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

Cover Story (view full-size image): Basic constructions of classical general relativity, especially the theory of spherically symmetric spacetimes, are revisited and extended. A Schwarzschild spacetime is considered as a 4-dimensional smooth manifold endowed with an action of the rotation group, and an invariant metric satisfying the Einstein equations. The main objective of this article is the mathematical structure of the theory; physical aspects and physical motivations are not considered. The theory describes the metric/gravitational field of stars and the Sun. Mathematical innovations include a complete classification of Schwarzschild metrics, parametrized by two real constants and a free function, on two topologically non-equivalent spacetimes. In general, the signature of a Schwarzschild metric may be chosen as an independent axiom. View this paper
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Article
Direct Constructions of Uniform Designs under the Weighted Discrete Discrepancy
Axioms 2022, 11(12), 747; https://doi.org/10.3390/axioms11120747 - 19 Dec 2022
Viewed by 462
Abstract
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 [...] Read more.
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
(This article belongs to the Special Issue Computational Statistics & Data Analysis)
Article
A New Parameterless Filled Function Method for Global Optimization
Axioms 2022, 11(12), 746; https://doi.org/10.3390/axioms11120746 - 19 Dec 2022
Viewed by 487
Abstract
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, [...] Read more.
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
(This article belongs to the Special Issue Optimization Algorithms and Applications)
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Article
The Boundary Homotopy Retract on the Scalar Hairy Charged Black Hole Spacetime
Axioms 2022, 11(12), 745; https://doi.org/10.3390/axioms11120745 - 19 Dec 2022
Viewed by 494
Abstract
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 [...] Read more.
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
(This article belongs to the Special Issue String Theory and Mathematical Physics)
Article
Classifying Topologies through G-Bases
Axioms 2022, 11(12), 744; https://doi.org/10.3390/axioms11120744 - 19 Dec 2022
Viewed by 475
Abstract
We classify several topological properties of a Tychonoff space X by means of certain locally convex topologies T with a G-base located between the pointwise topology τp and the bounded-open topology τb of the real-valued continuous function space CX [...] Read more.
We classify several topological properties of a Tychonoff space X by means of certain locally convex topologies T with a G-base located between the pointwise topology τp and the bounded-open topology τb of the real-valued continuous function space CX. Full article
(This article belongs to the Special Issue Mathematical Analysis and Applications III)
Article
New Formulas and Connections Involving Euler Polynomials
Axioms 2022, 11(12), 743; https://doi.org/10.3390/axioms11120743 - 18 Dec 2022
Viewed by 402
Abstract
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 [...] Read more.
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
(This article belongs to the Special Issue Theory of Functions and Applications)
Article
Ulam-Type Stability for a Boundary-Value Problem for Multi-Term Delay Fractional Differential Equations of Caputo Type
Axioms 2022, 11(12), 742; https://doi.org/10.3390/axioms11120742 - 18 Dec 2022
Viewed by 438
Abstract
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 [...] Read more.
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
(This article belongs to the Special Issue Impulsive, Delay and Fractional Order Systems)
Article
Analytical and Numerical Simulations of a Delay Model: The Pantograph Delay Equation
Axioms 2022, 11(12), 741; https://doi.org/10.3390/axioms11120741 - 17 Dec 2022
Viewed by 467
Abstract
In this paper, the pantograph delay differential equation y(t)=ay(t)+byct subject to the condition y(0)=λ is reanalyzed for the real constants a, b [...] Read more.
In this paper, the pantograph delay differential equation y(t)=ay(t)+byct subject to the condition y(0)=λ is reanalyzed for the real constants a, b, and c. In the literature, it has been shown that the pantograph delay differential equation, for λ=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 λ=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(1,1) such that ba<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 2πb2a2 when b>a. The current results are introduced for the first time and have not been reported in the relevant literature. Full article
(This article belongs to the Special Issue Mathematical Models and Simulations)
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Article
Statistical Inference of the Beta Binomial Exponential 2 Distribution with Application to Environmental Data
Axioms 2022, 11(12), 740; https://doi.org/10.3390/axioms11120740 - 17 Dec 2022
Viewed by 378
Abstract
A new four-parameter lifetime distribution called the beta binomial exponential 2 (BBE2) distribution is proposed. Some mathematical features, including quantile function, moments, generating function and characteristic function, of the BBE2 distribution, are computed. When the [...] Read more.
