Axioms

15 pages, 3403 KiB

Open AccessArticle

Edge DP-Coloring in K₄-Minor Free Graphs and Planar Graphs

by Jingxiang He and Ming Han

Axioms 2024, 13(6), 375; https://doi.org/10.3390/axioms13060375 (registering DOI) - 3 Jun 2024

The edge DP-chromatic number of G, denoted by

χ_{D P}^{'} (G)

, is the minimum k such that G is edge DP-k-colorable. In 1999, Juvan, Mohar, and Thomas proved that the edge list chromatic number of [...] Read more.

The edge DP-chromatic number of G, denoted by

χ_{D P}^{'} (G)

, is the minimum k such that G is edge DP-k-colorable. In 1999, Juvan, Mohar, and Thomas proved that the edge list chromatic number of

K_{4}

-minor free graph G with

Δ \geq 3

is

Δ

. In this paper, we prove that if G is a

K_{4}

-minor free graph, then

χ_{D P}^{'} (G) \in {Δ, Δ + 1}

, and equality

χ_{D P}^{'} (G) = Δ + 1

holds for some

K_{4}

-minor free graph G with

Δ = 3

. Moreover, if G is a planar graph with

Δ \geq 9

and with no intersecting triangles, then

χ_{D P}^{'} (G) = Δ

. Full article

(This article belongs to the Special Issue Advances in Mathematics: Theory and Applications)

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19 pages, 1277 KiB

Open AccessArticle

An Accelerated Dual-Integral Structure Zeroing Neural Network Resistant to Linear Noise for Dynamic Complex Matrix Inversion

by FeiXiang Yang, TingLei Wang and Yun Huang

Axioms 2024, 13(6), 374; https://doi.org/10.3390/axioms13060374 - 2 Jun 2024

Abstract

The problem of inverting dynamic complex matrices remains a central and intricate challenge that has garnered significant attention in scientific and mathematical research. The zeroing neural network (ZNN) has been a notable approach, utilizing time derivatives for real-time solutions in noiseless settings. However, [...] Read more.

The problem of inverting dynamic complex matrices remains a central and intricate challenge that has garnered significant attention in scientific and mathematical research. The zeroing neural network (ZNN) has been a notable approach, utilizing time derivatives for real-time solutions in noiseless settings. However, real-world disturbances pose a significant challenge to a ZNN’s convergence. We design an accelerated dual-integral structure zeroing neural network (ADISZNN), which can enhance convergence and restrict linear noise, particularly in complex domains. Based on the Lyapunov principle, theoretical analysis proves the convergence and robustness of ADISZNN. We have selectively integrated the SBPAF activation function, and through theoretical dissection and comparative experimental validation we have affirmed the efficacy and accuracy of our activation function selection strategy. After conducting numerous experiments, we discovered oscillations and improved the model accordingly, resulting in the ADISZNN-Stable model. This advanced model surpasses current models in both linear noisy and noise-free environments, delivering a more rapid and stable convergence, marking a significant leap forward in the field. Full article

(This article belongs to the Special Issue Differential Equations and Inverse Problems)

44 pages, 448 KiB

Open AccessArticle

On Properties and Classification of a Class of 4-Dimensional 3-Hom-Lie Algebras with a Nilpotent Twisting Map

by Abdennour Kitouni and Sergei Silvestrov

Axioms 2024, 13(6), 373; https://doi.org/10.3390/axioms13060373 - 2 Jun 2024

Abstract

The aim of this work is to investigate the properties and classification of an interesting class of 4-dimensional 3-Hom-Lie algebras with a nilpotent twisting map

α

and eight structure constants as parameters. Derived series and central descending series are studied for all algebras [...] Read more.

The aim of this work is to investigate the properties and classification of an interesting class of 4-dimensional 3-Hom-Lie algebras with a nilpotent twisting map

α

and eight structure constants as parameters. Derived series and central descending series are studied for all algebras in this class and are used to divide it into five non-isomorphic subclasses. The levels of solvability and nilpotency of the 3-Hom-Lie algebras in these five classes are obtained. Building upon that, all algebras of this class are classified up to Hom-algebra isomorphism. Necessary and sufficient conditions for multiplicativity of general

(n + 1)

-dimensional n-Hom-Lie algebras, as well as for algebras in the considered class, are obtained in terms of the structure constants and the twisting map. Furthermore, for some algebras in this class, it is determined whether the terms of the derived and central descending series are weak subalgebras, Hom-subalgebras, weak ideals, or Hom-ideals. Full article

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

23 pages, 7313 KiB

Open AccessArticle

Mathematical Model of the Evolution of a Simple Dynamic System with Dry Friction

by Stelian Alaci, Florina-Carmen Ciornei, Costica Lupascu and Ionut-Cristian Romanu

Axioms 2024, 13(6), 372; https://doi.org/10.3390/axioms13060372 - 31 May 2024

Abstract

A simple dynamic system with dry friction is studied theoretically and numerically. Models of systems including dry friction are not easily obtained, as defining the relationship between the friction force and the relative velocity presents a significant challenge. It is known that friction [...] Read more.

