Journal Description

Axioms

Axioms (ISSN 2075-1680) is an international, peer-reviewed, open access journal of mathematics, mathematical logic and mathematical physics, published quarterly online by MDPI. The European Society for Fuzzy Logic and Technology (EUSFLAT), International Fuzzy Systems Association (IFSA) and Union of Slovak Mathematicians and Physicists (JSMF) are affiliated with Axioms and their members receive discounts on the article processing charges.

Open Access— free for readers, with article processing charges (APC) paid by authors or their institutions.
High visibility: indexed within Scopus, SCIE (Web of Science), dblp, and many other databases.
Journal Rank: CiteScore - Q1 (Algebra and Number Theory)
Rapid Publication: manuscripts are peer-reviewed and a first decision provided to authors approximately 20.7 days after submission; acceptance to publication is undertaken in 4.7 days (median values for papers published in this journal in the second half of 2020).
Recognition of Reviewers: reviewers who provide timely, thorough peer-review reports receive vouchers entitling them to a discount on the APC of their next publication in any MDPI journal, in appreciation of the work done.

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Latest Articles

Open AccessArticle

Analyzing Uncertain Dynamical Systems after State-Space Transformations into Cooperative Form: Verification of Control and Fault Diagnosis

Julia Kersten

Andreas Rauh

and

Harald Aschemann

Axioms 2021, 10(2), 88; https://doi.org/10.3390/axioms10020088 - 10 May 2021

Abstract

When modeling real-life applications, uncertainty appears in the form of, for example, modeling approximations, measurement errors, or simply physical restrictions. Those uncertainties can either be treated as stochastic or as bounded, with known limits in the form of intervals. The latter is considered in this paper for a real-life application in the form of an electrical circuit. This is reasonable because the electrical circuit is subject to uncertainties, mainly due to circuit element tolerances and variable load conditions. Since conservative worst-case limits for such parameters are commonly known, interval methods can be applied. The aim of this paper is to demonstrate a possible overall handling of the given uncertain system. Firstly, this includes a control and a reliable computation of the states’ interval enclosures. On the one hand, this can be used to predict the system’s behavior, and on the other hand to verify the control numerically. Here, the implemented feedback control is based on linear matrix inequalities (LMIs) and the states are predicted using an interval enclosure technique based on cooperativity. Since the original system is not cooperative, a transformation is performed. Finally, an observer is implemented as a diagnosis tool regarding faulty measurements or component failures. Since adding a state-of-the-art observer would destroy this structure, a cooperativity-preserving method is applied. Overall, this paper combines methods from robust control design and interval-based evaluations, and presents a suitable observer technique to show the applicability of the presented methods. Full article

(This article belongs to the Special Issue Advances in Analysis and Control of Systems with Uncertainties)

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Open AccessArticle

The Ordered Weighted Average Human Development Index

Ernesto Leon-Castro

Fabio Blanco-Mesa

Alma Montserrat Romero-Serrano

and

Marlenne Velázquez-Cazares

Axioms 2021, 10(2), 87; https://doi.org/10.3390/axioms10020087 - 07 May 2021

Abstract

The main aim is to propose a new method for estimating the Human Development Index using ordered weighted average. To develop this method, ordered weighted geometric average (OWGA), induced OWGA prioritized OWA (POWA) operator are studied. Using Human Development Index formulation in combination to aggregations operators presented above is proposed the prioritized induced ordered weighted geometric average (PIOWGA) operator. A mathematical application is carried out to estimate the Human Development Index and compare it with the traditional method and other existing methods. Finally, it is noted that decision makers have an influence on the order given in the ranking by its attitude and criterion, and method can capture the subjective information prioritized by them. Full article

(This article belongs to the Special Issue Multiple-Criteria Decision Making)

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Open AccessArticle

Properties of λ-Pseudo-Starlike Functions of Complex Order Defined by Subordination

Kadhavoor R. Karthikeyan

Gangadharan Murugusundaramoorthy

and

Teodor Bulboacă

Axioms 2021, 10(2), 86; https://doi.org/10.3390/axioms10020086 - 07 May 2021

Abstract

In this paper, we defined a new class of

λ

-pseudo-Bazilevič functions of complex order using subordination. Various classes of analytic functions that map unit discs onto a conic domain and some classes of special functions were studied in dual. Some subordination results, inequalities for the initial Taylor–Maclaurin coefficients and the unified solution of the Fekete–Szegő problem for subclasses of analytic functions related to various conic regions, are our main results. Our main results have many applications which are presented in the form of corollaries. Full article

(This article belongs to the Special Issue Complex Analysis)

Open AccessArticle

Parrondo’s Paradox for Tent Maps

Jose S. Cánovas

Axioms 2021, 10(2), 85; https://doi.org/10.3390/axioms10020085 - 06 May 2021

Abstract

In this paper, we study the dynamic Parrondo’s paradox for the well-known family of tent maps. We prove that this paradox is impossible when we consider piecewise linear maps with constant slope. In addition, we analyze the paradox “simple + simple = complex” [...] Read more.

