Axioms doi: 10.3390/axioms12060530

Authors: Mohammad Sajid Harindri Chaudhary Santosh Kaushik

In this paper, we primarily investigate the methodology for the hybrid complex projective synchronization (HCPS) scheme in non-identical complex fractional order chaotic systems via an active complex synchronization technique (ACST). Appropriate controllers of a nonlinear type are designed in view of master&ndash;slave composition and Lyapunov&rsquo;s stability criterion (LSC). The HCPS is an extended version of the previously designed projective synchronization scheme. In the HCPS scheme, by using a complex scale matrix, the system taken as slave system is asymptotically synchronized with another system taken as the master system. By utilizing a complex scale matrix, the unpredictability and security of communication are increased along with image encryption. An efficient computational method has been employed to validate and visualize the HCPS method&rsquo;s efficacy by performing numerical simulation outcomes in MATLAB.

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Authors: Tamas Galli Francisco Chiclana Francois Siewe

The authors&rsquo; previously published research delved into the theory of software product quality modelling, model views, concepts, and terminologies. They also analysed this specific field from the point of view of uncertainty, and possible descriptions based on fuzzy set theory and fuzzy logic. Laying a theoretical foundation was necessary; however, software professionals need a more tangible and practical approach for their everyday work. Consequently, the authors devote this paper to filling in this gap; it aims to illustrate how to interpret and utilise the previous findings, including the established taxonomy of the software product quality models. The developed fuzzy model&rsquo;s simplification is also presented with a Generalized Additive Model approximation. The paper does not require any formal knowledge of uncertainty computations and reasoning under uncertainty, nor does it need a deep understanding of quality modelling in terms of terminology, concepts, and meta-models, which were necessary to prepare the taxonomy and relevance ranking. The paper investigates how to determine the validity of statements based on a given software product quality model; moreover, it considers how to tailor and adjust quality models to the particular project&rsquo;s needs. The paper also describes how to apply different software product quality models for different quality views to take advantage of the automation potential offered for the measurement and assessment of source code quality. Furthermore, frequent pitfalls are illustrated with their corresponding resolutions, including an unmeasured quality property that is found to be important and needs to be included in the measurement and assessment process.

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Authors: Huyen Trang Nguyen Ta-Chung Chu

In entrepreneurship management, the evaluation and selection of startups for acceleration programs, especially technology-based startups, are crucial. This process involves considering numerical and qualitative criteria such as sales, prior startup experience, demand validation, and product maturity. To effectively rank startups based on the varying importance of these criteria, a fuzzy multi-criteria decision-making (MCDM) approach is needed. Although MCDM methods have been successful in handling complex problems, their application in startup selection and evaluating criteria interrelationships from the accelerator perspective is underexplored. To address this gap, a hybrid DEMATEL-ANP-based fuzzy PROMETHEE II model is proposed in this study, facilitating startup ranking and examining interrelationships among factors. The resulting preference values are fuzzy numbers, necessitating a fuzzy ranking method for decision-making. An extension of ranking fuzzy numbers using a spread area-based relative maximizing and minimizing set is suggested to enhance the flexibility of existing ranking MCDM methods. Algorithms, formulas, and a comparative analysis validate the proposed method, while a numerical experiment verifies the viability of the hybrid model. The final ranking of four startup projects is A4&lt;A1&lt;A3&lt;A2 which indicates that startup project A2 has the highest comprehensive potential, followed by startup project A3.

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Authors: Muhammad Shoaib Arif Kamaleldin Abodayeh Yasir Nawaz

To boost productivity, commercial strategies, and social advancement, neural network techniques are gaining popularity among engineering and technical research groups. This work proposes a numerical scheme to solve linear and non-linear ordinary differential equations (ODEs). The scheme&rsquo;s primary benefit included its third-order accuracy in two stages, whereas most examples in the literature do not provide third-order accuracy in two stages. The scheme was explicit and correct to the third order. The stability region and consistency analysis of the scheme for linear ODE are provided in this paper. Moreover, a mathematical model of heat and mass transfer for the non-Newtonian Casson nanofluid flow is given under the effects of the induced magnetic field, which was explored quantitatively using the method of Levenberg&ndash;Marquardt back propagation artificial neural networks. The governing equations were reduced to ODEs using suitable similarity transformations and later solved by the proposed scheme with a third-order accuracy. Additionally, a neural network approach for input and output/predicted values is given. In addition, inputs for velocity, temperature, and concentration profiles were mapped to the outputs using a neural network. The results are displayed in different types of graphs. Absolute error, regression studies, mean square error, and error histogram analyses are presented to validate the suggested neural networks&rsquo; performance. The neural network technique is currently used on three of these four targets. Two hundred points were utilized, with 140 samples used for training, 30 samples used for validation, and 30 samples used for testing. These findings demonstrate the efficacy of artificial neural networks in forecasting and optimizing complex systems.

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Authors: Muhammad Amin Hajra Ashraf Hassan S. Bakouch Najla Qarmalah

The beta regression model (BRM) is used when the dependent variable may take continuous values and be bounded in the interval (0, 1), such as rates, proportions, percentages and fractions. Generally, the parameters of the BRM are estimated by the method of maximum likelihood estimation (MLE). However, the MLE does not offer accurate and reliable estimates when the explanatory variables in the BRM are correlated. To solve this problem, the ridge and Liu estimators for the BRM were proposed by different authors. In the current study, the James Stein Estimator (JSE) for the BRM is proposed. The matrix mean squared error (MSE) and the scalar MSE properties are derived and then compared to the available ridge estimator, Liu estimator and MLE. The performance of the proposed estimator is evaluated by conducting a simulation experiment and analyzing two real-life applications. The MSE of the estimators is considered as a performance evaluation criterion. The findings of the simulation experiment and applications indicate the superiority of the suggested estimator over the competitive estimators for estimating the parameters of the BRM.

]]>Axioms doi: 10.3390/axioms12060525

Authors: Shuai Wu Qingxia Li Wenhong Wei

Path planning is an important area of mobile robot research, and the ant colony optimization algorithm is essential for analyzing path planning. However, the current ant colony optimization algorithm applied to the path planning of mobile robots still has some limitations, including early blind search, slow convergence speed, and more turns. To overcome these problems, an improved ant colony optimization algorithm is proposed in this paper. In the improved algorithm, we introduce the idea of triangle inequality and a pseudo-random state transfer strategy to enhance the guidance of target points and improve the search efficiency and quality of the algorithm. In addition, we propose a pheromone update strategy based on the partition method with upper and lower limits on the pheromone concentration. This can not only improve the global search capability and convergence speed of the algorithm but also avoid the premature and stagnation phenomenon of the algorithm during the search. To prevent the ants from getting into a deadlock state, we introduce a backtracking mechanism to enable the ants to explore the solution space better. Finally, to verify the effectiveness of the proposed algorithm, the algorithm is compared with 11 existing methods for solving the robot path planning problem, including several ACO variants and two commonly used algorithms (A* algorithm and Dijkstra algorithm), and the experimental results show that the improved ACO algorithm can plan paths with faster convergence, shorter path lengths, and higher smoothness. Specifically, the algorithm produces the shortest path length with a standard deviation of zero while ensuring the most rapid convergence and the highest smoothness in the case of the shortest path in four different grid environments. These experimental results demonstrate the effectiveness of the proposed algorithm in path planning.

]]>Axioms doi: 10.3390/axioms12060524

Authors: Albertus Untadi Lily D. Li Michael Li Roland Dodd

Fires in buildings are significant public safety hazards and can result in fatalities and substantial financial losses. Studies have shown that the socioeconomic makeup of a region can impact the occurrence of building fires. However, existing models based on the classical stepwise regression procedure have limitations. This paper proposes a more accurate predictive model of building fire rates using a set of socioeconomic variables. To improve the model&rsquo;s forecasting ability, a backward elimination by robust final predictor error (RFPE) criterion is introduced. The proposed approach is applied to census and fire incident data from the South East Queensland region of Australia. A cross-validation procedure is used to assess the model&rsquo;s accuracy, and comparative analyses are conducted using other elimination criteria such as p-value, Akaike&rsquo;s information criterion (AIC), Bayesian information criterion (BIC), and predicted residual error sum of squares (PRESS). The results demonstrate that the RFPE criterion is a more accurate predictive model based on several goodness-of-fit measures. Overall, the RFPE equation was found to be a suitable criterion for the backward elimination procedure in the socioeconomic modeling of building fires.

]]>Axioms doi: 10.3390/axioms12060523

Authors: Dur-e-Shehwar Sagheer Isma Urooj Samina Batul Ahmad Aloqaily Nabil Mlaiki

In this study, we present a more general class of rational-type contractions in the domain of Hilbert spaces, along with a novel coupled implicit relation. We develop several intriguing results and consequences for the existence of unique coupled fixed points. Further, we investigate a necessary condition that guarantees the well-posedness of a coupled fixed-point problem of self-mappings in Hilbert spaces. Some new observations proposed in this research broaden and extend previously published results in the literature.

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Authors: Najla Altwaijry Silvestru Sever Dragomir Kais Feki

This paper presents new results related to Bombieri&rsquo;s generalization of Bessel&rsquo;s inequality in a semi-inner product space induced by a positive semidefinite operator A. Specifically, we establish new inequalities that generalize the classical Bessel inequality and extend previous results in this area. Furthermore, our findings have applications to the study of operators on positive semidefinite inner product spaces, also known as semi-Hilbert spaces, and contribute to a deeper understanding of their properties and applications. Our work has implications for various fields, including functional analysis and operator theory.

]]>Axioms doi: 10.3390/axioms12060521

Authors: Chenwei Liu Shuwen Xiang Yanlong Yang

In this paper, we propose a characteristic function of the maxmax defensive-equilibrium representation that maps every TU-game with strategies to a TU-game. This characteristic function is given by a two-step procedure in which each of any two complementary coalitions successively selects the equilibrium in a way that maximizes its utility. We then investigate the properties of this characteristic function and present the relations of the cores under three characteristic functions. Finally, as applications of our findings, we provide a firm production advertising game, a supply chain network game, a cost game with strategies, and a Cournot game.

]]>Axioms doi: 10.3390/axioms12060520

Authors: Maxim Korolev Antanas Laurinčikas

This paper is devoted to the approximation of a certain class of analytic functions by shifts Z(s+i&tau;), &tau;&isin;R, of the modified Mellin transform Z(s) of the square of the Riemann zeta-function &zeta;(1/2+it). More precisely, we prove the existence of a closed non-empty set F such that there are infinitely many shifts Z(s+i&tau;), which approximate a given analytic function from F with a given accuracy. In the proof, the weak convergence of measures in the space of analytic functions is applied. Then, the set F coincides with the support of a limit measure.