A simple dynamic system with dry friction is studied theoretically and numerically. Models of systems including dry friction are not easily obtained, as defining the relationship between the friction force and the relative velocity presents a significant challenge. It is known that friction forces exhibit notable discontinuities when there is a change in the direction of motion. Additionally, when the relative motion ceases, the friction force can assume any value within a certain range. In the literature, numerous models of dry friction are presented, and most of them assume a biunivocal dependency of the friction force with respect to relative velocity. The dynamic system considered here is a tilted rod with spherical ends, initially at rest. Dry friction forces are evident at the contact point with the horizontal plane. The ball–plane contact highlights the rolling friction or/and sliding friction. The problem is theoretically solved after adopting one of the two cases of friction: rolling friction or sliding friction. The nonlinear differential equations of motion have been derived, along with expressions for the magnitude of the normal reaction and the friction force. The results of the model are displayed graphically for three different sets of values for the coefficient of friction. It is revealed that there is a critical value of the coefficient of friction that determines the transition from rolling to sliding regimes. To validate the theoretical model, dynamic simulation software was utilised. The excellent match between the theoretical predictions and the results from the numerical simulation confirms the accuracy of the proposed analytical solution. Full article

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

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22 pages, 352 KiB

Open AccessArticle

On Approximate Variational Inequalities and Bilevel Programming Problems

by Balendu Bhooshan Upadhyay, Ioan Stancu-Minasian, Subham Poddar and Priyanka Mishra

Axioms 2024, 13(6), 371; https://doi.org/10.3390/axioms13060371 - 30 May 2024

Abstract

In this paper, we investigate a class of bilevel programming problems (BLPP) in the framework of Euclidean space. We derive relationships among the solutions of approximate Minty-type variational inequalities (AMTVI), approximate Stampacchia-type variational inequalities (ASTVI), and local

ϵ

-quasi solutions of the BLPP, [...] Read more.

In this paper, we investigate a class of bilevel programming problems (BLPP) in the framework of Euclidean space. We derive relationships among the solutions of approximate Minty-type variational inequalities (AMTVI), approximate Stampacchia-type variational inequalities (ASTVI), and local

ϵ

-quasi solutions of the BLPP, under generalized approximate convexity assumptions, via limiting subdifferentials. Moreover, by employing the generalized Knaster–Kuratowski–Mazurkiewicz (KKM)-Fan’s lemma, we derive some existence results for the solutions of AMTVI and ASTVI. We have furnished suitable, non-trivial, illustrative examples to demonstrate the importance of the established results. To the best of our knowledge, there is no research paper available in the literature that explores relationships between the approximate variational inequalities and BLPP under the assumptions of generalized approximate convexity by employing the powerful tool of limiting subdifferentials. Full article

(This article belongs to the Special Issue Research on Fixed Point Theory and Application)

11 pages, 281 KiB

Open AccessArticle

Solitonical Inequality on Submanifolds in Trans-Sasakian Manifolds Coupled with a Slant Factor

by Mohd Danish Siddiqi and Rawan Bossly

Axioms 2024, 13(6), 370; https://doi.org/10.3390/axioms13060370 - 30 May 2024

Abstract

In this article, we study the Ricci soliton on slant submanifolds of trans-Sasakian manifolds with a quarter symmetric non-metric connection. Moreover, we derive a lower-bound-type inequality for the slant submanifolds of trans-Sasakian manifolds with a quarter symmetric non-metric connection in terms of gradient [...] Read more.

In this article, we study the Ricci soliton on slant submanifolds of trans-Sasakian manifolds with a quarter symmetric non-metric connection. Moreover, we derive a lower-bound-type inequality for the slant submanifolds of trans-Sasakian manifolds with a quarter symmetric non-metric connection in terms of gradient Ricci solitons. We also characterize anti-invariant, invariant, quasi-umbilical submanifolds of trans-Sasakian manifolds with a quarter symmetric non-metric connection for which the same inequality case holds. Finally, we deduce the above inequalities in terms of a scalar concircular field on submanifolds of trans-Sasakian manifolds with a quarter symmetric non-metric connection. Full article

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

23 pages, 361 KiB

Open AccessArticle

A Discrete Cramér–Von Mises Statistic Related to Hahn Polynomials with Application to Goodness-of-Fit Testing for Hypergeometric Distributions

by Jean-Renaud Pycke

Axioms 2024, 13(6), 369; https://doi.org/10.3390/axioms13060369 - 30 May 2024

Viewed by 43

Abstract

We give the Karhunen–Loève expansion of the covariance function of a family of discrete weighted Brownian bridges, appearing as discrete analogues of continuous Gaussian processes related to Cramér –von Mises and Anderson–Darling statistics. This analogy enables us to introduce a discrete Cramér–von Mises [...] Read more.

