Axioms doi: 10.3390/axioms10030236

Authors: Robert Reynolds Allan Stauffer

A class of definite integrals involving a quotient function with a reducible polynomial, logarithm and nested logarithm functions are derived with a possible connection to contact problems for a wedge. The derivations are expressed in terms of the Lerch function. Special cases are also derived in terms fundamental constants. The majority of the results in this work are new.

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Authors: Rovana Boruga(Toma) Mihail Megan Daniela Maria-Magdalena Toth

The aim of this paper is to present some integral characterizations for the concept of uniform stability with growth rates in Banach spaces. In this sense, we prove necessary and sufficient conditions (of Barbashin and Datko type) for an evolution operator to be uniform h- stable. As particular cases of this notion, we obtain four characterizations for uniform exponential stability and two characterizations for uniform polynomial stability.

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Authors: Vladimir Vasilyev Nikolai Eberlein

We study a certain conjugation problem for a pair of elliptic pseudo-differential equations with homogeneous symbols inside and outside of a plane sector. The solution is sought in corresponding Sobolev–Slobodetskii spaces. Using the wave factorization concept for elliptic symbols, we derive a general solution of the conjugation problem. Adding some complementary conditions, we obtain a system of linear integral equations. If the symbols are homogeneous, then we can apply the Mellin transform to such a system to reduce it to a system of linear algebraic equations with respect to unknown functions.

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Authors: Rajat Kanti Nath Monalisha Sharma Parama Dutta Yilun Shang

Let R be a finite ring and r∈R. The r-noncommuting graph of R, denoted by ΓRr, is a simple undirected graph whose vertex set is R and two vertices x and y are adjacent if and only if [x,y]≠r and [x,y]≠−r. In this paper, we obtain expressions for vertex degrees and show that ΓRr is neither a regular graph nor a lollipop graph if R is noncommutative. We characterize finite noncommutative rings such that ΓRr is a tree, in particular a star graph. It is also shown that ΓR1r and ΓR2ψ(r) are isomorphic if R1 and R2 are two isoclinic rings with isoclinism (ϕ,ψ). Further, we consider the induced subgraph ΔRr of ΓRr (induced by the non-central elements of R) and obtain results on clique number and diameter of ΔRr along with certain characterizations of finite noncommutative rings such that ΔRr is n-regular for some positive integer n. As applications of our results, we characterize certain finite noncommutative rings such that their noncommuting graphs are n-regular for n≤6.

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Authors: Akhmed Dzhabrailov Yuri Luchko Elina Shishkina

In this paper, we treat a convolution-type operator called the generalized Bessel potential. Our main result is the derivation of two different forms of its inversion. The first inversion is provided in terms of an approximative inverse operator using the method of an improving multiplier. The second one employs the regularization technique for the divergent integrals in the form of the appropriate segments of the Taylor–Delsarte series.

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Authors: Cristian Chifu Erdal Karapınar Gabriela Petrusel

The purpose of this paper is to present some fixed point results for Frum-Ketkov type operators in complete b-metric spaces.

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Authors: Entsar A. Abdel-Rehim

In this paper, the time-fractional wave equation associated with the space-fractional Fokker–Planck operator and with the time-fractional-damped term is studied. The concept of the Green function is implemented to drive the analytic solution of the three-term time-fractional equation. The explicit expressions for the Green function G3(t) of the three-term time-fractional wave equation with constant coefficients is also studied for two physical and biological models. The explicit analytic solutions, for the two studied models, are expressed in terms of the Weber, hypergeometric, exponential, and Mittag–Leffler functions. The relation to the diffusion equation is given. The asymptotic behaviors of the Mittag–Leffler function, the hypergeometric function 1F1, and the exponential functions are compared numerically. The Grünwald–Letnikov scheme is used to derive the approximate difference schemes of the Caputo time-fractional operator and the Feller–Riesz space-fractional operator. The explicit difference scheme is numerically studied, and the simulations of the approximate solutions are plotted for different values of the fractional orders.

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Authors: Hari Mohan Srivastava Bidu Bhusan Jena Susanta Kumar Paikray

In this work we introduce and investigate the ideas of statistical Riemann integrability, statistical Riemann summability, statistical Lebesgue integrability and statistical Lebesgue summability via deferred weighted mean. We first establish some fundamental limit theorems connecting these beautiful and potentially useful notions. Furthermore, based upon our proposed techniques, we establish the Korovkin-type approximation theorems with algebraic test functions. Finally, we present two illustrative examples under the consideration of positive linear operators in association with the Bernstein polynomials to exhibit the effectiveness of our findings.

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Authors: Mdi Begum Jeelani Abeer S. Alnahdi Mohammed S. Abdo Mansour A. Abdulwasaa Kamal Shah Hanan A. Wahash

This manuscript is devoted to investigating a fractional-order mathematical model of COVID-19. The corresponding derivative is taken in Caputo sense with power-law of fractional order μ and fractal dimension χ. We give some detailed analysis on the existence and uniqueness of the solution to the proposed problem. Furthermore, some results regarding basic reproduction number and stability are given. For the proposed theoretical analysis, we use fixed point theory while for numerical analysis fractional Adams–Bashforth iterative techniques are utilized. Using our numerical scheme is verified by using some real values of the parameters to plot the approximate solution to the considered model. Graphical presentations corresponding to different values of fractional order and fractal dimensions are given. Moreover, we provide some information regarding the real data of Saudi Arabia from 1 March 2020 till 22 April 2021, then calculated the fatality rates by utilizing the SPSS, Eviews and Expert Modeler procedure. We also built forecasts of infection for the period 23 April 2021 to 30 May 2021, with 95% confidence.

]]>Axioms doi: 10.3390/axioms10030227

Authors: Mei Liu Bo Sang Ning Wang Irfan Ahmad

This paper is about the dynamical evolution of a family of chaotic jerk systems, which have different attractors for varying values of parameter a. By using Hopf bifurcation analysis, bifurcation diagrams, Lyapunov exponents, and cross sections, both self-excited and hidden attractors are explored. The self-exited chaotic attractors are found via a supercritical Hopf bifurcation and period-doubling cascades to chaos. The hidden chaotic attractors (related to a subcritical Hopf bifurcation, and with a unique stable equilibrium) are also found via period-doubling cascades to chaos. A circuit implementation is presented for the hidden chaotic attractor. The methods used in this paper will help understand and predict the chaotic dynamics of quadratic jerk systems.

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Authors: Efthimios Providas Stefanos Zaoutsos Ioannis Faraslis

This paper deals with the solution of boundary value problems for ordinary differential equations with general boundary conditions. We obtain closed-form solutions in a symbolic form of problems with the general n-th order differential operator, as well as the composition of linear operators. The method is based on the theory of the extensions of linear operators in Banach spaces.

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Authors: Alberto Castejón María Jesús Chasco Eusebio Corbacho Virgilio Rodríguez de Miguel

The usefulness of Fubini’s theorem as a measurement instrument is clearly understood from its multiple applications in Analysis, Convex Geometry, Statistics or Number Theory. This article is an expository paper based on a master class given by the second author at the University of Vigo and is devoted to presenting some Applications of Fubini’s theorem. In the first part, we present Brunn–Minkowski’s and Isoperimetric inequalities. The second part is devoted to the estimations of volumes of sections of balls in Rn.