]]>Axioms doi: 10.3390/axioms12060519

Authors: Yan-Nan Chen Kang-Jia Wang

In the present study, two effective methods, the Exp-function method and He&rsquo;s frequency formulation, are employed to investigate the dynamic behaviors of the (3+1)-dimensional Boiti&ndash;Leon&ndash;Manna&ndash;Pempinelli equation, which is used widely to describe the incompressible fluid. A variety of the wave structures, including the dark wave, bright-dark wave and periodic wave solutions, are successfully constructed. Compared with the results attained by the methods, the obtained solutions are all new and have not been presented in the other literature. The diverse wave structures of the solutions are presented through numerical results in the form of three-dimensional plots and two-dimensional curves. It reveals that the proposed methods are powerful and straightforward, which are expected to be helpful for the study of travelling-wave theory in fluid.

]]>Axioms doi: 10.3390/axioms12060518

Authors: Slobodanka Mitrović Nicola Fabiano Slobodan Radojević Stojan Radenović

Since 1964, when I.A. Perov introduced the so-called generalized metric space where d(x,y) is an element of the vector space Rm, many researchers have considered various contractive conditions in this type of space. In this paper, we generalize, extend and unify some of those established results. We are primarily concerned with examining the existence of a fixed point of some mapping from X to itself, but if (x,y) belongs to some relation R on the set X, then the binary relation R and some F contraction defined on the space cone Rm are combined. We start our consideration with the recently announced results and give them strict, critical remarks. In addition, we improve several announced results by weakening some of the given conditions.

]]>Axioms doi: 10.3390/axioms12060517

Authors: Bahtiyar Bayraktar Péter Kórus Juan Eduardo Nápoles Valdés

In this study, we present new variants of the Hermite&ndash;Hadamard inequality via non-conformable fractional integrals. These inequalities are proven for convex functions and differentiable functions whose derivatives in absolute value are generally convex. Our main results are established using the classical Jensen&ndash;Mercer inequality and its variants for (h,m)-convex modified functions proven in this paper. In addition to showing that our results support previously known results from the literature, we provide examples of their application.

]]>Axioms doi: 10.3390/axioms12060516

Authors: Maghsoud Amiri Mohammad Hashemi-Tabatabaei Mehdi Keshavarz-Ghorabaee Jurgita Antucheviciene Jonas Šaparauskas Mohsen Keramatpanah

Modern technologies have changed human life and created a generation of customers who have different needs compared to the past. Considering Industry 4.0 and its drivers, the implementation of digital banking (DB) has faced various challenges that are caused by emerging trends. Both Industry 4.0 and DB are contemporary concepts, and decision-makers are often faced with uncertainties in their decisions regarding the implementation of DB and its indicators. For this purpose, a novel multi-criteria group decision-making approach has been developed utilizing the best&ndash;worst method (BWM) and &alpha;-cut analysis as well as trapezoidal fuzzy numbers (TFNs). By reviewing the literature and using experts&rsquo; opinions, the DB implementation criteria are determined, and considering an uncertain environment, the criteria are prioritized using the proposed method. Then, the available DB models and alternatives are examined based on the decision criteria and the importance of each criterion. This research contributes to the existing literature by identifying and prioritizing the criteria necessary for the successful implementation of DB, taking into account emerging trends and technological advances driven by Industry 4.0. Subsequently, the study prioritizes the prevalent models of DB based on these criteria. This study proposes a decision-support framework for dealing with ambiguity, lack of information, insufficient knowledge, and uncertainty in decision-making. The framework uses TFNs to account for imprecision and doubt in decision-makers&rsquo; preferences. Additionally, the study presents a fuzzy multi-criteria group decision-making approach that enables a group of experts to arrive at more reliable results. The proposed approach can help improve the quality of decision-making in complex and uncertain situations. The results of this research show that human resources, rules and regulations, and customer satisfaction are the most important criteria for implementing DB. In addition, the open, blockchain, and social banking models are the crucial models that significantly cover the implementation criteria for DB.

]]>Axioms doi: 10.3390/axioms12060514

Authors: Mircea Merca

For each s&isin;{1,3,5}, we consider Rs(n) to be the number of the partitions of n into parts not congruent to 0, &plusmn;s(mod12). In recent years, some relations for computing the value of R3(n) were studied. In this paper, we investigate the parity of Rs(n) when s&isin;{1,5} and derive the following congruence identity: &sum;n=1&infin;(&minus;q;q)n&minus;12(1+qn)qn2(q;q)2n&equiv;&sum;n=1&infin;qn2+q3n2(mod2). For each s&isin;{1,5}, the number of the partitions of n into parts not congruent to 0, &plusmn;s(mod12) is connected with two truncated theta series. Some open problems involving R1(n) and R5(n) are introduced in this context.

]]>Axioms doi: 10.3390/axioms12060515

Authors: Shashi Bhushan Anoop Kumar Najwan Alsadat Manahil SidAhmed Mustafa Meshayil M. Alsolmi

Ranked set sampling (RSS) has been proven an efficient alternative to simple random sampling (SRS). The use of auxiliary information also helps to improve the efficiency of the estimation procedures. Therefore, to accomplish higher efficiency and discuss the optimality issues, we proffer some optimal classes of estimators under RSS by employing multi-auxiliary information. It is seen that the ordinary mean estimator, traditional regression, and ratio estimators are the subsets of the proffered estimators. The expressions of the bias and mean square error are reported. An analytical comparison under some optimality conditions points out the ascendancy of the proffered classes of estimators over all reviewed works. The theoretical results have been furnished with computational study by employing some artificial and natural populations. The computational results show that the proffered estimators outperform the conventional estimators reviewed in this study. Furthermore, apposite advices are suggested to the survey persons.

]]>Axioms doi: 10.3390/axioms12060513

Authors: Chunli Li Wenchang Chu

Two general transformations for hypergeometric series are examined by means of the coefficient extraction method. Several interesting closed formulae are shown for infinite series containing harmonic numbers and binomial/multinomial coefficients. Among them, three conjectured identities due to Z.-W. Sun are also confirmed.

]]>Axioms doi: 10.3390/axioms12060512

Authors: Abdullah Alsoboh Ala Amourah Fethiye Müge Sakar Osama Ogilat Gharib Mousa Gharib Nasser Zomot

The paper introduces a new family of analytic bi-univalent functions that are injective and possess analytic inverses, by employing a q-analogue of the derivative operator. Moreover, the article establishes the upper bounds of the Taylor&ndash;Maclaurin coefficients of these functions, which can aid in approximating the accuracy of approximations using a finite number of terms. The upper bounds are obtained by approximating analytic functions using Faber polynomial expansions. These bounds apply to both the initial few coefficients and all coefficients in the series, making them general and early, respectively.

]]>Axioms doi: 10.3390/axioms12060511

Authors: Wenyu Zhang Mengyao Cao Lei Wang

With the development of the cloud computing era, the decision-making environment and algorithm models have become increasingly complex, and traditional decision-making methods have been unable to meet the needs of large group decision-making (LGDM) problems. Firstly, in order to solve this problem, the concept of double hierarchy interval hesitant fuzzy language (DHIHFL) is proposed. Compared with the traditional double hierarchy hesitant fuzzy language (DHHFL), it contains all elements from the lower limit to the upper limit and more comprehensively characterizes the hesitation of language information. Secondly, for LGDM problems, a self-confident double hierarchy interval hesitant fuzzy language (SC-DHIHFL) is developed, and the integration of self-confident degree can better enrich the evaluation information and promote the achievement of group consensus. Thirdly, a new two-stage LGDM method is proposed. The first stage is clustering and grouping and reaching consensus within the group, and the second stage is the integration of LGDM information. The two-stage method contains novel methods such as expert clustering algorithm, subjective and objective comprehensive weight, consensus degree, and deviation weight considering minority opinions. Finally, the proposed LGDM consensus method is applied to a practical LGDM problem, and the effectiveness is verified by comparative analysis with existing methods.

]]>Axioms doi: 10.3390/axioms12060510

Authors: Abdullah Lotfi Abbe Mowshowitz Matthias Dehmer

This note is intended as a contribution to the study of quantitative measures of graph complexity that use entropy measures based on symmetry. Determining orbit sizes of graph automorphism groups is a key part of such studies. Here we focus on an extreme case where every orbit contains just a single vertex. A permutation of the vertices of a graph G is an automorphism if, and only if, the corresponding permutation matrix commutes with the adjacency matrix of G. This fact establishes a direct connection between the adjacency matrix and the automorphism group. In particular, it is known that if the eigenvalues of the adjacency matrix of G are all distinct, every non-trivial automorphism has order 2. In this note, we add a condition to the case of distinct eigenvalues that makes the graph asymmetric, i.e., reduces the automorphism group to the identity alone. In addition, we prove analogous results for the Google and Laplacian matrices. The condition is used to build an O(n3) algorithm for detecting identity graphs, and examples are given to demonstrate that it is sufficient, but not necessary.

]]>Axioms doi: 10.3390/axioms12060509

Authors: Ivan Košanin Milan Gnjatović Nemanja Maček Dušan Joksimović

This paper introduces a parameter-free clustering-based approach to detecting critical traffic road segments in urban areas, i.e., road segments of spatially prolonged and high traffic accident risk. In addition, it proposes a novel domain-specific criterion for evaluating the clustering results, which promotes the stability of the clustering results through time and inter-period accident spatial collocation, and penalizes the size of the selected clusters. To illustrate the proposed approach, it is applied to data on traffic accidents with injuries or death that occurred in three of the largest cities of Serbia over the three-year period.

]]>Axioms doi: 10.3390/axioms12060508

Authors: Yanni Guo Yinan Yan

In this paper, we propose a parameterized variable metric three-operator algorithm for finding a zero of the sum of three monotone operators in a real Hilbert space. Under some appropriate conditions, we prove the strong convergence of the proposed algorithm. Furthermore, we propose a parameterized variable metric three-operator algorithm with a multi-step inertial term and prove its strong convergence. Finally, we illustrate the effectiveness of the proposed algorithm with numerical examples.

]]>Axioms doi: 10.3390/axioms12060507

Authors: Joel Langer David Singer

We apply the theory of quadratic differentials, to present a classification of orthogonal pairs of foliations of the hyperbolic plane by hyperbolic conics. Light rays are represented by trajectories of meromorphic differentials, and mirrors are represented by trajectories of the quadratic differential that represents the geometric mean of two such differentials. Using the notion of a hyperbolic conic as a mirror, we classify the types of orthogonal pairs of foliations of the hyperbolic plane by confocal conics. Up to diffeomorphism, there are nine types: three of these types admit one parameter up to isometry; the remaining six types are unique up to isometry. The families include all possible hyperbolic conics.

