Axioms, Volume 11, Issue 12 (December 2022) – 88 articles

Uniform designs are widely used in many fields in view of their ability to reduce experimentalcosts. In a lot of practical cases, different factors may take different numbers of values, so a mixed-level uniform design is needed. Since it is not reasonable to use the uniformity measure with the same weight for factors with different levels, the weighted discrete discrepancy was proposed in the existing literature. This paper discusses the construction method of mixed-level uniform designs under the weighted discrete discrepancy. The underlying method is to utilize some properties of partitioned difference families (PDFs) to obtain an infinite class of uniformly resolvable weighted balanced designs (URWBDs), which can directly produce corresponding uniform designs. Some examples are presented to illustrate the methods. Full article

The filled function method is an effective way to solve global optimization problems. However, its effectiveness is greatly affected by the selection of parameters, and the non-continuous or non-differentiable properties of the constructed filled function. To overcome the above-mentioned drawbacks, in this paper, a new parameterless filled function is proposed that is continuous and differentiable. Theoretical proofs have been made to show the properties of the proposed filled function. Based on the new filled function, a filled function algorithm is proposed to solve unconstrained global optimization problems. Experiments are carried out on widely used test problems and an application of supply chain problems with equality and inequality constraints. The numerical results show that the proposed filled function is effective. Full article

In this paper, we investigate and define the topology of some astrophysical phenomena, like the hairy (scalarized) charged black hole spacetime, to improve our understanding of the kinematics and dynamics of their nature. We use the Lagrangian equation to find different types of geodesic equations. This can be done under some conditions for the variations of the Cosmological constant and Newton’s constant. We show how to induce the two types (null and spacelike) of geodesics as boundary retractions, in order to obtain the boundary homotopy retract of the scalar charged black hole. These types are used the Lagrangian equation in a 4-D scalar charged black hole to explain the event horizon for this black hole. Full article

We classify several topological properties of a Tychonoff space X by means of certain locally convex topologies $\mathcal{T}$ with a $\mathfrak{G}$-base located between the pointwise topology ${\tau }_p$ and the bounded-open topology ${\tau }_b$ of the real-valued continuous function space $C\left(X\right)$. Full article

The major goal of the current article is to create new formulas and connections between several well-known polynomials and the Euler polynomials. These formulas are developed using some of these polynomials’ well-known fundamental characteristics as well as those of the Euler polynomials. In terms of the Euler polynomials, new formulas for the derivatives of various symmetric and non-symmetric polynomials, including the well-known classical orthogonal polynomials, are given. This leads to the deduction of several new connection formulas between various polynomials and the Euler polynomials. As an important application, new closed forms for the definite integrals for the product of various symmetric and non-symmetric polynomials with the Euler polynomials are established based on the newly derived connection formulas. Full article

A boundary-value problem for a couple of scalar nonlinear differential equations with a delay and several generalized proportional Caputo fractional derivatives is studied. Ulam-type stability of the given problem is investigated. Sufficient conditions for the existence of the boundary-value problem with an arbitrary parameter are obtained. In the study of Ulam-type stability, this parameter was chosen to depend on the solution of the corresponding fractional differential inequality. We provide sufficient conditions for Ulam–Hyers stability, Ulam–Hyers–Rassias stability and generalized Ulam–Hyers–Rassias stability for the given problem on a finite interval. As a partial case, sufficient conditions for Ulam-type stability for a couple of multi-term delay, Caputo fractional differential equations are obtained. An example is illustrating the results. Full article

In this paper, the pantograph delay differential equation $y^{\prime }\left(t\right)=ay\left(t\right)+by\left(ct\right)$ subject to the condition $y\left(0\right)=\lambda$ is reanalyzed for the real constants a, b, and c. In the literature, it has been shown that the pantograph delay differential equation, for $\lambda =1$, is well-posed if $c<1$, but not if $c>1$. In addition, the solution is available in the form of a standard power series when $\lambda =1$. In the present research, we are able to determine the solution of the pantograph delay differential equation in a closed series form in terms of exponential functions. The convergence of such a series is analysed. It is found that the solution converges for $c\in (-1,1)$ such that $\left|\frac{b}{a}\right|<1$ and it also converges for $c>1$ when $a<0$. For $c=-1$, the exact solution is obtained in terms of trigonometric functions, i.e., a periodic solution with periodicity $\frac{2\pi }{\sqrt{b^2-a^2}}$ when $b>a$. The current results are introduced for the first time and have not been reported in the relevant literature. Full article