]]>Axioms doi: 10.3390/axioms10030224

Authors: Yang Shen Pengjiang Wang Weixiong Zheng Xiaodong Ji Hai Jiang Miao Wu

The strapdown inertial navigation system can provide the navigation information for the boom-type roadheader in the unmanned roadway tunneling working face of the coal mine. However, the complex vibration caused by the cutting process of the boom-type roadheader may result in significant errors of its attitude and position measured by the strapdown inertial navigation system. Thus, an error compensation method based on the vibration characteristics of the roadheader is proposed in this paper. In order to further analyze the angular and linear vibration of the fuselage, as the main vibration sources of the roadheader, the dynamic model of the roadheader is formulated based on the cutting load. Following that, multiple sub-samples compensation algorithms for the coning and sculling errors are constructed. Simulation experiments were carried out under different subsample compensation algorithms, different coal and rock characteristics, and different types of roadheader. The experimental results show that the proposed error compensation algorithm can eliminate the effect of the angular and linear vibration on the measurement accuracy. The coning and sculling error of the strapdown inertial navigation system can reduce at least 52.21% and 42.89%, respectively. Finally, a strapdown inertial navigation error compensation accuracy experiment system is built, and the validity and superiority of the method proposed in this paper are verified through calculation and analysis of the data collected on the actual tunneling work face.

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Authors: Erhan Set Ahmet Ocak Akdemir Ali Karaoǧlan Thabet Abdeljawad Wasfi Shatanawi

Fractional operators are one of the frequently used tools to obtain new generalizations of clasical inequalities in recent years and many new fractional operators are defined in the literature. This development in the field of fractional analysis has led to a new orientation in various branches of mathematics and in many of the applied sciences. Thanks to this orientation, it has brought a whole new dimension to the field of inequality theory as well as many other disciplines. In this study, a new lemma has been proved for the fractional integral operator defined by Atangana and Baleanu. Later with the help of this lemma and known inequalities such as Young, Jensen, Hölder, new generalizations of Hermite-Hadamard inequality are obtained. Many reduced corollaries about the main findings are presented for classical integrals.

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Authors: Feliz Minhós Nuno Oliveira

This work concerns with the solvability of third-order periodic fully problems with a weighted parameter, where the nonlinearity must verify only a local monotone condition and no periodic, coercivity or super or sublinearity restrictions are assumed, as usual in the literature. The arguments are based on a new type of lower and upper solutions method, not necessarily well ordered. A Nagumo growth condition and Leray–Schauder’s topological degree theory are the existence tools. Only the existence of solution is studied here and it will remain open the discussion on the non-existence and the multiplicity of solutions. Last section contains a nonlinear third-order differential model for periodic catatonic phenomena, depending on biological and/or chemical parameters.

]]>Axioms doi: 10.3390/axioms10030221

Authors: David Yost

We discuss two facets of the interaction between geometry and algebra in Banach algebras. In the class of unital Banach algebras, there is essentially one known example which is also strictly convex as a Banach space. We recall this example, which is finite-dimensional, and consider the open question of generalising it to infinite dimensions. In C∗-algebras, we exhibit one striking example of the tighter relationship that exists between algebra and geometry there.

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Authors: Hongying Xiao Weidong Wang Zhaofeng Li

In this article, we introduce the concept of general Lp-mixed chord integral difference of star bodies. Further, we establish the Brunn–Minkowski type, Aleksandrov–Fenchel type and cyclic inequalities for the Lp-mixed chord integral difference.

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Authors: Paolo Emilio Ricci Rekha Srivastava Pierpaolo Natalini

In this article, we derive representation formulas for a class of r-associated Stirling numbers of the second kind and examine their connections with a class of generalized Bernoulli polynomials. Herein, we use the Blissard umbral approach and the familiar Bell polynomials. Links with available literature on this subject are also pointed out. The extension to the bivariate case is discussed.

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Authors: Ali Fares Ali Ayad Bruno de Malafosse

Given any sequence z=znn≥1 of positive real numbers and any set E of complex sequences, we write Ez for the set of all sequences y=ynn≥1 such that y/z=yn/znn≥1∈E; in particular, sz0 denotes the set of all sequences y such that y/z tends to zero. Here, we consider the infinite tridiagonal matrix Br,s,t˜, obtained from the triangle Br,s,t, by deleting its first row. Then we determine the sets of all positive sequences a=ann≥1 such that EaBr,s,t˜⊂Ea, where E=ℓ∞, c0, or c. These results extend some recent results.

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Authors: Saak Gabriyelyan

It is well known that every normed (even quasibarrelled) space is a Mackey space. However, in the more general realm of locally quasi-convex abelian groups an analogous result does not hold. We give the first examples of normed spaces which are not Mackey groups.

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Authors: Hoang Pham

The immune system is a complex interconnected network consisting of many parts including organs, tissues, cells, molecules and proteins that work together to protect the body from illness when germs enter the body. An autoimmune disease is a disease in which the body’s immune system attacks healthy cells. It is known that when the immune system is working properly, it can clearly recognize and kill the abnormal cells and virus-infected cells. But when it doesn’t work properly, the human body will not be able to recognize the virus-infected cells and, therefore, it can attack the body’s healthy cells when there is no invader or does not stop an attack after the invader has been killed, resulting in autoimmune disease.; This paper presents a mathematical modeling of the virus-infected development in the body’s immune system considering the multiple time-delay interactions between the immune cells and virus-infected cells with autoimmune disease. The proposed model aims to determine the dynamic progression of virus-infected cell growth in the immune system. The patterns of how the virus-infected cells spread and the development of the body’s immune cells with respect to time delays will be derived in the form of a system of delay partial differential equations. The model can be used to determine whether the virus-infected free state can be reached or not as time progresses. It also can be used to predict the number of the body’s immune cells at any given time. Several numerical examples are discussed to illustrate the proposed model. The model can provide a real understanding of the transmission dynamics and other significant factors of the virus-infected disease and the body’s immune system subject to the time delay, including approaches to reduce the growth rate of virus-infected cell and the autoimmune disease as well as to enhance the immune effector cells.

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Authors: Andrés Romero-Arellano Ernesto Moya-Albor Jorge Brieva Ivan Cruz-Aceves Juan Gabriel Avina-Cervantes Martha Alicia Hernandez-Gonzalez Luis Miguel Lopez-Montero

In this work, a new medical image encryption/decryption algorithm was proposed. It is based on three main parts: the Jigsaw transform, Langton’s ant, and a novel way to add deterministic noise. The Jigsaw transform was used to hide visual information effectively, whereas Langton’s ant and the deterministic noise algorithm give a reliable and secure approach. As a case study, the proposal was applied to high-resolution retinal fundus images, where a zero mean square error was obtained between the original and decrypted image. The method performance has been proven through several testing methods, such as statistical analysis (histograms and correlation distributions), entropy computation, keyspace assessment, robustness to differential attack, and key sensitivity analysis, showing in each one a high security level. In addition, the method was compared against other works showing a competitive performance and highlighting with a large keyspace (&gt;1×101,134,190.38). Besides, the method has demonstrated adequate handling of high-resolution images, obtaining entropy values between 7.999988 and 7.999989, an average Number of Pixel Change Rate (NPCR) of 99.5796%±0.000674, and a mean Uniform Average Change Intensity (UACI) of 33.4469%±0.00229. In addition, when there is a small change in the key, the method does not give additional information to decrypt the image.