]]>Axioms doi: 10.3390/axioms12060506

Authors: Limin Wang Wenqi Wang

In this paper, we consider a variant of dominating set problem, i.e., the total dominating set problem. Given an undirected graph G=(V,E), a subset of vertices T&sube;V is called a total dominating set if every vertex in V is adjacent to at least one vertex in T. Based on LP relaxation techniques, this paper gives a distributed approximation algorithm for the total dominating set problem in general graphs. The presented algorithm obtains a fractional total dominating set that is, at most, k(1+&Delta;1k)&Delta;1k times the size of the optimal solution to this problem, where k is a positive integer and &Delta; is the maximum degree of G. The running time of this algorithm is constant communication rounds under the assumption of a synchronous communication model.

]]>Axioms doi: 10.3390/axioms12060505

Authors: Maryam M. Abuelwafa Ravi P. Agarwal Safi S. Rabie Samir H. Saker

In this paper, we develop a new technique on a time scale T to prove that the self-improving properties of the Muckenhoupt weights hold. The results contain the properties of the weights when T=R and when T=N, and also can be extended to cover different spaces such as T=hN, T=qN, etc. The results will be proved by employing some new refinements of Hardy&rsquo;s type dynamic inequalities with negative powers proven and designed for this purpose. The results give the exact value of the limit exponent as well as the new constants of the new classes.

]]>Axioms doi: 10.3390/axioms12050504

Authors: Yilan Cui Jianping Ou Saihua Liu

A 3-restricted edge cut is an edge cut of a connected graph that separates this graph into components, each having an order of at least 3. The minimum size of all 3-restricted edge cuts of a graph is called its 3-restricted edge connectivity. This work determines the upper and lower bounds on the 3-restricted edge connectivity of replacement product graphs and presents sufficient conditions for replacement product graphs to be maximally 3-restricted edge connected. As a result, the 3-restricted edge connectivity of replacement product graphs of some special graphs are determined.

]]>Axioms doi: 10.3390/axioms12050503

Authors: Nanami Taketomi Takeshi Emura

Fixed-effect meta-analyses aim to estimate the common mean parameter by the best linear unbiased estimator. Besides unbiasedness, consistency is one of the most fundamental requirements for the common mean estimator to be valid. However, conditions for the consistency of the common mean estimator have not been discussed in the literature. This article fills this gap by clarifying conditions for making the common mean estimator consistent in fixed-effect meta-analyses. In this article, five theorems are devised, which state regularity conditions for the common mean estimator to be consistent. These theorems are novel applications of the classical large sample theory to meta-analyses. Numerical illustrations are also given to help understand the needs of the regularity conditions. Three real datasets illustrate the practical consequences of the devised theorems. This article concludes that the inconsistency of the common mean estimator occurs under some conditions in real meta-analyses.

]]>Axioms doi: 10.3390/axioms12050502

Authors: Najwan Alsadat Mohammed Elgarhy Kadir Karakaya Ahmed M. Gemeay Christophe Chesneau M. M. Abd El-Raouf

In this paper, we emphasize a new one-parameter distribution with support as [1,+&infin;). It is constructed from the inverse method applied to an understudied one-parameter unit distribution, the unit Teissier distribution. Some properties are investigated, such as the mode, quantiles, stochastic dominance, heavy-tailed nature, moments, etc. Among the strengths of the distribution are the following: (i) the closed-form expressions and flexibility of the main functions, and in particular, the probability density function is unimodal and the hazard rate function is increasing or unimodal; (ii) the manageability of the moments; and, more importantly, (iii) it provides a real alternative to the famous Pareto distribution, also with support as [1,+&infin;). Indeed, the proposed distribution has different functionalities but also benefits from the heavy-right-tailed nature, which is demanded in many applied fields (finance, the actuarial field, quality control, medicine, etc.). Furthermore, it can be used quite efficiently in a statistical setting. To support this claim, the maximum likelihood, Anderson&ndash;Darling, right-tailed Anderson&ndash;Darling, left-tailed Anderson&ndash;Darling, Cram&eacute;r&ndash;Von Mises, least squares, weighted least-squares, maximum product of spacing, minimum spacing absolute distance, and minimum spacing absolute-log distance estimation methods are examined to estimate the unknown unique parameter. A Monte Carlo simulation is used to compare the performance of the obtained estimates. Additionally, the Bayesian estimation method using an informative gamma prior distribution under the squared error loss function is discussed. Data on the COVID mortality rate and the timing of pain relief after receiving an analgesic are considered to illustrate the applicability of the proposed distribution. Favorable results are highlighted, supporting the importance of the findings.

]]>Axioms doi: 10.3390/axioms12050501

Authors: Zhao Jiang Azhar Halik Ahmadjan Muhammadhaji

We studied a class of generalized n-species non-autonomous cooperative Lotka&ndash;Volterra (L-V) systems with time delays. We obtained new criteria on the dynamic properties of the systems. First, we obtained the boundedness and permanence of the system using the inequality analysis technique and comparison method. Then, the existence of positive periodic solutions was investigated using the coincidence degree theory. The global attractivity of the system was obtained by constructing suitable Lyapunov functionals and utilizing Barbalat&rsquo;s lemma. The existence and global attractivity of the periodic solutions were also obtained. Finally, we conducted two numerical simulations to validate the feasibility and practicability of our results.

]]>Axioms doi: 10.3390/axioms12050500

Authors: Jer-Rong Chang Te-Wen Tu Chun-Jung Huang

The purpose of this study is to derive an analytical solution for a cantilever beam with a novel spring-like actuator that behaves like a time-dependent spring and to study the dynamic behavior of the system. A time-dependent spring was set at the free end of the cantilever beam to model the novel spring-like actuator. First, the boundary conditions were transformed from being nonhomogeneous to being homogeneous using the shifting function method. The solution of the analytic series was then obtained by using the expansion theorem method. The correctness of the proposed analytical solution was verified by comparing the results with those obtained via the separation of variables in the special extreme case of a constant spring coefficient. We took the free end of a cantilever beam with harmonic spring stiffness and an external periodic unit load as an example. The influence of the actuator parameters, such as the effect of the magnitude and the frequency of the time-dependent spring stiffness on the resonance frequency, was investigated. An important new result was found, i.e., that the resonance frequency is clearly dependent on the magnitude and the frequency of the spring-like actuator in the first two modes, but not in the third and fourth modes. In practical engineering applications, system resonance can be avoided by adjusting the magnitude and frequency of the actuator.

]]>Axioms doi: 10.3390/axioms12050499

Authors: Bicheng Yang Michael Th. Rassias

Using weight functions and parameters, as well as applying real analytic techniques, we derive a new Hardy&ndash;Hilbert-type integral inequality with the homogeneous kernel 1(x+y)&lambda;+n involving one multiple upper limit function and one derivative function of higher order. Certain equivalent statements of the optimal constant factor related to some parameters are considered. A few particular inequalities and the case of reverses are also provided.

]]>Axioms doi: 10.3390/axioms12050498

Authors: Mo Chen Frank Werner Mohammad Shokouhifar

University course scheduling (UCS) is one of the most important and time-consuming issues that all educational institutions face yearly. Most of the existing techniques to model and solve UCS problems have applied approximate methods, which differ in terms of efficiency, performance, and optimization speed. Accordingly, this research aims to apply an exact optimization method to provide an optimal solution to the course scheduling problem. In other words, in this research, an integer programming model is presented to solve the USC problem. In this model, the constraints include the facilities of classrooms, courses of different levels and compression of students&rsquo; curriculum, courses outside the faculty and planning for them, and the limited time allocated to the professors. The objective is to maximize the weighted sum of allocating available times to professors based on their preferences in all periods. To evaluate the presented model&rsquo;s feasibility, it is implemented using the GAMS software. Finally, the presented model is solved in a larger dimension using a real data set from a college in China and compared with the current program in the same college. The obtained results show that considering the mathematical model&rsquo;s constraints and objective function, the faculty courses&rsquo; timetable is reduced from 4 days a week to 3 working days. Moreover, master courses are planned in two days, and the courses in the educational groups do not interfere with each other. Furthermore, by implementing the proposed model for the real case study, the maximum teaching hours of the professors are significantly reduced. The results demonstrate the efficiency of the proposed model and solution method in terms of optimization speed and solution accuracy.

]]>Axioms doi: 10.3390/axioms12050497

Authors: Lazhar Bougoffa Smail Bougouffa Ammar Khanfer

Approximate solutions are obtained in implicit forms for the following general form of the nonlinear Stefan problem ddx(1+&delta;1yp)dydx+2x(1+&delta;2yp)dydx=4Ste&beta;(x),0&lt;x&lt;&lambda;, with y(0)=1,y(&lambda;)=0, where &lambda;&gt;0 is a solution to the nonlinear equation y&prime;(&lambda;)=&minus;2&lambda;Ste, where &delta;i&gt;&minus;1,i=1,2,p&gt;0, and Ste is the Stefan number, which represents a phase-change problem with a nonlinear temperature-dependent thermal parameters (i.e., thermal conductivity and specific heat) on (0,&lambda;).

]]>Axioms doi: 10.3390/axioms12050496

Authors: Enrique Calderín-Ojeda Emilio Gómez-Déniz Francisco J. Vázquez-Polo

In this paper, we calculate premiums that are based on the Conditional Tail Expectation (CTE) and asymmetric loss functions to account for the risk of both underestimation and overestimation losses. After selecting an appropriate loss function, the premium is calculated as the quantity minimizing an objective function related to the conditional tail expectation of the loss. The premium satisfies desirable properties, i.e., it is a coherent risk measure, and it helps the practitioner to quantify the global risk of the insurer. Finally, this methodology is applied to quantify the risks associated to the total claims amount that are modelled via composite models and comparisons with the usual risk measures, i.e., Value-at-Risk (VaR) and Tail Value-at-Risk (TVaR) are carried out.

]]>Axioms doi: 10.3390/axioms12050495

Authors: Oscar Humberto Montiel Ross

Deep Learning (DL) is an essential topic of increasing interest in science, industry, and academia [...]

]]>Axioms doi: 10.3390/axioms12050494

Authors: Alina Alb Lupaş

Zadeh&rsquo;s fuzzy set theory offers a logical, adaptable solution to the challenge of defining, assessing and contrasting various sustainability scenarios. The results presented in this paper use the fuzzy set concept embedded into the theories of differential subordination and superordination established and developed in geometric function theory. As an extension of the classical concept of differential subordination, fuzzy differential subordination was first introduced in geometric function theory in 2011. In order to generalize the idea of fuzzy differential superordination, the dual notion of fuzzy differential superordination was developed later, in 2017. The two dual concepts are applied in this article making use of the previously introduced operator defined as the convolution product of the generalized S&#259;lgean operator and the Ruscheweyh derivative. Using this operator, a new subclass of functions, normalized analytic in U, is defined and investigated. It is proved that this class is convex, and new fuzzy differential subordinations are established by applying known lemmas and using the functions from the new class and the aforementioned operator. When possible, the fuzzy best dominants are also indicated for the fuzzy differential subordinations. Furthermore, dual results involving the theory of fuzzy differential superordinations and the convolution operator are established for which the best subordinants are also given. Certain corollaries obtained by using particular convex functions as fuzzy best dominants or fuzzy best subordinants in the proved theorems and the numerous examples constructed both for the fuzzy differential subordinations and for the fuzzy differential superordinations prove the applicability of the new theoretical results presented in this study.

