Axioms doi: 10.3390/axioms10030163

Authors: Li Zhou Chuanxi Zhu

In this paper, we consider the following Kirchhoff-type equation:{u∈H1(RN),−(a+b∫RN|∇u|2dx)Δu+V(x)u=(Iα*F(u))f(u)+λg(u),inRN, where a&gt;0, b≥0, λ&gt;0, α∈(N−2,N), N≥3, V:RN→R is a potential function and Iα is a Riesz potential of order α∈(N−2,N). Under certain assumptions on V(x), f(u) and g(u), we prove that the equation has at least one nontrivial solution by variational methods.

]]>Axioms doi: 10.3390/axioms10030164

Authors: Songsong Dai

This paper studies rough approximation via join and meet on a complete orthomodular lattice. Different from Boolean algebra, the distributive law of join over meet does not hold in orthomodular lattices. Some properties of rough approximation rely on the distributive law. Furthermore, we study the relationship among the distributive law, rough approximation and orthomodular lattice-valued relation.

]]>Axioms doi: 10.3390/axioms10030162

Authors: Simon Gluzman

“Odd” factor approximants of the special form suggested by Gluzman and Yukalov (J. Math. Chem. 2006, 39, 47) are amenable to optimization by power transformation and can be successfully applied to critical phenomena. The approach is based on the idea that the critical index by itself should be optimized through the parameters of power transform to be calculated from the minimal sensitivity (derivative) optimization condition. The critical index is a product of the algebraic self-similar renormalization which contributes to the expressions the set of control parameters typical to the algebraic self-similar renormalization, and of the power transform which corrects them even further. The parameter of power transformation is, in a nutshell, the multiplier connecting the critical exponent and the correction-to-scaling exponent. We mostly study the minimal model of critical phenomena based on expansions with only two coefficients and critical points. The optimization appears to bring quite accurate, uniquely defined results given by simple formulas. Many important cases of critical phenomena are covered by the simple formula. For the longer series, the optimization condition possesses multiple solutions, and additional constraints should be applied. In particular, we constrain the sought solution by requiring it to be the best in prediction of the coefficients not employed in its construction. In principle, the error/measure of such prediction can be optimized by itself, with respect to the parameter of power transform. Methods of calculation based on optimized power-transformed factors are applied and results presented for critical indices of several key models of conductivity and viscosity of random media, swelling of polymers, permeability in two-dimensional channels. Several quantum mechanical problems are discussed as well.

]]>Axioms doi: 10.3390/axioms10030161

Authors: Alicia Cordero Javier G. Maimó Eulalia Martínez Juan R. Torregrosa María P. Vassileva

In this work, we use the technique of recurrence relations to prove the semilocal convergence in Banach spaces of the multidimensional extension of Chun’s iterative method. This is an iterative method of fourth order, that can be transferred to the multivariable case by using the divided difference operator. We obtain the domain of existence and uniqueness by taking a suitable starting point and imposing a Lipschitz condition to the first Fréchet derivative in the whole domain. Moreover, we apply the theoretical results obtained to a nonlinear integral equation of Hammerstein type, showing the applicability of our results.

]]>Axioms doi: 10.3390/axioms10030160

Authors: Likai Liu Jin-Lin Liu

Using differential subordination, we consider conditions of β so that some multivalent analytic functions are subordinate to (1+z)γ (0&lt;γ≤1). Notably, these results are applied to derive sufficient conditions for f∈A to satisfy the condition zf′(z)f(z)2−1&lt;1. Several previous results are extended.

]]>Axioms doi: 10.3390/axioms10030159

Authors: Yingdan Shang Bin Zhou Ye Wang Aiping Li Kai Chen Yichen Song Changjian Lin

Predicting the popularity of online content is an important task for content recommendation, social influence prediction and so on. Recent deep learning models generally utilize graph neural networks to model the complex relationship between information cascade graph and future popularity, and have shown better prediction results compared with traditional methods. However, existing models adopt simple graph pooling strategies, e.g., summation or average, which prone to generate inefficient cascade graph representation and lead to unsatisfactory prediction results. Meanwhile, they often overlook the temporal information in the diffusion process which has been proved to be a salient predictor for popularity prediction. To focus attention on the important users and exclude noises caused by other less relevant users when generating cascade graph representation, we learn the importance coefficient of users and adopt sample mechanism in graph pooling process. In order to capture the temporal features in the diffusion process, we incorporate the inter-infection duration time information into our model by using LSTM neural network. The results show that temporal information rather than cascade graph information is a better predictor for popularity. The experimental results on real datasets show that our model significantly improves the prediction accuracy compared with other state-of-the-art methods.

]]>Axioms doi: 10.3390/axioms10030158

Authors: Ioannis K. Argyros Stepan Shakhno Roman Iakymchuk Halyna Yarmola Michael I. Argyros

We develop a local convergence of an iterative method for solving nonlinear least squares problems with operator decomposition under the classical and generalized Lipschitz conditions. We consider the case of both zero and nonzero residuals and determine their convergence orders. We use two types of Lipschitz conditions (center and restricted region conditions) to study the convergence of the method. Moreover, we obtain a larger radius of convergence and tighter error estimates than in previous works. Hence, we extend the applicability of this method under the same computational effort.

]]>Axioms doi: 10.3390/axioms10030157

Authors: Bruno de Malafosse

Given any sequence a=(an)n≥1 of positive real numbers and any set E of complex sequences, we can use Ea to represent the set of all sequences y=(yn)n≥1 such that y/a=(yn/an)n≥1∈E. In this paper, we use the spaces w∞, w0 and w of strongly bounded, summable to zero and summable sequences, which are the sets of all sequences y such that n−1∑k=1nykn is bounded and tends to zero, and such that y−le∈w0, for some scalarl . These sets were used in the statistical convergence. Then we deal with the solvability of each of the SSIE FΔ⊂E+Fx′, where E is a linear space of sequences, F=c0, c, ℓ∞, w0, w or w∞, and F′=c0, c or ℓ∞. For instance, the solvability of the SSIE wΔ⊂w0+sxc relies on determining the set of all sequences x=xnn≥1∈U+ that satisfy the following statement. For every sequence y that satisfies the condition limn→∞n−1∑k=1nyk−yk−1−l=0, there are two sequences u and v, with y=u+v such that limn→∞n−1∑k=1nuk=0 and limn→∞vn/xn=L for some scalars l and L.

]]>Axioms doi: 10.3390/axioms10030156

Authors: Alexander J. Zaslavski

We study the behavior of inexact products of uniformly continuous self-mappings of a complete metric space that is uniformly continuous and bounded on bounded sets. It is shown that previously established convergence theorems for products of non-expansive mappings continue to hold even under the presence of computational errors.

]]>Axioms doi: 10.3390/axioms10030155

Authors: Rafael Dahmen Gábor Lukács

The group of compactly supported homeomorphisms on a Tychonoff space can be topologized in a number of ways, including as a colimit of homeomorphism groups with a given compact support or as a subgroup of the homeomorphism group of its Stone-Čech compactification. A space is said to have the Compactly Supported Homeomorphism Property (CSHP) if these two topologies coincide. The authors provide necessary and sufficient conditions for finite products of ordinals equipped with the order topology to have CSHP. In addition, necessary conditions are presented for finite products and coproducts of spaces to have CSHP.

]]>Axioms doi: 10.3390/axioms10030154

Authors: Anderson Fonseca Paulo Henrique Ferreira Diego Carvalho do Nascimento Rosemeire Fiaccone Christopher Ulloa-Correa Ayón García-Piña Francisco Louzada

Statistical monitoring tools are well established in the literature, creating organizational cultures such as Six Sigma or Total Quality Management. Nevertheless, most of this literature is based on the normality assumption, e.g., based on the law of large numbers, and brings limitations towards truncated processes as open questions in this field. This work was motivated by the register of elements related to the water particles monitoring (relative humidity), an important source of moisture for the Copiapó watershed, and the Atacama region of Chile (the Atacama Desert), and presenting high asymmetry for rates and proportions data. This paper proposes a new control chart for interval data about rates and proportions (symbolic interval data) when they are not results of a Bernoulli process. The unit-Lindley distribution has many interesting properties, such as having only one parameter, from which we develop the unit-Lindley chart for both classical and symbolic data. The performance of the proposed control chart is analyzed using the average run length (ARL), median run length (MRL), and standard deviation of the run length (SDRL) metrics calculated through an extensive Monte Carlo simulation study. Results from the real data applications reveal the tool’s potential to be adopted to estimate the control limits in a Statistical Process Control (SPC) framework.