A new four-parameter lifetime distribution called the beta binomial exponential 2 (BBE2) 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
(This article belongs to the Special Issue Computational Statistics & Data Analysis)
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Article
Nonhomogeneous Dirichlet Problems with Unbounded Coefficient in the Principal Part
Axioms 2022, 11(12), 739; https://doi.org/10.3390/axioms11120739 - 17 Dec 2022
Viewed by 404
Abstract
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 u in the reaction term, which is driven by a p-Laplacian-type operator [...] Read more.
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 u in the reaction term, which is driven by a p-Laplacian-type operator with a coefficient G(u) 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(u) 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
(This article belongs to the Special Issue 10th Anniversary of Axioms: Mathematical Analysis)
Article
The Synchronization of a Class of Time-Delayed Chaotic Systems Using Sliding Mode Control Based on a Fractional-Order Nonlinear PID Sliding Surface and Its Application in Secure Communication
Axioms 2022, 11(12), 738; https://doi.org/10.3390/axioms11120738 - 16 Dec 2022
Viewed by 626
Abstract
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 [...] Read more.
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
(This article belongs to the Special Issue Optimization Models and Applications)
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Article
Discrete Single-Factor Extension of the Exponential Distribution: Features and Modeling
Axioms 2022, 11(12), 737; https://doi.org/10.3390/axioms11120737 - 16 Dec 2022
Viewed by 385
Abstract
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 [...] Read more.
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
(This article belongs to the Special Issue Computational Statistics & Data Analysis)
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Editorial
Approximation Theory and Related Applications
Axioms 2022, 11(12), 736; https://doi.org/10.3390/axioms11120736 - 16 Dec 2022
Viewed by 411
Abstract
The theory of approximation of functions is one of the central branches of mathematical analysis [...] Full article
(This article belongs to the Special Issue Approximation Theory and Related Applications)
Article
Linear Diophantine Fuzzy Fairly Averaging Operator for Suitable Biomedical Material Selection
Axioms 2022, 11(12), 735; https://doi.org/10.3390/axioms11120735 - 15 Dec 2022
Cited by 1 | Viewed by 422
Abstract
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 [...] Read more.
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
(This article belongs to the Special Issue Multiple-Criteria Decision Making II)
Article
Bayesian Statistical Method Enhance the Decision-Making for Imperfect Preventive Maintenance with a Hybrid Competing Failure Mode
Axioms 2022, 11(12), 734; https://doi.org/10.3390/axioms11120734 - 15 Dec 2022
Viewed by 380
Abstract
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 [...] Read more.
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
(This article belongs to the Special Issue A Hybrid Analysis of Information Technology and Decision Making)
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Article
Orbit Tracing Properties on Hyperspaces and Fuzzy Dynamical Systems
Axioms 2022, 11(12), 733; https://doi.org/10.3390/axioms11120733 - 15 Dec 2022
Viewed by 366
Abstract
Let X be a compact metric space and a continuous map f:XX which defines a discrete dynamical system (X,f). The map f induces two natural maps, namely [...] Read more.
Let X be a compact metric space and a continuous map f:XX which defines a discrete dynamical system (X,f). The map f induces two natural maps, namely f¯:K(X)K(X) on the hyperspace K(X) of non-empty compact subspaces of X and the Zadeh’s extension f^:F(X)F(X) on the space F(X) 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 (K(X),f¯) and (F(X),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
(This article belongs to the Special Issue Topological Groups and Dynamics)
Article
Modified Inequalities on Center-Radius Order Interval-Valued Functions Pertaining to Riemann–Liouville Fractional Integrals
Axioms 2022, 11(12), 732; https://doi.org/10.3390/axioms11120732 - 15 Dec 2022
Cited by 1 | Viewed by 603
Abstract
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., cr [...] Read more.
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., 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
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Article
Subclasses of Uniformly Convex Functions with Negative Coefficients Based on Deniz–Özkan Differential Operator
Axioms 2022, 11(12), 731; https://doi.org/10.3390/axioms11120731 - 14 Dec 2022
Viewed by 444
Abstract
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 [...] Read more.
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
Article
A Fresh Approach to a Special Type of the Luria–Delbrück Distribution
Axioms 2022, 11(12), 730; https://doi.org/10.3390/axioms11120730 - 14 Dec 2022
Viewed by 326
Abstract
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 [...] Read more.