We give the Karhunen–Loève expansion of the covariance function of a family of discrete weighted Brownian bridges, appearing as discrete analogues of continuous Gaussian processes related to Cramér –von Mises and Anderson–Darling statistics. This analogy enables us to introduce a discrete Cramér–von Mises statistic and show that this statistic satisfies a property of local asymptotic Bahadur optimality for a statistical test involving the classical hypergeometric distributions. Our statistic and the goodness-of-fit problem we deal with are based on basic properties of Hahn polynomials and are, therefore, subject to some extension to all families of classical orthogonal polynomials, as well as their q-analogues. Due probably to computational difficulties, the family of discrete Cramér–von Mises statistics has received less attention than its continuous counterpart—the aim of this article is to bridge part of this gap. Full article

(This article belongs to the Special Issue New Trends in Discrete Probability and Statistics)

16 pages, 1367 KiB

Open AccessArticle

A New Hybrid Approach for Clustering, Classification, and Prediction of World Development Indicators Combining General Type-2 Fuzzy Systems and Neural Networks

by Martha Ramírez, Patricia Melin and Oscar Castillo

Axioms 2024, 13(6), 368; https://doi.org/10.3390/axioms13060368 - 30 May 2024

Viewed by 167

Abstract

Economic risk is a probability that measures the possible alterations, as well as the uncertainty, generated by multiple internal or external factors. Sometimes it could cause the impossibility of guaranteeing the level of compliance with organizational goals and objectives, which is why for [...] Read more.

Economic risk is a probability that measures the possible alterations, as well as the uncertainty, generated by multiple internal or external factors. Sometimes it could cause the impossibility of guaranteeing the level of compliance with organizational goals and objectives, which is why for their administration they are frequently divided into multiple categories according to their consequences and impact. Global indicators are dynamic and sometimes the correlation is uncertain because they depend largely on a combination of economic, social, and environmental factors. Thus, our proposal consists of a model for prediction and classification of multivariate risk factors such as birth rate and population growth, among others, using multiple neural networks and General Type-2 fuzzy systems. The contribution is the proposal to integrate multiple variables of several time series using both supervised and unsupervised neural networks, and a generalized Type-2 fuzzy integration. Results show the advantages of utilizing the method for the fuzzy integration of multiple time series attributes, with which the user can then prevent future threats from the global environment that impact the scheduled compliance process. Full article

(This article belongs to the Special Issue Editorial Board Members’ Collection Series: Fuzzy Modeling, Optimization and Computational Intelligence)

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47 pages, 781 KiB

Open AccessArticle

Bivariate Random Coefficient Integer-Valued Autoregressive Model Based on a ρ-Thinning Operator

by Chang Liu and Dehui Wang

Axioms 2024, 13(6), 367; https://doi.org/10.3390/axioms13060367 - 29 May 2024

Viewed by 133

Abstract

While overdispersion is a common phenomenon in univariate count time series data, its exploration within bivariate contexts remains limited. To fill this gap, we propose a bivariate integer-valued autoregressive model. The model leverages a modified binomial thinning operator with a dispersion parameter

ρ

[...] Read more.

While overdispersion is a common phenomenon in univariate count time series data, its exploration within bivariate contexts remains limited. To fill this gap, we propose a bivariate integer-valued autoregressive model. The model leverages a modified binomial thinning operator with a dispersion parameter

ρ

and integrates random coefficients. This approach combines characteristics from both binomial and negative binomial thinning operators, thereby offering a flexible framework capable of generating counting series exhibiting equidispersion, overdispersion, or underdispersion. Notably, our model includes two distinct classes of first-order bivariate geometric integer-valued autoregressive models: one class employs binomial thinning (BVGINAR(1)), and the other adopts negative binomial thinning (BVNGINAR(1)). We establish the stationarity and ergodicity of the model and estimate its parameters using a combination of the Yule–Walker (YW) and conditional maximum likelihood (CML) methods. Furthermore, Monte Carlo simulation experiments are conducted to evaluate the finite sample performances of the proposed estimators across various parameter configurations, and the Anderson-Darling (AD) test is employed to assess the asymptotic normality of the estimators under large sample sizes. Ultimately, we highlight the practical applicability of the examined model by analyzing two real-world datasets on crime counts in New South Wales (NSW) and comparing its performance with other popular overdispersed BINAR(1) models. Full article

(This article belongs to the Section Mathematical Analysis)

19 pages, 289 KiB

Open AccessArticle

Certain New Applications of Symmetric q-Calculus for New Subclasses of Multivalent Functions Associated with the Cardioid Domain

by Hari M. Srivastava, Daniel Breaz, Shahid Khan and Fairouz Tchier

Axioms 2024, 13(6), 366; https://doi.org/10.3390/axioms13060366 - 29 May 2024

Viewed by 152

Abstract

In this work, we study some new applications of symmetric quantum calculus in the field of Geometric Function Theory. We use the cardioid domain and the symmetric quantum difference operator to generate new classes of multivalent q-starlike and q-convex functions. We [...] Read more.

In this work, we study some new applications of symmetric quantum calculus in the field of Geometric Function Theory. We use the cardioid domain and the symmetric quantum difference operator to generate new classes of multivalent q-starlike and q-convex functions. We examine a wide range of interesting properties for functions that can be classified into these newly defined classes, such as estimates for the bounds for the first two coefficients, Fekete–Szego-type functional and coefficient inequalities. All the results found in this research are sharp. A number of well-known corollaries are additionally taken into consideration to show how the findings of this research relate to those of earlier studies. Full article

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

25 pages, 5968 KiB

Open AccessArticle

Analyzing Richtmyer–Meshkov Phenomena Triggered by Forward-Triangular Light Gas Bubbles: A Numerical Perspective

by Satyvir Singh and Ahmed Hussein Msmali

Axioms 2024, 13(6), 365; https://doi.org/10.3390/axioms13060365 - 29 May 2024

Viewed by 140

Abstract

In this paper, we present a numerical investigation into elucidating the complex dynamics of Richtmyer–Meshkov (RM) phenomena initiated by the interaction of shock waves with forward-triangular light gas bubbles. The triangular bubble is filled with neon, helium, or hydrogen gas, and is surrounded [...] Read more.