A new four-parameter lifetime distribution called the beta binomial exponential 2 $\left(BBE2\right)$ distribution is proposed. Some mathematical features, including quantile function, moments, generating function and characteristic function, of the $BBE2$ distribution, are computed. When the life test is truncated at a predetermined time, acceptance sampling plans (ASP) are constructed for the $BBE2$ distribution. The truncation time is supposed to represent the median lifetime of the $BBE2$ distribution with predetermined factors for the smallest sample size required to guarantee that the prescribed life test is achieved at a given consumer’s risk. Some numerical results for a given consumer’s risk, $BBE2$ distribution parameters and truncation time are derived. Classical (maximum likelihood and maximum product of spacing estimation methods) and Bayesian estimation approaches are utilized to estimate the model parameters. The performance of the model parameters is examined through the simulation study by using the three different approaches of estimation. Subsequently, we examine real-world data applications to demonstrate the versatility and potential of the $BBE2$ model. A real-world application demonstrates that the new distribution can offer a better fit than other competitive lifetime models. Full article

The main result of the paper establishes the existence of a bounded weak solution for a nonlinear Dirichlet problem exhibiting full dependence on the solution u and its gradient $\nabla u$ in the reaction term, which is driven by a p-Laplacian-type operator with a coefficient $G\left(u\right)$ that can be unbounded. Through a special Moser iteration procedure, it is shown that the solution set is uniformly bounded. A truncated problem is formulated that drops that $G\left(u\right)$ be unbounded. The existence of a bounded weak solution to the truncated problem is proven via the theory of pseudomonotone operators. It is noted that the bound of the solution for the truncated problem coincides with the uniform bound of the original problem. This estimate allows us to deduce that for an appropriate choice of truncation, one actually resolves the original problem. Full article

A novel approach for the synchronization of a class of chaotic systems with uncertainty, unknown time delays, and external disturbances is presented. The control method given here is expressed by combining sliding mode control approaches with adaptive rules. A sliding surface of fractional order has been developed to construct the control strategy of the abovementioned sliding mode by employing the structure of nonlinear fractional PID (NLPID) controllers. The suggested control mechanism using Lyapunov’s theorem developed robust adaptive rules in such a way that the estimation error of the system’s unknown parameters and time delays tends to be zero. Furthermore, the proposed robust control approach’s stability has been demonstrated using Lyapunov stability criteria and Lipschitz conditions. Then, in order to assess the performance of the proposed mechanism, the presented control approach was used to simulate the synchronization of two chaotic jerk systems with uncertainty, unknown time delays, and external distortion. The results of the simulation confirm the robust and desirable synchronization performance. Finally, a secure communications mechanism based on the proposed technique is shown as a practical implementation of the introduced control strategy, in which the message signal is disguised in the transmitter with high security and well recovered in the receiver with high quality, according to the mean squared error (MES) criteria. Full article

The importance of counting data modeling and its applications to real-world phenomena has been highlighted in several research studies. The present study focuses on a one-parameter discrete distribution that can be derived via the survival discretization approach. The proposed model has explicit forms for its statistical properties. It can be applied to discuss asymmetric “right skewed” data with long “heavy” tails. Its failure rate function can be used to discuss the phenomena with a monotonically decreasing or unimodal failure rate shape. Further, it can be utilized as a probability tool to model and discuss over- and under-dispersed data. Various estimation techniques are reported and discussed in detail. A simulation study is performed to test the property of the estimator. Finally, three real data sets are analyzed to prove the notability of the introduced model. Full article