]]>Axioms doi: 10.3390/axioms10030152

Authors: Li-Jun Zhu Yeong-Cheng Liou

In this paper, we survey the split problem of fixed points of two pseudocontractive operators and variational inequalities of two pseudomonotone operators in Hilbert spaces. We present a Tseng-type iterative algorithm for solving the split problem by using self-adaptive techniques. Under certain assumptions, we show that the proposed algorithm converges weakly to a solution of the split problem. An application is included.

]]>Axioms doi: 10.3390/axioms10030153

Authors: Jeong Ryeol Choi

Quantum characteristics of a mass-accreting oscillator are investigated using the invariant operator theory, which is a rigorous mathematical tool for unfolding quantum theory for time-dependent Hamiltonian systems. In particular, the quantum energy of the system is analyzed in detail and compared to the classical one. We focus on two particular cases; one is a linearly mass-accreting oscillator and the other is an exponentially mass-accreting one. It is confirmed that the quantum energy is in agreement with the classical one in the limit ℏ→0. We showed that not only the classical but also the quantum energy oscillates with time. It is carefully analyzed why the energy oscillates with time, and a reasonable explanation for that outcome is given.

]]>Axioms doi: 10.3390/axioms10030151

Authors: Salvador López-Alfonso Manuel López-Pellicer Santiago Moll-López

A local convex space E is said to be distinguished if its strong dual Eβ′ has the topology β(E′,(Eβ′)′), i.e., if Eβ′ is barrelled. The distinguished property of the local convex space CpX of real-valued functions on a Tychonoff space X, equipped with the pointwise topology on X, has recently aroused great interest among analysts and Cp-theorists, obtaining very interesting properties and nice characterizations. For instance, it has recently been obtained that a space CpX is distinguished if and only if any function f∈RX belongs to the pointwise closure of a pointwise bounded set in CX. The extensively studied distinguished properties in the injective tensor products CpX⊗εE and in Cp(X,E) contrasts with the few distinguished properties of injective tensor products related to the dual space LpX of CpX endowed with the weak* topology, as well as to the weak* dual of Cp(X,E). To partially fill this gap, some distinguished properties in the injective tensor product space LpX⊗εE are presented and a characterization of the distinguished property of the weak* dual of Cp(X,E) for wide classes of spaces X and E is provided.

]]>Axioms doi: 10.3390/axioms10030150

Authors: Andriy Zagorodnyuk Anna Hihliuk

In the paper we establish some conditions under which a given sequence of polynomials on a Banach space X supports entire functions of unbounded type, and construct some counter examples. We show that if X is an infinite dimensional Banach space, then the set of entire functions of unbounded type can be represented as a union of infinite dimensional linear subspaces (without the origin). Moreover, we show that for some cases, the set of entire functions of unbounded type generated by a given sequence of polynomials contains an infinite dimensional algebra (without the origin). Some applications for symmetric analytic functions on Banach spaces are obtained.

]]>Axioms doi: 10.3390/axioms10030149

Authors: Eliana Costa e Silva Aldina Correia Ana Borges

Entrepreneurship is a theme of global interest, and it is the subject of investigations conducted by many researchers and projects. In particular, the Global Entrepreneurship Monitor project is a global project that involves several countries and years of surveys on entrepreneurship indicators. This study focuses on the 12 indicators of the entrepreneurial ecosystem defined by the Entrepreneurial Framework Conditions (EFCs). The EFCs are specifically related to the quality of the entrepreneurial ecosystem. Using clustering techniques, the present study analyzes how European experts’ perceptions on the EFCs of their home country have changed between 2000 and 2019. The main finding is the existence of significant differences between the clusters obtained over the years and between countries. Therefore, in theoretical terms, this dynamical behavior in relation to the entrepreneurial conditions of economies should be considered in future works, namely, those concerning the definition of the number of clusters, which, according to the internal validation measures computed in this work, should be two.

]]>Axioms doi: 10.3390/axioms10030148

Authors: Vasile Dragan Samir Aberkane

This note is devoted to a robust stability analysis, as well as to the problem of the robust stabilization of a class of continuous-time Markovian jump linear systems subject to block-diagonal stochastic parameter perturbations. The considered parametric uncertainties are of multiplicative white noise type with unknown intensity. In order to effectively address the multi-perturbations case, we use scaling techniques. These techniques allow us to obtain an estimation of the lower bound of the stability radius. A first characterization of a lower bound of the stability radius is obtained in terms of the unique bounded and positive semidefinite solutions of adequately defined parameterized backward Lyapunov differential equations. A second characterization is given in terms of the existence of positive solutions of adequately defined parameterized backward Lyapunov differential inequalities. This second result is then exploited in order to solve a robust control synthesis problem.

]]>Axioms doi: 10.3390/axioms10030147

Authors: Murtala Haruna Harbau Godwin Chidi Ugwunnadi Lateef Olakunle Jolaoso Ahmad Abdulwahab

In this work, we introduce a new inertial accelerated Mann algorithm for finding a point in the set of fixed points of asymptotically nonexpansive mapping in a real uniformly convex Banach space. We also establish weak and strong convergence theorems of the scheme. Finally, we give a numerical experiment to validate the performance of our algorithm and compare with some existing methods. Our results generalize and improve some recent results in the literature.

]]>Axioms doi: 10.3390/axioms10030146

Authors: Laszlo Barna Iantovics Florin Felix Nichita

This paper is related to several articles published in AXIOMS, SCI, etc. The main concepts of the current paper are the colored Yang–Baxter equation and the set-theoretical Yang–Baxter equation. The Euler formula, colagebra structures, and means play an important role in our study. We show that some new solutions for a certain system of equations lead to colored Yang–Baxter operators, which are related to an Euler formula for matrices, and the set-theoretical solutions to the Yang–Baxter equation are related to means. A new coalgebra is obtained and studied.

]]>Axioms doi: 10.3390/axioms10030145

Authors: Yun Jin Zareena Kousar Kifayat Ullah Tahir Mahmood Nimet Yapici Pehlivan Zeeshan Ali

Interval-valued T-spherical fuzzy set (IVTSFS) handles uncertain and vague information by discussing their membership degree (MD), abstinence degree (AD), non-membership degree (NMD), and refusal degree (RD). MD, AD, NMD, and RD are defined in terms of closed subintervals of [0,&nbsp;1] that reduce information loss compared to the T-spherical fuzzy set (TSFS), which takes crisp values from [0,&nbsp;1] intervals; hence, some information may be lost. The purpose of this manuscript is to develop some Hamacher aggregation operators (HAOs) in the environment of IVTSFSs. To do so, some Hamacher operational laws based on Hamacher t-norms (HTNs) and Hamacher t-conorms (HTCNs) are introduced. Using Hamacher operational laws, we develop some aggregation operators (AOs), including an interval-valued T-spherical fuzzy Hamacher (IVTSFH) weighted averaging (IVTSFHWA) operator, an IVTSFH-ordered weighted averaging (IVTSFHOWA) operator, an IVTSFH hybrid averaging (IVTSFHHA) operator, an IVTSFH-weighted geometric (IVTSFHWG) operator, an IVTSFH-ordered weighted geometric (IVTSFHOWG) operator, and an IVTSFH hybrid geometric (IVTSFHHG) operator. The validation of the newly developed HAOs is investigated, and their basic properties are examined. In view of some restrictions, the generalization and proposed HAOs are shown, and a multi-attribute decision-making (MADM) procedure is explored based on the HAOs, which are further exemplified. Finally, a comparative analysis of the proposed work is also discussed with previous literature to show the superiority of our work.