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Authors: José Ruiz-Meza Karen Meza-Peralta Jairo R. Montoya-Torres Jesus Gonzalez-Feliu

The main concern in city logistics is the need to optimize the movement of goods in urban contexts, and to minimize the multiple costs inherent in logistics operations. Inspired by an application in a medium-sized city in Latin America, this paper develops a bi-objective mixed linear integer programming (MILP) model to locate different types of urban logistics spaces (ULS) for the configuration of a two-echelon urban distribution system. The objective functions seek to minimize the costs associated with distance traveled and relocation, in addition to the costs of violation of time windows. This model considers heterogeneous transport, speed assignment, and time windows. For experimental evaluation, two operational scenarios are considered, and Pareto frontiers are obtained to identify the efficient non-dominated solutions to select the most feasible ones from such a set. A case study of a distribution company of goods for supermarkets in the city of Barranquilla, Colombia, is also used to validate the proposed model. These solutions allow decision-makers to define the configuration of ULS networks for urban product delivery.

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Authors: Mücahit Akbıyık Seda Yamaç Akbıyık Emel Karaca Fatih Yılmaz

It is known that the hybrid numbers are generalizations of complex, hyperbolic and dual numbers. Recently, they have attracted the attention of many scientists. At this paper, we provide the Euler’s and De Moivre’s formulas for the 4×4 matrices associated with hybrid numbers by using trigonometric identities. Also, we give the roots of the matrices of hybrid numbers. Moreover, we give some illustrative examples to support the main formulas.

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Authors: Yaé Ulrich Gaba Hassen Aydi Nabil Mlaiki

We point out a vital error in the paper of Gaba et al. (2019), showing that a (ρ,η,μ) interpolative Kannan contraction in a complete metric space need not have a fixed point. Then we give an appropriate restriction on a (ρ,η,μ)-interpolative Kannan contraction that guarantees the existence of a fixed point and provide an equivalent formulation. Moreover, we show that this formulation can be extended to the interpolative Reich-Rus-Ćirić type contraction.

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Authors: Asuka Ohashi Tomohiro Sogabe

We consider computing an arbitrary singular value of a tensor sum: T:=In⊗Im⊗A+In⊗B⊗Iℓ+C⊗Im⊗Iℓ∈Rℓmn×ℓmn, where A∈Rℓ×ℓ, B∈Rm×m, C∈Rn×n. We focus on the shift-and-invert Lanczos method, which solves a shift-and-invert eigenvalue problem of (TTT−σ˜2Iℓmn)−1, where σ˜ is set to a scalar value close to the desired singular value. The desired singular value is computed by the maximum eigenvalue of the eigenvalue problem. This shift-and-invert Lanczos method needs to solve large-scale linear systems with the coefficient matrix TTT−σ˜2Iℓmn. The preconditioned conjugate gradient (PCG) method is applied since the direct methods cannot be applied due to the nonzero structure of the coefficient matrix. However, it is difficult in terms of memory requirements to simply implement the shift-and-invert Lanczos and the PCG methods since the size of T grows rapidly by the sizes of A, B, and C. In this paper, we present the following two techniques: (1) efficient implementations of the shift-and-invert Lanczos method for the eigenvalue problem of TTT and the PCG method for TTT−σ˜2Iℓmn using three-dimensional arrays (third-order tensors) and the n-mode products, and (2) preconditioning matrices of the PCG method based on the eigenvalue and the Schur decomposition of T. Finally, we show the effectiveness of the proposed methods through numerical experiments.

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Authors: Taye Samuel Faniran Leontine Nkague Nkamba Thomas Timothee Manga

COVID-19 is a highly contagious disease which has spread across the world. A deterministic model that considers an important component of individuals with vertically transmitted underlying diseases (high-risk susceptible individuals), rather than the general public, is formulated in this paper. We also consider key parameters that are concerned with the disease. An epidemiological threshold, R0, is computed using next-generation matrix approach. This is used to establish the existence and global stability of equilibria. We identify the most sensitive parameters which effectively contribute to change the disease dynamics with the help of sensitivity analysis. Our results reveal that increasing contact tracing of the exposed individuals who are tested for COVID-19 and hospitalizing them, largely has a negative impact on R0. Results further reveal that transmission rate between low-risk/high-risk susceptible individuals and symptomatic infectious individuals β and incubation rate of the exposed individuals σ have positive impact on R0. Numerical simulations show that there are fewer high-risk susceptible individuals than the general public when R0&lt;1. This may be due to the fact that high-risk susceptible individuals may prove a bit more difficult to control than the low-risk susceptible individuals as a result of inherited underlying diseases present in them. We thus conclude that high level of tracing and hospitalizing the exposed individuals, as well as adherence to standard precautions and wearing appropriate Personal Protective Equipment (PPE) while handling emergency cases, are needed to flatten the epidemic curve.

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Authors: Atiya Perveen Waleed M. Alfaqih Salvatore Sessa Mohammad Imdad

In this paper, the notion of θ*-weak contraction is introduced, which is utilized to prove some fixed point results. These results are helpful to give a positive response to certain open question raised by Kannan and Rhoades on the existence of contractive definition which does not force the mapping to be continuous at the fixed point. Some illustrative examples are also given to support our results. As applications of our result, we investigate the existence and uniqueness of a solution of non-linear matrix equations and integral equations of Volterra type as well.

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Authors: Muhammad Hamza Naseem Jiaqi Yang Ziquan Xiang

Recently, the demand for third-party logistics providers has become extremely relevant and the key subject for businesses to enhance their service quality and minimize logistics costs. The key success factor for an e-commerce business is product delivery, and the third-party logistics service provider is responsible for that. Each 3PLP has its own business characteristics, meaning it is important to select the most suitable logistics provider for the e-commerce business. This study uses a combination of grey relational analysis (GRA) and the Technique for Order Preference by Similarity to Ideal Solution (TOPSIS) method, assisting decision makers in choosing the best logistics service provider for their e-business. A case study of an e-commerce company based in Faisalabad, Pakistan, was selected to demonstrate the steps of the proposed methods. In this process, seven criteria of logistics suppliers were considered, and then the best alternatives among four logistics provider companies were selected using the proposed method.

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Authors: Takao Komatsu

There are many kinds of generalizations of Cauchy numbers and polynomials. Recently, a parametric type of the Bernoulli numbers with level 3 was introduced and studied as a kind of generalization of Bernoulli polynomials. A parametric type of Cauchy numbers with level 3 is its analogue. In this paper, as an analogue of a parametric type of Bernoulli polynomials with level 3 and its extension, we introduce a parametric type of Cauchy polynomials with a higher level. We present their characteristic and combinatorial properties. By using recursions, we show some determinant expressions.

