Axioms, Volume 11, Issue 7 (July 2022) – 53 articles

The goal of this paper is to propose and investigate new iterative methods for examining an approximate solution of a fixed-point problem, an equilibrium problem, and a finite collection of variational inclusions in the Hadamard manifold’s structure. Operating under some assumptions, we extend the proximal point algorithm to estimate the common solution of stated problems and obtain a strong convergence theorem for the common solution. We also present several consequences of the proposed iterative methods and their convergence results. Full article

We consider the foundational relation between arithmetic and set theory. Our goal is to criticize the construction of standard arithmetic models as providing grounds for arithmetic truth. Our method is to emphasize the incomplete picture of both theories and to treat models as their syntactical counterparts. Insisting on the incomplete picture will allow us to argue in favor of the revisability of the standard-model interpretation. We start briefly characterizing the expansion of arithmetic ‘truth’ provided by the interpretation in a set theory. Interpreted versions of an arithmetic theory into set theories generally have more theorems than the original. This theorem expansion is not complete however. Using this, the set theoretic multiversalist concludes that there are multiple legitimate standard models of arithmetic. We suggest a different multiversalist conclusion: while there is a single arithmetic structure, its interpretation in each universe may vary or even not be possible. We continue by defining the coordination problem. We consider two independent communities of mathematicians responsible for deciding over new axioms for ZF and PA. How likely are they to be coordinated regarding PA’s interpretation in ZF? We prove that it is possible to have extensions of PA not interpretable in a given set theory ST. We further show that the number of extensions of arithmetic is uncountable, while interpretable extensions in ST are countable. We finally argue that this fact suggests that coordination can only work if it is assumed from the start. Full article

The fractional Langevin equation has more advantages than its classical equation in representing the random motion of Brownian particles in complex viscoelastic fluid. The Mittag–Leffler (ML) fractional equation without singularity is more accurate and effective than Riemann–Caputo (RC) and Riemann–Liouville (RL) fractional equation in portraying Brownian motion. This paper focuses on a nonlinear ML-fractional Langevin system with distributed lag and integral control. Employing the fixed-point theorem of generalised metric space established by Diaz and Margolis, we built the Hyers–Ulam–Rassias (HUR) stability along with Hyers–Ulam (HU) stability of this ML-fractional Langevin system. Applying our main results and MATLAB software, we have carried out theoretical analysis and numerical simulation on an example. By comparing with the numerical simulation of the corresponding classical Langevin system, it can be seen that the ML-fractional Langevin system can better reflect the stationarity of random particles in the statistical sense. Full article

Let R be a commutative ring with unity. The unit graph $G\left(R\right)$ is defined such that the vertex set of $G\left(R\right)$ is the set of all elements of R, and two distinct vertices are adjacent if their sum is a unit in $R.$ In this paper, we show that for each prime, $p,G\left(Z_p\right)$ and $G\left(Z_{2p}\right)$ are eigensharp graphs. Likewise, we show that the unit graph associated with the ring ${}^{Z_p\left[x\right]}{∕}_{⟨x^2⟩}$ is an eigensharp graph. Full article

An implicit time–fractal–fractional differential equation involving the Atangana’s fractal–fractional derivative in the sense of Caputo with the Mittag–Leffler law type kernel is studied. Using the Banach fixed point theorem, the well-posedness of the solution is proved. We show that the solution exhibits an exponential growth bound, and, consequently, the long-time (asymptotic) property of the solution. We also give examples to illustrate our problem. Full article

In this paper, based on the Euler equation and mass conservation equation in spherical coordinates, the ratio of the stratospheric average width to the planetary radius and the ratio of the vertical velocity to the horizontal velocity are selected as parameters under appropriate boundary conditions. We establish the approximate system using these two small parameters. In addition, we consider the time dependence of the system and establish the governing equations describing the atmospheric flow. By introducing a flow function to code the system, a nonlinear vorticity equation describing the planetary flow in the stratosphere is obtained. The governing equations describing the atmospheric flow are transformed into a second-order homogeneous linear ordinary differential equation and a Legendre’s differential equation by applying the method of separating variables based on the concepts of spherical harmonic functions and weak solutions. The Gronwall inequality and the Cauchy–Schwartz inequality are applied to priori estimates for the vorticity equation describing the stratospheric planetary flow under the appropriate initial and boundary conditions. The existence and non-uniqueness of weak solutions to the vorticity equation are obtained by using the functional analysis technique. Full article