]]>Axioms doi: 10.3390/axioms12050493

Authors: Angelo Plastino Diana Monteoliva Angel Ricardo Plastino

This work scrutinizes, using statistical mechanics indicators, important traits displayed by quantum many-body systems. Our statistical mechanics quantifiers are employed, in the context of Gibbs&rsquo; canonical ensemble at temperature T. A new quantifier of this sort is also presented here. The present discussion focuses attention on the role played by the fermion number N in many-fermion dynamics, that is, N is our protagonist. We have discovered discovers particular values of N for which the thermal indicators exhibit unexpected abrupt variations. Such a fact reflects an unanticipated characteristic of fermionic dynamics.

]]>Axioms doi: 10.3390/axioms12050492

Authors: Ilaria Cacciari Anedio Ranfagni

Further measurements of delay time, in the transfer of modulation between microwave beams, are reported even considering the angular dependence in the orientation of the F1 c.w. launcher. The obtained results allow for a better interpretation of the observed phenomenology on the basis of a more sophisticated analysis, which takes into account the presence of pole singularities in field-amplitude evaluations according to the saddle point method. The model already presented in one of our previous publications, consisting of a photon&ndash;photon scattering mechanism as concomitant with a stochastic process, is then confirmed.

]]>Axioms doi: 10.3390/axioms12050491

Authors: Stevo Stević

We present some formulas for the norm, as well as the essential norm, of a product of composition and an integral operator between some Bloch-type spaces of analytic functions on the unit ball, in terms of given symbols and weights.

]]>Axioms doi: 10.3390/axioms12050490

Authors: Songsong Dai

A novel concept of quaternionic fuzzy sets (QFSs) is presented in this paper. QFSs are a generalization of traditional fuzzy sets and complex fuzzy sets based on quaternions. The novelty of QFSs is that the range of the membership function is the set of quaternions with modulus less than or equal to one, of which the real and quaternionic imaginary parts can be used for four different features. A discussion is made on the intuitive interpretation of quaternion-valued membership grades and the possible applications of QFSs. Several operations, including quaternionic fuzzy complement, union, intersection, and aggregation of QFSs, are presented. Quaternionic fuzzy relations and their composition are also investigated. QFS is designed to maintain the advantages of traditional FS and CFS, while benefiting from the properties of quaternions. Cuts of QFSs and rotational invariance of quaternionic fuzzy operations demonstrate the particularity of quaternion-valued grades of membership.

]]>Axioms doi: 10.3390/axioms12050489

Authors: Shan Ma Feng Ma Chaoyu Tang

Train operation control is of great importance in reducing train operation energy consumption and improving railway operation efficiency. This paper investigates the design of optimal control inputs for multiple trains on a single railway line with several stations. Firstly, a distributed optimal control problem for multiple train operation is formulated to reduce the energy consumption and improve the punctuality of trains. Then, we propose an efficient algorithm based on the framework of the symmetric alternating direction method of multipliers to solve this optimization problem. Finally, numerical simulations show that the method can obtain the optimal train control sequence in fewer iterative steps compared to the alternating direction multiplier method, thus illustrating the effectiveness of the algorithm.

]]>Axioms doi: 10.3390/axioms12050488

Authors: Iqbal M. Batiha Ahmad A. Abubaker Iqbal H. Jebril Suha B. Al-Shaikh Khaled Matarneh

This work purposes to establish two small numerical modifications for the Fractional Euler method (FEM) and the Modified Fractional Euler Method (MFEM) to deal with fractional initial value problems. Two such modifications, which are named Improved Modified Fractional Euler Method 1 (IMFEM 1) and Improved Modified Fractional Euler Method 2 (IMFEM 2), endeavor to further enhance FEM and MFEM in terms of attaining more accuracy. By utilizing certain theoretical results, the resultant error bounds of the proposed methods are analyzed and estimated. Several numerical comparisons are carried out to validate the efficiency of our proposed methods.

]]>Axioms doi: 10.3390/axioms12050487

Authors: Dan Yu Li Jin Jin Li Xixi Qin Zhichuan Zhu Jiujun Zhang

In industrial production, the exponentially weighted moving average scheme is widely used to monitor shifts in product quality, especially small-to-moderate shifts. In this paper, we propose a modified one-sided EWMA scheme for Type I right-censored Weibull lifetime data for detecting shifts in the scale parameter with the shape parameter fixed. A comparative analysis with existing cumulative sum and exponentially weighted moving average results from the literature is provided. The zero-state and steady-state behaviour of the new scheme are considered with regard to the average run length, the standard deviation of the run length, and other performance measures. Our simulation shows stronger power in detecting changes in the censored lifetime data using the modified scheme than that using the traditional exponentially weighted moving average scheme, and the new scheme is superior to the cumulative sum scheme in most situations. A real-data example further demonstrates the effectiveness of the proposed method.

]]>Axioms doi: 10.3390/axioms12050486

Authors: Yanlin Li Abdussamet Çalışkan

In this article, we examine the relationship between Darboux frames along parameter curves and the Darboux frame of the base curve of the ruled surface. We derive the equations of the quaternionic shape operators, which can rotate tangent vectors around the normal vector, and find the corresponding rotation matrices. Using these operators, we examine the Gauss curvature and mean curvature of the ruled surface. We explore how these properties are found by the use of Frenet vectors instead of generator vectors. We provide illustrative examples to better demonstrate the concepts and results discussed.

]]>Axioms doi: 10.3390/axioms12050485

Authors: Xinzhu Zhao Bo Dong Bo Yu Yan Yu

A linear transformation from vector space to another vector space can be represented as a matrix. This close relationship between the matrix and the linear transformation is helpful for the study of matrices. In this paper, the tensor is regarded as a generalization of the matrix from the viewpoint of the linear transformation instead of the quadratic form in matrix theory; we discuss some operations and present some definitions and theorems related to tensors. For example, we provide the definitions of the triangular form and the eigenvalue of a tensor, and the theorems of the tensor QR decomposition and the tensor singular value decomposition. Furthermore, we explain the significance of our definitions and their differences from existing definitions.

]]>Axioms doi: 10.3390/axioms12050483

Authors: Alit Kartiwa Asep K. Supriatna Endang Rusyaman Jumat Sulaiman

Quaternion is a four-dimensional and an extension of the complex number system. It is often viewed from various fields, such as analysis, algebra, and geometry. Several applications of quaternions are related to an object&rsquo;s rotation and motion in three-dimensional space in the form of a differential equation. In this paper, we do a systematic literature review on the development of quaternion differential equations. We utilize PRISMA (preferred reporting items for systematic review and meta-analyses) framework in the review process as well as content analysis. The expected result is a state-of-the-art and the gap of concepts or problems that still need to develop or answer. It was concluded that there are still some opportunities to develop a quaternion differential equation using a quaternion function domain.

]]>Axioms doi: 10.3390/axioms12050484

Authors: Adrià Torrens-Urrutia Maria Dolores Jiménez-López Susana Campillo-Muñoz

We introduce a Fuzzy Property Grammar System (FPGS), a formalism that integrates a Fuzzy Property Grammar into a linguistic grammar system to formally characterize metaphorical evaluative expressions. The main scope of this paper is to present the formalism of FPGS and to show how it might provide a formal characterization of hate speech linguistic evaluative expressions with metaphors (as fuzzy concepts), together with evaluating their degree of linguistic violence. Linguistic metaphors are full of semantic coercions. It is necessary to formally characterize the context of the communication to acknowledge the extralinguistic constraints of the pragmatic domain, which establishes whether an utterance is violent. To show the applicability of our formalism, we present a proof of concept. By compiling and tagging a 3000-tweet corpus, we have extracted a lexicon of hate speech metaphors. Furthermore, we show how FPGS architecture can deal with different types of hate speech and can identify implicit violent figurative evaluative expressions by context and type. Although we are still in the experimental phase of our project and cannot present conclusive results at the computational level, the proof-of-concept results show that our formalism can achieve the desired outcome.

]]>Axioms doi: 10.3390/axioms12050482

Authors: Hans G. Feichtinger

For the characterization of multipliers of Lp(Rd) or more generally, of Lp(G) for some locally compact Abelian group G, the so-called Figa-Talamanca&ndash;Herz algebra Ap(G) plays an important role. Following Larsen&rsquo;s book, we describe multipliers as bounded linear operators that commute with translations. The main result of this paper is the characterization of the multipliers of Ap(G). In fact, we demonstrate that it coincides with the space of multipliers of Lp(G),&#8741;&middot;&#8741;p. Given a multiplier T of (Ap(G),&#8741;&middot;&#8741;Ap(G)) and using the embedding (Ap(G),&#8741;&middot;&#8741;Ap(G))&#8618;C0(G),&#8741;&middot;&#8741;&infin;, the linear functional f&#8614;[T(f)(0)] is bounded, and T can be written as a moving average for some element in the dual PMp(G) of (Ap(G),&#8741;&middot;&#8741;Ap(G)). A key step for this identification is another elementary fact: showing that the multipliers from Lp(G),&#8741;&middot;&#8741;p to C0(G),&#8741;&middot;&#8741;&infin; are exactly the convolution operators with kernels in Lq(G),&#8741;&middot;&#8741;q for 1&lt;p&lt;&infin; and 1/p+1/q=1. The proofs make use of the space of mild distributions, which is the dual of the Segal algebra S0(G),&#8741;&middot;&#8741;S0, and the fact that multipliers T from S0(G) to S0&prime;(G) are convolution operators of the form T:f&#8614;&sigma;&lowast;f for some uniquely determined &sigma;&isin;S0&prime;. This setting also allows us to switch from the description of these multipliers as convolution operators (by suitable pseudomeasures) to their description as Fourier multipliers, using the extended Fourier transform in the setting of S0&prime;(G),&#8741;&middot;&#8741;S0&prime;. The approach presented here extends to other function spaces, but a more detailed discussion is left to future publications.

]]>Axioms doi: 10.3390/axioms12050481

Authors: Jiahang Zhang Shengai Cui

The number of random fields required to capture the spatial variability of soil properties and their impact on the performance of geotechnical systems is often varied. However, the number of random fields required to obtain higher-order statistical moments of model outputs has not yet been studied. This research aims to investigate the number of Monte Carlo simulations needed to achieve stationary higher-order statistics of a pore pressure head in an unsaturated soil slope under steady-state infiltration. The study recommends using at least 500 Monte Carlo samples for the probabilistic analysis of geotechnical engineering models. A more conservative choice for up to second-moment analysis is 1000 samples. The analysis reveals significant variations in skewness, which become stationary for all mesh grids when the number of samples exceeds 15,000. Kurtosis stabilizes only when the number of samples reaches 25,000. The pore pressure head in the unsaturated zone is less uncertain. Additionally, the probability density function of the pore pressure head follows a leptokurtic distribution.