In this paper, we present a numerical investigation into elucidating the complex dynamics of Richtmyer–Meshkov (RM) phenomena initiated by the interaction of shock waves with forward-triangular light gas bubbles. The triangular bubble is filled with neon, helium, or hydrogen gas, and is surrounded by nitrogen gas. Three different shock Mach numbers are considered:

M_{s} = 1.12, 1.21,

and 1.41. For the numerical simulations, a two-dimensional system of compressible Euler equations for two-component gas flows is solved by utilizing the high-fidelity explicit modal discontinuous Galerkin technique. For validation, the numerical results are compared with the existing experimental results and are found to be in good agreement. The numerical model explores the impact of the Atwood number on the underlying mechanisms of the shock-induced forward-triangle bubble, encompassing aspects such as flow evolution, wave characteristics, jet formation, generation of vorticity, interface features, and integral diagnostics. Furthermore, the impacts of shock strengths and positive Atwood numbers on the flow evolution are also analyzed. Insights gained from this numerical perspective enhance our understanding of RM phenomena triggered by forward-triangular light gas bubbles, with implications for diverse applications in engineering, astrophysics, and fusion research. Full article

(This article belongs to the Special Issue Fluid Dynamics: Mathematics and Numerical Experiment)

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15 pages, 332 KiB

Open AccessArticle

Finding Set Extreme 3-Uniform Hypergraphs Cardinality through Second-Order Signatures

by Evgeniya Egorova, Vladislav Leonov, Aleksey Mokryakov and Vladimir Tsurkov

Axioms 2024, 13(6), 364; https://doi.org/10.3390/axioms13060364 - 29 May 2024

Viewed by 123

Abstract

This paper continues the study of second-order signature properties—the characterization of the extreme 3-uniform hypergraph. Previously, bases were used to count extreme 3-uniform hypergraphs. However, the algorithm using this mechanism is extremely labor-intensive. The structure of the signature allows us to use it [...] Read more.

This paper continues the study of second-order signature properties—the characterization of the extreme 3-uniform hypergraph. Previously, bases were used to count extreme 3-uniform hypergraphs. However, the algorithm using this mechanism is extremely labor-intensive. The structure of the signature allows us to use it as a more efficient basis for the same problem. Here, we establish the nature of the mutual correspondence between the kind of second-order signature and extreme hypergraphs, and we present a new algorithm to find the power of the set of extreme 3-uniform hypergraphs through the set of their characteristic-signatures. New results obtained with the proposed tool are also presented. Full article

(This article belongs to the Special Issue Advances in Graph Theory and Combinatorial Optimization)

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14 pages, 270 KiB

Open AccessArticle

Perturbed Dirac Operators and Boundary Value Problems

by Xiaopeng Liu and Yuanyuan Liu

Axioms 2024, 13(6), 363; https://doi.org/10.3390/axioms13060363 - 29 May 2024

Viewed by 218

Abstract

In this paper, the time-independent Klein-Gordon equation in

R^{3}

is treated with a decomposition of the operator

Δ - γ^{2} I

by the Clifford algebra

C l (V_{3, 3})

. Some properties of integral operators associated the [...] Read more.

In this paper, the time-independent Klein-Gordon equation in

R^{3}

is treated with a decomposition of the operator

Δ - γ^{2} I

by the Clifford algebra

C l (V_{3, 3})

. Some properties of integral operators associated the kind of equations and some Riemann-Hilbert boundary value problems for perturbed Dirac operators are investigated. Full article

(This article belongs to the Special Issue Differential Equations and Its Application)

24 pages, 393 KiB

Open AccessArticle

Steady Solutions to Equations of Viscous Compressible Multifluids

by Alexander Mamontov and Dmitriy Prokudin

Axioms 2024, 13(6), 362; https://doi.org/10.3390/axioms13060362 - 28 May 2024

Viewed by 180

Abstract

For the differential equations of the barotropic dynamics of compressible viscous multifluids in a bounded three-dimensional domain with an immobile rigid boundary, a study of the solvability of the boundary value problem is made. Weak generalized solutions to the boundary value problem are [...] Read more.

For the differential equations of the barotropic dynamics of compressible viscous multifluids in a bounded three-dimensional domain with an immobile rigid boundary, a study of the solvability of the boundary value problem is made. Weak generalized solutions to the boundary value problem are shown to exist with weak constraints on the types of viscosity matrices and constitutive equations for pressure and momentum exchange. Full article

(This article belongs to the Special Issue Fluid Dynamics: Mathematics and Numerical Experiment)

44 pages, 10325 KiB

Open AccessArticle

Multi-Strategy-Improved Growth Optimizer and Its Applications

by Rongxiang Xie, Liya Yu, Shaobo Li, Fengbin Wu, Tao Zhang and Panliang Yuan

Axioms 2024, 13(6), 361; https://doi.org/10.3390/axioms13060361 - 28 May 2024

Viewed by 150

Abstract

The growth optimizer (GO) is a novel metaheuristic algorithm designed to tackle complex optimization problems. Despite its advantages of simplicity and high efficiency, GO often encounters localized stagnation when dealing with discretized, high-dimensional, and multi-constraint problems. To address these issues, this paper proposes [...] Read more.

