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Axioms, Volume 10, Issue 1 (March 2021) – 41 articles

Cover Story (view full-size image): Empirical traffic data collected from three locations in Europe and the USA are used to reveal a three-phase fundamental diagram for vehicular traffic flow. Model-based clustering, hypothesis testing, and regression analyses are applied to the speed-flow-occupancy data represented in the three-dimensional space to rigorously validate the three phases and identify their gaps. The findings are consistent across the different geographical locations. Accordingly, a three-phase macroscopic traffic flow model is proposed, and a characterization of solutions to the Riemann problems is shown. This work identifies critical structures in the fundamental diagram that are typically ignored in first- and higher-order models, and which could significantly impact travel time estimation on highways. View this paper
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Article
Gradation of Fuzzy Preconcept Lattices
Axioms 2021, 10(1), 41; https://0-doi-org.brum.beds.ac.uk/10.3390/axioms10010041 - 22 Mar 2021
Viewed by 583
Abstract
Noticing certain limitations of concept lattices in the fuzzy context, especially in view of their practical applications, in this paper, we propose a more general approach based on what we call graded fuzzy preconcept lattices. We believe that this approach is more adequate [...] Read more.
Noticing certain limitations of concept lattices in the fuzzy context, especially in view of their practical applications, in this paper, we propose a more general approach based on what we call graded fuzzy preconcept lattices. We believe that this approach is more adequate for dealing with fuzzy information then the one based on fuzzy concept lattices. We consider two possible gradation methods of fuzzy preconcept lattice—an inner one, called D-gradation and an outer one, called M-gradation, study their properties, and illustrate by a series of examples, in particular, of practical nature. Full article
(This article belongs to the Special Issue Fuzzy Set Theory and Applications)
Article
Generalization of the Regularization Method to Singularly Perturbed Integro-Differential Systems of Equations with Rapidly Oscillating Inhomogeneity
Axioms 2021, 10(1), 40; https://0-doi-org.brum.beds.ac.uk/10.3390/axioms10010040 - 22 Mar 2021
Cited by 2 | Viewed by 480
Abstract
In this paper, we consider systems of singularly perturbed integro-differential equations with a rapidly oscillating right-hand side, including an integral operator with a slowly varying kernel. Differential equations of this type and integro-differential equations with slowly varying inhomogeneity and with a rapidly oscillating [...] Read more.
In this paper, we consider systems of singularly perturbed integro-differential equations with a rapidly oscillating right-hand side, including an integral operator with a slowly varying kernel. Differential equations of this type and integro-differential equations with slowly varying inhomogeneity and with a rapidly oscillating coefficient at an unknown function are studied. The main goal of this work is to generalize the Lomov’s regularization method and to reveal the influence of the rapidly oscillating right-hand side on the asymptotics of the solution to the original problem. Full article
Article
Existence of Coupled Best Proximity Points of p-Cyclic Contractions
Axioms 2021, 10(1), 39; https://0-doi-org.brum.beds.ac.uk/10.3390/axioms10010039 - 22 Mar 2021
Viewed by 488
Abstract
We generalize the notion of coupled fixed (or best proximity) points for cyclic ordered pairs of maps to p-cyclic ordered pairs of maps. We find sufficient conditions for the existence and uniqueness of the coupled fixed (or best proximity) points. We illustrate [...] Read more.
We generalize the notion of coupled fixed (or best proximity) points for cyclic ordered pairs of maps to p-cyclic ordered pairs of maps. We find sufficient conditions for the existence and uniqueness of the coupled fixed (or best proximity) points. We illustrate the results with an example that covers a wide class of maps. Full article
(This article belongs to the Special Issue Theory and Application of Fixed Point)
Article
Filtrated Pseudo-Orbit Shadowing Property and Approximately Shadowable Measures
Axioms 2021, 10(1), 38; https://0-doi-org.brum.beds.ac.uk/10.3390/axioms10010038 - 20 Mar 2021
Viewed by 528
Abstract
In this paper, it is proved that every diffeomorphism possessing the filtrated pseudo-orbit shadowing property admits an approximately shadowable Lebesgue measure. Furthermore, the C1-interior of the set of diffeomorphisms possessing the filtrated pseudo-orbit shadowing property is characterized as the set of [...] Read more.
In this paper, it is proved that every diffeomorphism possessing the filtrated pseudo-orbit shadowing property admits an approximately shadowable Lebesgue measure. Furthermore, the C1-interior of the set of diffeomorphisms possessing the filtrated pseudo-orbit shadowing property is characterized as the set of diffeomorphisms satisfying both Axiom A and the no-cycle condition. As a corollary, it is proved that there exists a C1-open set of diffeomorphisms, any element of which does not have the shadowing property but admits an approximately shadowable Lebesgue measure. Full article
(This article belongs to the Special Issue Topological Theory of Dynamical Systems)
Article
Explicit, Determinantal, and Recurrent Formulas of Generalized Eulerian Polynomials
Axioms 2021, 10(1), 37; https://0-doi-org.brum.beds.ac.uk/10.3390/axioms10010037 - 18 Mar 2021
Cited by 3 | Viewed by 1009
Abstract
In the paper, by virtue of the Faà di Bruno formula, with the aid of some properties of the Bell polynomials of the second kind, and by means of a general formula for derivatives of the ratio between two differentiable functions, the authors [...] Read more.