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Authors: Ji-Eun Kim

The step derivative of a complex function can be defined with various methods. The step direction defines a basis that is distinct from that of a complex number; the derivative can then be treated by using Taylor series expansion in this direction. In this study, we define step derivatives based on complex numbers and quaternions that are orthogonal to the complex basis while simultaneously being distinct from it. Considering previous studies, the step derivative defined using quaternions was insufficient for applying the properties of quaternions by setting a quaternion basis distinct from the complex basis or setting the step direction to which only a part of the quaternion basis was applied. Therefore, in this study, we examine the definition of quaternions and define the step derivative in the direction of a generalized quaternion basis including a complex basis. We find that the step derivative based on the definition of a quaternion has a relative error in some domains; however, it can be used as a substitute derivative in specific domains.

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Authors: Aníbal Coronel Fernando Huancas Alex Tello Marko Rojas-Medar

We introduce new necessary conditions for the existence and uniqueness of stationary weak solutions and the existence of the weak solutions for the evolution problem in the system arising from the modeling of the bioconvective flow problem. Our analysis is based on the application of the Galerkin method, and the system considered consists of three equations: the nonlinear Navier–Stokes equation, the incompressibility equation, and a parabolic conservation equation, where the unknowns are the fluid velocity, the hydrostatic pressure, and the concentration of microorganisms. The boundary conditions are homogeneous and of zero-flux-type, for the cases of fluid velocity and microorganism concentration, respectively.

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Authors: Bootan Rahman Sarbaz H. A. Khoshnaw Grace O. Agaba Fahad Al Basir

In this paper, the aim is to capture the global pandemic of COVID-19 with parameters that consider the interactions among individuals by proposing a mathematical model. The introduction of a parsimonious model captures both the isolation of symptomatic infected individuals and population lockdown practices in response to containment policies. Local stability and basic reproduction numbers are analyzed. Local sensitivity indices of the parameters of the proposed model are calculated, using the non-normalization, half-normalization, and full-normalization techniques. Numerical investigations show that the dynamics of the system depend on the model parameters. The infection transmission rate (as a function of the lockdown parameter) for both reported and unreported symptomatic infected peoples is a significant parameter in spreading the infection. A nationwide public lockdown decreases the number of infected cases and stops the pandemic’s peak from occurring. The results obtained from this study are beneficial worldwide for developing different COVID-19 management programs.

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Authors: Erdoğan Mehmet Özkan Ayten Özkan

Nonlinear fractional differential equations have gained a significant place in mathematical physics. Finding the solutions to these equations has emerged as a field of study that has attracted a lot of attention lately. In this work, He’s semi-inverse variation method and the ansatz method have been applied to find the soliton solutions for fractional Korteweg–de Vries equation, fractional equal width equation, and fractional modified equal width equation defined by Atangana’s conformable derivative (beta-derivative). These two methods are effective methods employed to get the soliton solutions of these nonlinear equations. All of the calculations in this work have been obtained using the Maple program and the solutions have been replaced in the equations and their accuracy has been confirmed. In addition, graphics of some of the solutions are also included. The found solutions in this study have the potential to be useful in mathematical physics and engineering.

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Authors: Mufutau Ajani Rufai Higinio Ramos

This manuscript presents an efficient pair of hybrid Nyström techniques to solve second-order Lane–Emden singular boundary value problems directly. One of the proposed strategies uses three off-step points. The obtained formulas are paired with an appropriate set of formulas implemented for the first step to avoid singularity at the left end of the integration interval. The fundamental properties of the proposed scheme are analyzed. Some test problems, including chemical kinetics and physical model problems, are solved numerically to determine the efficiency and validity of the proposed approach.

]]>Axioms doi: 10.3390/axioms10030201

Authors: Carlos Bejines Sergio Ardanza-Trevijano Jorge Elorza

Preservation of structures under aggregation functions is an active area of research with applications in many fields. Among such structures, min-subgroups play an important role, for instance, in mathematical morphology, where they can be used to model translation invariance. Aggregation of min-subgroups has only been studied for binary aggregation functions. However, results concerning preservation of the min-subgroup structure under binary aggregations do not generalize to aggregation functions with arbitrary input size since they are not associative. In this article, we prove that arbitrary self-aggregation functions preserve the min-subgroup structure. Moreover, we show that whenever the aggregation function is strictly increasing on its diagonal, a min-subgroup and its self-aggregation have the same level sets.

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Authors: Ji-Huan He Mahmoud H. Taha Mohamed A. Ramadan Galal M. Moatimid

The present paper employs a numerical method based on the improved block–pulse basis functions (IBPFs). This was mainly performed to resolve the Volterra–Fredholm integral equations of the second kind. Those equations are often simplified into a linear system of algebraic equations through the use of IBPFs in addition to the operational matrix of integration. Typically, the classical alterations have enhanced the time taken by the computer program to solve the system of algebraic equations. The current modification works perfectly and has improved the efficiency over the regular block–pulse basis functions (BPF). Additionally, the paper handles the uniqueness plus the convergence theorems of the solution. Numerical examples have been presented to illustrate the efficiency as well as the accuracy of the method. Furthermore, tables and graphs are used to show and confirm how the method is highly efficient.

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Authors: Jewgeni H. Dshalalow Ryan T. White

In this paper, we study a reliability system subject to occasional random shocks hitting an underlying device in accordance with a general marked point process with position dependent marking. In addition, the system ages according to a linear path that eventually fails even without any external shocks that accelerate the total failure. The approach for obtaining the distribution of the failure time falls into the area of random walk analysis. The results obtained are in closed form. A special case of a marked Poisson process with exponentially distributed marks is discussed that supports our claim of analytical tractability. The example is further confirmed by simulation. We also provide a classification of the literature pertaining to various reliability systems with degradation and shocks.

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Authors: Yinbin Lei Jun Zhang

It is well known that topological spaces are axiomatically characterized by the topological closure operator satisfying the Kuratowski Closure Axioms. Equivalently, they can be axiomatized by other set operators encoding primitive semantics of topology, such as interior operator, exterior operator, boundary operator, or derived-set operator (or dually, co-derived-set operator). It is also known that a topological closure operator (and dually, a topological interior operator) can be weakened into generalized closure (interior) systems. What about boundary operator, exterior operator, and derived-set (and co-derived-set) operator in the weakened systems? Our paper completely answers this question by showing that the above six set operators can all be weakened (from their topological counterparts) in an appropriate way such that their inter-relationships remain essentially the same as in topological systems. Moreover, we show that the semantics of an interior point, an exterior point, a boundary point, an accumulation point, a co-accumulation point, an isolated point, a repelling point, etc. with respect to a given set, can be extended to an arbitrary subset system simply by treating the subset system as a base of a generalized interior system (and hence its dual, a generalized closure system). This allows us to extend topological semantics, namely the characterization of points with respect to an arbitrary set, in terms of both its spatial relations (interior, exterior, or boundary) and its dynamic convergence of any sequence (accumulation, co-accumulation, and isolation), to much weakened systems and hence with wider applicability. Examples from the theory of matroid and of Knowledge/Learning Spaces are used as an illustration.

]]>Axioms doi: 10.3390/axioms10030197

Authors: Yingying Li Yaxuan Zhang

In this paper, we present some modified relaxed CQ algorithms with different kinds of step size and perturbation to solve the Multiple-sets Split Feasibility Problem (MSSFP). Under mild assumptions, we establish weak convergence and prove the bounded perturbation resilience of the proposed algorithms in Hilbert spaces. Treating appropriate inertial terms as bounded perturbations, we construct the inertial acceleration versions of the corresponding algorithms. Finally, for the LASSO problem and three experimental examples, numerical computations are given to demonstrate the efficiency of the proposed algorithms and the validity of the inertial perturbation.