]]>Axioms doi: 10.3390/axioms12050480

Authors: Muhammad Usman Mujahid Abbas Andrew Omame

In this paper, a vaccination model for SARS-CoV-2 variants is proposed and is studied using fractional differential operators involving a non-singular kernel. It is worth mentioning that variability in transmission rates occurs because of the particular population that is vaccinated, and hence, the asymptomatic infected classes are classified on the basis of their vaccination history. Using the Banach contraction principle and the Arzela&ndash;Ascoli theorem, existence and uniqueness results for the proposed model are presented. Two different numerical approaches, the fractional Euler and Lagrange polynomial methods, are employed to approximate the model&rsquo;s solution. The model is then fitted to data associated with COVID-19 deaths in Pakistan between 1 January 2022 and 10 April 2022. It is concluded that our model is much aligned with the data when the order of the fractional derivative &zeta;=0.96. The two different approaches are then compared with different step sizes. It is observed that they behave alike for small step sizes and exhibit different behaviour for larger step sizes. Based on the numerical assessment of the model presented herein, the impact of vaccination and the fractional order are highlighted. It is also noted that vaccination could remarkably decrease the spikes of different emerging variants of SARS-CoV-2 within the population.

]]>Axioms doi: 10.3390/axioms12050479

Authors: Shuang Li Jinming Cai Kun Li

Matrix representations for a class of Sturm&ndash;Liouville problems with eigenparameters contained in the boundary and interface conditions were studied. Given any matrix eigenvalue problem of a certain type and an eigenparameter-dependent condition, a class of Sturm&ndash;Liouville problems with this specified condition was constructed. It has been proven that each Sturm&ndash;Liouville problem is equivalent to the given matrix eigenvalue problem.

]]>Axioms doi: 10.3390/axioms12050478

Authors: Ebrahem Ateatullah Algehyne Mounirah Areshi Faizan Ahmad Khan

This manuscript includes certain results on fixed points under a generalized contraction involving a pair of shifting distance functions in the framework of metric space endowed with a class of transitive relation. The results presented herein are illustrated by an example. Finally, we apply our result to compute a unique solution of certain first order boundary value problems.

]]>Axioms doi: 10.3390/axioms12050477

Authors: Huda M. Alshanbari Omalsad Hamood Odhah Zubair Ahmad Faridoon Khan Abd Al-Aziz Hosni El-Bagoury

Probability models are frequently used in numerous healthcare, sports, and policy studies. These probability models use datasets to identify patterns, analyze lifetime scenarios, predict outcomes of interest, etc. Therefore, numerous probability models have been studied, introduced, and implemented. In this paper, we also propose a novel probability model for analyzing data in different sectors, particularly in biomedical and sports sciences. The probability model is called a new modified exponential-Weibull distribution. The heavy-tailed characteristics along with some other mathematical properties are derived. Furthermore, the estimators of the new modified exponential-Weibull are derived. A simulation study of the new modified exponential-Weibull model is also provided. To illustrate the new modified exponential-Weibull model, a practical dataset is analyzed. The dataset consists of seventy-eight observations and represents the recovery time after the injuries in different basketball matches.

]]>Axioms doi: 10.3390/axioms12050476

Authors: Tongwei Zhang Lianyan Fu Dehui Wang Zhuoxi Yu

In this article, we consider the nonparametric inference for the time-varying coefficient double-threshold generalized autoregressive conditional heteroscedastic models. The quasi-maximum exponential likelihood estimators (QMELEs) of the model&rsquo;s parameters and the asymptotic properties of the estimators are obtained. The simulation study implies that the distribution of the estimators is asymptotically normal. A real data application to stock returns is given. Both the simulations and real data example imply that the model and the QMELE are proper, compatible and accurately fit the financial time series data of the Nikkei 225.

]]>Axioms doi: 10.3390/axioms12050475

Authors: Rashmi Rekha Devi Surajit Chattopadhyay

This paper reports a study to interpret the surface temperature based on time series and fuzzy measures. We demonstrated a method to identify the uncertainty around the surface temperature data concerning the summer monsoon in India. The random variables were standardized, and the Dempster-Shafer Theory was used to generate common goals. Two criteria, represented as fuzzy numbers, were used for this purpose. We constructed three polynomials to illustrate a functional connection between time series and the measure of joint belief. The analysis of the obtained results showed that the certainty increased over time. It confirmed that the degree of the evidence is a more predictable parameter at a more extended period.

]]>Axioms doi: 10.3390/axioms12050474

Authors: Xiaoming Wang Jehad Alzabut Mahammad Khuddush Michal Fečkan

This work explores the possibility that iterative classes of elliptic equations have both single and coupled positive radial solutions. Our approach is based on using the well-known Guo&ndash;Krasnoselskii and Avery&ndash;Henderson fixed-point theorems in a Banach space. Furthermore, we utilize Rus&rsquo; theorem in a metric space, to prove the uniqueness of solutions for the problem. Examples are constructed for the sake of verification.

]]>Axioms doi: 10.3390/axioms12050472

Authors: Areej A. Almoneef Rashad A. Abdel-Baky

This paper investigates the kinematic differential geometry of a line trajectory in spatial movement. Specifically, we provide a theoretical expression of inflection line congruence, which is the spatial equivalent of the inflection circle of planar kinematics. Additionally, we introduce new proofs for the Euler&ndash;Savary and Disteli formulae and thoroughly analyze their spatial equivalence.

]]>Axioms doi: 10.3390/axioms12050473

Authors: Mohamed Abdelsabour Fahmy Mohammed O. Alsulami Ahmed E. Abouelregal

The main goal of this work is to develop a novel boundary element method (BEM) model for analyzing ultrasonic wave propagation in three-temperature anisotropic viscoelastic porous media. Due to the problems of the strong nonlinearity of ultrasonic wave propagation in three-temperature porous media, the analytical or numerical solutions to the problems under consideration are always challenging, necessitating the development of new computational techniques. As a result, we use a new BEM model to solve such problems. A time-stepping procedure based on the linear multistep method is obtained after solving the discretized boundary integral equation with the quadrature rule. The calculation of a double integral is required to obtain fundamental solutions, but this increases the total BEM computation time. Our proposed BEM technique is used to solve the current problem and improve the formulation efficiency. The numerical results are graphed to demonstrate the effects of viscosity and anisotropy on the nonlinear ultrasonic stress waves in three-temperature porous media. The validity, accuracy, and efficiency of the proposed methodology are demonstrated by comparing the obtained results to a corresponding solution obtained from the finite difference method (FDM).

]]>Axioms doi: 10.3390/axioms12050471

Authors: Stef Frijters Lorenz Demey

In this paper, we introduce and study AD-logic, i.e., a system of (hybrid) modal logic that can be used to reason about Aristotelian diagrams. The language of AD-logic, LAD, is interpreted on a kind of birelational Kripke frames, which we call &ldquo;AD-frames&rdquo;. We establish a sound and strongly complete axiomatization for AD-logic, and prove that there exists a bijection between finite Aristotelian diagrams (up to Aristotelian isomorphism) and finite AD-frames (up to modal isomorphism). We then show how AD-logic can express several major insights about Aristotelian diagrams; for example, for every well-known Aristotelian family A, we exhibit a formula &chi;A&isin;LAD and show that an Aristotelian diagram D belongs to the family A iff &chi;A is validated by D (when the latter is viewed as an AD-frame). Finally, we show that AD-logic itself gives rise to new and interesting Aristotelian diagrams, and we reflect on their profoundly peculiar status.

]]>Axioms doi: 10.3390/axioms12050469

Authors: Alexander D. Bruno Alijon A. Azimov

Presently, there is a method based on Power Geometry that allows one to find asymptotic forms and asymptotic expansions of solutions to different kinds of non-linear equations near their singularities. The method contains three algorithms: (1) Reducing the equation to its normal form, (2) separating truncated equations, and (3) power transformations of coordinates. Here, we describe the method for the simplest case, a single algebraic equation, and apply it to an algebraic variety, as described by an algebraic equation of order 12 in three variables. The variety was considered in study of Einstein&rsquo;s metrics and has several singular points and singular curves. Near some of them, we compute a local parametric expansion of the variety.

]]>Axioms doi: 10.3390/axioms12050470

Authors: Alina Alb Lupaş

In this paper, the author combines the geometric theory of analytic function regarding differential superordination and subordination with fuzzy theory for the convolution product of Ruscheweyh derivative and multiplier transformation. Interesting fuzzy inequalities are obtained by the author.

]]>Axioms doi: 10.3390/axioms12050468

Authors: Stanislawa Kanas Kamaljeet Gangania

We find the sharp radius of uniformly convex &gamma;-spirallikeness for N&nu;(z)=az2J&nu;&Prime;(z)+bzJ&nu;&prime;(z)+cJ&nu;(z) (here J&nu;(z) is the Bessel function of the first kind of order &nu;) with three different kinds of normalizations of the function N&nu;(z). As an application, we derive sufficient conditions on the parameters for the functions to be uniformly convex &gamma;-spirallikeness and, consequently, generate examples of uniform convex &gamma;-spirallike via N&nu;(z). Results are well-supported by the relevant graphs and tables.

]]>Axioms doi: 10.3390/axioms12050467

Authors: Alptekin Ulutaş Ayse Topal Darjan Karabasevic Figen Balo

Material handling is a cost-intensive operation for businesses. There are several alternative types of equipment for material handling, therefore it is important to select the best one among them to decrease the cost. As there are several different alternatives and criteria which are used to assess these alternatives, multi-criteria decision making (MCDM) techniques are useful to determine the optimal material handling equipment (MHE) for businesses. In this study, fuzzy BWM for determining weights of criteria and the fuzzy Multiple Criteria Ranking by Alternative Trace (MCRAT) method have been used for ranking forklift alternatives. This study&rsquo;s significance in the literature will be the creation of a novel fuzzy MCDM technique with the application of fuzzy MCRAT. Furthermore, there are relatively few studies employing the MCRAT approach in the literature; therefore, this study will provide additional data and outcomes from this method to the literature. The findings present that the forklift with the code FLT-3 performed the best, whereas the forklift with the code FLT-2 had the worst performance, according to the fuzzy MCRAT technique. According to the comparison analysis, the fuzzy MCRAT produced the same results as the fuzzy ARAS and had a few subtle differences to fuzzy MARCOS.