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
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Article
A Peptides Prediction Methodology with Fragments and CNN for Tertiary Structure Based on GRSA2
Axioms 2022, 11(12), 729; https://doi.org/10.3390/axioms11120729 - 14 Dec 2022
Viewed by 352
Abstract
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 [...] Read more.
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
(This article belongs to the Special Issue Computational and Mathematical Methods in Science and Engineering)
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Article
Solution to Integral Equation in an O-Complete Branciari b-Metric Spaces
Axioms 2022, 11(12), 728; https://doi.org/10.3390/axioms11120728 - 13 Dec 2022
Viewed by 388
Abstract
In this paper, we prove fixed point theorem via orthogonal Geraghty type α-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 [...] Read more.
In this paper, we prove fixed point theorem via orthogonal Geraghty type α-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
(This article belongs to the Special Issue Fixed Point Theory and Its Related Topics III)
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Article
Parameterized Quantum Fractional Integral Inequalities Defined by Using n-Polynomial Convex Functions
Axioms 2022, 11(12), 727; https://doi.org/10.3390/axioms11120727 - 13 Dec 2022
Viewed by 421
Abstract
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 [...] Read more.
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
Article
Coincidence Theory of a Nonlinear Periodic Sturm–Liouville System and Its Applications
Axioms 2022, 11(12), 726; https://doi.org/10.3390/axioms11120726 - 13 Dec 2022
Viewed by 402
Abstract
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. [...] Read more.
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
(This article belongs to the Special Issue Differential Equations in Applied Mathematics)
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Article
An Improved Whale Optimization Algorithm for Web Service Composition
Axioms 2022, 11(12), 725; https://doi.org/10.3390/axioms11120725 - 13 Dec 2022
Viewed by 418
Abstract
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 [...] Read more.
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
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Article
New Results for Multivalued Mappings in Hausdorff Neutrosophic Metric Spaces
Axioms 2022, 11(12), 724; https://doi.org/10.3390/axioms11120724 - 13 Dec 2022
Viewed by 448
Abstract
The fundamental goal of this paper is to derive common fixed-point results for a sequence of multivalued mappings contained in a closed ball over a complete neutrosophic metric space. A basic and distinctive procedure has been used to prove the proposed results. Full article
(This article belongs to the Special Issue Fixed Point Theory and Its Related Topics III)
Article
Dynamical Behaviour of a Modified Tuberculosis Model with Impact of Public Health Education and Hospital Treatment
Axioms 2022, 11(12), 723; https://doi.org/10.3390/axioms11120723 - 13 Dec 2022
Viewed by 581
Abstract
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, [...] Read more.
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, Rph, 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 (Rph) 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
(This article belongs to the Topic Mathematical Modeling)
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Article
Latent Multi-View Semi-Nonnegative Matrix Factorization with Block Diagonal Constraint
Axioms 2022, 11(12), 722; https://doi.org/10.3390/axioms11120722 - 12 Dec 2022
Viewed by 586
Abstract
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 [...] Read more.
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 article belongs to the Special Issue Soft Computing with Applications to Decision Making and Data Mining)
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Article
A New Topological Approach to Target the Existence of Solutions for Nonlinear Fractional Impulsive Wave Equations
Axioms 2022, 11(12), 721; https://doi.org/10.3390/axioms11120721 - 12 Dec 2022
Viewed by 459
Abstract
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 [...] Read more.
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
(This article belongs to the Special Issue Recent Advances in Stochastic Differential Equations)
Article
Global Well-Posedness of the Dissipative Quasi-Geostrophic Equation with Dispersive Forcing
Axioms 2022, 11(12), 720; https://doi.org/10.3390/axioms11120720 - 12 Dec 2022
Viewed by 380
Abstract
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 [...] Read more.
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
(This article belongs to the Collection Differential Equations and Dynamical Systems)
Article
Criteria for Oscillation of Half-Linear Functional Differential Equations of Second-Order
Axioms 2022, 11(12), 719; https://doi.org/10.3390/axioms11120719 - 12 Dec 2022
Viewed by 454
Abstract
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 [...] Read more.
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
(This article belongs to the Special Issue Mathematical Analysis and Applications III)
Article
Amended Criteria for Testing the Asymptotic and Oscillatory Behavior of Solutions of Higher-Order Functional Differential Equations
Axioms 2022, 11(12), 718; https://doi.org/10.3390/axioms11120718 - 12 Dec 2022
Viewed by 358
Abstract
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 [...] Read more.
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
(This article belongs to the Special Issue 10th Anniversary of Axioms: Mathematical Analysis)
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