]]>Axioms doi: 10.3390/axioms10030196

Authors: Hua Guo Guolin Liu Luyao Wang

In this work, we investigate the ill-conditioned problem of a separable, nonlinear least squares model by using the variable projection method. Based on the truncated singular value decomposition method and the Tikhonov regularization method, we propose an improved Tikhonov regularization method, which neither discards small singular values, nor treats all singular value corrections. By fitting the Mackey–Glass time series in an exponential model, we compare the three regularization methods, and the numerically simulated results indicate that the improved regularization method is more effective at reducing the mean square error of the solution and increasing the accuracy of unknowns.

]]>Axioms doi: 10.3390/axioms10030195

Authors: Lili Chen Shilei Lin Yanfeng Zhao

This paper investigates the problem of the global directed dynamic behaviors of a Lotka-Volterra competition-diffusion-advection system between two organisms in heterogeneous environments. The two organisms not only compete for different basic resources, but also the advection and diffusion strategies follow the dispersal towards a positive distribution. By virtue of the principal eigenvalue theory, the linear stability of the co-existing steady state is established. Furthermore, the classification of dynamical behaviors is shown by utilizing the monotone dynamical system theory. This work can be seen as a further development of a competition-diffusion system.

]]>Axioms doi: 10.3390/axioms10030194

Authors: Patricia Ochoa Oscar Castillo Patricia Melin José Soria

This work is mainly focused on improving the differential evolution algorithm with the utilization of shadowed and general type 2 fuzzy systems to dynamically adapt one of the parameters of the evolutionary method. Previously, we have worked with both kinds of fuzzy systems in different types of benchmark problems and it has been found that the use of fuzzy logic in combination with the differential evolution algorithm gives good results. In some of the studies, it is clearly shown that, when compared to other algorithms, our methodology turns out to be statistically better. In this case, the mutation parameter is dynamically moved during the evolution process by using shadowed and general type-2 fuzzy systems. The main contribution of this work is the ability to determine, through experimentation in a benchmark control problem, which of the two kinds of the used fuzzy systems has better results when combined with the differential evolution algorithm. This is because there are no similar works to our proposal in which shadowed and general type 2 fuzzy systems are used and compared. Moreover, to validate the performance of both fuzzy systems, a noise level is used in the controller, which simulates the disturbances that may exist in the real world and is thus able to validate statistically if there are significant differences between shadowed and general type 2 fuzzy systems.

]]>Axioms doi: 10.3390/axioms10030193

Authors: Xue Jiang Kai Cui

Multivariate polynomial interpolation plays a crucial role both in scientific computation and engineering application. Exploring the structure of the D-invariant (closed under differentiation) polynomial subspaces has significant meaning for multivariate Hermite-type interpolation (especially ideal interpolation). We analyze the structure of a D-invariant polynomial subspace Pn in terms of Cartesian tensors, where Pn is a subspace with a maximal total degree equal to n,n≥1. For an arbitrary homogeneous polynomial p(k) of total degree k in Pn, p(k) can be rewritten as the inner products of a kth order symmetric Cartesian tensor and k column vectors of indeterminates. We show that p(k) can be determined by all polynomials of a total degree one in Pn. Namely, if we treat all linear polynomials on the basis of Pn as a column vector, then this vector can be written as a product of a coefficient matrix A(1) and a column vector of indeterminates; our main result shows that the kth order symmetric Cartesian tensor corresponds to p(k) is a product of some so-called relational matrices and A(1).

]]>Axioms doi: 10.3390/axioms10030192

Authors: R. Elayaraja V. Ganesan Omar Bazighifan Clemente Cesarano

The main purpose of this study is aimed at developing new criteria of the iterative nature to test the asymptotic and oscillation of nonlinear neutral delay differential equations of third order with noncanonical operator (a(ι)[(b(ι)x(ι)+p(ι)x(ι−τ)′)′]β)′+∫cdq(ι,μ)xβ(σ(ι,μ))dμ=0, where ι≥ι0 and w(ι):=x(ι)+p(ι)x(ι−τ). New oscillation results are established by using the generalized Riccati technique under the assumption of ∫ι0ιa−1/β(s)ds&lt;∫ι0ι1b(s)ds=∞asι→∞. Our new results complement the related contributions to the subject. An example is given to prove the significance of new theorem.

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Authors: Ji-Huan He Tarek S. Amer Shimaa Elnaggar Abdallah A. Galal

The current paper investigates the dynamical property of a pendulum attached to a rotating rigid frame with a constant angular velocity about the vertical axis passing to the pivot point of the pendulum. He’s homotopy perturbation method is used to obtain the analytic solution of the governing nonlinear differential equation of motion. The fourth-order Runge-Kutta method (RKM) and He’s frequency formulation are used to verify the high accuracy of the obtained solution. The stability condition of the motion is examined and discussed. Some plots of the time histories of the gained solutions are portrayed graphically to reveal the impact of the distinct parameters on the dynamical motion.

]]>Axioms doi: 10.3390/axioms10030190

Authors: Karl H. Hofmann Sidney A. Morris

This article surveys the development of the theory of compact groups and pro-Lie groups, contextualizing the major achievements over 125 years and focusing on some progress in the last quarter century. It begins with developments in the 18th and 19th centuries. Next is from Hilbert’s Fifth Problem in 1900 to its solution in 1952 by Montgomery, Zippin, and Gleason and Yamabe’s important structure theorem on almost connected locally compact groups. This half century included profound contributions by Weyl and Peter, Haar, Pontryagin, van Kampen, Weil, and Iwasawa. The focus in the last quarter century has been structure theory, largely resulting from extending Lie Theory to compact groups and then to pro-Lie groups, which are projective limits of finite-dimensional Lie groups. The category of pro-Lie groups is the smallest complete category containing Lie groups and includes all compact groups, locally compact abelian groups, and connected locally compact groups. Amongst the structure theorems is that each almost connected pro-Lie group G is homeomorphic to RI×C for a suitable set I and some compact subgroup C. Finally, there is a perfect generalization to compact groups G of the age-old natural duality of the group algebra R[G] of a finite group G to its representation algebra R(G,R), via the natural duality of the topological vector space RI to the vector space R(I), for any set I, thus opening a new approach to the Hochschild-Tannaka duality of compact groups.

]]>Axioms doi: 10.3390/axioms10030189

Authors: Sittisak Injan Angkool Wangwongchai Usa Humphries Amir Khan Abdullahi Yusuf

The Ensemble Intermediate Coupled Model (EICM) is a model used for studying the El Niño-Southern Oscillation (ENSO) phenomenon in the Pacific Ocean, which is anomalies in the Sea Surface Temperature (SST) are observed. This research aims to implement Cressman to improve SST forecasts. The simulation considers two cases in this work: the control case and the Cressman initialized case. These cases are simulations using different inputs where the two inputs differ in terms of their resolution and data source. The Cressman method is used to initialize the model with an analysis product based on satellite data and in situ data such as ships, buoys, and Argo floats, with a resolution of 0.25 × 0.25 degrees. The results of this inclusion are the Cressman Initialized Ensemble Intermediate Coupled Model (CIEICM). Forecasting of the sea surface temperature anomalies was conducted using both the EICM and the CIEICM. The results show that the calculation of SST field from the CIEICM was more accurate than that from the EICM. The forecast using the CIEICM initialization with the higher-resolution satellite-based analysis at a 6-month lead time improved the root mean square deviation to 0.794 from 0.808 and the correlation coefficient to 0.630 from 0.611, compared the control model that was directly initialized with the low-resolution in-situ-based analysis.