Nowadays, there is an ever-increasing diversity of materials available, each with its own set of features, capabilities, benefits, and drawbacks. There is no single definitive criteria for selecting the perfect biomedical material; designers and engineers must consider a vast array of distinct biomedical material selection qualities. The goal of this study is to establish fairly operational rules and aggregation operators (AOs) in a linear Diophantine fuzzy context. To achieve this goal, we devised innovative operational principles that make use of the notion of proportional distribution to provide an equitable or fair aggregate for linear Diophantine fuzzy numbers (LDFNs). Furthermore, a multi-criteria decision-making (MCDM) approach is built by combining recommended fairly AOs with evaluations from multiple decision-makers (DMs) and partial weight information under the linear Diophantine fuzzy paradigm. The weights of the criterion are determined using incomplete data with the help of a linear programming model. The enhanced technique might be used in the selection of compounds in a variety of applications, including biomedical programmes where the chemicals used in prostheses must have qualities similar to those of human tissues. The approach presented for the femoral component of the hip joint prosthesis may be used by orthopaedists and practitioners who will choose bio-materials. This is due to the fact that biomedical materials are employed in many sections of the human body for various functions. Full article

The study aims to provide a Bayesian statistical method with natural conjugate for facilities’ preventive maintenance scheduling related to the hybrid competing failure mode. An effective preventive maintenance strategy not only can improve a system’s health condition but also can increase a system’s efficiency, and therefore a firm needs to make an appropriate strategy for increasing the utilization of a system with reasonable costs. In the last decades, preventive maintenance issues of deteriorating systems have been studied in the related literature, and hundreds of maintenance/replacement models have been created. However, few studies focused on the issue of hybrid deteriorating systems which are composed of maintainable and non-maintainable failure modes. Moreover, due to the situations of the scarcity of historical failure data, the related analyses of preventive maintenance would be difficult to perform. Based on the above two reasons, this study proposed a Bayesian statistical method to deal with such preventive maintenance problems. Non-homogeneous Poisson processes (NHPP) with power law failure intensity functions are employed to describe the system’s deterioration behavior. Accordingly, the study can provide useful ways to help managers to make effective decisions for preventive maintenance. To apply the proposed models in actual cases, the study provides solution algorithms and a computerized architecture design for decision-makers to realize the computerization of decision-making. Full article

Let X be a compact metric space and a continuous map $f:X\to X$ which defines a discrete dynamical system $(X,f)$. The map f induces two natural maps, namely $\overline{f}:\mathcal{K}\left(X\right)\to \mathcal{K}\left(X\right)$ on the hyperspace $\mathcal{K}\left(X\right)$ of non-empty compact subspaces of X and the Zadeh’s extension $\widehat{f}:\mathcal{F}\left(X\right)\to \mathcal{F}\left(X\right)$ on the space $\mathcal{F}\left(X\right)$ of normal fuzzy set. In this work, we analyze the interaction of some orbit tracing dynamical properties, namely the specification and shadowing properties of the discrete dynamical system $(X,f)$ and its induced discrete dynamical systems $(\mathcal{K}\left(X\right),\overline{f})$ and $(\mathcal{F}\left(X\right),\widehat{f})$. Adding an algebraic structure yields stronger conclusions, and we obtain a full characterization of the specification property in the hyperspace, in the fuzzy space, and in the phase space X if we assume that the later is a convex compact subset of a (metrizable and complete) locally convex space and f is a linear operator. Full article

In this paper, we shall discuss a newly introduced concept of center-radius total-ordered relations between two intervals. Here, we address the Hermite–Hadamard-, Fejér- and Pachpatte-type inequalities by considering interval-valued Riemann–Liouville fractional integrals. Interval-valued fractional inequalities for a new class of preinvexity, i.e., $\mathrm{cr}$-h-preinvexity, are estimated. The fractional operator is used for the first time to prove such inequalities involving center–radius-ordered functions. Some numerical examples are also provided to validate the presented inequalities. Full article

We introduce in this paper a new family of uniformly convex functions related to the Deniz–Özkan differential operator. By using this family of functions with a negative coefficient, we obtain coefficient estimates, the radius of starlikeness, convexity, and close-to-convexity, and we find their extreme points. Moreover, the neighborhood, partial sums, and integral means of functions for this new family are studied. Full article

