14(2), 103; https://doi.org/10.3390/axioms14020103 - 29 Jan 2025
Viewed by 237
Abstract
Let τ be a topology on the finite set Xn. We consider the open-set polynomial associated with the topology τ. Its coefficients are the cardinalities of sets Uj=Uj(τ) of open sets of size [...] Read more.
Let τ be a topology on the finite set Xn. We consider the open-set polynomial associated with the topology τ. Its coefficients are the cardinalities of sets Uj=Uj(τ) of open sets of size j=0,,n. We prove that this polynomial has only real zeros only in the trivial case where τ is the discrete topology. Hence, we answer a question raised by J. Brown. We give a partial answer to the question: for which topology is this polynomial log-concave, or at least unimodal? More specifically, we prove that if the topology has a large number of open sets, its open polynomial is unimodal. The idea of degree of log-concavity is introduced and it is shown to be limited for polynomials of non-trivial topologies. Furthermore, the maximum-sized topologies that omit open sets of given sizes are derived. Moreover, all topologies over n points with at least (3/8)2n open sets are proved to be unimodal, completing previous results. Full article
19 pages, 331 KiB  
Article
In Search of L-Fuzzy Contexts Adaptable to Variable Information: A Tool for Time-Varying Data Analysis
by Cristina Alcalde and Ana Burusco
Axioms 2025, 14(2), 102; https://doi.org/10.3390/axioms14020102 - 29 Jan 2025
Viewed by 308
Abstract
This paper sheds light on the study of a new structure, called L-fuzzy hypercontext, which provides an extension of the range of applications of fuzzy concept analysis. The advantage of working with L-fuzzy hypercontexts lies in the fact that we can [...] Read more.
This paper sheds light on the study of a new structure, called L-fuzzy hypercontext, which provides an extension of the range of applications of fuzzy concept analysis. The advantage of working with L-fuzzy hypercontexts lies in the fact that we can establish relation among elements such that their values are, in turn, other relations. Thus, they are easily adaptable to different situations that vary over time. The usefulness of the developed theory is illustrated by a practical case in which the valuation made by the different clients of a hotel company is analyzed. Full article
(This article belongs to the Special Issue Recent Advances in Fuzzy Sets and Related Topics)
20 pages, 667 KiB  
Article
EM Algorithm in the Slash 2S-Lindley Distribution with Applications
by Héctor A. Muñoz, Jaime S. Castillo, Diego I. Gallardo, Osvaldo Venegas and Héctor W. Gómez
Axioms 2025, 14(2), 101; https://doi.org/10.3390/axioms14020101 - 29 Jan 2025
Viewed by 282
Abstract
In this work, we present a new distribution, which is a slash extension of the distribution of the sum of two independent Lindley random variables. This new distribution is developed using the slash methodology, resulting in a distribution with more flexible kurtosis, i.e., [...] Read more.
In this work, we present a new distribution, which is a slash extension of the distribution of the sum of two independent Lindley random variables. This new distribution is developed using the slash methodology, resulting in a distribution with more flexible kurtosis, i.e., the ability to model atypical data. We study the density function of the new model and some of its properties, such as the cumulative distribution function, moments, and its asymmetry and kurtosis coefficients. The parameters are estimated by the maximum likelihood method with the EM algorithm. Finally, we apply the proposed model to two real datasets with high kurtosis, showing that it provides a better fit than two distributions known in the literature. Full article
(This article belongs to the Special Issue Probability, Statistics and Estimations, 2nd Edition)
27 pages, 1806 KiB  
Article
Efficient Tensor Robust Principal Analysis via Right-Invertible Matrix-Based Tensor Products
by Zhang Huang, Jun Feng and Wei Li
Axioms 2025, 14(2), 99; https://doi.org/10.3390/axioms14020099 - 28 Jan 2025
Viewed by 368
Abstract
In this paper, we extend the definition of tensor products from using an invertible matrix to utilising right-invertible matrices, exploring the algebraic properties of these new tensor products. Based on this novel definition, we define the concepts of tensor rank and tensor nuclear [...] Read more.