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

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Open AccessArticle

Controllability of Fuzzy Solutions for Neutral Impulsive Functional Differential Equations with Nonlocal Conditions

Falguni Acharya

Vandana Kushawaha

Jitendra Panchal

and

Dimplekumar Chalishajar

Axioms 2021, 10(2), 84; https://doi.org/10.3390/axioms10020084 - 06 May 2021

Abstract

In this paper, the controllability of fuzzy solutions for first order nonlocal impulsive neutral functional differential equations is explored using the Banach fixed point theorem. We utilized the concepts of the fuzzy set theory, functional analysis, and the Hausdorff metric. In the conclusion, [...] Read more.

(This article belongs to the Special Issue Advances in Applied Mathematical Analysis)

Open AccessArticle

About the Normal Projectivity and Injectivity of Krasner Hypermodules

Hashem Bordbar

and

Irina Cristea

Axioms 2021, 10(2), 83; https://doi.org/10.3390/axioms10020083 - 04 May 2021

Abstract

Inspired by the concepts of projective and injective modules in classical algebraic structure theory, in this paper we initiate the study of the chains of hypermodules over a Krasner hyperring R, endowing first the set

H o m_{R}^{n} (M, N)

of all normal homomorphisms between two R-hypermodules M and N with a structure of R-hypermodule. Then, our study focuses on the concepts of normal injectivity and projectivity of hypermodules over a Krasner hyperring R, characterizing them by the mean of chains of R-hypermodules. Full article

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Open AccessArticle

Regularization of the Ill-Posed Cauchy Problem for Matrix Factorizations of the Helmholtz Equation on the Plane

Davron Aslonqulovich Juraev

and

Samad Noeiaghdam

Axioms 2021, 10(2), 82; https://doi.org/10.3390/axioms10020082 - 02 May 2021

Abstract

In this paper, we present an explicit formula for the approximate solution of the Cauchy problem for the matrix factorizations of the Helmholtz equation in a bounded domain on the plane. Our formula for an approximate solution also includes the construction of a [...] Read more.

K (w)

which depends on the space dimension. In this paper, based on the results of previous works, the better results can be obtained by choosing the function

K (w)

. Full article

(This article belongs to the Special Issue Modern Problems of Mathematical Physics and Their Applications)

Open AccessArticle

Certain Unified Integrals Involving a Multivariate Mittag–Leffler Function

and

Axioms 2021, 10(2), 81; https://doi.org/10.3390/axioms10020081 - 02 May 2021

Abstract

A remarkably large number of unified integrals involving the Mittag–Leffler function have been presented. Here, with the same technique as Choi and Agarwal, we propose the establishment of two generalized integral formulas involving a multivariate generalized Mittag–Leffler function, which are expressed in terms [...] Read more.

(This article belongs to the Special Issue Special Functions Associated with Fractional Calculus)

Open AccessArticle

Dynamics of Systems with a Discontinuous Hysteresis Operator and Interval Translation Maps

and

Axioms 2021, 10(2), 80; https://doi.org/10.3390/axioms10020080 - 02 May 2021

Abstract

We studied topological and metric properties of the so-called interval translation maps (ITMs). For these maps, we introduced the maximal invariant measure and demonstrated that an ITM, endowed with such a measure, is metrically conjugated to an interval exchange map (IEM). This allowed us to extend some properties of IEMs (e.g., an estimate of the number of ergodic measures and the minimality of the symbolic model) to ITMs. Further, we proved a version of the closing lemma and studied how the invariant measures depend on the parameters of the system. These results were illustrated by a simple example or a risk management model where interval translation maps appear naturally. Full article

(This article belongs to the Special Issue Topological Theory of Dynamical Systems)

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Open AccessArticle

An Information-Theoretic Framework for Optimal Design: Analysis of Protocols for Estimating Soft Tissue Parameters in Biaxial Experiments