The growth optimizer (GO) is a novel metaheuristic algorithm designed to tackle complex optimization problems. Despite its advantages of simplicity and high efficiency, GO often encounters localized stagnation when dealing with discretized, high-dimensional, and multi-constraint problems. To address these issues, this paper proposes an enhanced version of GO called CODGBGO. This algorithm incorporates three strategies to enhance its performance. Firstly, the Circle-OBL initialization strategy is employed to enhance the quality of the initial population. Secondly, an exploration strategy is implemented to improve population diversity and the algorithm’s ability to escape local optimum traps. Finally, the exploitation strategy is utilized to enhance the convergence speed and accuracy of the algorithm. To validate the performance of CODGBGO, it is applied to solve the CEC2017, CEC2020, 18 feature selection problems, and 4 real engineering optimization problems. The experiments demonstrate that the novel CODGBGO algorithm effectively addresses the challenges posed by complex optimization problems, offering a promising approach. Full article

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

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13 pages, 296 KiB

Open AccessArticle

Skew Cyclic and Skew Constacyclic Codes over a Mixed Alphabet

by Karthick Gowdhaman, Cruz Mohan, Chinnapillai Durairajan, Selda Çalkavur and Patrick Solé

Axioms 2024, 13(6), 360; https://doi.org/10.3390/axioms13060360 - 28 May 2024

Viewed by 258

Abstract

In this note, we study skew cyclic and skew constacyclic codes over the mixed alphabet

R = F_{q} R_{1} R_{2}

, where

q = p^{m},

p is an odd prime with m odd and [...] Read more.

In this note, we study skew cyclic and skew constacyclic codes over the mixed alphabet

R = F_{q} R_{1} R_{2}

, where

q = p^{m},

p is an odd prime with m odd and

R_{1} = F_{q} + u F_{q}

with

u^{2} = u

, and

R_{2} = F_{q} + u F_{q} + v F_{q}

with

u^{2} = u, v^{2} = v, u v = v u = 0 .

Such codes consist of the juxtaposition of three codes of the same size over

F_{q},

R_{1},

and

R_{2}

, respectively. We investigate the generator polynomial for skew cyclic codes over

R

. Furthermore, we discuss the structural properties of the skew cyclic and skew constacyclic codes over

R .

We also study their q-ary images under suitable Gray maps. Full article

12 pages, 280 KiB

Open AccessArticle

Generalized Bounded Turning Functions Connected with Gregory Coefficients

by Huo Tang, Zeeshan Mujahid, Nazar Khan, Fairouz Tchier and Muhammad Ghaffar Khan

Axioms 2024, 13(6), 359; https://doi.org/10.3390/axioms13060359 - 28 May 2024

Viewed by 177

Abstract

In this research article, we introduce new family

R_{G}

of holomorphic functions, which is related to the generalized bounded turning and generating functions of Gregory coefficients. Leveraging the concept of functions with positive real parts, we acquire the first five coefficients for [...] Read more.

In this research article, we introduce new family

R_{G}

of holomorphic functions, which is related to the generalized bounded turning and generating functions of Gregory coefficients. Leveraging the concept of functions with positive real parts, we acquire the first five coefficients for the functions belonging to this newly defined family, demonstrating their sharpness. Furthermore, we find the third Hankel determinant for functions in the class

R_{G}

. Moreover, the sharp bounds for logarithmic and inverse coefficients of functions belonging to the under-considered class

R_{G}

are estimated. Full article

(This article belongs to the Special Issue New Developments in Geometric Function Theory III)

13 pages, 287 KiB

Open AccessArticle

On the Kantorovich Theory for Nonsingular and Singular Equations

by Ioannis K. Argyros, Santhosh George, Samundra Regmi and Michael I. Argyros

Axioms 2024, 13(6), 358; https://doi.org/10.3390/axioms13060358 - 28 May 2024

Viewed by 168

Abstract

We develop a new Kantorovich-like convergence analysis of Newton-type methods to solve nonsingular and singular nonlinear equations in Banach spaces. The outer or generalized inverses are exchanged by a finite sum of linear operators making the implementation of these methods easier than in [...] Read more.

We develop a new Kantorovich-like convergence analysis of Newton-type methods to solve nonsingular and singular nonlinear equations in Banach spaces. The outer or generalized inverses are exchanged by a finite sum of linear operators making the implementation of these methods easier than in earlier studies. The analysis uses relaxed generalized continuity of the derivatives of operators involved required to control the derivative and on real majorizing sequences. The same approach can also be implemented on other iterative methods with inverses. The examples complement the theory by verifying the convergence conditions and demonstrating the performance of the methods. Full article

(This article belongs to the Special Issue Differential Equations and Inverse Problems)

17 pages, 327 KiB

Open AccessArticle

An Intuitionistic Fuzzy Multi-Criteria Approach for Prioritizing Failures That Cause Overproduction: A Case Study in Process Manufacturing

by Ranka Sudžum, Snežana Nestić, Nikola Komatina and Milija Kraišnik

Axioms 2024, 13(6), 357; https://doi.org/10.3390/axioms13060357 - 27 May 2024

Viewed by 198

Abstract

Overproduction is one of the most significant wastes of Lean that can occur in any manufacturing company. Identifying and prioritizing failures that lead to overproduction are crucial tasks for operational managers and engineers. Therefore, this paper presents a new approach for determining the [...] Read more.