In this paper, we extend the definition of tensor products from using an invertible matrix to utilising right-invertible matrices, exploring the algebraic properties of these new tensor products. Based on this novel definition, we define the concepts of tensor rank and tensor nuclear norm, ensuring consistency with their matrix counterparts, and derive a singular value thresholding (*L,R SVT) formula to approximately solve the subproblems in the alternating direction method of multipliers (ADMM), which is integral to our proposed tensor robust principal component analysis (*LR TRPCA) algorithm. The computational complexity of the *LR TRPCA algorithm is O(k·(n1n2n3+p·min(n12n2,n1n22))) for k iterations. According to this complexity analysis, by using a right-invertible matrix that selects p rows from the n3 rows of the invertible matrix used in the tensor product with an invertible matrix, the computational load is approximately reduced to p/n3 of what it would be with an invertible matrix, highlighting the efficiency gain in terms of computational resources. We apply this efficient algorithm to grayscale video denoising and motion detection problems, where it demonstrates significant improvements in processing speed while maintaining comparable quality levels to existing methods, thereby providing a promising approach for handling multi-linear data and offering valuable insights for advanced data analysis tasks. Full article
(This article belongs to the Special Issue Advances in Linear Algebra with Applications, 2nd Edition)
21 pages, 304 KiB  
Article
Ergodicity and Mixing Properties for SDEs with α-StableLévy Noises
by Siyan Xu and Huiyan Zhao
Axioms 2025, 14(2), 98; https://doi.org/10.3390/axioms14020098 - 28 Jan 2025
Viewed by 252
Abstract
In this paper, we consider a class of stochastic differential equations driven by multiplicative α-stable (0<α<2) Lévy noises. Firstly, we show that there exists a unique strong solution under a local one-sided Lipschitz condition and a [...] Read more.
In this paper, we consider a class of stochastic differential equations driven by multiplicative α-stable (0<α<2) Lévy noises. Firstly, we show that there exists a unique strong solution under a local one-sided Lipschitz condition and a general non-explosion condition. Next, the weak Feller and stationary properties are derived. Furthermore, a concrete sufficient condition for the coefficients is presented, which is different from the conditions for SDEs driven by Brownian motion or general squared-integrable martingales. Finally, some ergodic and mixing properties are obtained by using the Foster–Lyapunov criteria. Full article
27 pages, 769 KiB  
Article
Some New Geometric State-Space Properties of the Classical Linear Time-Optimal Control Problem with One Input and Real Non-Positive Eigenvalues of the System Following from Pontryagin’s Maximum Principle
by Borislav G. Penev
Axioms 2025, 14(2), 97; https://doi.org/10.3390/axioms14020097 - 28 Jan 2025
Viewed by 350
Abstract
This purely theoretical study considers two new geometric state-space properties of the classical linear time-optimal control problem with one input and real non-positive eigenvalues of the system, with constraints only on the control input and without constraints on the state-space variables, following from [...] Read more.
This purely theoretical study considers two new geometric state-space properties of the classical linear time-optimal control problem with one input and real non-positive eigenvalues of the system, with constraints only on the control input and without constraints on the state-space variables, following from Pontryagin’s maximum principle. These properties complement the well-known facts from the maximum principle about the number of switchings of the control function and the character of the optimal phase trajectories of the system leading it to the state-space origin. They lay the foundation of a new method for synthesizing the time-optimal control without the need to describe the switching hyper-surfaces. The new technique is demonstrated on two examples. The so-called “axes initialization” and the synthesis technique are illustrated on the double integrator system in its entirety. The second one is on a hypothetical seventh-order system. Full article
(This article belongs to the Special Issue Advances in Mathematical Methods in Optimal Control and Applications)
30 pages, 397 KiB  
Article
Asymptotic Stability of the Magnetohydrodynamic Flows with Temperature-Dependent Transport Coefficients
by Mingyu Zhang
Axioms 2025, 14(2), 100; https://doi.org/10.3390/axioms14020100 - 28 Jan 2025
Viewed by 372
Abstract
The objective of this paper is to analyze the asymptotic stability of global strong solutions to the boundary value problem of the compressible magnetohydrodynamic (MHD) equations for the ideal polytropic gas in which the viscosity λ and heat conductivity κ depend on temperature, [...] Read more.
The objective of this paper is to analyze the asymptotic stability of global strong solutions to the boundary value problem of the compressible magnetohydrodynamic (MHD) equations for the ideal polytropic gas in which the viscosity λ and heat conductivity κ depend on temperature, i.e., λ=θα and κ=θβ with α,β[0,+). Both the global-in-time existence and uniqueness of strong solutions are obtained under certain assumptions on the parameter α and initial data. Moreover, based on accurate uniform-in-time estimates, we show that the global large solutions decay exponentially in time to the equilibrium states. Compared with the existing results, the initial data could be large if α is small and the growth exponent β can be arbitrarily large. Full article
16 pages, 321 KiB  
Article
Exploring Star Filters of Almost Distributive Lattices
by Ali Al Khabyah, Noorbhasha Rafi and Moin A. Ansari
Axioms 2025, 14(2), 96; https://doi.org/10.3390/axioms14020096 - 27 Jan 2025
Viewed by 286
Abstract
In an almost distributive lattice (ADL), we have presented and explored the notions of star filters and starlets. Further, we have characterized star filters through their starlets. A set of equivalent conditions is established for a filter in an ADL to become a [...] Read more.