The mutant distribution that accommodates both fitness and plating efficiency is an important class of the Luria–Delbrück distribution. Practical algorithms for computing this distribution do not coincide with the theoretically most elegant ones, as existing generic methods often either produce unreliable results or freeze the computational process altogether when employed to solve real-world research problems. Exploiting properties of the hypergeometric function, this paper offers an algorithm that considerably expands the scope of application of this important class of the Luria–Delbrück distribution. An integration method is also devised to complement the novel algorithm. Asymptotic properties of the mutant probability are derived to help gauge the new algorithm. An illustrative example and simulation results provide further guidelines on the use of the new algorithm. Full article

Proteins are macromolecules essential for living organisms. However, to perform their function, proteins need to achieve their Native Structure (NS). The NS is reached fast in nature. By contrast, in silico, it is obtained by solving the Protein Folding problem (PFP) which currently has a long execution time. PFP is computationally an NP-hard problem and is considered one of the biggest current challenges. There are several methods following different strategies for solving PFP. The most successful combine computational methods and biological information: I-TASSER, Rosetta (Robetta server), AlphaFold2 (CASP14 Champion), QUARK, PEP-FOLD3, TopModel, and GRSA2-SSP. The first three named methods obtained the highest quality at CASP events, and all apply the Simulated Annealing or Monte Carlo method, Neural Network, and fragments assembly methodologies. In the present work, we propose the GRSA2-FCNN methodology, which assembles fragments applied to peptides and is based on the GRSA2 and Convolutional Neural Networks (CNN). We compare GRSA2-FCNN with the best state-of-the-art algorithms for PFP, such as I-TASSER, Rosetta, AlphaFold2, QUARK, PEP-FOLD3, TopModel, and GRSA2-SSP. Our methodology is applied to a dataset of 60 peptides and achieves the best performance of all methods tested based on the common metrics TM-score, RMSD, and GDT-TS of the area. Full article

In this paper, we prove fixed point theorem via orthogonal Geraghty type $\alpha$-admissible contraction map in an orthogonal complete Branciari b-metric spaces context. An example is presented to strengthen our main result. We provided an application to find the existence and uniqueness of a solution to the Volterra integral equation. We have compared the approximate solution and exact solution numerically. Full article

Convexity performs the appropriate role in the theoretical study of inequalities according to the nature and behaviour. There is a strong relation between symmetry and convexity. In this article, we consider a new parameterized quantum fractional integral identity. Following that, our main results are established, which consist of some integral inequalities of Ostrowski and midpoint type pertaining to n-polynomial convex functions. From our main results, we discuss in detail several special cases. Finally, an example and an application to special means of positive real numbers are presented to support our theoretical results. Full article

Based on the second derivative, this paper directly establishes the coincidence degree theory of a nonlinear periodic Sturm–Liouville (SL) system. As applications, we study the existence of periodic solutions to the S–L system with some special nonlinear functions by applying Mawhin’s continuation theorem. Some examples and simulations are furnished to inspect the correctness and availability of the chief findings. Full article

In the current circumstance, the Web Service Composition (WSC) was introduced to address complex user needs concerning the Quality of Services (QoS). In the WSC problem, the user needs are divided into a set of tasks. The corresponding web services are retrieved from the web services discovery according to the functionality of each task, and have different non-functional constraints, such as QoS. The WSC problem is a multi-objective optimization problem and is classified as an NP-hard problem. The whale optimization algorithm (WOA) is proven to solve complex multi-objective optimization problems, and it has the advantage of easy implementation with few control parameters. In this work, we contribute to improving the WOA algorithm, where different strategies are introduced to enhance its performance and address its shortcomings, namely its slow convergence speed, which produces low solution accuracy for the WSC problem. The proposed algorithm is named Improved Whale Optimization Algorithm (IWOA) and has three different strategies to enhance the performance of the WOA. Firstly, the Sine chaos theory is proposed to initiate the WOA’s population and enhance the initialization diversity. Secondly, a Lévy flight mechanism is proposed to enhance the exploitation and exploration of WOA by maintaining the whales’ diversity. Further, a neighborhood search mechanism is introduced to address the trade-off between exploration and exploitation searching mechanisms. Different experiments are conducted with datasets on 12 different scales (small, medium, and large), and the proposed algorithm is compared with standard WOA and five state-of-the-art swarm-based algorithms on 30 different independent runs. Furthermore, four evaluation criteria are used to validate the comparison: the average fitness value, best fitness values, standard deviation, and average execution time. The results show that the IWOA enhanced the WOA algorithm’s performance, where it got the better average and best fitness values with a low variation on all datasets. However, it ranked second regarding average execution time after the WOA, and sometimes third after the WOA and OABC, which is reasonable because of the proposed strategies. Full article