Regular physical activity has a positive impact on our physical and mental health. Adhering to a fixed physical activity regimen is essential for good health and mental wellbeing. Today, fitness trackers and smartphone applications are used to promote physical activity. These applications use step counts recorded by accelerometers to estimate physical activity. In this research, we performed a two-level clustering on a dataset based on individuals’ physical and physiological features, as well as past daily activity patterns. The proposed model exploits the user data with partial or complete features. To include the user with partial features, we trained the proposed model with the data of users who possess exclusive features. Additionally, we classified the users into several clusters to produce more accurate results for the users. This enables the proposed system to provide data-driven and personalized activity planning recommendations every day. A personalized physical activity plan is generated on the basis of hourly patterns for users according to their adherence and past recommended activity plans. Customization of activity plans can be achieved according to the user’s historical activity habits and current activity objective, as well as the likelihood of sticking to the plan. The proposed physical activity recommendation system was evaluated in real time, and the results demonstrated the improved performance over existing baselines. Full article

Many immigrants have risked their lives searching for a better future by crossing the Mediterranean Sea or the Atlantic Ocean. The Canary Islands became the centre of another emerging humanitarian and human rights crisis at Europe’s frontier in 2020. The study aims to analyse whether attitudes towards immigrants are affected by territories close to these humanitarian crises. To this end, the study is based on previous studies using a Fuzzy-Hybrid TOPSIS method to analyse attitudes toward immigrants. The synthetic indicator will be built upon a set of eight indicators that proxy the ethnic, economic, cultural, and religious threats experienced by the citizens. The International Social Survey Program (ISSP) dataset for the year 2013 for six countries, namely Belgium, Germany, Spain, France, United Kingdom, and Portugal, will be used. Results show that the attitude toward immigrants is affected by the territorial dimension as classified by the nomenclature of territorial units for statistics at NUTS2 and NUTS3 levels, and that attitudes are very different between those of some of the archipelagos and islands considered in the study. In particular, our results point out a sort of duality between the Balearic Islands—the most open territory toward immigrants, and Corse—the least open territory toward immigrants. Full article

In this paper, we first give some results on monic generalized Hermite polynomials (GHP) ${\{H_n^{(\mu )}(x)\}}_{n\ge 0}$, orthogonal with respect to the positive weight ${\left|x\right|}^{2\mu }{e}^{-x^2},\mu >-\frac{1}{2},x\in \mathbb{R}$, which will lead to the formulation of the second-order spectralvectorial differential equation (SVDE) that the GHP satisfies. This SVDE differs from the one given in G. Szego (problem 25. p. 380), which is a pseudo-spectral equation. Second, we give the SVDE, as conjecture, satisfied by the generalized Jacobi polynomials $J_n^{(\alpha ,\alpha +1)}(x,\mu )$, orthogonal with respect to the positive weight $w(x,\alpha ;\mu )={\left|x\right|}^{-\mu }{(1-x^2)}^{\alpha }(1-x),$$\mu <1,$$\alpha >-1$ on $[-1,1]$. Full article

This paper searches for optimal strategies for the minimization of the number of high-risk latent and active tuberculosis (TB) infectious individuals using real data from Ethiopia. Optimal control theory is harnessed for investigation and analysis of the optimal combination of interventions for controlling the transmission of TB using distancing, case finding, and case holding as controls. We calculate and compare the incremental cost-effectiveness ratio (ICER) for each of the strategies to determine the most effective combination of interventions for curbing the spread of the disease. Our findings suggest that, for optimal cost-effective management of the TB disease, the government of Ethiopia must focus more on prevention strategies such as isolation of infectious people, early TB patient detection, treatment, and educational programs. The optimal strategy is quantified through simulation. Full article