]]>Axioms doi: 10.3390/axioms12050466

Authors: Farah M. Al-Askar Clemente Cesarano Wael W. Mohammed

In this work, we consider the Boiti&ndash;Leon&ndash;Manna&ndash;Pempinelli equation with the M-truncated derivative (BLMPE-MTD). Our aim here is to obtain trigonometric, rational and hyperbolic solutions of BLMPE-MTD by employing two diverse methods, namely, He&rsquo;s semi-inverse method and the extended tanh function method. In addition, we generalize some previous results. As the Boiti&ndash;Leon&ndash;Manna&ndash;Pempinelli equation is a model for an incompressible fluid, the solutions obtained may be utilized to represent a wide variety of fascinating physical phenomena. We construct a large number of 2D and 3D figures to demonstrate the impact of the M-truncated derivative on the exact solution of the BLMPE-MTD.

]]>Axioms doi: 10.3390/axioms12050465

Authors: Victor Orlov

This paper considers a theoretical substantiation of the influence of a perturbation of a moving singular point on the analytical approximate solution to the Van der Pol equation obtained earlier by the author. A priori estimates of the error of the analytical approximate solution are obtained, which allows the solving of the inverse problem of the theory of error: what should the structure of the analytical approximate solution be in order to obtain a result with a given accuracy? Thanks to a new approach for obtaining a priori evaluations of errors, based on elements of differential calculus, the domain, used to obtain an analytical approximate solution, was substantially expanded. A variant of optimizing a priori estimates using a posteriori estimates is illustrated. The results of a numerical experiment are also presented.

]]>Axioms doi: 10.3390/axioms12050464

Authors: Yue Xu Shi-Cai Gong

Let G be a graph of order n and L(G) be its Laplacian matrix. The Laplacian polynomial of G is defined as P(G;&lambda;)=det(&lambda;I&minus;L(G))=&sum;i=0n(&minus;1)ici(G)&lambda;n&minus;i, where ci(G) is called the i-th Laplacian coefficient of G. Denoted by Gn,m the set of all (n,m)-graphs, in which each of them contains n vertices and m edges. The graph G is called uniformly minimal if, for each i(i=0,1,&hellip;,n), H is ci(G)-minimal in Gn,m. The Laplacian matrix and eigenvalues of graphs have numerous applications in various interdisciplinary fields, such as chemistry and physics. Specifically, these matrices and eigenvalues are widely utilized to calculate the energy of molecular energy and analyze the physical properties of materials. The Laplacian-like energy shares a number of properties with the usual graph energy. In this paper, we investigate the existence of uniformly minimal graphs in Gn,m because such graphs have minimal Laplacian-like energy. We determine that the c2(G)-c3(G) successive minimal graph is exactly one of the four classes of threshold graphs.

]]>Axioms doi: 10.3390/axioms12050463

Authors: Samet Memiş Burak Arslan Tuğçe Aydın Serdar Enginoğlu Çetin Camcı

Intuitionistic fuzzy parameterized intuitionistic fuzzy soft matrices (ifpifs-matrices), proposed by Engino&#287;lu and Arslan in 2020, are worth utilizing in data classification in supervised learning due to coming into prominence with their ability to model decision-making problems. This study aims to define the concepts metrics, quasi-, semi-, and pseudo-metrics and similarities, quasi-, semi-, and pseudo-similarities over ifpifs-matrices; develop a new classifier by using them; and apply it to data classification. To this end, it develops a new classifier, i.e., Intuitionistic Fuzzy Parameterized Intuitionistic Fuzzy Soft Classifier (IFPIFSC), based on six pseudo-similarities proposed herein. Moreover, this study performs IFPIFSC&rsquo;s simulations using 20 datasets provided in the UCI Machine Learning Repository and obtains its performance results via five performance metrics, accuracy (Acc), precision (Pre), recall (Rec), macro F-score (MacF), and micro F-score (MicF). It also compares the aforementioned results with those of 10 well-known fuzzy-based classifiers and 5 non-fuzzy-based classifiers. As a result, the mean Acc, Pre, Rec, MacF, and MicF results of IFPIFSC, in comparison with fuzzy-based classifiers, are 94.45%, 88.21%, 86.11%, 87.98%, and 89.62%, the best scores, respectively, and with non-fuzzy-based classifiers, are 94.34%, 88.02%, 85.86%, 87.65%, and 89.44%, the best scores, respectively. Later, this study conducts the statistical evaluations of the performance results using a non-parametric test (Friedman) and a post hoc test (Nemenyi). The critical diagrams of the Nemenyi test manifest the performance differences between the average rankings of IFPIFSC and 10 of the 15 are greater than the critical distance (4.0798). Consequently, IFPIFSC is a convenient method for data classification. Finally, to present opportunities for further research, this study discusses the applications of ifpifs-matrices for machine learning and how to improve IFPIFSC.

]]>Axioms doi: 10.3390/axioms12050462

Authors: Miguel-Angel Gil-Rios Claire Chalopin Ivan Cruz-Aceves Juan-Manuel Lopez-Hernandez Martha-Alicia Hernandez-Gonzalez Sergio-Eduardo Solorio-Meza

In this paper, a novel method for the automatic classification of coronary stenosis based on a feature selection strategy driven by a hybrid evolutionary algorithm is proposed. The main contribution is the characterization of the coronary stenosis anomaly based on the automatic selection of an efficient feature subset. The initial feature set consists of 49 features involving intensity, texture and morphology. Since the feature selection search space was O(2n), being n=49, it was treated as a high-dimensional combinatorial problem. For this reason, different single and hybrid evolutionary algorithms were compared, where the hybrid method based on the Boltzmann univariate marginal distribution algorithm (BUMDA) and simulated annealing (SA) achieved the best performance using a training set of X-ray coronary angiograms. Moreover, two different databases with 500 and 2700 stenosis images, respectively, were used for training and testing of the proposed method. In the experimental results, the proposed method for feature selection obtained a subset of 11 features, achieving a feature reduction rate of 77.5% and a classification accuracy of 0.96 using the training set. In the testing step, the proposed method was compared with different state-of-the-art classification methods in both databases, obtaining a classification accuracy and Jaccard coefficient of 0.90 and 0.81 in the first one, and 0.92 and 0.85 in the second one, respectively. In addition, based on the proposed method&rsquo;s execution time for testing images (0.02 s per image), it can be highly suitable for use as part of a clinical decision support system.

]]>Axioms doi: 10.3390/axioms12050461

Authors: Thomas Kotoulas

We study three-dimensional potentials of the form V=U(xp+yp+zp), where U is an arbitrary function of C2-class, and p&isin;Z, which produces a preassigned two-parametric family of spatial regular orbits given in the solved form f(x,y,z) = c1, g(x,y,z) = c2 (c1, c2 = const). These potentials have to satisfy two linear PDEs, which are the basic equations of the 3D inverse problem of Newtonian dynamics. The functions f and g can be represented uniquely by the &rdquo;slope functions&rdquo; &alpha;(x,y,z) and &beta;(x,y,z). The orbital functions &alpha;(x,y,z) and &beta;(x,y,z) have to satisfy three differential conditions according to the theory of the inverse problem. If these conditions are satisfied, then we can find such a potential analytically. We offer pertinent examples of potentials that are mainly used in physical problems. The values obtained for p lead to cases of well-known potentials, such as the Newtonian, cored, logarithmic, polynomial and quadratic ones. New families of orbits produced by the 3D harmonic oscillator are found. Pertinent examples are given and cover all cases. Two-dimensional potentials belong to a special category of potentials and are studied separately. The families of straight lines in 3D space are also examined.

]]>Axioms doi: 10.3390/axioms12050460

Authors: Muhammad Shoaib Arif Kamaleldin Abodayeh Yasir Nawaz

The main aim of this contribution is to construct a numerical scheme for solving stochastic time-dependent partial differential equations (PDEs). This has the advantage of solving problems with positive solutions. The scheme provides conditions for obtaining positive solutions, which the existing Euler&ndash;Maruyama method cannot do. In addition, it is more accurate than the existing stochastic non-standard finite difference (NSFD) method. Theoretically, the suggested scheme is more accurate than the current NSFD method, and its stability and consistency analysis are also shown. The scheme is applied to the linear scalar stochastic time-dependent parabolic equation and the nonlinear auto-catalytic Brusselator model. The deficiency of the NSFD in terms of accuracy is also shown by providing different graphs. Many observable occurrences in the physical world can be traced back to certain chemical concentrations. Examining and understanding the inter-diffusion between chemical concentrations is important, especially when they coincide. The Brusselator model is the gold standard for describing the relationship between chemical concentrations and other variables in chemical systems. A computational code for the proposed model scheme may be made available to readers upon request for convenience.

]]>Axioms doi: 10.3390/axioms12050459

Authors: Paulina Gonzalez-Ayala Avelina Alejo-Reyes Erik Cuevas Abraham Mendoza

Economic Order Quantity (EOQ) is an important optimization problem for inventory management with an impact on various industries; however, their mathematical models may be complex with non-convex, non-linear, and non-differentiable objective functions. Metaheuristic algorithms have emerged as powerful tools for solving complex optimization problems (including EOQ). They are iterative search techniques that can efficiently explore large solution spaces and obtain near-optimal solutions. Simulated Annealing (SA) is a widely used metaheuristic method able to avoid local suboptimal solutions. The traditional SA algorithm is based on a single agent, which may result in a low convergence rate for complex problems. This article proposes a modified multiple-agent (population-based) adaptive SA algorithm; the adaptive algorithm imposes a slight attraction of all agents to the current best solution. As a proof of concept, the proposed algorithm was tested on a particular EOQ problem (recently studied in the literature and interesting by itself) in which the objective function is non-linear, non-convex, and non-differentiable. With these new mechanisms, the algorithm allows for the exploration of different regions of the solution space and determines the global optimum in a faster manner. The analysis showed that the proposed algorithm performed well in finding good solutions in a reasonably short amount of time.

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Authors: Atif Ali Wagan Qianmu Li Zubair Zaland Shah Marjan Dadan Khan Bozdar Aamir Hussain Aamir Mehmood Mirza Mehmood Baryalai

The DNS firewall plays an important role in network security. It is based on a list of known malicious domain names, and, based on these lists, the firewall blocks communication with these domain names. However, DNS firewalls can only block known malicious domain names, excluding communication with unknown malicious domain names. Prior research has found that machine learning techniques are effective for detecting unknown malicious domain names. However, those methods have limited capabilities to learn from both textual and numerical data. To solve this issue, we present a novel unified learning approach that uses both numerical and textual features of the domain name to classify whether a domain name pair is malicious or not. The experiments were conducted on a benchmark domain names dataset consisting of 90,000 domain names. The experimental results show that the proposed approach performs significantly better than the six comparative methods in terms of accuracy, precision, recall, and F1-Score.