]]>Axioms doi: 10.3390/axioms10030188

Authors: Kulandhivel Karthikeyan Dhatchinamoorthy Tamizharasan Dimplekumar N. Chalishajar

The functional abstract second order impulsive differential equation with state dependent delay is studied in this paper. First, we consider a second order system and use a control to determine the controllability result. Then, using Sadovskii’s fixed point theorem, we get sufficient conditions for the controllability of the proposed system in a Banach space. The major goal of this study is to demonstrate the controllability of an abstract second-order impulsive differential system with a state dependent delay mechanism. The wellposed condition is then defined. Next, we studied whether the defined problem is wellposed. Finally, we apply our results to examine the controllability of the second order state dependent delay impulsive equation.

]]>Axioms doi: 10.3390/axioms10030187

Authors: Rahul Goyal Shaher Momani Praveen Agarwal Michael Th. Rassias

The main purpose of this paper is to study extension of the extended beta function by Shadab et al. by using 2-parameter Mittag-Leffler function given by Wiman. In particular, we study some functional relations, integral representation, Mellin transform and derivative formulas for this extended beta function.

]]>Axioms doi: 10.3390/axioms10030186

Authors: Erhan Güler

We introduce the fourth fundamental form of a Dini-type helicoidal hypersurface in the four dimensional Euclidean space E4. We find the Gauss map of helicoidal hypersurface in E4. We obtain the characteristic polynomial of shape operator matrix. Then, we compute the fourth fundamental form matrix IV of the Dini-type helicoidal hypersurface. Moreover, we obtain the Dini-type rotational hypersurface, and reveal its differential geometric objects.

]]>Axioms doi: 10.3390/axioms10030185

Authors: Masooma Raza Hashmi Syeda Tayyba Tehrim Muhammad Riaz Dragan Pamucar Goran Cirovic

Modeling uncertainties with spherical linear Diophantine fuzzy sets (SLDFSs) is a robust approach towards engineering, information management, medicine, multi-criteria decision-making (MCDM) applications. The existing concepts of neutrosophic sets (NSs), picture fuzzy sets (PFSs), and spherical fuzzy sets (SFSs) are strong models for MCDM. Nevertheless, these models have certain limitations for three indexes, satisfaction (membership), dissatisfaction (non-membership), refusal/abstain (indeterminacy) grades. A SLDFS with the use of reference parameters becomes an advanced approach to deal with uncertainties in MCDM and to remove strict limitations of above grades. In this approach the decision makers (DMs) have the freedom for the selection of above three indexes in [0,1]. The addition of reference parameters with three index/grades is a more effective approach to analyze DMs opinion. We discuss the concept of spherical linear Diophantine fuzzy numbers (SLDFNs) and certain properties of SLDFSs and SLDFNs. These concepts are illustrated by examples and graphical representation. Some score functions for comparison of LDFNs are developed. We introduce the novel concepts of spherical linear Diophantine fuzzy soft rough set (SLDFSRS) and spherical linear Diophantine fuzzy soft approximation space. The proposed model of SLDFSRS is a robust hybrid model of SLDFS, soft set, and rough set. We develop new algorithms for MCDM of suitable clean energy technology. We use the concepts of score functions, reduct, and core for the optimal decision. A brief comparative analysis of the proposed approach with some existing techniques is established to indicate the validity, flexibility, and superiority of the suggested MCDM approach.

]]>Axioms doi: 10.3390/axioms10030184

Authors: Alexander O. Spiridonov Anna I. Repina Ilya V. Ketov Sergey I. Solov’ev Evgenii M. Karchevskii

The paper investigates an algorithm for the numerical solution of a parametric eigenvalue problem for the Helmholtz equation on the plane specially tailored for the accurate mathematical modeling of lasing modes of microring lasers. The original problem is reduced to a nonlinear eigenvalue problem for a system of Muller boundary integral equations. For the numerical solution of the obtained problem, we use a trigonometric Galerkin method, prove its convergence, and derive error estimates in the eigenvalue and eigenfunction approximation. Previous numerical experiments have shown that the method converges exponentially. In the current paper, we prove that if the generalized eigenfunctions are analytic, then the approximate eigenvalues and eigenfunctions exponentially converge to the exact ones as the number of basis functions increases. To demonstrate the practical effectiveness of the algorithm, we find geometrical characteristics of microring lasers that provide a significant increase in the directivity of lasing emission, while maintaining low lasing thresholds.

]]>Axioms doi: 10.3390/axioms10030183

Authors: José Ángel Sánchez Martín Victor Mitrana

In this paper, we propose direct simulations between a given network of evolutionary processors with an arbitrary topology of the underlying graph and a network of evolutionary processors with underlying graphs—that is, a complete graph, a star graph and a grid graph, respectively. All of these simulations are time complexity preserving—namely, each computational step in the given network is simulated by a constant number of computational steps in the constructed network. These results might be used to efficiently convert a solution of a problem based on networks of evolutionary processors provided that the underlying graph of the solution is not desired.

]]>Axioms doi: 10.3390/axioms10030182

Authors: Tímea Melinda Személy Fülöp Mihail Megan Diana Ioana Borlea(Pătraşcu)

The main purpose of this paper is to study a more general concept of uniform stability in mean in which the uniform behavior in the classical sense is replaced by a weaker requirement with respect to some probability measure. This concept includes, as particular cases, the concepts of uniform exponential stability in mean and uniform polynomial stability in mean. Extending techniques employed in the deterministic case, we obtain variants of some results for the general cases of uniform stability in mean for stochastic skew-evolution semiflows in Banach spaces.

]]>Axioms doi: 10.3390/axioms10030181

Authors: Abdelkader Djerad Ameur Memou Ali Hameida

The aim of this work is to prove the well-posedness of some linear and nonlinear mixed problems with integral conditions defined only on two parts of the considered boundary. First, we establish for the associated linear problem a priori estimate and prove that the range of the operator generated by the considered problem is dense using a functional analysis method. Then by applying an iterative process based on the obtained results for the linear problem, we establish the existence, uniqueness and continuous dependence of the weak solution of the nonlinear problem.

]]>Axioms doi: 10.3390/axioms10030180

Authors: Yoshio Rubio Oscar Montiel

Breast segmentation plays a vital role in the automatic analysis of mammograms. Accurate segmentation of the breast region increments the probability of a correct diagnostic and minimizes computational cost. Traditionally, model-based approaches dominated the landscape for breast segmentation, but recent studies seem to benefit from using robust deep learning models for this task. In this work, we present an extensive evaluation of deep learning architectures for semantic segmentation of mammograms, including segmentation metrics, memory requirements, and average inference time. We used several combinations of two-stage segmentation architectures composed of a feature extraction net (VGG16 and ResNet50) and a segmentation net (FCN-8, U-Net, and PSPNet). The training examples were taken from the mini Mammographic Image Analysis Society (MIAS) database. Experimental results using the mini-MIAS database show that the best net scored a Dice similarity coefficient of 99.37% for breast boundary segmentation and 95.45% for pectoral muscle segmentation.