In this paper, we explore Ramanujan-type congruences modulo 4 for the function ${\sigma }_0\left(n\right)$, counting the positive divisors of n. We consider relations of the form ${\sigma }_0\left(8(\alpha n+\beta )+r\right)\equiv 0(mod4),$ with $(\alpha ,\beta )\in {\mathbb{N}}^2$ and $r\in \{1,3,5,7\}$. In this context, some conjectures are made and some Ramanujan-type congruences involving overpartitions are obtained. Full article

Much attention is focused on the relationship between rough sets and many-valued modal logic to deal with approximate reasoning. This paper discusses the graded modal logic and puts forward the graded many-valued modal logic G(S5). Secondly, by employing the graded operators that correspond to graded modal operations in G(S5), we introduce the concept of graded upper and lower rough truth degrees of a logical formula. Then, we propose the graded upper and lower conditional rough truth degrees. Several basic interesting properties are addressed. Finally, in order to make a distinction between any two rough formulas in graded many-valued modal logic, the graded upper and lower rough similarity degrees between two graded modal formulas are established in a very natural way. Full article

This paper introduces the implicative derivations and gives some of their characterizations on MTL-algebras. Furthermore, we provide some representation of MTL-algebras by implicative derivations and obtain some representation of Boolean algebra via the algebra of all implicative derivations. Finally, we explore the relationship between implicative derivation and other operators on MTL-algebras and show that there exists a bijection between the sets of multiplier and implicative derivations on IMTL-algebras. The results of this paper can provide the common properties of implicative derivations in the t-norm-based fuzzy logical algebras. Full article

This study analyzes whether Bitcoin, gold, oil, and stock have the ability to hedge against inflation in high cryptocurrency adoption countries in the periods from January 2010 to March 2021. It is hypothesized that the assets behave differently and thereby respond differently to inflation in different market conditions. Therefore, we employ the Markov Switching Vector Autoregressive to examine these assets’ hedging ability against inflation in both stable and turbulent market regimes. Our main findings are threefold: We show that there exists a structural change and nonlinear relationship between the returns of hedging assets and inflation. Second, all assets can hedge against inflation more effectively in the short run than in the long run. We find that the inflation hedging ability of these assets are weak in the long run for both market regimes. We also find some evidence that the rigidity between the assets and inflation is relatively high in the stable regime. Third, according to the impulse response analysis, we also find that the responses of assets to inflation shock are heterogeneous across two market regimes. Full article

The advent of intelligent technology has spurred most large companies to introduce business intelligence systems (BIS), but those with low information maturity still have a wait-and-see attitude towards BIS. In order to accelerate the introduction of BIS, this study found and analyzed the critical factors (CFs) considered by companies when introducing BIS. First, the literature on factors considered by companies to introduce BIS was reviewed. The three stages before, during, and after introduction in marketing that organizations undergo during the procurement process were developed into a three-layer hierarchy factor table. An expert questionnaire with pairwise factors was then designed and sent to senior executives in companies that had introduced BIS, and the weights of all factors were calculated by the fuzzy analytic hierarchy process (FAHP) based on the collected questionnaire data. After this, four critical factors—system function integrity, approaching corporate strategy, licensing fee, and information technology maturity—were determined objectively by using the conditions for the acceptable advantage of Vlse Kriterijumska Optimizacija Kompromisno Resenje (VIKOR) and further explored in order to help companies input fewer resources, introduce BIS efficiently, and thus increase their decision-making power. Full article

This article revisits the stability property of a symbiotic model of commensalism with Michaelis–Menten type harvesting in the first commensal populations. By constructing some suitable Lyapunov functions, we provide a thorough analysis of the dynamic behaviors of the subsystem composed of the second and third species. After that, by applying the stability results of this subsystem and combining with the differential inequality theory, sufficient conditions which ensure the global attractivity of the equilibria are obtained. The results obtained here essentially improve and generalize some known results. Full article

In the present paper, we prove some new reverse type dynamic inequalities on $\mathbb{T}$. Our main inequalities are proved by using the chain rule and Fubini’s theorem on time scales $\mathbb{T}$. Our results extend some existing results in the literature. As special cases, we obtain some new discrete inequalities, quantum inequalities and integral inequalities. Full article