Tuberculosis (TB), caused by Mycobacterium tuberculosis is one of the treacherous infectious diseases of global concern. In this paper, we consider a deterministic model of TB infection with the public health education and hospital treatment impact. The effective reproductive number, $R_{ph},$ that measures the potential spread of TB is presented by employing the next generation matrix approach. We investigate local and global stability of the TB-free equilibrium point, endemic equilibrium point, and sensitivity analysis. The analyses of the proposed model show that the model undergoes the phenomenon of backward bifurcation when the effective reproduction number $\left(R_{ph}\right)$ is less than one, where two stable equilibria, namely, the DFE and an EEP coexist. Further, we compute the sensitivity of the impact of each parameter on the effective reproductive number of the model by employing a normalized sensitivity index formula. Numerical simulation of the proposed model was conducted using Maple 2016 and MatLab R2020b software and compared with the theoretical results for illustration purposes. The investigation results can be useful in providing information to policy makers and public health authorities in mitigating the spread of TB infection by public health education and hospital treatment. Full article

Multi-view clustering algorithms based on matrix factorization have gained enormous development in recent years. Although these algorithms have gained impressive results, they typically neglect the spatial structures that the latent data representation should have, for example, the ideal data representation owns a block structure just like the indicator matrix has. To address this issue, a new algorithm named latent multi-view semi-nonnegative matrix factorization with block diagonal constraint (LMSNB) is proposed. First, latent representation learning and Semi-NMF are combined to get a lower-dimensional representation with consistent information from different views. Second, the block diagonal constraint is able to capture the global structure of original data. In addition, the graph regularization is considered in our model to preserve the local structure. LMSNB can deal with negative data matrix and be applied to more fields. Although the low dimensional representation from semi-nonnegative matrix factorization loses some valuable information, it still has same structure as original data with the help of block diagonal constraint and graph regularization. Finally, an iterative optimization algorithm is proposed for our objective problem. Experiments on several multi-view benchmark datasets demonstrate the effectiveness of our approach against other state-of-the-art methods. Full article

This paper considers a class of fractional impulsive wave equations and improves a previous results. In fact, this paper adopts a new topological approach to prove the existence of classical solutions with a complex arguments caused by impulsive perturbations. To the best of our knowledge, there is a severe lack of results related to such impulsive equations. Full article

The dissipative quasi-geostrophic equation with dispersive forcing is considered. By striking new balances between the dispersive effects of the dispersive forcing and the smoothing effects of the viscous dissipation, we obtain the global well-posedness for Cauchy problem of the dissipative quasi-geostrophic equation with dispersive forcing for arbitrary initial data, provided that the dispersive parameter is large enough. Full article

The present article aims to establish more effective criteria for testing the oscillation of a class of functional differential equations with delay arguments. In the non-canonical case, we deduce some improved monotonic and asymptotic properties of the class of decreasing positive solutions of the studied equation. Depending on both the new properties and the linear representation of the studied equation, we obtain new oscillation criteria. Moreover, we test the effectiveness of the new criteria by applying them to some special cases of the studied equation. Full article

Our interest in this article is to develop oscillation conditions for solutions of higher order differential equations and to extend recent results in the literature to differential equations of several delays. We obtain new asymptotic properties of a class from the positive solutions of an even higher order neutral delay differential equation. Then we use these properties to create more effective criteria for studying oscillation. Finally, we present some special cases of the studied equation and apply the new results to them. Full article