]]>Axioms doi: 10.3390/axioms10030144

Authors: Pavel Trojovský

For r≥2 and a≥1 integers, let (tn(r,a))n≥1 be the sequence of the (r,a)-generalized Fibonacci numbers which is defined by the recurrence tn(r,a)=tn−1(r,a)+⋯+tn−r(r,a) for n&gt;r, with initial values ti(r,a)=1, for all i∈[1,r−1] and tr(r,a)=a. In this paper, we shall prove (in particular) that, for any given r≥2, there exists a positive proportion of positive integers which can not be written as tn(r,a) for any (n,a)∈Z≥r+2×Z≥1.

]]>Axioms doi: 10.3390/axioms10030141

Authors: Rabha W. Ibrahim Dumitru Baleanu

(1) Background: symmetry breaking (self-organized transformation of symmetric stats) is a global phenomenon that arises in an extensive diversity of essentially symmetric physical structures. We investigate the symmetry breaking of time-2D space fractional wave equation in a complex domain; (2) Methods: a fractional differential operator is used together with a symmetric operator to define a new fractional symmetric operator. Then by applying the new operator, we formulate a generalized time-2D space fractional wave equation. We shall utilize the two concepts: subordination and majorization to present our results; (3) Results: we obtain different formulas of analytic solutions using the geometric analysis. The solution suggests univalent (1-1) in the open unit disk. Moreover, under certain conditions, it was starlike and dominated by a chaotic function type sine. In addition, the authors formulated a fractional time wave equation by using the Atangana–Baleanu fractional operators in terms of the Riemann–Liouville and Caputo derivatives.

]]>Axioms doi: 10.3390/axioms10030142

Authors: Jinhua Qian Mingyu Sun Pei Yin Young-Ho Kim

Based on the fundamental theories of null curves in Minkowski 3-space, the null Darboux mate curves of a null curve are defined which can be regarded as a kind of extension for Bertrand curves and Mannheim curves in Minkowski 3-space. The relationships of null Darboux curve pairs are explored and their expression forms are presented explicitly.

]]>Axioms doi: 10.3390/axioms10030143

Authors: Gergely Pataki

In this paper, we define uniformities and proximities as relators and show the equivalences of these definitions with classical ones. For this, we summarize the essential properties of relators, using their theory from earlier works of Á. Száz. Moreover, we prove implications between important topological properties of relators and disprove others. Finally, we add an analogous definition for uniformly and proximally filtered properties.

]]>Axioms doi: 10.3390/axioms10030140

Authors: Sun-Weng Huang James J. H. Liou Shih-Hsiung Cheng William Tang Jessica C. Y. Ma Gwo-Hshiung Tzeng

The global economy has been hit by the unexpected COVID-19 outbreak, and foreign investment has been seen as one of the most important tools to boost the economy. However, in the highly uncertain post-epidemic era, determining how to attract foreign investment is the key to revitalizing the economy. What are the important factors for governments to attract investment, and how to improve them? This will be an important decision in the post-epidemic era. Therefore, this study develops a novel decision-making model to explore the key factors in attracting foreign investment. The model first uses fuzzy Delphi to explore the key factors of attracting foreign investment in the post-epidemic era, and then uses DEMATEL to construct the causal relationships among these factors. To overcome the uncertainty of various information sources and inconsistent messages from decision-makers, this study combined neutrosophic set theory to conduct quantitative analysis. The results of the study show that the model is suitable for analyzing the key factors of investment attraction in the post-epidemic period. Based on the results of the study, we also propose strategies that will help the relevant policy-making departments to understand the root causes of the problem and to formulate appropriate investment strategies in advance. In addition, the model is also used for comparative analysis, which reveals that this novel approach can integrate more incomplete information and present expert opinions in a more objective way.

]]>Axioms doi: 10.3390/axioms10030139

Authors: Jonathan Fregoso Claudia I. Gonzalez Gabriela E. Martinez

This paper presents an approach to design convolutional neural network architectures, using the particle swarm optimization algorithm. The adjustment of the hyper-parameters and finding the optimal network architecture of convolutional neural networks represents an important challenge. Network performance and achieving efficient learning models for a particular problem depends on setting hyper-parameter values and this implies exploring a huge and complex search space. The use of heuristic-based searches supports these types of problems; therefore, the main contribution of this research work is to apply the PSO algorithm to find the optimal parameters of the convolutional neural networks which include the number of convolutional layers, the filter size used in the convolutional process, the number of convolutional filters, and the batch size. This work describes two optimization approaches; the first, the parameters obtained by PSO are kept under the same conditions in each convolutional layer, and the objective function evaluated by PSO is given by the classification rate; in the second, the PSO generates different parameters per layer, and the objective function is composed of the recognition rate in conjunction with the Akaike information criterion, the latter helps to find the best network performance but with the minimum parameters. The optimized architectures are implemented in three study cases of sign language databases, in which are included the Mexican Sign Language alphabet, the American Sign Language MNIST, and the American Sign Language alphabet. According to the results, the proposed methodologies achieved favorable results with a recognition rate higher than 99%, showing competitive results compared to other state-of-the-art approaches.

]]>Axioms doi: 10.3390/axioms10030138

Authors: Osman Tunç Cemil Tunç Yuanheng Wang

This paper deals with non-perturbed and perturbed systems of nonlinear differential systems of first order with multiple time-varying delays. Here, for the considered systems, easily verifiable and applicable uniformly asymptotic stability, integrability, and boundedness criteria are obtained via defining an appropriate Lyapunov–Krasovskiĭ functional (LKF) and using the Lyapunov–Krasovskiĭ method (LKM). Comparisons with a former result that can be found in the literature illustrate the novelty of the stability theorem and show new contributions to the qualitative theory of solutions. A discussion of two illustrative examples and the obtained results are presented.

]]>Axioms doi: 10.3390/axioms10030136

Authors: Ying Wu Hong-Ping Yin Bai-Ni Guo

In the paper, with the help of two known integral identities and by virtue of the classical Hölder integral inequality, the authors establish several new integral inequalities of the Hermite–Hadamard type for convex functions. These newly established inequalities generalize some known results.

]]>Axioms doi: 10.3390/axioms10030137

Authors: Vladimir Turetsky

Two inverse ill-posed problems are considered. The first problem is an input restoration of a linear system. The second one is a restoration of time-dependent coefficients of a linear ordinary differential equation. Both problems are reformulated as auxiliary optimal control problems with regularizing cost functional. For the coefficients restoration problem, two control models are proposed. In the first model, the control coefficients are approximated by the output and the estimates of its derivatives. This model yields an approximating linear-quadratic optimal control problem having a known explicit solution. The derivatives are also obtained as auxiliary linear-quadratic tracking controls. The second control model is accurate and leads to a bilinear-quadratic optimal control problem. The latter is tackled in two ways: by an iterative procedure and by a feedback linearization. Simulation results show that a bilinear model provides more accurate coefficients estimates.

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Authors: Faïçal Ndaïrou Delfim F. M. Torres

We propose a qualitative analysis of a recent fractional-order COVID-19 model. We start by showing that the model is mathematically and biologically well posed. Then, we give a proof on the global stability of the disease free equilibrium point. Finally, some numerical simulations are performed to ensure stability and convergence of the disease free equilibrium point.

]]>Axioms doi: 10.3390/axioms10030134

Authors: Qiu Jin Lingqiang Li

For L a complete co-residuated lattice and R an L-fuzzy relation, an L-fuzzy upper approximation operator based on co-implication adjoint with L is constructed and discussed. It is proved that, when L is regular, the new approximation operator is the dual operator of the Qiao–Hu L-fuzzy lower approximation operator defined in 2018. Then, the new approximation operator is characterized by using an axiom set (in particular, by single axiom). Furthermore, the L-fuzzy upper approximation operators generated by serial, symmetric, reflexive, mediate, transitive, and Euclidean L-fuzzy relations and their compositions are characterize through axiom set (single axiom), respectively.