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Authors: Ričardas Krikštolaitis Gintautas Mozgeris Edmundas Petrauskas Petras Rupšys

Stochastic differential equations and Copula theories are important topics that have many advantages for applications in almost every discipline. Many studies in forestry collect longitudinal, multi-dimensional, and discrete data for which the amount of measurement of individual variables does not match. For example, during sampling experiments, the diameters of all trees, the heights of approximately 10% of the trees, and the tree crown base height and crown width for a significantly smaller number of trees are measured. In this study, for estimating five-dimensional dependencies, we used a normal copula approach, where the dynamics of individual tree variables (diameter, potentially available area, height, crown base height, and crown width) are described by a stochastic differential equation with mixed-effect parameters. The approximate maximum likelihood method was used to obtain parameter estimates of the presented stochastic differential equations, and the normal copula dependence parameters were estimated using the pseudo-maximum likelihood method. This study introduced the normalized multi-dimensional interaction information index based on differential entropy to capture dependencies between state variables. Using conditional copula-type probability density functions, the exact form equations defining the links among the diameter, potentially available area, height, crown base height, and crown width were derived. All results were implemented in the symbolic algebra system MAPLE.

]]>Axioms doi: 10.3390/axioms12050456

Authors: Zulqurnain Sabir Tareq Saeed Juan L. G. Guirao Juan M. Sánchez Adrián Valverde

The motive of this work is to provide the numerical performances of the reactive transport model that carries trucks with goods on roads by exploiting the stochastic procedures based on the Meyer wavelet (MW) neural network. An objective function is constructed by using the differential model and its boundary conditions. The optimization of the objective function is performed through the hybridization of the global and local search procedures, i.e., swarming and interior point algorithms. Three different cases of the model have been obtained, and the exactness of the stochastic procedure is observed by using the comparison of the obtained and Adams solutions. The negligible absolute error enhances the exactness of the proposed MW neural networks along with the hybridization of the global and local search schemes. Moreover, statistical interpretations based on different operators, histograms, and boxplots are provided to validate the constancy of the designed stochastic structure.

]]>Axioms doi: 10.3390/axioms12050455

Authors: Oscar Castillo

Published for the first time in 2012, Axioms is celebrating its 10th anniversary [...]

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Authors: Asif Ali Shaikh Evren Hincal Sotiris K. Ntouyas Jessada Tariboon Muhammad Tariq

The term convexity and theory of inequalities is an enormous and intriguing domain of research in the realm of mathematical comprehension. Due to its applications in multiple areas of science, the theory of convexity and inequalities have recently attracted a lot of attention from historians and modern researchers. This article explores the concept of a new group of modified harmonic exponential s-convex functions. Some of its significant algebraic properties are elegantly elaborated to maintain the newly described idea. A new sort of Hermite&ndash;Hadamard-type integral inequality using this new concept of the function is investigated. In addition, several new estimates of Hermite&ndash;Hadamard inequality are presented to improve the study. These new results illustrate some generalizations of prior findings in the literature.

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Authors: Tareq Hamadneh Ibraheem Abu Falahah Yazan Alaya AL-Khassawneh Abdallah Al-Husban Abbas Kareem Wanas Teodor Bulboacă

In this article, we introduce and study the behavior of the modules of the first two coefficients for the classes N&Sigma;(&gamma;,&lambda;,&delta;,&mu;;&alpha;) and N&Sigma;*(&gamma;,&lambda;,&delta;,&mu;;&beta;) of normalized holomorphic and bi-univalent functions that are connected with the prestarlike functions. We determine the upper bounds for the initial Taylor&ndash;Maclaurin coefficients |a2| and |a3| for the functions of each of these families, and we also point out some special cases and consequences of our main results. The study of these classes is closely connected with those of Ruscheweyh who in 1977 introduced the classes of prestarlike functions of order &mu; using a convolution operator and the proofs of our results are based on the well-known Carath&eacute;dory&rsquo;s inequality for the functions with real positive part in the open unit disk. Our results generalize a few of the earlier ones obtained by Li and Wang, Murugusundaramoorthy et al., Brannan and Taha, and could be useful for those that work with the geometric function theory of one-variable functions.

]]>Axioms doi: 10.3390/axioms12050452

Authors: Durkbin Cho

We construct an overlapping additive Schwarz preconditioner for the biharmonic Dirichlet problems discretized by isogeometric analysis based on generalized B-splines (GB-splines) and analyze its optimal convergence rate bound that is cubic in the ratio between subdomains and overlap sizes. Our analysis is validated through a set of numerical experiments that illustrate good behavior of the proposed preconditioner with respect to the model parameters.

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Authors: Laura Pezza Simmaco Di Lillo

A dynamical system is a particle or set of particles whose state changes over time. The dynamics of the system is described by a set of differential equations. If the derivatives involved are of non-integer order, we obtain a fractional dynamical system. In this paper, we considered a fractional dynamical system with the Caputo fractional derivative. We collocated the fractional differential problem in dyadic nodes and used refinable functions as approximation functions to achieve a good degree of freedom in the choice of the regularity. The collocation method stands out as a particularly useful and attractive tool for solving fractional differential problems of various forms. A numerical result is presented to show that the numerical solution fits the analytical one very well. We collocated the fractional differential problem in dyadic nodes using refinable functions as approximation functions to achieve a good degree of freedom in the choice of regularity.

]]>Axioms doi: 10.3390/axioms12050450

Authors: Lina Zheng Yiqiao Wang Weifan Wang

The difference of Zagreb indices of a graph G is defined as &Delta;M(G)=&sum;u&isin;V(G)(d(u))2&minus;&sum;uv&isin;E(G)d(u)d(v), where d(x) denotes the degree of a vertex x in G. A Halin graph G is a graph that results from a plane tree T without vertices of degree two and with at least one vertex of degree at least three such that all leaves are joined through a cycle C in the embedded order. In this paper, we establish both lower and upper bounds on the difference of Zagreb indices for general Halin graphs and some special Halin graphs with fewer inner vertices. Furthermore, extremal graphs attaining related bounds are found.

]]>Axioms doi: 10.3390/axioms12050449

Authors: Barakah Almarri Ahmed A. El-Deeb

We investigated several novel conformable fractional gamma-nabla dynamic Hardy&ndash;Hilbert inequalities on time scales in this study. Several continuous inequalities and their corresponding discrete analogues in the literature are combined and expanded by these inequalities. H&ouml;lder&rsquo;s inequality on time scales and a few algebraic inequalities are used to demonstrate our findings.

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Authors: Gabriel Marín Díaz Ramón Alberto Carrasco González

In the literature, the Information Technology Infrastructure Library (ITIL) methodology recommends determining the priority of incident resolution based on the impact and urgency of interactions. The RFID model, based on the parameters of Recency, Frequency, Importance and Duration in the resolution of incidents, provides an individual assessment and a clustering of customers based on these factors. We can improve the traditional concept of waiting queues for customer service management by using a procedure that adds to the evaluation provided by RFID such additional factors as Impact, Urgency and Emotional character of each interaction. If we also include aspects such as Waiting Time and Contact Center Workload, we have a procedure that allows prioritizing interactions between the customer and the Contact Center dynamically and in real time. In this paper we propose to apply a model of unification of heterogeneous information in 2-tuple linguistic evaluations, to obtain a global evaluation of each interaction by applying the Analytic Hierarchy Process (AHP), and in this way be able to have a dynamic process of prioritization of interactions.

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Authors: Farah M. Al-Askar Clemente Cesarano Wael W. Mohammed

In the current study, we investigate the stochastic Benjamin&ndash;Bona&ndash;Mahony equation with beta derivative (SBBME-BD). The considered stochastic term is the multiplicative noise in the It&ocirc; sense. By combining the F-expansion approach with two separate equations, such as the Riccati and elliptic equations, new hyperbolic, trigonometric, rational, and Jacobi elliptic solutions for SBBME-BD can be generated. The solutions to the Benjamin&ndash;Bona&ndash;Mahony equation are useful in understanding various scientific phenomena, including Rossby waves in spinning fluids and drift waves in plasma. Our results are presented using MATLAB, with numerous 3D and 2D figures illustrating the impacts of white noise and the beta derivative on the obtained solutions of SBBME-BD.

]]>Axioms doi: 10.3390/axioms12050446

Authors: Caixia Zhang Yanlin Shi

Recent research suggests that long memory can be caused by regime switching and is easily confused with it. However, if the causes of confusion were properly controlled, they could be distinguished. Motivated by this idea, our study aims to distinguish between the long memory and regime switching of financial volatility. We firstly modeled the long memory and regime switching of volatility using the Fractionally Integrated Exponential GARCH (FIEGARCH) and Markov Regime-Switching EGARCH (MRS-EGARCH) frameworks, respectively, and performed a simulation study on their finite-sample properties when innovations followed a non-normal distribution. Subsequently, we demonstrated the confusion between the FIEGARCH and MRS-EGARCH processes using simulations. A recent study theoretically proved that the time-varying smoothing probability series can induce the presence of significant long memory in the regime-switching process. To control for its effect, the two-stage two-state FIEGARCH and MRS-FIEGARCH frameworks are proposed. The Monte Carlo studies showed that both frameworks can effectively distinguish between the pure FIEGARCH and pure MRS-EGARCH processes. When the MRS-FIEGARCH model was further employed to fit series generated with the MRS-FIEGARCH process, it outperformed the ordinary FIEGARCH model. Finally, an empirical study of NASDAQ index return was conducted to demonstrate that our MRS-FIEGARCH model can provide potentially more reliable long-memory estimates, identify the volatility states and outperform both the FIEGARCH and MRS-EGARCH models.

]]>Axioms doi: 10.3390/axioms12050444

Authors: Mohamed Karek Sadok Otmani Keltoum Bouhali Khaled Zennir Hatim M. Elkhair Eltegani I. Hassan Alnadhief H. A. Alfedeel Almonther Alarfaj

This article is devoted to a study of the question of existence (in time) of weak solutions and the derivation of qualitative properties of such solutions for the nonlinear viscoelastic wave equation with variable exponents and minor damping terms. By using the energy method combined with the Faedo&ndash;Galerkin method, the local and global existence of solutions are established. Then, the stability estimate of the solution is obtained by introducing a suitable Lyapunov function.

]]>Axioms doi: 10.3390/axioms12050445

Authors: Davide Falessi Fabien Schang

This article aims at providing some extension of the modal square of opposition in the light of Ockham&rsquo;s account of modal operators. Moreover, we set forth some significant remarks on the de re&ndash;de dicto distinction and on the modal operator of contingency by means of a set-theoretic algebra called numbering semantics. This generalization starting from Ockham&rsquo;s account of modalities will allow us to take into consideration whether Ockham&rsquo;s account holds water or not, and in which case it should be changed.