]]>Axioms doi: 10.3390/axioms10030179

Authors: Hsueh-Li Huang Sin-Jin Lin Ming-Fu Hsu

Compared to widely examined topics in the related literature, such as financial crises/difficulties in accurate prediction, studies on corporate performance forecasting are quite scarce. To fill the research gap, this study introduces an advanced decision making framework that incorporates context-dependent data envelopment analysis (CD-DEA), fuzzy robust principal component analysis (FRPCA), latent Dirichlet allocation (LDA), and stochastic gradient twin support vector machine (SGTSVM) for corporate performance forecasting. Ratio analysis with the merits of easy-to-use and intuitiveness plays an essential role in performance analysis, but it typically has one input variable and one output variable, which is unable to appropriately depict the inherent status of a corporate’s operations. To combat this, we consider CD-DEA as it can handle multiple input and multiple output variables simultaneously and yields an attainable target to analyze decision making units (DMUs) when the data present great variations. To strengthen the discriminant ability of CD-DEA, we also conduct FRPCA, and because numerical messages based on historical principles normally cannot transmit future corporate messages, we execute LDA to decompose the accounting narratives into many topics and preserve those topics that are relevant to corporate operations. Sequentially, the process matches the preserved topics with a sentimental dictionary to exploit the hidden sentiments in each topic. The analyzed data are then fed into SGTSVM to construct the forecasting model. The result herein reveals that the introduced decision making framework is a promising alternative for performance forecasting.

]]>Axioms doi: 10.3390/axioms10030178

Authors: Shih-Hsien Tseng Tien Son Nguyen

Corporate fraud is not only curtailed investors’ rights and privileges but also disrupts the overall market economy. For this reason, the formulation of a model that could help detect any unusual market fluctuations would be essential for investors. Thus, we propose an early warning system for predicting fraud associated with financial statements based on the Bayesian probit model while examining historical data from 1999 to 2017 with 327 businesses in Taiwan to create a visual method to aid in decision making. In this study, we utilize a parametric estimation via the Markov Chain Monte Carlo (MCMC). The result show that it can reduce over or under-confidence within the decision-making process when standard logistic regression is utilized. In addition, the Bayesian probit model in this study is found to offer more accurate calculations and not only represent the prediction value of the responses but also possible ranges of these responses via a simple plot.

]]>Axioms doi: 10.3390/axioms10030177

Authors: Francisco J. Fernández Miguel E. Vázquez-Méndez

This work deals aims to present a methodology for source identification of chemical incidents in urban areas. We propose an approximation of the problem within the framework of the optimal control theory and we provide an algorithm for its numerical resolution. Finally, we analyze the validity of the algorithm in several academic situations.

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Authors: Boyan Dimitrov

This is a discussion article that should raise more questions than answers. We write our own point of view about the concept of axioms. We list several examples, mostly known to readers, and focus on examples where the axioms produce separate areas of studies and applications. The classic definitions are schematically presented since these are well known. We briefly notice how they generated various other fields of development. Set theory is, in our opinion, the fundamental for new areas of development. Our focus is on some recent axioms such as uncertainty, probability, and new concepts and results related to these fields. The emphasis is on the meaning of an undefined concept and on its measuring.

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Authors: Muhammad Bilal Khan Pshtiwan Othman Mohammed Muhammad Aslam Noor Dumitru Baleanu Juan Luis García Guirao

It is a familiar fact that interval analysis provides tools to deal with data uncertainty. In general, interval analysis is typically used to deal with the models whose data are composed of inaccuracies that may occur from certain kinds of measurements. In interval analysis, both the inclusion relation (⊆) and pseudo order relation (≤p) are two different concepts. In this article, by using pseudo order relation, we introduce the new class of nonconvex functions known as LR-p-convex interval-valued functions (LR-p-convex-IVFs). With the help of this relation, we establish a strong relationship between LR-p-convex-IVFs and Hermite-Hadamard type inequalities (HH-type inequalities) via Katugampola fractional integral operator. Moreover, we have shown that our results include a wide class of new and known inequalities for LR-p-convex-IVFs and their variant forms as special cases. Useful examples that demonstrate the applicability of the theory proposed in this study are given. The concepts and techniques of this paper may be a starting point for further research in this area.

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Authors: Chanakarn Kiataramkul Weera Yukunthorn Sotiris K. Ntouyas Jessada Tariboon

In this paper, we initiate the study of existence of solutions for a fractional differential system which contains mixed Riemann–Liouville and Hadamard–Caputo fractional derivatives, complemented with nonlocal coupled fractional integral boundary conditions. We derive necessary conditions for the existence and uniqueness of solutions of the considered system, by using standard fixed point theorems, such as Banach contraction mapping principle and Leray–Schauder alternative. Numerical examples illustrating the obtained results are also presented.

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Authors: Larry Bates Richard Cushman Jędrzej Śniatycki

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Authors: Delfim F. M. Torres

The calculus of variations is a field of mathematical analysis born in 1687 with Newton’s problem of minimal resistance, which is concerned with the maxima or minima of integral functionals. Finding the solution of such problems leads to solving the associated Euler–Lagrange equations. The subject has found many applications over the centuries, e.g., in physics, economics, engineering and biology. Up to this moment, however, the theory of the calculus of variations has been confined to Newton’s approach to calculus. As in many applications negative values of admissible functions are not physically plausible, we propose here to develop an alternative calculus of variations based on the non-Newtonian approach first introduced by Grossman and Katz in the period between 1967 and 1970, which provides a calculus defined, from the very beginning, for positive real numbers only, and it is based on a (non-Newtonian) derivative that permits one to compare relative changes between a dependent positive variable and an independent variable that is also positive. In this way, the non-Newtonian calculus of variations we introduce here provides a natural framework for problems involving functions with positive images. Our main result is a first-order optimality condition of Euler–Lagrange type. The new calculus of variations complements the standard one in a nontrivial/multiplicative way, guaranteeing that the solution remains in the physically admissible positive range. An illustrative example is given.