]]>Axioms doi: 10.3390/axioms10030133

Authors: Zahoor Ahmad Rather Rais Ahmad Ching-Feng Wen

This article deals with the study of a variational-like inequality problem which involves the generalized Cayley operator. We compare our problem with a fixed point equation, and based on it we construct an iterative algorithm to obtain the solution of our problem. Convergence analysis as well as stability analysis are studied.

]]>Axioms doi: 10.3390/axioms10030132

Authors: Valery Y. Glizer

A finite-horizon two-person non-zero-sum differential game is considered. The dynamics of the game is linear. Each of the players has a quadratic functional on its own disposal, which should be minimized. The case where weight matrices in control costs of one player are singular in both functionals is studied. Hence, the game under the consideration is singular. A novel definition of the Nash equilibrium in this game (a Nash equilibrium sequence) is proposed. The game is solved by application of the regularization method. This method yields a new differential game, which is a regular Nash equilibrium game. Moreover, the new game is a partial cheap control game. An asymptotic analysis of this game is carried out. Based on this analysis, the Nash equilibrium sequence of the pairs of the players’ state-feedback controls in the singular game is constructed. The expressions for the optimal values of the functionals in the singular game are obtained. Illustrative examples are presented.

]]>Axioms doi: 10.3390/axioms10030131

Authors: Chia-Nan Wang Ngoc-Ai-Thy Nguyen Thanh-Tuan Dang Thi-Thuy-Quynh Trinh

The interactive relationship between the banking system and enterprise makes up the role that affects a national economy. Significantly, the relationship between banking and technology has become tighter over the past few decades. An assessment of bank performance is critical for understanding their position and provides valuable information to practitioners. In this paper, we assess the performance of the top 18 commercial banks in Vietnam during 2015–2019. The assessment utilizes two data envelopment analysis (DEA) models while involving the banks’ performance in six dimensions, including assets, deposits, operating expenses, liabilities as inputs, while treating loans and net income as outputs. Using the Malmquist measurement, the total productivity growth indexes of the banks are obtained, which are decomposed into technical and technological evolutions. Window analysis is used to compute the efficiencies of the banks in every single year in 2015–2019. From the results of Malmquist, most banks are found to decrease their Malmquist productivity indexes from 2015 to 2019, wherein both of their technical and technological indexes declined. Window analysis indicates B6-SHBank, B1-Vietinbank, and B18-PetrolimexGroup as the most efficient banks during 2015–2019, and in the interim, B16-BaoVietBank, B11-NationalCitizen, and B13-VietnamMaritime ranked on the bottom line. The managerial implications of this research help to reflect the comprehensive insights of the top Vietnamese commercial bank performance and offer a strategic guideline for decision-makers toward sustainable development in the banking industry.

]]>Axioms doi: 10.3390/axioms10030130

Authors: Suphawat Asawasamrit Yasintorn Thadang Sotiris Ntouyas Jessada Tariboon

In the present article we study existence and uniqueness results for a new class of boundary value problems consisting by non-instantaneous impulses and Caputo fractional derivative of a function with respect to another function, supplemented with Riemann–Stieltjes fractional integral boundary conditions. The existence of a unique solution is obtained via Banach’s contraction mapping principle, while an existence result is established by using Leray–Schauder nonlinear alternative. Examples illustrating the main results are also constructed.

]]>Axioms doi: 10.3390/axioms10030129

Authors: Shu-Kun Lin

This year we publish the tenth volume of Axioms (ISSN 2075-1680) [...]

]]>Axioms doi: 10.3390/axioms10030128

Authors: Lorenz Demey

Aristotelian diagrams, such as the square of opposition, are well-known in the context of normal modal logics (i.e., systems of modal logic which can be given a relational semantics in terms of Kripke models). This paper studies Aristotelian diagrams for non-normal systems of modal logic (based on neighborhood semantics, a topologically inspired generalization of relational semantics). In particular, we investigate the phenomenon of logic-sensitivity of Aristotelian diagrams. We distinguish between four different types of logic-sensitivity, viz. with respect to (i) Aristotelian families, (ii) logical equivalence of formulas, (iii) contingency of formulas, and (iv) Boolean subfamilies of a given Aristotelian family. We provide concrete examples of Aristotelian diagrams that illustrate these four types of logic-sensitivity in the realm of normal modal logic. Next, we discuss more subtle examples of Aristotelian diagrams, which are not sensitive with respect to normal modal logics, but which nevertheless turn out to be highly logic-sensitive once we turn to non-normal systems of modal logic.

]]>Axioms doi: 10.3390/axioms10020127

Authors: Nikola Mirkov Stojan Radenović Slobodan Radojević

The main purpose of this article is to improve, generalize and complement some recently established results for Perov’s type F-contractions. In our approach, we use only the property (F1) of Wardowski while other authors employed all three conditions. Working only with the fact that the function F is strictly increasing on 0,+∞m, we obtain as a consequence new families of contractive conditions in the realm of vector-valued metric spaces of Perov’s type. At the end of the article, we present an example that supports obtained theoretical results and genuinely generalizes several known results in existing literature.

]]>Axioms doi: 10.3390/axioms10020126

Authors: Hong Li Hongyan Xu

This article is to investigate the existence of entire solutions of several quadratic trinomial difference equations f(z+c)2+2αf(z)f(z+c)+f(z)2=eg(z), and the partial differential difference equations f(z+c)2+2αf(z+c)∂f(z)∂z1+∂f(z)∂z12=eg(z),f(z+c)2+2αf(z+c)∂f(z)∂z1+∂f(z)∂z2+∂f(z)∂z1+∂f(z)∂z22=eg(z). We establish some theorems about the forms of the finite order transcendental entire solutions of these functional equations. We also list a series of examples to explain the existence of the finite order transcendental entire solutions of such equations. Meantime, some examples show that there exists a very significant difference with the previous literature on the growth order of the finite order transcendental entire solutions. Our results show that some functional equations can admit the transcendental entire solutions with any positive integer order. These results make a few improvements of the previous theorems given by Xu and Cao, Liu and Yang.

]]>Axioms doi: 10.3390/axioms10020125

Authors: Kwang-Wu Chen

We establish two recurrence relations for some Clausen’s hypergeometric functions with unit argument. We solve them to give the explicit formulas. Additionally, we use the moments of Ramanujan’s generalized elliptic integrals to obtain these recurrence relations.

]]>Axioms doi: 10.3390/axioms10020124

Authors: Dragiša Stanujkić Darjan Karabašević Gabrijela Popović Predrag S. Stanimirović Florentin Smarandache Muzafer Saračević Alptekin Ulutaş Vasilios N. Katsikis

Some decision-making problems, i.e., multi-criteria decision analysis (MCDA) problems, require taking into account the attitudes of a large number of decision-makers and/or respondents. Therefore, an approach to the transformation of crisp ratings, collected from respondents, in grey interval numbers form based on the median of collected scores, i.e., ratings, is considered in this article. In this way, the simplicity of collecting respondents’ attitudes using crisp values, i.e., by applying some form of Likert scale, is combined with the advantages that can be achieved by using grey interval numbers. In this way, a grey extension of MCDA methods is obtained. The application of the proposed approach was considered in the example of evaluating the websites of tourism organizations by using several MCDA methods. Additionally, an analysis of the application of the proposed approach in the case of a large number of respondents, done in Python, is presented. The advantages of the proposed method, as well as its possible limitations, are summarized.

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Authors: Pundikala Veeresha Haci Mehmet Baskonus Wei Gao

The main objective of the present study is to analyze the nature and capture the corresponding consequences of the solution obtained for the Gardner–Ostrovsky equation with the help of the q-homotopy analysis transform technique (q-HATT). In the rotating ocean, the considered equations exemplify strong interacting internal waves. The fractional operator employed in the present study is used in order to illustrate its importance in generalizing the models associated with kernel singular. The fixed-point theorem and the Banach space are considered to present the existence and uniqueness within the frame of the Caputo–Fabrizio (CF) fractional operator. Furthermore, for different fractional orders, the nature has been captured in plots. The realized consequences confirm that the considered procedure is reliable and highly methodical for investigating the consequences related to the nonlinear models of both integer and fractional order.