Overproduction is one of the most significant wastes of Lean that can occur in any manufacturing company. Identifying and prioritizing failures that lead to overproduction are crucial tasks for operational managers and engineers. Therefore, this paper presents a new approach for determining the priority of failures that cause overproduction, based on an intuitionistic fuzzy Multi-Criteria Optimization model and the Failure Mode and Effects Analysis framework. The existing vagueness in the relative importance of risk factors and their values is described using natural language words, which are modeled with trapezoidal intuitionistic fuzzy numbers. Determining the relative importance of risk factors is defined as a fuzzy group decision-making problem, and the weight vector is obtained by applying the proposed Analytical Hierarchy Process with trapezoidal intuitionistic fuzzy numbers. The compromise solution, as well as the stability check of the obtained compromise solution, is achieved using the proposed Multi-Criteria Optimization and Compromise Solution with trapezoidal intuitionistic fuzzy numbers. The proposed model was applied to data collected from a process manufacturing company. Full article

(This article belongs to the Special Issue Editorial Board Members’ Collection Series: Fuzzy Modeling, Optimization and Computational Intelligence)

18 pages, 309 KiB

Open AccessArticle

New Nonlinear Retarded Integral Inequalities and Their Applications to Nonlinear Retarded Integro-Differential Equations

by Mahvish Samar, Xinzhong Zhu, Abdul Shakoor and Mawia Osman

Axioms 2024, 13(6), 356; https://doi.org/10.3390/axioms13060356 - 27 May 2024

Viewed by 210

Abstract

The purpose of this article is to present some new nonlinear retarded integral inequalities which can be utilized to study the existence, stability, boundedness, uniqueness, and asymptotic behavior of solutions of nonlinear retarded integro-differential equations, and these inequalities can be used in the [...] Read more.

The purpose of this article is to present some new nonlinear retarded integral inequalities which can be utilized to study the existence, stability, boundedness, uniqueness, and asymptotic behavior of solutions of nonlinear retarded integro-differential equations, and these inequalities can be used in the symmetrical properties of functions. These inequalities also generalize some former famous inequalities in the literature. Two examples as applications will be provided to demonstrate the strength of our inequalities in estimating the boundedness and global existence of the solution to initial value problems for nonlinear integro-differential equations and differential equations which can be seen in graphs. This research work will ensure opening new opportunities for studying nonlinear dynamic inequalities on a time-scale structure of a varying nature. Full article

(This article belongs to the Special Issue Advances in Difference Equations)

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21 pages, 399 KiB

Open AccessArticle

Randomly Stopped Sums, Minima and Maxima for Heavy-Tailed and Light-Tailed Distributions

by Remigijus Leipus, Jonas Šiaulys, Svetlana Danilenko and Jūratė Karasevičienė

Axioms 2024, 13(6), 355; https://doi.org/10.3390/axioms13060355 - 25 May 2024

Viewed by 214

Abstract

This paper investigates the randomly stopped sums, minima and maxima of heavy- and light-tailed random variables. The conditions on the primary random variables, which are independent but generally not identically distributed, and counting random variable are given in order that the randomly stopped [...] Read more.

This paper investigates the randomly stopped sums, minima and maxima of heavy- and light-tailed random variables. The conditions on the primary random variables, which are independent but generally not identically distributed, and counting random variable are given in order that the randomly stopped sum, random minimum and maximum is heavy/light tailed. The results generalize some existing ones in the literature. The examples illustrating the results are provided. Full article

(This article belongs to the Special Issue Stochastic Modeling and Optimization Techniques)

31 pages, 392 KiB

Open AccessArticle

One-Dimensional BSDEs with Jumps and Logarithmic Growth

by El Mountasar Billah Bouhadjar, Nabil Khelfallah and Mhamed Eddahbi

Axioms 2024, 13(6), 354; https://doi.org/10.3390/axioms13060354 - 24 May 2024

Viewed by 233

Abstract

In this study, we explore backward stochastic differential equations driven by a Poisson process and an independent Brownian motion, denoted for short as BSDEJs. The generator exhibits logarithmic growth in both the state variable and the Brownian component while maintaining Lipschitz continuity with [...] Read more.

In this study, we explore backward stochastic differential equations driven by a Poisson process and an independent Brownian motion, denoted for short as BSDEJs. The generator exhibits logarithmic growth in both the state variable and the Brownian component while maintaining Lipschitz continuity with respect to the jump component. Our study rigorously establishes the existence and uniqueness of solutions within suitable functional spaces. Additionally, we relax the Lipschitz condition on the Poisson component, permitting the generator to exhibit logarithmic growth with respect to all variables. Taking a step further, we employ an exponential transformation to establish an equivalence between a solution of a BSDEJ exhibiting quadratic growth in the z-variable and a BSDEJ showing a logarithmic growth with respect to y and z. Full article

(This article belongs to the Special Issue Stochastic Modeling and Its Analysis)

15 pages, 337 KiB

Open AccessArticle

Dynamical Behaviors of Stochastic SIS Epidemic Model with Ornstein–Uhlenbeck Process

by Huina Zhang, Jianguo Sun, Peng Yu and Daqing Jiang

Axioms 2024, 13(6), 353; https://doi.org/10.3390/axioms13060353 - 24 May 2024

Viewed by 228

Abstract

Controlling infectious diseases has become an increasingly complex issue, and vaccination has become a common preventive measure to reduce infection rates. It has been thought that vaccination protects the population. However, there is no fully effective vaccine. This is based on the fact [...] Read more.