Ankush Aggarwal

Damiano Lombardi

and

Sanjay Pant

Axioms 2021, 10(2), 79; https://doi.org/10.3390/axioms10020079 - 01 May 2021

Abstract

A new framework for optimal design based on the information-theoretic measures of mutual information, conditional mutual information and their combination is proposed. The framework is tested on the analysis of protocols—a combination of angles along which strain measurements can be acquired—in a biaxial experiment of soft tissues for the estimation of hyperelastic constitutive model parameters. The proposed framework considers the information gain about the parameters from the experiment as the key criterion to be maximised, which can be directly used for optimal design. Information gain is computed through k-nearest neighbour algorithms applied to the joint samples of the parameters and measurements produced by the forward and observation models. For biaxial experiments, the results show that low angles have a relatively low information content compared to high angles. The results also show that a smaller number of angles with suitably chosen combinations can result in higher information gains when compared to a larger number of angles which are poorly combined. Finally, it is shown that the proposed framework is consistent with classical approaches, particularly D-optimal design. Full article

(This article belongs to the Special Issue Differential Models, Numerical Simulations and Applications)

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Open AccessArticle

A Fractional-in-Time Prey–Predator Model with Hunting Cooperation: Qualitative Analysis, Stability and Numerical Approximations

Maria Francesca Carfora

and

Isabella Torcicollo

Axioms 2021, 10(2), 78; https://doi.org/10.3390/axioms10020078 - 30 Apr 2021

Abstract

A prey–predator system with logistic growth of prey and hunting cooperation of predators is studied. The introduction of fractional time derivatives and the related persistent memory strongly characterize the model behavior, as many dynamical systems in the applied sciences are well described by such fractional-order models. Mathematical analysis and numerical simulations are performed to highlight the characteristics of the proposed model. The existence, uniqueness and boundedness of solutions is proved; the stability of the coexistence equilibrium and the occurrence of Hopf bifurcation is investigated. Some numerical approximations of the solution are finally considered; the obtained trajectories confirm the theoretical findings. It is observed that the fractional-order derivative has a stabilizing effect and can be useful to control the coexistence between species. Full article

(This article belongs to the Special Issue Differential Models, Numerical Simulations and Applications)

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Open AccessArticle

Trees in Positive Entropy Subshifts

Ville Salo

Axioms 2021, 10(2), 77; https://doi.org/10.3390/axioms10020077 - 29 Apr 2021

Abstract

I give a simple proof for the fact that positive entropy subshifts contain infinite binary trees where branching happens synchronously in each branch, and that the branching times form a set with positive lower asymptotic density. Full article

(This article belongs to the Special Issue Topological Theory of Dynamical Systems)

Open AccessArticle

Approximations of an Equilibrium Problem without Prior Knowledge of Lipschitz Constants in Hilbert Spaces with Applications

and

Axioms 2021, 10(2), 76; https://doi.org/10.3390/axioms10020076 - 27 Apr 2021

Abstract

The objective of this paper is to introduce an iterative method with the addition of an inertial term to solve equilibrium problems in a real Hilbert space. The proposed iterative scheme is based on the Mann-type iterative scheme and the extragradient method. By imposing certain mild conditions on a bifunction, the corresponding theorem of strong convergence in real Hilbert space is well-established. The proposed method has the advantage of requiring no knowledge of Lipschitz-type constants. The applications of our results to solve particular classes of equilibrium problems is presented. Numerical results are established to validate the proposed method’s efficiency and to compare it to other methods in the literature. Full article

(This article belongs to the Special Issue Numerical Analysis and Computational Mathematics)

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Open AccessArticle

A Comparison of a Priori Estimates of the Solutions of a Linear Fractional System with Distributed Delays and Application to the Stability Analysis

and

Axioms 2021, 10(2), 75; https://doi.org/10.3390/axioms10020075 - 27 Apr 2021

Abstract

In this article, we consider a retarded linear fractional differential system with distributed delays and Caputo type derivatives of incommensurate orders. For this system, several a priori estimates for the solutions, applying the two traditional approaches—by the use of the Gronwall’s inequality and by the use of integral representations of the solutions are obtained. As application of the obtained estimates, different sufficient conditions which guaranty finite-time stability of the solutions are established. A comparison of the obtained different conditions in respect to the used estimates and norms is made. Full article

(This article belongs to the Special Issue Fractional Calculus - Theory and Applications)