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Authors: Maryamsadat Hedayati Reza Ezzati Samad Noeiaghdam

Coronaviruses are a group of RNA (ribonucleic acid) viruses with the capacity for rapid mutation and recombination. Coronaviruses are known to cause respiratory or intestinal infections in humans and animals. In this paper, a biologically compatible set of nonlinear fractional differential equations governing the outbreak of the novel coronavirus is suggested based on a model previously proposed in the literature. Then, this set is numerically solved utilizing two new methods employing sine–cosine and Bernoulli wavelets and their operational matrices. Moreover, the convergence of the solution is experimentally studied. Furthermore, the accuracy of the solution is proved via comparing the results with those obtained in previous research for the primary model. Furthermore, the computational costs are compared by measuring the CPU running time. Finally, the effects of the fractional orders on the outbreak of the COVID-19 are investigated.

]]>Axioms doi: 10.3390/axioms10020121

Authors: Mir Hameeda Angelo Plastino Mario Carlos Rocca Javier Zamora

We considered the canonical gravitational partition function Z associated to the classical Boltzmann–Gibbs (BG) distribution e−βHZ. It is popularly thought that it cannot be built up because the integral involved in constructing Z diverges at the origin. Contrariwise, it was shown in (Physica A 497 (2018) 310), by appeal to sophisticated mathematics developed in the second half of the last century, that this is not so. Z can indeed be computed by recourse to (A) the analytical extension treatments of Gradshteyn and Rizhik and Guelfand and Shilov, that permit tackling some divergent integrals and (B) the dimensional regularization approach. Only one special instance was discussed in the above reference. In this work, we obtain the classical partition function for Newton’s gravity in the four cases that immediately come to mind.

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Authors: Wenjun Pan Miao Lin

This paper focuses on the pricing problem of a two-stage closed-loop supply chain (CLSC) considering the cross-channel recycling and channel preference based on a single manufacturer and a single traditional retailer. The pricing decision problem raises from the manufacturer’s direct sales and the retailer’s retailing including recycling. Managers need to focus on intelligible management considering consumer channel preferences, cross-channel recovery and pricing strategies. According to game theory, centralized and decentralized CLSC decision models are used to provide an efficient solution to managers for the pricing problem. The centralized model consists of differential and uniform pricing strategy and the decentralized model consists of manufacturer-led Stackelberg, retailer-led Stackelberg and Nash equilibrium game, respectively. The impact of cross-channel recycling rate and channel preference on pricing and profitability in a two-stage CLSC system is explained elaborately in this study. The results show that cross-channel recovery rates and consumer channel preferences have a direct significant impact on pricing strategies including profit allocation decisions in CLSC. It demonstrated that different channel preferences leading to different pricing strategies and decision for manufacturers and retailers choices. Manufacturer’s pricing decreases when channel preferences are constant and cross-channel recovery rates increase. Retailer’s pricing remains stable as the cross-channel recovery rate has less affected on it. Furthermore, if the cross-channel recovery rates increase, then the manufacturers pricing decreases and retailers pricing increases. This information will be a helpful guideline for the manager to select suitable pricing strategies based on the company scenario.

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Authors: Marcoen J. T. F. Cabbolet

It is well known that Zermelo-Fraenkel Set Theory (ZF), despite its usefulness as a foundational theory for mathematics, has two unwanted features: it cannot be written down explicitly due to its infinitely many axioms, and it has a countable model due to the Löwenheim–Skolem theorem. This paper presents the axioms one has to accept to get rid of these two features. For that matter, some twenty axioms are formulated in a non-classical first-order language with countably many constants: to this collection of axioms is associated a universe of discourse consisting of a class of objects, each of which is a set, and a class of arrows, each of which is a function. The axioms of ZF are derived from this finite axiom schema, and it is shown that it does not have a countable model—if it has a model at all, that is. Furthermore, the axioms of category theory are proven to hold: the present universe may therefore serve as an ontological basis for category theory. However, it has not been investigated whether any of the soundness and completeness properties hold for the present theory: the inevitable conclusion is therefore that only further research can establish whether the present results indeed constitute an advancement in the foundations of mathematics.

]]>Axioms doi: 10.3390/axioms10020118

Authors: Larry Bates Richard Cushman Jędrzej Śniatycki

In this paper, we study differential forms and vector fields on the orbit space of a proper action of a Lie group on a smooth manifold, defining them as multilinear maps on the generators of infinitesimal diffeomorphisms, respectively. This yields an intrinsic view of vector fields and differential forms on the orbit space.

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Authors: Vasily Gorelov

The notions of cogredience and contragredience, which have great importance to the question of algebraic independence of linear differential equation solutions, are discussed in the paper. Conditions of equivalence of two definitions of cogredience and contragredience are found.

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Authors: Michele Bufalo Daniele Bufalo Giuseppe Orlando

In literature, there are a number of cryptographic algorithms (RSA, ElGamal, NTRU, etc.) that require multiple computations of modulo multiplicative inverses. In this paper, we describe the modulo operation and we recollect the main approaches to computing the modulus. Then, given a and n positive integers, we present the sequence (zj)j≥0, where zj=zj−1+aβj−n, a&lt;n and GCD(a,n)=1. Regarding the above sequence, we show that it is bounded and admits a simple explicit, periodic solution. The main result is that the inverse of a modulo n is given by a−1=⌊im⌋+1 with m=n/a. The computational cost of such an index i is O(a), which is less than O(nlnn) of the Euler’s phi function. Furthermore, we suggest an algorithm for the computation of a−1 using plain multiplications instead of modular multiplications. The latter, still, has complexity O(a) versus complexity O(n) (naive algorithm) or complexity O(lnn) (extended Euclidean algorithm). Therefore, the above procedure is more convenient when a&lt;&lt;n (e.g., a&lt;lnn).

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Authors: Dilip Kumar Hans Haubold

The closed forms of the non-resonant thermonuclear function in the Maxwell–Boltzmann and Tsallis case with depleted tail are obtained in generalized special functions. The results are written in terms of H-function of two variables. The importance of the results in this paper lies in the fact that the reaction rate probability integrals in Maxwell-Boltzmann and Tsallis cases are not obtained by the conventional method of approximation or by means of a single variable transform technique but by means of a two variable transform method. The behaviour of the depleted non-resonant thermonuclear functions are examined using graphs. The results in the paper are of much interest to astrophysicists and statisticians in their future work in this area.

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Authors: Emmanuel A. Bakare Snehashish Chakraverty Radovan Potucek

This work proposes an interval-based uncertain Susceptible–Infected–Recovered (SIR) epidemic model. The interval model has been numerically solved by the homotopy analysis method (HAM). The SIR epidemic model is proposed and solved under different uncertain intervals by the HAM to obtain the numerical solution of the model. Furthermore, the SIR ODE model was transformed into a stochastic differential equation (SDE) model and the results of the stochastic and deterministic models were compared using numerical simulations. The results obtained were compared with the numerical solution and found to be in good agreement. Finally, various simulations were done to discuss the solution.