Controlling infectious diseases has become an increasingly complex issue, and vaccination has become a common preventive measure to reduce infection rates. It has been thought that vaccination protects the population. However, there is no fully effective vaccine. This is based on the fact that it has long been assumed that the immune system produces corresponding antibodies after vaccination, but usually does not achieve the level of complete protection for undergoing environmental fluctuations. In this paper, we investigate a stochastic SIS epidemic model with incomplete inoculation, which is perturbed by the Ornstein–Uhlenbeck process and Brownian motion. We determine the existence of a unique global solution for the stochastic SIS epidemic model and derive control conditions for the extinction. By constructing two suitable Lyapunov functions and using the ergodicity of the Ornstein–Uhlenbeck process, we establish sufficient conditions for the existence of stationary distribution, which means the disease will prevail. Furthermore, we obtain the exact expression of the probability density function near the pseudo-equilibrium point of the stochastic model while addressing the four-dimensional Fokker–Planck equation under the same conditions. Finally, we conduct several numerical simulations to validate the theoretical results. Full article

(This article belongs to the Special Issue Advances in Dynamical Systems and Control)

24 pages, 369 KiB

Open AccessArticle

An Introduction to Extended Gevrey Regularity

by Nenad Teofanov, Filip Tomić and Milica Žigić

Axioms 2024, 13(6), 352; https://doi.org/10.3390/axioms13060352 - 24 May 2024

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Abstract

Gevrey classes are the most common choice when considering the regularities of smooth functions that are not analytic. However, in various situations, it is important to consider smoothness properties that go beyond Gevrey regularity, for example, when initial value problems are ill-posed in [...] Read more.

Gevrey classes are the most common choice when considering the regularities of smooth functions that are not analytic. However, in various situations, it is important to consider smoothness properties that go beyond Gevrey regularity, for example, when initial value problems are ill-posed in Gevrey settings. In this paper, we consider a convenient framework for studying smooth functions that possess weaker regularity than any Gevrey function. Since the available literature on this topic is scattered, our aim is to provide an overview of extended Gevrey regularity, highlighting its most important features. Additionally, we consider related dual spaces of ultra distributions and review some results on micro-local analysis in the context of extended Gevrey regularity. We conclude the paper with a few selected applications that may motivate further study of the topic. Full article

(This article belongs to the Special Issue Research on Functional Analysis and Its Applications)

10 pages, 253 KiB

Open AccessArticle

Some Remarks Regarding Special Elements in Algebras Obtained by the Cayley–Dickson Process over Z_p

by Cristina Flaut and Andreea Baias

Axioms 2024, 13(6), 351; https://doi.org/10.3390/axioms13060351 - 24 May 2024

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Abstract

In this paper, we provide some properties of k-potent elements in algebras obtained by the Cayley–Dickson process over

Z_{p}

. Moreover, we find a structure of nonunitary ring over Fibonacci quaternions over

Z_{3}

and we present a method to encrypt [...] Read more.

In this paper, we provide some properties of k-potent elements in algebras obtained by the Cayley–Dickson process over

Z_{p}

. Moreover, we find a structure of nonunitary ring over Fibonacci quaternions over

Z_{3}

and we present a method to encrypt plain texts, by using invertible elements in some of these algebras. Full article

(This article belongs to the Special Issue Advances in Classical and Applied Mathematics)

4 pages, 170 KiB

Open AccessEditorial

Editorial Conclusion for the Special Issue “New Theory and Applications of Nonlinear Analysis, Fractional Calculus and Optimization”

by Wei-Shih Du

Axioms 2024, 13(6), 350; https://doi.org/10.3390/axioms13060350 - 24 May 2024

Viewed by 205

Abstract

Nonlinear analysis has widespread and significant applications in many areas at the core of many branches of pure and applied mathematics and modern science, including nonlinear ordinary and partial differential equations, critical point theory, functional analysis, fixed point theory, nonlinear optimization, fractional calculus, [...] Read more.

Nonlinear analysis has widespread and significant applications in many areas at the core of many branches of pure and applied mathematics and modern science, including nonlinear ordinary and partial differential equations, critical point theory, functional analysis, fixed point theory, nonlinear optimization, fractional calculus, variational analysis, convex analysis, dynamical system theory, mathematical economics, data mining, signal processing, control theory, and many more [...] Full article

(This article belongs to the Special Issue New Theory and Applications of Nonlinear Analysis, Fractional Calculus and Optimization)

17 pages, 377 KiB

Open AccessArticle

Isoptic Point of the Complete Quadrangle

by Ema Jurkin, Marija Šimić Horvath and Vladimir Volenec

Axioms 2024, 13(6), 349; https://doi.org/10.3390/axioms13060349 - 24 May 2024

Viewed by 218

Abstract

In this paper, we study the complete quadrangle. We started this investigation in a few of our previous papers. In those papers and here, the rectangular coordinates are used to enable us to prove the properties of the rich geometry of a quadrangle [...] Read more.