In an almost distributive lattice (ADL), we have presented and explored the notions of star filters and starlets. Further, we have characterized star filters through their starlets. A set of equivalent conditions is established for a filter in an ADL to become a star filter. Additionally, this paper investigates the topological properties of the prime spectrum associated with star filters in an ADL. Full article
(This article belongs to the Section Algebra and Number Theory)
15 pages, 256 KiB  
Article
Extrinsic Geometry of a Riemannian Manifold and Ricci Solitons
by Ibrahim Al-Dayel and Sharief Deshmukh
Axioms 2025, 14(2), 95; https://doi.org/10.3390/axioms14020095 - 27 Jan 2025
Viewed by 277
Abstract
The object of this paper is to find a vector field ξ and a constant λ on an n-dimensional compact Riemannian manifold Mn,g such that we obtain the Ricci soliton Mn,g,ξ,λ. [...] Read more.
The object of this paper is to find a vector field ξ and a constant λ on an n-dimensional compact Riemannian manifold Mn,g such that we obtain the Ricci soliton Mn,g,ξ,λ. In order to achieve this objective, we choose an isometric embedding provided in the work of Kuiper and Nash in the Euclidean space Rm,g¯ and choose ξ as the tangential component of a constant unit vector on Rm and call it a Kuiper–Nash vector. If τ is the scalar curvature of the compact Riemannian manifold Mn,g with a Kuiper–Nash vector ξ, we show that if the integral of the function ξτ has a suitable lower bound containing a constant λ, then Mn,g,ξ,λ is a Ricci soliton; we call this a Kuiper–Nash Ricci soliton. We find a necessary and sufficient condition involving the scalar curvature τ under which a compact Kuiper–Nash Ricci soliton Mn,g,ξ,λ is a trivial soliton. Finally, we find a characterization of an n-dimensional compact trivial Kuiper–Nash Ricci soliton Mn,g,ξ,λ using an upper bound on the integral of divξ2 containing the scalar curvature τ. Full article
(This article belongs to the Special Issue Differential Geometry and Its Application, 3rd Edition)
37 pages, 2252 KiB  
Article
Rogue Waves in the Nonlinear Schrödinger, Kadomtsev–Petviashvili, Lakshmanan–Porsezian–Daniel and Hirota Equations
by Pierre Gaillard
Axioms 2025, 14(2), 94; https://doi.org/10.3390/axioms14020094 - 27 Jan 2025
Viewed by 443
Abstract
We give some of our results over the past few years about rogue waves concerning some partial differential equations, such as the focusing nonlinear Schrödinger equation (NLS), the Kadomtsev–Petviashvili equation (KPI), the Lakshmanan–Porsezian–Daniel equation (LPD) and the Hirota equation (H). For the NLS [...] Read more.
We give some of our results over the past few years about rogue waves concerning some partial differential equations, such as the focusing nonlinear Schrödinger equation (NLS), the Kadomtsev–Petviashvili equation (KPI), the Lakshmanan–Porsezian–Daniel equation (LPD) and the Hirota equation (H). For the NLS and KP equations, we give different types of representations of the solutions, in terms of Fredholm determinants, Wronskians and degenerate determinants of order 2N. These solutions are called solutions of order N. In the case of the NLS equation, the solutions, explicitly constructed, appear as deformations of the Peregrine breathers PN as the last one can be obtained when all parameters are equal to zero. At order N, these solutions are the product of a ratio of two polynomials of degree N(N+1) in x and t by an exponential depending on time t and depending on 2N2 real parameters: they are called quasi-rational solutions. For the KPI equation, we explicitly obtain solutions at order N depending on 2N2 real parameters. We present different examples of rogue waves for the LPD and Hirota equations. Full article
(This article belongs to the Special Issue Differential Equations and Its Application)
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18 pages, 268 KiB  
Article
Strong k-Skew Commutativity Preserving Maps on Standard Operator Algebras
by Ting Zhang and Xiaofei Qi
Axioms 2025, 14(2), 93; https://doi.org/10.3390/axioms14020093 - 26 Jan 2025
Viewed by 231
Abstract
Let A be a self-adjoint standard operator algebra on a real or complex Hilbert space of dimension 2, and let k{1,2,3}. The k-skew commutator for A,BA is [...] Read more.