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Authors: Rajkumar Verma

Fermatean fuzzy linguistic (FFL) set theory provides an efficient tool for modeling a higher level of uncertain and imprecise information, which cannot be represented using intuitionistic fuzzy linguistic (IFL)/Pythagorean fuzzy linguistic (PFL) sets. On the other hand, the linguistic scale function (LSF) is the better way to consider the semantics of the linguistic terms during the evaluation process. It is worth noting that the existing operational laws and aggregation operators (AOs) for Fermatean fuzzy linguistic numbers (FFLNs) are not valid in many situations, which can generate errors in real-life applications. The present study aims to define new robust operational laws and AOs under Fermatean fuzzy linguistic environment. To do so, first, we define some new modified operational laws for FFLNs based on LSF and prove some important mathematical properties of them. Next, the work defines several new AOs, namely, the FFL-weighted averaging (FFLWA) operator, the FFL-weighted geometric (FFLWG) operator, the FFL-ordered weighted averaging (FFLOWA) operator, the FFL-ordered weighted geometric (FFLOWG) operator, the FFL-hybrid averaging (FFLHA) operator and the FFL-hybrid geometric (FFLHG) operator under Fermatean fuzzy linguistic environment. Several properties of these AOs are investigated in detail. Further, based on the proposed AOs, a new decision-making approach with Fermatean fuzzy linguistic information is developed to solve group decision-making problems with multiple attributes. Finally, to illustrate the effectiveness of the present approach, a real-life supplier selection problem is presented where the evaluation information of the alternatives is given in terms of FFLNs. Compared to the existing methods, the salient features of the developed approach are (1) it can solve decision-making problems with qualitative information data using FFLNs; (2) It can consider the attitudinal character of the decision-makers during the solution process; (3) It has a solid ability to distinguish the optimal alternative.

]]>Axioms doi: 10.3390/axioms10020112

Authors: Savin Treanţă

In this paper, we investigate the Lagrange dynamics generated by a class of isoperimetric constrained controlled optimization problems involving second-order partial derivatives and boundary conditions. More precisely, we derive necessary optimality conditions for the considered class of variational control problems governed by path-independent curvilinear integral functionals. Moreover, the theoretical results presented in the paper are accompanied by an illustrative example. Furthermore, an algorithm is proposed to emphasize the steps to be followed to solve a control problem such as the one studied in this paper.

]]>Axioms doi: 10.3390/axioms10020111

Authors: Elvis Aponte Jhixon Macías José Sanabria José Soto

In this article, we consider Drazin invertible operators for study of the relationship between their B-Fredholm spectra and the transfer between some of the spectral properties defined through B-Fredholm spectra of this class of operators. Among other results, we investigate the transfer of generalized a-Weyl’s theorem from T to their Drazin inverse S, if it exists.

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Authors: Abdukomil Risbekovich Khashimov Dana Smetanová

The article considers third-order equations with multiple characteristics with general boundary value conditions and non-local initial data. A regular solution to the problem with known methods is constructed here. The uniqueness of the solution to the problem is proved by the method of energy integrals. This uses the theory of non-negative quadratic forms. The existence of a solution to the problem is proved by reducing the problem to Fredholm integral equations of the second kind. In this case, the method of Green’s function and potential is used.

]]>Axioms doi: 10.3390/axioms10020109

Authors: Nattakarn Kaewyong Kanokwan Sitthithakerngkiet

In this paper, a new self-adaptive step size algorithm to approximate the solution of the split minimization problem and the fixed point problem of nonexpansive mappings was constructed, which combined the proximal algorithm and a modified Mann’s iterative method with the inertial extrapolation. The strong convergence theorem was provided in the framework of Hilbert spaces and then proven under some suitable conditions. Our result improved related results in the literature. Moreover, some numerical experiments were also provided to show our algorithm’s consistency, accuracy, and performance compared to the existing algorithms in the literature.

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Authors: Benoît Fabrèges Frédéric Lagoutière Sébastien Tran Tien Nicolas Vauchelet

This work was devoted to the study of a relaxation limit of the so-called aggregation equation with a pointy potential in one-dimensional space. The aggregation equation is today widely used to model the dynamics of a density of individuals attracting each other through a potential. When this potential is pointy, solutions are known to blow up in final time. For this reason, measure-valued solutions have been defined. In this paper, we investigated an approximation of such measure-valued solutions thanks to a relaxation limit in the spirit of Jin and Xin. We study the convergence of this approximation and give a rigorous estimate of the speed of convergence in one dimension with the Newtonian potential. We also investigated the numerical discretization of this relaxation limit by uniformly accurate schemes.

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Authors: Juan Carlos García-Ardila Francisco Marcellán

Given a quasi-definite linear functional u in the linear space of polynomials with complex coefficients, let us consider the corresponding sequence of monic orthogonal polynomials (SMOP in short) (Pn)n≥0. For a canonical Christoffel transformation u˜=(x−c)u with SMOP (P˜n)n≥0, we are interested to study the relation between u˜ and u(1)˜, where u(1) is the linear functional for the associated orthogonal polynomials of the first kind (Pn(1))n≥0, and u(1)˜=(x−c)u(1) is its Christoffel transformation. This problem is also studied for canonical Geronimus transformations.

]]>Axioms doi: 10.3390/axioms10020106

Authors: Tinggui Chen Xiaohua Yin Lijuan Peng Jingtao Rong Jianjun Yang Guodong Cong

With the rapid development of “We media” technology, netizens can freely express their opinions regarding enterprise products on a network platform. Consequently, online public opinion about enterprises has become a prominent issue. Negative comments posted by some netizens may trigger negative public opinion, which can have a significant impact on an enterprise’s image. From the perspective of helping enterprises deal with negative public opinion, this paper combines user portrait technology and a random forest algorithm to help enterprises identify high-risk users who have posted negative comments and thus may trigger negative public opinion. In this way, enterprises can monitor the public opinion of high-risk users to prevent negative public opinion events. Firstly, we crawled the information of users participating in discussions of product experience, and we constructed a portrait of enterprise public opinion users. Then, the characteristics of the portraits were quantified into indicators such as the user’s activity, the user’s influence, and the user’s emotional tendency, and the indicators were sorted. According to the order of the indicators, the users were divided into high-risk, moderate-risk, and low-risk categories. Next, a supervised high-risk user identification model for this classification was established, based on a random forest algorithm. In turn, the trained random forest identifier can be used to predict whether the authors of newly published public opinion information are high-risk users. Finally, a back propagation neural network algorithm was used to identify users and compared with the results of model recognition in this paper. The results showed that the average recognition accuracy of the back propagation neural network is only 72.33%, while the average recognition accuracy of the model constructed in this paper is as high as 98.49%, which verifies the feasibility and accuracy of the proposed random forest recognition method.

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Authors: Lokesh Singh Dhirendra Bahuguna

In this article, we construct a C1 stable invariant manifold for the delay differential equation x′=Ax(t)+Lxt+f(t,xt) assuming the ρ-nonuniform exponential dichotomy for the corresponding solution operator. We also assume that the C1 perturbation, f(t,xt), and its derivative are sufficiently small and satisfy smoothness conditions. To obtain the invariant manifold, we follow the method developed by Lyapunov and Perron. We also show the dependence of invariant manifold on the perturbation f(t,xt).

]]>Axioms doi: 10.3390/axioms10020104

Authors: Efrain Solares Liliana Guerrero Alberto Aguilera Juana María Hernández Sandra Rodríguez Víctor De-León-Gómez

Correctly allocating times to the main activities of a manager is a crucial task that directly affects the possibility of success for any company. Decision support based on state-of-the-art methods can lead to better performance in this activity. However, allocating times to managerial activities is not straightforward; the decision support should provide a flexible recommendation so the manager can make a final decision while ensuring robustness. This paper describes and assesses a novel approach where a search for the best distribution of the manager’s time is performed by an intelligent decision support system. The approach consists of eliciting manager preferences to define the value of the manager’s main activities and, by using a portfolio-like optimization based on differential evolution, obtaining the best time allocation. Aiming at applicability in practical scenarios, the approach can deal with many activities, group decisions, cope with imprecision, vagueness, ill-determination, and other types of uncertainty. We present evidence of the approach’s applicability exploiting a real case study with the participation of several managers. The approach is assessed through the satisfaction level of each manager.

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Authors: Lei Hu Yaozhen Han Shuqin Zhang

By coincidence degree theory due to Mawhin, some sufficient conditions for the existence of solution for a class of coupled jerk equations with multi-point conditions are established. The new existence results have not yet been reported before. Novel coupled fractional jerk equations with resonant boundary value conditions are discussed in detail for the first time. Our work is interesting and complements known results.