In this work, we study the global existence of solutions reaction-diffusion systems with control of mass on multiple domains. Some of these domains overlap, and as a result, an unknown defined on one subdomain can impact another unknown defined on a different domain that intersects with the first. The question addressed is related to the long standing question of global existence for reaction-diffusion systems with quasi-positive reaction vector fields that dissipate mass, in the setting of a single bounded spatial domain. The results extend recent work of the authors and others for systems on a single domain with $L^{\infty }$ diffusion and quasi-positive reaction vector fields that dissipate mass, in the setting of multiple domains. Full article

This paper deals with the mathematical modelling of the red palm weevil (RPW), Rhynchophorus ferrugineus (Olivier) (Coleoptera: Curculionidae), in date palms using chemical control by utilizing injection and sex pheromone traps. A deterministic and stochastic model for RPW is proposed and analyzed. The existence of a positive global solution for the stochastic RPW model is investigated, and the conditions for the extinction of RPWs from the stochastic system are obtained. The adequate criteria for the presence of a unique ergodic stationary distribution for the RPW system are established by creating suitable Lyapunov functions. The impact of chemical injection and pheromone traps on RPW is demonstrated. The importance of environmental noise on RPW is highlighted and simulated using the Milstein method. Full article

Based on GM (0,N) grey model and grey structure model in grey system theory, this study takes Chinese restaurant in tourist hotel as a case to analyze service role behavior. A total of 241 questionnaires were collected to calculate index weighted coefficients, and then 12 experts carried out an investigation to construct clusters. There were 12 dimensions of professional competencies, and a total of 50 indicator factors were analyzed for role behavior in a restaurant. According to the results, there are three role behaviors for service staff in Chinese restaurants: supportive, interactive, and integrative role behaviors. In theory, this reinterprets the meaning of catering service competencies and defines the role types of catering service staff. In practical applications, restaurant managers could apply this result to help service staff to understand their current role, in order to reduce their role pressure and to increase their job satisfaction and performance. Full article

The purpose of this article is to introduce to the literature a new extension of the Simple WISP method adapted for utilizing the triangular fuzzy numbers. This extension is proposed to allow the use of the Simple WISP method for addressing decision-making problems related to uncertainties and inaccuracies, as well as for solving problems related to predictions. In addition, this article also discusses the use of linguistic variables to collect the attitudes of the respondents, as well as their transformation into appropriate triangular fuzzy numbers. The article discusses the use of two defuzzification procedures. The first normalization procedure is easy to use, while the second procedure uses the advantages that the application of asymmetric fuzzy numbers gives in terms of analysis. The usability of the proposed extension is presented through two examples. Full article

The Brazilian Federal Highway Patrol is an organ of public administration with the constitutional mission to carry out the extensive patrolling of federal highways. Stress and physical and emotional exhaustion are constant, causing illnesses along with frustration, demotivation, and depression. The objective of this research is the development of a self-evaluation model of performance for the Federal Highway Patrols, using their perceptions to enhance their motivation at work considering the factors under their control. The constructivist multi-criteria decision aid (MCDA-C) methodology was used to elaborate the model. The proposed model identifies, establishes, and structures a process to measure the performance of patrol officers on the relevant aspects that they can manage, to guide their decisions toward the desired consequences, thus regulating their stress levels. Full article

In this article, we prove that the $⟨p,q⟩$ condition holds, first by using the Fuchs index of the complex Kawahara equation, and then proving that all meromorphic solutions of complex Kawahara equations belong to the class W. Moreover, the complex method is employed to get all meromorphic solutions of complex Kawahara equation and all traveling wave exact solutions of Kawahara equation. Our results reveal that all rational solutions $u_r(x+\nu t)$ and simply periodic solutions $u_{s,1}(x+\nu t)$ of Kawahara equation are solitary wave solutions, while simply periodic solutions $u_{s,2}(x+\nu t)$ are not real-valued. Finally, computer simulations are given to demonstrate the main results of this paper. At the same time, we believe that this method is a very effective and powerful method of looking for exact solutions to the mathematical physics equations, and the search process is simpler than other methods. Full article