Let A be a self-adjoint standard operator algebra on a real or complex Hilbert space of dimension 2, and let k{1,2,3}. The k-skew commutator for A,BA is defined by *[A,B]1=ABBA* and *[A,B]k=*[A,*[A,B]k1]1. Assume that Φ:AA is a map whose range contains all rank-one projections. In this paper, we prove that Φ is strong k-skew-commutativity preserving, that is, *[Φ(A),Φ(B)]k=*[A,B]k for all A,BA if and only if one of the following statements holds: (i) Φ is either the identity map or the negative identity map whenever k{1,3}; (ii) Φ is the identity map whenever k=2. Full article
(This article belongs to the Special Issue Recent Advances in Functional Analysis and Operator Theory)
20 pages, 307 KiB  
Article
Existence and Asymptotic Estimates of the Maximal and Minimal Solutions for a Coupled Tempered Fractional Differential System with Different Orders
by Peng Chen, Xinguang Zhang, Lishuang Li, Yongsheng Jiang and Yonghong Wu
Axioms 2025, 14(2), 92; https://doi.org/10.3390/axioms14020092 - 26 Jan 2025
Viewed by 337
Abstract
In this paper, we focus on the existence and asymptotic estimates of the maximal and minimal solutions for a coupled tempered fractional differential system with different orders. By introducing an order reduction technique and some new growth conditions, we establish some new results [...] Read more.
In this paper, we focus on the existence and asymptotic estimates of the maximal and minimal solutions for a coupled tempered fractional differential system with different orders. By introducing an order reduction technique and some new growth conditions, we establish some new results on the existence of positive extremal solutions for the tempered fractional differential system, meanwhile, we also obtain the asymptotic estimate of the positive extreme solution by an iterative technique, which possesses a sharp asymptotic estimate. In particular, the iterative sequences converging to maximal and minimal solutions starting from two known initial values are easy to compute. Moreover, the weight function i is allowed to have an infinite number of singular points in [0,1]. Full article
(This article belongs to the Special Issue Fractional Calculus—Theory and Applications, 3rd Edition)
13 pages, 242 KiB  
Article
Noncanonical Third-Order Advanced Differential Equations of Unstable Type: Oscillation and Property B via Canonical Transform
by Bose Rani, George E. Chatzarakis and Ethiraju Thandapani
Axioms 2025, 14(2), 91; https://doi.org/10.3390/axioms14020091 - 26 Jan 2025
Viewed by 231
Abstract
In this paper, without assuming any extra conditions, the third-order unstable noncaonical advanced differential equation is changed into a canonical form that reduces the number of classes of nonoscillatory solutions into two instead of four. Using comparison and integral averaging method, new sufficient [...] Read more.
In this paper, without assuming any extra conditions, the third-order unstable noncaonical advanced differential equation is changed into a canonical form that reduces the number of classes of nonoscillatory solutions into two instead of four. Using comparison and integral averaging method, new sufficient conditions are obtained so that all solutions to have Property B or oscillate. Specific numerical examples are provided to demonstrate the importance and the significance of the main results. Full article
(This article belongs to the Section Mathematical Analysis)
36 pages, 500 KiB  
Review
Abelian Function Fields on Jacobian Varieties
by Julia Bernatska
Axioms 2025, 14(2), 90; https://doi.org/10.3390/axioms14020090 - 26 Jan 2025
Viewed by 220
Abstract
The aim of this paper is an exposition of fields of multiply periodic, or Kleinian, -functions. Such a field arises on the Jacobian variety of an algebraic curve, providing natural algebraic models for the Jacobian and Kummer varieties, possessing the addition law, [...] Read more.
The aim of this paper is an exposition of fields of multiply periodic, or Kleinian, -functions. Such a field arises on the Jacobian variety of an algebraic curve, providing natural algebraic models for the Jacobian and Kummer varieties, possessing the addition law, and accommodating dynamical equations with solutions. All of this will be explained in detail for plane algebraic curves in their canonical forms. Examples of hyperelliptic and non-hyperelliptic curves are presented. Full article
(This article belongs to the Special Issue Recent Advances in Function Spaces and Their Applications)
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