In this paper, we study the complete quadrangle. We started this investigation in a few of our previous papers. In those papers and here, the rectangular coordinates are used to enable us to prove the properties of the rich geometry of a quadrangle using the same method. Now, we are focused on the isoptic point of the complete quadrangle

A B C D

, which is the inverse point to

A^{'}, B^{'}, C^{'},

and

D^{'}

with respect to circumscribed circles of the triangles

B C D

,

A C D

,

A B D

, and

A B C

, respectively, where

A^{'}, B^{'}, C^{'},

and

D^{'}

are isogonal points to

A, B, C,

and D with respect to these triangles. In studying the properties of the quadrangle regarding its isoptic point, some new results are obtained as well. Full article

(This article belongs to the Special Issue Advances in Geometry and Its Applications)

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21 pages, 826 KiB

Open AccessArticle

On Certain Properties of Parametric Kinds of Apostol-Type Frobenius–Euler–Fibonacci Polynomials

by Hao Guan, Waseem Ahmad Khan, Can Kızılateş and Cheon Seoung Ryoo

Axioms 2024, 13(6), 348; https://doi.org/10.3390/axioms13060348 - 24 May 2024

Viewed by 249

Abstract

This paper presents an overview of cosine and sine Apostol-type Frobenius–Euler–Fibonacci polynomials, as well as several identities that are associated with these polynomials. By applying a partial derivative operator to the generating functions, the authors obtain derivative formulae and finite combinatorial sums involving [...] Read more.

This paper presents an overview of cosine and sine Apostol-type Frobenius–Euler–Fibonacci polynomials, as well as several identities that are associated with these polynomials. By applying a partial derivative operator to the generating functions, the authors obtain derivative formulae and finite combinatorial sums involving these polynomials and numbers. Additionally, the paper establishes connections between cosine and sine Apostol-type Frobenius–Euler–Fibonacci polynomials of order

α

and several other polynomial sequences, such as the Apostol-type Bernoulli–Fibonacci polynomials, the Apostol-type Euler–Fibonacci polynomials, the Apostol-type Genocchi–Fibonacci polynomials, and the Stirling–Fibonacci numbers of the second kind. The authors also provide computational formulae and graphical representations of these polynomials using the Mathematica program. Full article

(This article belongs to the Special Issue Fractional and Stochastic Differential Equations in Mathematics)

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20 pages, 316 KiB

Open AccessArticle

Strong Comonotonic Additive Systemic Risk Measures

by Heyan Wang, Shuo Gong and Yijun Hu

Axioms 2024, 13(6), 347; https://doi.org/10.3390/axioms13060347 - 23 May 2024

Viewed by 267

Abstract

In this paper, we propose a new class of systemic risk measures, which we refer to as strong comonotonic additive systemic risk measures. First, we introduce the notion of strong comonotonic additive systemic risk measures by proposing new axioms. Second, we establish a [...] Read more.

In this paper, we propose a new class of systemic risk measures, which we refer to as strong comonotonic additive systemic risk measures. First, we introduce the notion of strong comonotonic additive systemic risk measures by proposing new axioms. Second, we establish a structural decomposition for strong comonotonic additive systemic risk measures. Third, when both the single-firm risk measure and the aggregation function in the structural decomposition are convex, we also provide a dual representation for it. Last, examples are given to illustrate the proposed systemic risk measures. Comparisons with existing systemic risk measures are also provided. Full article

(This article belongs to the Special Issue Advances in Financial Mathematics)

20 pages, 859 KiB

Open AccessArticle

Local Influence for the Thin-Plate Spline Generalized Linear Model

by Germán Ibacache-Pulgar, Pablo Pacheco, Orietta Nicolis and Miguel Angel Uribe-Opazo

Axioms 2024, 13(6), 346; https://doi.org/10.3390/axioms13060346 - 23 May 2024

Viewed by 239

Abstract

Thin-Plate Spline Generalized Linear Models (TPS-GLMs) are an extension of Semiparametric Generalized Linear Models (SGLMs), because they allow a smoothing spline to be extended to two or more dimensions. This class of models allows modeling a set of data in which it is [...] Read more.

Thin-Plate Spline Generalized Linear Models (TPS-GLMs) are an extension of Semiparametric Generalized Linear Models (SGLMs), because they allow a smoothing spline to be extended to two or more dimensions. This class of models allows modeling a set of data in which it is desired to incorporate the non-linear joint effects of some covariates to explain the variability of a certain variable of interest. In the spatial context, these models are quite useful, since they allow the effects of locations to be included, both in trend and dispersion, using a smooth surface. In this work, we extend the local influence technique for the TPS-GLM model in order to evaluate the sensitivity of the maximum penalized likelihood estimators against small perturbations in the model and data. We fit our model through a joint iterative process based on Fisher Scoring and weighted backfitting algorithms. In addition, we obtained the normal curvature for the case-weight perturbation and response variable additive perturbation schemes, in order to detect influential observations on the model fit. Finally, two data sets from different areas (agronomy and environment) were used to illustrate the methodology proposed here. Full article

(This article belongs to the Special Issue Mathematical Models and Simulations II)

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Axioms, Volume 13, Issue 6 (June 2024) – 37 articles

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