In this paper, a mathematical model for African swine fever is modified by considering the swine farm with the contaminated human vector that is able to infect and spread the disease among swine farms. In the developed model, we have divided the swine farm density into three related groups, namely the susceptible swine farm compartment, latent swine farm compartment, and infectious swine farm compartment. On the other hand, the human vector population density has been separated into two classes, namely the susceptible human vector compartment and the infectious human vector compartment. After that, we use this model and a quarantine strategy to analyze the spread of the infection. In addition, the basic reproduction number $R_0$ is determined by using the next-generation matrix, which can analyze the stability of the model. Finally, the numerical simulations of the proposed model are illustrated to confirm the results from theorems. The results showed that the transmission coefficient values per unit of time per individual between the human vector and the swine farm resulted in the spread of African swine fever. Full article

Let $\mathcal{R}$ be a commutative ring with unity and $\mathcal{T}$ be a triangular algebra over $\mathcal{R}$. Let a sequence $\Delta ={\left\{{\delta }_n\right\}}_{n\in \mathbb{N}}$ of nonlinear mappings ${\delta }_n:\mathcal{T}\to \mathcal{T}$ is a Lie triple higher derivation by local actions satisfying the equation. Under some mild conditions on $\mathcal{T}$, we prove in this paper that every Lie triple higher derivation by local actions on the triangular algebras is proper. As an application, we shall give a characterization of Lie triple higher derivations by local actions on upper triangular matrix algebras and nest algebras, respectively. Full article

Existence and uniqueness of solutions for a simplified model of immiscible two-phase flow in porous media are obtained in this paper. The mathematical model is a simplified physical model with hysteresis in the flux functions. The resulting semilinear hyperbolic-parabolic equation is expected from numerical work to admit non-monotone imbibition-drainage fronts. We prove the local existence of imbibition-drainage fronts. The uniqueness, global existence, maximal regularity and boundedness of the solutions are also discussed. Methodically, the results are established by means of semigroup theory and fractional interpolation spaces. Full article

In this paper, we define surfaces of revolution without parabolic points in three-dimensional Lorentz–Minkowski space. Then, we classify this class of surfaces under the condition ${\Delta }^{III}\mathit{x}=A\mathit{x}$, where ${\Delta }^{III}$ is the Laplace operator regarding the third fundamental form, and A is a real square matrix of order 3. We prove that such surfaces are either catenoids or surfaces of Enneper, or pseudo spheres or hyperbolic spaces centered at the origin. Full article

In recent years, efficient processes have become increasingly important because of high-level competition in the production industry. The concept of Industry 4.0 is a relatively new and effective method for managing production processes. Because the Industry 4.0 implementation process includes connections between objects, humans, and systems, it is quite difficult to evaluate and measure the performance. At this stage, performance criteria can be applied. However, linguistic evaluation of criteria makes the problem too complicated to solve. The purpose of this paper is to present a novel fuzzy performance measurement model for Industry 4.0 in small and medium-sized manufacturing firms. A hybrid spherical fuzzy analytic hierarchy process (SF-AHP)—weighted score methodology (WSM) is proposed for the performance measurement and scoring process. In the application part of this paper, the propounded methodology was applied to five companies. The results of this study can be used as a reference for experts in the performance measurement of the Industry 4.0 process. Full article

In this article, we derive Chen’s inequalities involving Chen’s $\delta$-invariant ${\delta }_M$, Riemannian invariant $\delta (m_1,\cdots ,m_k)$, Ricci curvature, Riemannian invariant ${\mathsf{\Theta }}_k(2\le k\le m)$, the scalar curvature and the squared of the mean curvature for submanifolds of generalized Sasakian-space-forms endowed with a quarter-symmetric connection. As an application of the obtain inequality, we first derived the Chen inequality for the bi-slant submanifold of generalized Sasakian-space-forms. Full article

In this paper, we extend some Steffensen-type inequalities to time scales by using the diamond-$\alpha$-dynamic integral. Further, we prove some new Steffensen-type inequalities for convex functions utilizing positive $\sigma$-finite measures in time scale calculus. Moreover, as a special case, we obtain these inequalities for the delta and the nabla integral. By using the relation between calculus on time scales $\mathbb{T}$ and differential calculus on $\mathbb{R}$, we obtain already-known Steffensen-type inequalities. Full article