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Authors: Maya Briani Emiliano Cristiani Paolo Ranut

In this paper, we propose two models describing the dynamics of heavy and light vehicles on a road network, taking into account the interactions between the two classes. The models are tailored for two-lane highways where heavy vehicles cannot overtake. This means that heavy vehicles cannot saturate the whole road space, while light vehicles can. In these conditions, the creeping phenomenon can appear, i.e., one class of vehicles can proceed even if the other class has reached the maximal density. The first model we propose couples two first-order macroscopic LWR models, while the second model couples a second-order microscopic follow-the-leader model with a first-order macroscopic LWR model. Numerical results show that both models are able to catch some second-order (inertial) phenomena such as stop and go waves. Models are calibrated by means of real data measured by fixed sensors placed along the A4 Italian highway Trieste–Venice and its branches, provided by Autovie Venete S.p.A.

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Authors: Samera M. Saleh Salvatore Sessa Waleed M. Alfaqih Fawzia Shaddad

In this paper, we define almost Rg-Geraghty type contractions and utilize the same to establish some coincidence and common fixed point results in the setting of b2-metric spaces endowed with binary relations. As consequences of our newly proved results, we deduce some coincidence and common fixed point results for almost g-α-η Geraghty type contraction mappings in b2-metric spaces. In addition, we derive some coincidence and common fixed point results in partially ordered b2-metric spaces. Moreover, to show the utility of our main results, we provide an example and an application to non-linear integral equations.

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Authors: Hisham M. Almongy Fatma Y. Alshenawy Ehab M. Almetwally Doaa A. Abdo

In this paper, the Weibull extension distribution parameters are estimated under a progressive type-II censoring scheme with random removal. The parameters of the model are estimated using the maximum likelihood method, maximum product spacing, and Bayesian estimation methods. In classical estimation (maximum likelihood method and maximum product spacing), we did use the Newton–Raphson algorithm. The Bayesian estimation is done using the Metropolis–Hastings algorithm based on the square error loss function. The proposed estimation methods are compared using Monte Carlo simulations under a progressive type-II censoring scheme. An empirical study using a real data set of transformer insulation and a simulation study is performed to validate the introduced methods of inference. Based on the result of our study, it can be concluded that the Bayesian method outperforms the maximum likelihood and maximum product-spacing methods for estimating the Weibull extension parameters under a progressive type-II censoring scheme in both simulation and empirical studies.

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Authors: Michael Gil’

The paper is a survey of the recent results of the author on the perturbations of matrices. A part of the results presented in the paper is new. In particular, we suggest a bound for the difference of the determinants of two matrices which refines the well-known Bhatia inequality. We also derive new estimates for the spectral variation of a perturbed matrix with respect to a given one, as well as estimates for the Hausdorff and matching distances between the spectra of two matrices. These estimates are formulated in the terms of the entries of matrices and via so called departure from normality. In appropriate situations they improve the well-known results. We also suggest a bound for the angular sectors containing the spectra of matrices. In addition, we suggest a new bound for the similarity condition numbers of diagonalizable matrices. The paper also contains a generalization of the famous Kahan inequality on perturbations of Hermitian matrices by non-normal matrices. Finally, taking into account that any matrix having more than one eigenvalue is similar to a block-diagonal matrix, we obtain a bound for the condition numbers in the case of non-diagonalizable matrices, and discuss applications of that bound to matrix functions and spectrum perturbations. The main methodology presented in the paper is based on a combined usage of the recent norm estimates for matrix-valued functions with the traditional methods and results.

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Authors: Tsung-Yin Ou Yenming J. Chen

This paper investigates the impact of consumer preferences on the intensity of competition for companies in a duopoly market. A classical Hotelling’s competition problem will be different if consumers are allowed to distribute non-uniformly. New results in competition intensity are established and conditions for the existence of a subgame perfect Nash equilibrium is identified through a model that considers generic distribution in consumer preferences. A competition strategy is demonstrated to depend on the signs of local change rates of the density function at the endpoints of market segments.

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Authors: Katarína Čunderlíková

The conditional mean value has applications in regression analysis and in financial mathematics, because they are used in it. We can find papers from recent years that use the conditional mean value in fuzzy cases. As the intuitionstic fuzzy sets are an extension of fuzzy sets, we will try to define a conditional mean value for the intuitionistic fuzzy case. The conditional mean value in crisp intuitionistic fuzzy events was first studied by V. Valenčáková in 2009. She used Gödel connectives. Her approach can only be used for special cases of intuitionistic fuzzy events, therefore, we want to define a conditional mean value for all elements of a family of intuitionistic fuzzy events. In this paper, we define the conditional mean value for intuitionistic fuzzy events using Lukasiewicz connectives. We use a Kolmogorov approach and the notions from a classical probability theory for construction. B. Riečan formulated a conditional intuitionistic fuzzy probability for intuitionistic fuzzy events using an intuitionistic fuzzy state in 2012. In classical cases, there exists a connection between the conditional probability and the conditional mean value, therefore we show a connection between the conditional intuitionistic fuzzy probability induced by the intuitionistic fuzzy state and the conditional intuitionistic fuzzy mean value.

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Authors: Nataša Kontrec Stefan Panić Biljana Panić Aleksandar Marković Dejan Stošović

Reliability, the number of spare parts and repair time have a great impact on system availability. In this paper, we observed a repairable system comprised of several components. The aim was to determine the repair rate by emphasizing its stochastic nature. A model for the statistical analysis of the component repair rate in function of the desired level of availability is presented. Furthermore, based on the presented model, the approach for the calculation of probability density functions of maximal and minimal repair times for a system comprised of observed components was developed as an important measure that unambiguously defines the total annual repair time. The obtained generalized analytical expressions that can be used to predict the total repair time for an observed entity are the main contributions of the manuscript. The outputs of the model can be useful for making decisions in which time interval repair or replacement should be done to maintain the system and component availability. In addition to planning maintenance activities, the presented models could be used for service capacity planning and the dynamic forecasting of system characteristics.

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Authors: Alexander Ramm

The aim of this paper is to explain for broad audience the author’s result concerning the Navier–Stokes problem (NSP) in R3 without boundaries. It is proved that the NSP is contradictory in the following sense: if one assumes that the initial data v(x,0)≢0, ∇·v(x,0)=0 and the solution to the NSP exists for all t≥0, then one proves that the solution v(x,t) to the NSP has the property v(x,0)=0. This paradox shows that the NSP is not a correct description of the fluid mechanics problem and the NSP does not have a solution. In the exceptional case, when the data are equal to zero, the solution v(x,t) to the NSP exists for all t≥0 and is equal to zero, v(x,t)≡0. Thus, one of the millennium problems is solved.

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Authors: Dimitris M. Christodoulou Eric Kehoe Qutaibeh D. Katatbeh

For each fundamental and widely used ordinary second-order linear homogeneous differential equation of mathematical physics, we derive a family of associated differential equations that share the same “degenerate” canonical form. These equations can be solved easily if the original equation is known to possess analytic solutions, otherwise their properties and the properties of their solutions are de facto known as they are comparable to those already deduced for the fundamental equation. We analyze several particular cases of new families related to some of the famous differential equations applied to physical problems, and the degenerate eigenstates of the radial Schrödinger equation for the hydrogen atom in N dimensions.

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Authors: Rafael A. Espin-Andrade Witold Pedrycz Efrain Solares Laura Cruz-Reyes

This research is a review and analysis paper that offers a transdisciplinary, methodological, and strategic vision for soft computing development towards a wider favorable impact in data analytics. Strategies are defined, explained, and illustrated by examples. The paper also shows how these strategies are expressed in three dimensions of an ambitious actions plan. They are all integrated into a master strategy called wide knowledge discovery, which offers a way towards the augmented analytics paradigm. Some contributions of this work are defining what kind of mathematical elements should be introduced into soft computing towards a better impact on the area of data analytics, offering orientation towards building new mathematical elements, and defining why and how they can be introduced.