Open AccessArticle

Singular Integral Neumann Boundary Conditions for Semilinear Elliptic PDEs

Praveen Agarwal

Jochen Merker

and

Gregor Schuldt

Axioms 2021, 10(2), 74; https://doi.org/10.3390/axioms10020074 - 24 Apr 2021

Abstract

In this article, we discuss semilinear elliptic partial differential equations with singular integral Neumann boundary conditions. Such boundary value problems occur in applications as mathematical models of nonlocal interaction between interior points and boundary points. Particularly, we are interested in the uniqueness of solutions to such problems. For the sublinear and subcritical case, we calculate, on the one hand, illustrative, rather explicit solutions in the one-dimensional case. On the other hand, we prove in the general case the existence and—via the strong solution of an integro-PDE with a kind of fractional divergence as a lower order term—uniqueness up to a constant. Full article

(This article belongs to the Special Issue Special Functions Associated with Fractional Calculus)

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Open AccessArticle

Coupled Optimal Results with an Application to Nonlinear Integral Equations

and

Axioms 2021, 10(2), 73; https://doi.org/10.3390/axioms10020073 - 22 Apr 2021

Abstract

In the present work, we consider the best proximal problem related to a coupled mapping, which we define using control functions and weak inequalities. As a consequence, we obtain some results on coupled fixed points. Our results generalize some recent results in the literature. Also, as an application of the results obtained, we present the solution to a system of a coupled Fredholm nonlinear integral equation. Our work is supported by several illustrations. Full article

(This article belongs to the Special Issue Fixed Point Theory and Its Related Topics III)

Open AccessArticle

Fixed Points Results for Various Types of Tricyclic Contractions

and

Axioms 2021, 10(2), 72; https://doi.org/10.3390/axioms10020072 - 20 Apr 2021

Abstract

In this paper, we introduce four new types of contractions called in this order Kanan-S-type tricyclic contraction, Chattergea-S-type tricyclic contraction, Riech-S-type tricyclic contraction, Cirić-S-type tricyclic contraction, and we prove the existence and uniqueness for a fixed point for each situation. Full article

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

Open AccessArticle

On Convex F-Contraction in b-Metric Spaces

and

Axioms 2021, 10(2), 71; https://doi.org/10.3390/axioms10020071 - 19 Apr 2021

Abstract

In this paper, we introduce a notion of convex F-contraction and establish some fixed point results for such contractions in b-metric spaces. Moreover, we give a supportive example to show that our convex F-contraction is quite different from the F-contraction used in the existing literature since our convex F-contraction does not necessarily contain the continuous mapping but the F-contraction contains such mapping. In addition, via some facts, we claim that our results indeed generalize and improve some previous results in the literature. Full article

(This article belongs to the Special Issue Special Issue in Honor of the 60th Birthday of Professor Hong-Kun Xu)

Open AccessArticle

q-Binomial Convolution and Transformations of q-Appell Polynomials

Alaa Mohammed Obad

Asif Khan

Kottakkaran Sooppy Nisar

and

Ahmed Morsy

Axioms 2021, 10(2), 70; https://doi.org/10.3390/axioms10020070 - 19 Apr 2021

Abstract

In this paper, binomial convolution in the frame of quantum calculus is studied for the set

A_{q}

of q-Appell sequences. It has been shown that the set

A_{q}

of q-Appell sequences forms an Abelian group under the operation of binomial convolution. Several properties for this Abelian group structure

A_{q}

have been studied. A new definition of the q-Appell polynomials associated with a random variable is proposed. Scale transformation as well as transformation based on expectation with respect to a random variable is used to present the determinantal form of q-Appell sequences. Full article

(This article belongs to the Special Issue p-adic Analysis and q-Calculus with Their Applications)

Open AccessArticle

The χ-Hessian Quotient for Riemannian Metrics

Pişcoran Laurian-Ioan

Akram Ali

Barbu Cătălin

and

Ali H. Alkhaldi

Axioms 2021, 10(2), 69; https://doi.org/10.3390/axioms10020069 - 19 Apr 2021

Abstract

Pseudo-Riemannian geometry and Hilbert–Schmidt norms are two important fields of research in applied mathematics. One of the main goals of this paper will be to find a link between these two research fields. In this respect, in the present paper, we will introduce [...] Read more.

χ

-quotient. This second quantity will be investigated using the Frobenius (Hilbert–Schmidt) norm. Some important examples will be also given, which will prove the validity of the developed theory along the paper. Full article

(This article belongs to the Special Issue Applications of Differential Geometry II)

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Non-associative Structures, Yang–Baxter Equations and Related Topics Guest Editor: Florin Felix Nichita
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