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Authors: Ibtisam Aldawish Mohamed Jleli Bessem Samet

Hermite&ndash;Hadamard inequality is a double inequality that provides an upper and lower bounds of the mean (integral) of a convex function over a certain interval. Moreover, the convexity of a function can be characterized by each of the two sides of this inequality. On the other hand, it is well known that a twice differentiable function is convex, if and only if it admits a nonnegative second-order derivative. In this paper, we obtain a characterization of a class of twice differentiable functions (including the class of convex functions) satisfying second-order differential inequalities. Some special cases are also discussed.

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Authors: Ramzy M. Abumandour Adel M. El-Reafay Khaled M. Salem Ahmed S. Dawood

The expanded wall channel backward-facing step (BFS) and axisymmetric diffuser plays an important role in the society of fluid dynamics. Using a cut-cell technique is an established new method to treat the inclined wall of an axisymmetric diffuser. Cut-cell handle to reach the shape of the inclined wall, an axisymmetric diffuser and complex geometry. It helps treat the boundary condition at the wall in an accurate physical way. The turbulent flow through the geometries is solved by using Reynolds averaged Navier-Stokes equations (RANS) with the standard k-&epsilon; model. A self-built FOTRAN code based on the finite volume method with the Semi-Implicit Method for Pressure Linked Equations (SIMPLE) algorithm for pressure velocity coupling is established and examined with published experimental data for two different geometries backward-facing step (BFS) and axisymmetric diffuser. The results of the new technique reflect good agreement between the numerical results and the experimental data. A parametric study of the impact of area ratios (2, 2.5, 3, 3.5) in a backward-facing step on pressure, velocity, and turbulent kinetic energy. The angles (7&deg;, 10&deg;, 14&deg;) and area ratios (2, 2.5, 3, 3.5) effect of an axisymmetric diffuser on the streamlines, local skin friction, pressure, velocity, turbulent kinetic energy, and separation zone.

]]>Axioms doi: 10.3390/axioms12050440

Authors: Thanasak Mouktonglang Kanyuta Poochinapan Suriyon Yimnet

The stability problem of switched systems plays an essential role in the study of long-term behavior. In fact, systems containing both time delay and uncertainty terms may lead to performance degradation of those systems. Therefore, we are interested in the robust stability for discrete-time switched positive time-varying delay systems with interval uncertainties in the case of all modes being unstable. Based on the proposed time-scheduled multiple co-positive Lyapunov&ndash;Krasovskii functional of each mode, new sufficient conditions for the global uniform asymptotic stability of the systems are derived. An effective time-dependent switching law utilized in this work is mode-dependent dwell time. In addition, the robust stability criteria in an asymptotic sense are formulated for the systems without time-varying delay. Compared with the existing related works, our results are less conservative and more general than some previous research. Finally, two numerical examples are provided to illustrate the effectiveness and correctness of the developed theoretical results.

]]>Axioms doi: 10.3390/axioms12050441

Authors: Basem Aref Frasin Luminiţa-Ioana Cotîrlă

Recently, some researchers determined lower bounds for the normalized version of some special functions to its sequence of partial sums, e.g., Struve and Dini functions, Wright functions and Miller&ndash;Ross functions. In this paper, we determine lower bounds for the normalized Le Roy-type Mittag-Leffler function F&alpha;,&beta;&gamma;(z)=z+&sum;n=1&infin;Anzn+1, where An=&Gamma;&beta;&Gamma;&alpha;(n&minus;1)+&beta;&gamma; and its sequence of partial sums (F&alpha;,&beta;&gamma;(z))m(z)=z+&sum;n=1mAnzn+1. Several examples of the main results are also considered.

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Authors: Bahady I. Mohammed Yusra A. Tashkandy Mohmoud M. Abd El-Raouf Md. Moyazzem Hossain Mahmoud E. Bakr

In this article, we present a Markov Bernoulli Lomax (MB-L) model, which is obtained by a countable mixture of Markov Bernoulli and Lomax distributions, with decreasing and unimodal hazard rate function (HRF). The new model contains Marshall- Olkin Lomax and Lomax distributions as a special case. The mathematical properties, as behavior of probability density function (PDF), HRF, rth moments, moment generating function (MGF) and minimum (maximum) Markov-Bernoulli Geometric (MBG) stable are studied. Moreover, the estimates of the model parameters by maximum likelihood are obtained. The maximum likelihood estimation (MLE), bias and mean squared error (MSE) of MB-L parameters are inspected by simulation study. Finally, a MB-L distribution was fitted to the randomly censored and COVID-19 (complete) data.

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Authors: Svyatoslav Nykorovych Oleh Nykyforchyn Andriy Zagorodnyuk

In this paper we study pseudoultrametrics, which are a natural mixture of ultrametrics and pseudometrics. They satisfy a stronger form of the triangle inequality than usual pseudometrics and naturally arise in problems of classification and recognition. The text focuses on the natural partial order on the set of all pseudoultrametrics on a fixed (not necessarily finite) set. In addition to the &ldquo;way below&rdquo; relation induced by a partial order, we introduce its version which we call &ldquo;weakly way below&rdquo;. It is shown that a pseudoultrametric should satisfy natural conditions closely related to compactness, for the set of all pseudoultrametric weakly way below it to be non-trivial (to consist not only of the zero pseudoultrametric). For non-triviality of the set of all pseudoultrametrics way below a given one, the latter must be compact. On the other hand, each compact pseudoultrametric is the least upper bound of the directed set of all pseudoultrametrics way below it, which are compact as well. Thus it is proved that the set CPsU(X) of all compact pseudoultrametric on a set X is a continuous poset. This shows that compactness is a crucial requirement for efficiency of approximation in methods of classification by means of ultrapseudometrics.

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Authors: Juan F. R. Archilla Jānis Bajārs

In this paper, we study the spectral properties of polarobreathers, that is, breathers carrying charge in a one-dimensional semiclassical model. We adapt recently developed numerical methods that preserve the charge probability at every step of time integration without using the Born&ndash;Oppenheimer approximation, which is the assumption that the electron is not at equilibrium with the atoms or ions. We develop an algorithm to obtain exact polarobreather solutions. The properties of polarobreathers, both stationary and moving ones, are deduced from the lattice and charge variable spectra in the frequency&ndash;momentum space. We consider an efficient approach to produce approximate polarobreathers with long lifespans. Their spectrum allows for the determination of the initial conditions and the necessary parameters to obtain numerically exact polarobreathers. The spectra of exact polarobreathers become extremely simple and easy to interpret. We also solve the problem that the charge frequency is not an observable, but the frequency of the charge probability certainly is an observable.

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Authors: Osama Abdulaziz Alamri

Fundamentally, newborn items that are used commercially, such as chicken, fish, and small camel, grow day by day in size and also increase their weight. The seller offers a credit policy to the buyer to increase sales for a particular growing item (fish), and in this paper, it is assumed that the buyer accepts the policy of the trade credit. In this paper, the buyer acquires the newborn items (fish) from the seller and then sells them when the newborn items have increased their size and weight. From this point of view, the present paper reveals a fuzzy-based supply chain model that includes carbon emissions and a permissible delay in payment for defective growing items (fish) under the effect of learning where the demand rate is imprecise in nature and is treated as a triangular fuzzy number. Finally, the buyer&rsquo;s total profit is optimized with respect to the number of newborn items. A numerical example has been presented for the justification of the model. The findings clearly suggest that the presence of trade credit, learning, and a fuzzy environment have an affirmative effect on the ordering policy. The buyer should order more to avoid higher interest charges after the grace period, which eventually increases their profit, while at the same time, it is also beneficial for the buyer to order less to gain the benefit of the trade credit period. The fuzziness theory controls the uncertainty situation of inventory parameters with the help of a de-fuzzified method. The lower and upper deviation of demand affects the total fuzzy profit. The effect of learning gives a positive response concerning the size of the order and the buyer&rsquo;s total fuzzy profit. This means that the decision-maker should be aware of the size of the newborn items, rate of learning, and trade credit period during the supply chain because these directly affect the buyer&rsquo;s total fuzzy profit. The impact of the inventory parameter of this model is presented with the help of sensitivity analysis.

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Authors: Ehsan Movahednia Manuel De la Sen

This article explores the stability of involution in fuzzy C&#9733;-algebras through the use of a functional inequality. We present an approach to obtaining an approximate involution in fuzzy C&#9733;-algebras by utilizing a fixed-point method. Moreover, for greater clarity, we implemented Python code for the main theorem.

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Authors: Kristina Krulić Himmelreich Josip Pečarić Dora Pokaz Marjan Praljak

In this paper we extend general Hardy&rsquo;s inequality by appropriately combining Montgomery&rsquo;s identity and Green functions. Related Gr&uuml;ss and Ostrowski-type inequalities are also derived.

]]>Axioms doi: 10.3390/axioms12050433

Authors: Likai Liu Jie Zhai Jin-Lin Liu

A new subclass of bi-univalent functions associated with the Hohlov operator is introduced. Certain properties such as the coefficient bounds, Fekete-Szeg&ouml; inequality and the second Hankel determinant for functions in the subclass are obtained. In particular, several known results are generalized.

]]>Axioms doi: 10.3390/axioms12050432

Authors: Dimitar Razpopov Georgi Dzhelepov Iva Dokuzova

Our research focuses on the tangent space of a point on a four-dimensional Riemannian manifold. Besides having a positive definite metric, the manifold is endowed with an additional tensor structure of type (1,1), whose fourth power is minus the identity. The additional structure is skew-circulant and compatible with the metric, such that an isometry is induced in every tangent space on the manifold. Both structures define an indefinite metric. With the help of the indefinite metric, we determine circles in different two-planes in the tangent space on the manifold. We also calculate the length and area of the circles. On a smooth closed curve, such as a circle, we define a vector force field. Further, we obtain the circulation of the vector force field along the curve, as well as the flux of the curl of this vector force field across the curve. Finally, we find a relation between these two values, which is an analog of the well-known Green&rsquo;s formula in the Euclidean space.

]]>Axioms doi: 10.3390/axioms12050431

Authors: Guimei Jiao Jiajuan Liang Fanjuan Wang Xiaoli Chen Shaokang Chen Hao Li Jing Jin Jiali Cai Fangjie Zhang

A Bayesian semiparametric model framework is proposed to analyze multivariate longitudinal data. The new framework leads to simple explicit posterior distributions of model parameters. It results in easy implementation of the MCMC algorithm for estimation of model parameters and demonstrates fast convergence. The proposed model framework associated with the MCMC algorithm is validated by four covariance structures and a real-life dataset. A simple Monte Carlo study of the model under four covariance structures and an analysis of the real dataset show that the new model framework and its associated Bayesian posterior inferential method through the MCMC algorithm perform fairly well in the sense of easy implementation, fast convergence, and smaller root mean square errors compared with the same model without the specified autoregression structure.

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