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Authors: Sabahudin Vrtagić Edis Softić Marko Subotić Željko Stević Milan Dordevic Mirza Ponjavic

Traffic management is a significantly difficult and demanding task. It is necessary to know the main parameters of road networks in order to adequately meet traffic management requirements. Through this paper, an integrated fuzzy model for ranking road sections based on four inputs and four outputs was developed. The goal was to determine the safety degree of the observed road sections by the methodology developed. The greatest contribution of the paper is reflected in the development of the improved fuzzy step-wise weight assessment ratio analysis (IMF SWARA) method and integration with the fuzzy measurement alternatives and ranking according to the compromise solution (fuzzy MARCOS) method. First, the data envelopment analysis (DEA) model was applied, showing that three road sections have a high traffic risk. After that, IMF SWARA was applied to determine the values of the weight coefficients of the criteria, and the fuzzy MARCOS method was used for the final ranking of the sections. The obtained results were verified through a three-phase sensitivity analysis with an emphasis on forming 40 new scenarios in which input values were simulated. The stability of the model was proven in all phases of sensitivity analysis.

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Authors: Rafał Palak Krystian Wojtkiewicz

Automated reasoning is becoming crucial for information systems. Building one uniform decision support system has become too complicated. The natural approach is to divide the task and combine the results from different subsystems into one uniform answer. It is the basic idea behind the system approach, where one solution is a composition of multiple subsystems. In this paper, the main emphasis is on establishing the theoretical framework that combines various reasoning methods into a collective system. The system’s formal abstraction uses graph theory and provides a discussion on possible aggregation function definitions. The proposed framework is a tool for building and testing specific approaches rather than the solution itself.

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Authors: Han-Khanh Nguyen

During the months of the COVID-19 epidemic, the number of processing and manufacturing agricultural products enterprises in Vietnam faced many difficulties in the consumption of agricultural products, even when they were unable to sell. Therefore, the enterprises are more and more difficult. Many enterprises are not strong enough to restore production, so it is necessary to find solutions to overcome this difficult period. In this research, the author used the application of modern statistical techniques, along with the Grey method, to predict enterprises’ business results in the future, combined with the model of Super-slacks-based-measure efficiency (Super-SBM) to help businesses select the right partners in a supply chain to achieve their business goals. By our proposed approach, the selected solution (AG6 combined with AG10) should be implemented in the future to upgrade efficiency to help stabilize output and raise productivity; thus, both parties are able not only to improve their product quality but also achieve business goals and sustainable development. In fact, it is necessary to further this study, in combination with these factors and other quantitative models, to give investors a more comprehensive view, helping them to make the right decisions and appropriately develop their businesses and social and economic development.

]]>Axioms doi: 10.3390/axioms10020089

Authors: Igor Protasov

A subset X of a group G is called thin if, for every finite subset F of G, there exists a finite subset H of G such that Fx∩Fy=∅, xF∩yF=∅ for all distinct x,y∈X\H. We prove that every countable topologizable group G can be factorized G=AB into thin subsets A,B.

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Authors: Julia Kersten Andreas Rauh Harald Aschemann

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.

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Authors: Ernesto Leon-Castro Fabio Blanco-Mesa Alma Montserrat Romero-Serrano Marlenne Velázquez-Cazares

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.

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Authors: Kadhavoor R. Karthikeyan Gangadharan Murugusundaramoorthy Teodor Bulboacă

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.

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Authors: Jose S. Cánovas

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” when a tent map with constant slope and a piecewise linear homeomorphism with two different slopes are considered.

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Authors: Falguni Acharya Vandana Kushawaha Jitendra Panchal Dimplekumar Chalishajar

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, an illustration is given to bolster the hypothesis.

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Authors: Hashem Bordbar Irina Cristea

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 HomRn(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.

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Authors: Davron Aslonqulovich Juraev Samad Noeiaghdam

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 family of fundamental solutions for the Helmholtz operator on the plane. This family is parameterized by function 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).

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Authors: Shilpi Jain Ravi P. Agarwal Praveen Agarwal Prakash Singh

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 of the generalized Lauricella series due to Srivastava and Daoust. We also present some interesting special cases.

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Authors: Sergey Kryzhevich Viktor Avrutin Nikita Begun Dmitrii Rachinskii Khosro Tajbakhsh

We studied topological and metric properties of the so-called interval translation maps (ITMs). For these maps, we introduced the maximal invariant measure and study its properties. Further, we study 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.

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Authors: Ankush Aggarwal Damiano Lombardi Sanjay Pant

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.

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Authors: Maria Carfora Isabella Torcicollo

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.

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Authors: Ville Salo

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.

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Authors: Chainarong Khanpanuk Nuttapol Pakkaranang Nopparat Wairojjana Nattawut Pholasa

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.

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Authors: Hristo Kiskinov Magdalena Veselinova Ekaterina Madamlieva Andrey Zahariev

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.

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Authors: Praveen Agarwal Jochen Merker Gregor Schuldt

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.

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Authors: Pulak Konar Sumit Chandok Shrutinil Dutta Manuel De la Sen

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.

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Authors: Mustapha Sabiri Abdelhafid Bassou Jamal Mouline Taoufik Sabar

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.

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Authors: Huaping Huang Zoran D. Mitrović Kastriot Zoto Stojan Radenović

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.

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Authors: Alaa Mohammed Obad Asif Khan Kottakkaran Sooppy Nisar Ahmed Morsy

In this paper, binomial convolution in the frame of quantum calculus is studied for the set Aq of q-Appell sequences. It has been shown that the set Aq of q-Appell sequences forms an Abelian group under the operation of binomial convolution. Several properties for this Abelian group structure Aq 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.

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Authors: Pişcoran Laurian-Ioan Akram Ali Barbu Cătălin Ali H. Alkhaldi

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 and analyze two important quantities in pseudo-Riemannian geometry, namely the H-distorsion and, respectively, the Hessian 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.

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Authors: Fabio Camilli

We consider a Mean Field Games model where the dynamics of the agents is given by a controlled Langevin equation and the cost is quadratic. An appropriate change of variables transforms the Mean Field Games system into a system of two coupled kinetic Fokker–Planck equations. We prove an existence result for the latter system, obtaining consequently existence of a solution for the Mean Field Games system.

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Authors: Lu-Chuan Ceng Jen-Chih Yao

Suppose that in a real Hilbert space H, the variational inequality problem with Lipschitzian and pseudomonotone mapping A and the common fixed-point problem of a finite family of nonexpansive mappings and a quasi-nonexpansive mapping with a demiclosedness property are represented by the notations VIP and CFPP, respectively. In this article, we suggest two Mann-type inertial subgradient extragradient iterations for finding a common solution of the VIP and CFPP. Our iterative schemes require only calculating one projection onto the feasible set for every iteration, and the strong convergence theorems are established without the assumption of sequentially weak continuity for A. Finally, in order to support the applicability and implementability of our algorithms, we make use of our main results to solve the VIP and CFPP in two illustrating examples.

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Authors: Aviv Gibali Oleg Kelis

In this paper we present an appropriate singular, zero-sum, linear-quadratic differential game. One of the main features of this game is that the weight matrix of the minimizer’s control cost in the cost functional is singular. Due to this singularity, the game cannot be solved either by applying the Isaacs MinMax principle, or the Bellman–Isaacs equation approach. As an application, we introduced an interception differential game with an appropriate regularized cost functional and developed an appropriate dual representation. By developing the variational derivatives of this regularized cost functional, we apply Popov’s approximation method and show how the numerical results coincide with the dual representation.

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Authors: Mohadeseh Paknazar Manuel De La Sen

The Sturm–Liouville differential equation is an important tool for physics, applied mathematics, and other fields of engineering and science and has wide applications in quantum mechanics, classical mechanics, and wave phenomena. In this paper, we investigate the coupled hybrid version of the Sturm–Liouville differential equation. Indeed, we study the existence of solutions for the coupled hybrid Sturm–Liouville differential equation with multi-point boundary coupled hybrid condition. Furthermore, we study the existence of solutions for the coupled hybrid Sturm–Liouville differential equation with an integral boundary coupled hybrid condition. We give an application and some examples to illustrate our results.

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