]]>Axioms doi: 10.3390/axioms10030172

Authors: Siti Nurul Fitriah Mohamad Roslan Hasni Florentin Smarandache Binyamin Yusoff

The energy of a graph is defined as the sum of the absolute values of its eigenvalues. Recently, there has been a lot of interest in graph energy research. Previous literature has suggested integrating energy, Laplacian energy, and signless Laplacian energy with single-valued neutrosophic graphs (SVNGs). This integration is used to solve problems that are characterized by indeterminate and inconsistent information. However, when the information is endowed with both positive and negative uncertainty, then bipolar single-valued neutrosophic sets (BSVNs) constitute an appropriate knowledge representation of this framework. A BSVNs is a generalized bipolar fuzzy structure that deals with positive and negative uncertainty in real-life problems with a larger domain. In contrast to the previous study, which directly used truth and indeterminate and false membership, this paper proposes integrating energy, Laplacian energy, and signless Laplacian energy with BSVNs to graph structure considering the positive and negative membership degree to greatly improve decisions in certain problems. Moreover, this paper intends to elaborate on characteristics of eigenvalues, upper and lower bound of energy, Laplacian energy, and signless Laplacian energy. We introduced the concept of a bipolar single-valued neutrosophic graph (BSVNG) for an energy graph and discussed its relevant ideas with the help of examples. Furthermore, the significance of using bipolar concepts over non-bipolar concepts is compared numerically. Finally, the application of energy, Laplacian energy, and signless Laplacian energy in BSVNG are demonstrated in selecting renewable energy sources, while optimal selection is suggested to illustrate the proposed method. This indicates the usefulness and practicality of this proposed approach in real life.

]]>Axioms doi: 10.3390/axioms10030170

Authors: Ahmed Salem Aeshah Al-Dosari

The monotonicity of multi-valued operators serves as a guideline to prove the existence of the results in this article. This theory focuses on the existence of solutions without continuity and compactness conditions. We study these results for the (k,n−k) conjugate fractional differential inclusion type with λ&gt;0,1≤k≤n−1.

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Authors: Avram Sidi

The secant method is a very effective numerical procedure used for solving nonlinear equations of the form f(x)=0. In a recent work (A. Sidi, Generalization of the secant method for nonlinear equations. Appl. Math. E-Notes, 8:115–123, 2008), we presented a generalization of the secant method that uses only one evaluation of f(x) per iteration, and we provided a local convergence theory for it that concerns real roots. For each integer k, this method generates a sequence {xn} of approximations to a real root of f(x), where, for n≥k, xn+1=xn−f(xn)/pn,k′(xn), pn,k(x) being the polynomial of degree k that interpolates f(x) at xn,xn−1,…,xn−k, the order sk of this method satisfying 1&lt;sk&lt;2. Clearly, when k=1, this method reduces to the secant method with s1=(1+5)/2. In addition, s1&lt;s2&lt;s3&lt;⋯, such that limk→∞sk=2. In this note, we study the application of this method to simple complex roots of a function f(z). We show that the local convergence theory developed for real roots can be extended almost as is to complex roots, provided suitable assumptions and justifications are made. We illustrate the theory with two numerical examples.

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Authors: Yingjie Hu Shouzhen Zeng Llopis-Albert Carlos Kifayat Ullah Yuqi Yang

As q-rung orthopair fuzzy set (q-ROFS) theory can effectively express complex fuzzy information, this study explores its application to social network environments and proposes a social network group decision-making (SNGDM) method based on the q-ROFS. Firstly, the q-rung orthopair fuzzy value is used to represent the trust relationships between experts in the social network, and a trust q-rung orthopair fuzzy value is defined. Secondly, considering the decreasing and multipath of trust in the process of trust propagation, this study designs a trust propagation mechanism by using its multiplication operation in the q-ROFS environment and proposes a trust q-ROFS aggregation approach. Moreover, based on the trust scores and confidence levels of experts, a new integration operator called q-rung orthopair fuzzy-induced ordered weighted average operator is proposed to fuse experts’ evaluation information. Additionally, considering the impact of consensus interaction on decision-making results, a consensus interaction model based on the q-ROF distance measure and trust relationship is proposed, including consistency measurement, identification of inconsistent expert decision-making opinions and a personalized adjustment mechanism. Finally, the SNGDM method is applied to solve the problem of evaluating online teaching quality.

]]>Axioms doi: 10.3390/axioms10030167

Authors: Mikhail G. Tkachenko

This study is on the factorization properties of continuous homomorphisms defined on subgroups (or submonoids) of products of (para)topological groups (or monoids). A typical result is the following one: Let D=∏i∈IDi be a product of paratopological groups, S be a dense subgroup of D, and χ a continuous character of S. Then one can find a finite set E⊂I and continuous characters χi of Di, for i∈E, such that χ=∏i∈Eχi∘piS, where pi:D→Di is the projection.

]]>Axioms doi: 10.3390/axioms10030166

Authors: Lili Chen Shilei Lin Yanfeng Zhao

In this paper, the problem of a Lotka–Volterra competition–diffusion–advection system between two competing biological organisms in a spatially heterogeneous environments is investigated. When two biological organisms are competing for different fundamental resources, and their advection and diffusion strategies follow different positive diffusion distributions, the functions of specific competition ability are variable. By virtue of the Lyapunov functional method, we discuss the global stability of a non-homogeneous steady-state. Furthermore, the global stability result is also obtained when one of the two organisms has no diffusion ability and is not affected by advection.

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Authors: Mutaz Mohammad Alexandre Trounev Mohammed Alshbool

In this work, a new numerical method for the fractional diffusion-wave equation and nonlinear Fredholm and Volterra integro-differential equations is proposed. The method is based on Euler wavelet approximation and matrix inversion of an M×M collocation points. The proposed equations are presented based on Caputo fractional derivative where we reduce the resulting system to a system of algebraic equations by implementing the Gaussian quadrature discretization. The reduced system is generated via the truncated Euler wavelet expansion. Several examples with known exact solutions have been solved with zero absolute error. This method is also applied to the Fredholm and Volterra nonlinear integral equations and achieves the desired absolute error of 0×10−31 for all tested examples. The new numerical scheme is exceptional in terms of its novelty, efficiency and accuracy in the field of numerical approximation.

]]>Axioms doi: 10.3390/axioms10030163

Authors: Li Zhou Chuanxi Zhu

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

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Authors: Songsong Dai

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

]]>Axioms doi: 10.3390/axioms10030162

Authors: Simon Gluzman

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

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

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

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Authors: Likai Liu Jin-Lin Liu

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

]]>Axioms doi: 10.3390/axioms10030159

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

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

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

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

]]>Axioms doi: 10.3390/axioms10030157

Authors: Bruno de Malafosse

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

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Authors: Alexander J. Zaslavski

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

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Authors: Rafael Dahmen Gábor Lukács

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

]]>Axioms doi: 10.3390/axioms10030154

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

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

]]>Axioms doi: 10.3390/axioms10030152

Authors: Li-Jun Zhu Yeong-Cheng Liou

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

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Authors: Jeong Ryeol Choi

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

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

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

]]>Axioms doi: 10.3390/axioms10030150

Authors: Andriy Zagorodnyuk Anna Hihliuk

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

]]>Axioms doi: 10.3390/axioms10030149

Authors: Eliana Costa e Silva Aldina Correia Ana Borges

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

]]>Axioms doi: 10.3390/axioms10030148

Authors: Vasile Dragan Samir Aberkane

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

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

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

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Authors: Laszlo Barna Iantovics Florin Felix Nichita

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

]]>Axioms doi: 10.3390/axioms10030145

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

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

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Authors: Pavel Trojovský

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

]]>Axioms doi: 10.3390/axioms10030141

Authors: Rabha W. Ibrahim Dumitru Baleanu

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

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

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

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Authors: Gergely Pataki

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

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

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

]]>Axioms doi: 10.3390/axioms10030139

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

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

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Authors: Osman Tunç Cemil Tunç Yuanheng Wang

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

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

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

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