In the paper, by virtue of the Faà di Bruno formula, with the aid of some properties of the Bell polynomials of the second kind, and by means of a general formula for derivatives of the ratio between two differentiable functions, the authors establish explicit, determinantal, and recurrent formulas for generalized Eulerian polynomials. Full article
(This article belongs to the Special Issue p-adic Analysis and q-Calculus with Their Applications)
Article
A Compensatory Fuzzy Logic Model in Technical Trading
Axioms 2021, 10(1), 36; https://0-doi-org.brum.beds.ac.uk/10.3390/axioms10010036 - 18 Mar 2021
Cited by 1 | Viewed by 821
Abstract
This work presents a novel approach to prediction of financial asset prices. Its main contribution is the combination of compensatory fuzzy logic and the classical technical analysis to build an efficient prediction model. The interpretability properties of the model allow its users to [...] Read more.
This work presents a novel approach to prediction of financial asset prices. Its main contribution is the combination of compensatory fuzzy logic and the classical technical analysis to build an efficient prediction model. The interpretability properties of the model allow its users to incorporate and consider virtually any set of rules from technical analysis, in addition to the investors’ knowledge related to the actual market conditions. This knowledge can be incorporated into the model in the form of subjective assessments made by investors. Such assessments can be obtained, for example, from the graphical analysis commonly performed by traders. The effectiveness of the model was assessed through its systematic application in the stock and cryptocurrency markets. From the results, we conclude that when the model shows a high degree of recommendation, the actual financial assets show high effectiveness. Full article
(This article belongs to the Special Issue Softcomputing: Theories and Applications II)
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Article
The Role of Spectral Complexity in Connectivity Estimation
Axioms 2021, 10(1), 35; https://0-doi-org.brum.beds.ac.uk/10.3390/axioms10010035 - 16 Mar 2021
Viewed by 529
Abstract
The study of functional connectivity from magnetoecenphalographic (MEG) data consists of quantifying the statistical dependencies among time series describing the activity of different neural sources from the magnetic field recorded outside the scalp. This problem can be addressed by utilizing connectivity measures whose [...] Read more.
The study of functional connectivity from magnetoecenphalographic (MEG) data consists of quantifying the statistical dependencies among time series describing the activity of different neural sources from the magnetic field recorded outside the scalp. This problem can be addressed by utilizing connectivity measures whose computation in the frequency domain often relies on the evaluation of the cross-power spectrum of the neural time series estimated by solving the MEG inverse problem. Recent studies have focused on the optimal determination of the cross-power spectrum in the framework of regularization theory for ill-posed inverse problems, providing indications that, rather surprisingly, the regularization process that leads to the optimal estimate of the neural activity does not lead to the optimal estimate of the corresponding functional connectivity. Along these lines, the present paper utilizes synthetic time series simulating the neural activity recorded by an MEG device to show that the regularization of the cross-power spectrum is significantly correlated with the signal-to-noise ratio of the measurements and that, as a consequence, this regularization correspondingly depends on the spectral complexity of the neural activity. Full article
(This article belongs to the Special Issue Differential Models, Numerical Simulations and Applications)
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Article
Outsourcing Reverse Logistics for E-Commerce Retailers: A Two-Stage Fuzzy Optimization Approach
Axioms 2021, 10(1), 34; https://0-doi-org.brum.beds.ac.uk/10.3390/axioms10010034 - 14 Mar 2021
Cited by 9 | Viewed by 1716
Abstract
On the heels of the online shopping boom during the Covid-19 pandemic, the electronic commerce (e-commerce) surge has many businesses facing an influx in product returns. Thus, relevant companies must implement robust reverse logistics strategies to reflect the increased importance of the capability. [...] Read more.
On the heels of the online shopping boom during the Covid-19 pandemic, the electronic commerce (e-commerce) surge has many businesses facing an influx in product returns. Thus, relevant companies must implement robust reverse logistics strategies to reflect the increased importance of the capability. Reverse logistics also plays a radical role in any business’s sustainable development as a process of reusing, remanufacturing, and redistributing products. Within this context, outsourcing to a third-party reverse logistics provider (3PRLP) has been identified as one of the most important management strategies for today’s organizations, especially e-commerce players. The objective of this study is to develop a decision support system to assist businesses in the selection and evaluation of different 3PRLPs by a hybrid fuzzy multicriteria decision-making (MCDM) approach. Relevant criteria concerning the economic, environmental, social, and risk factors are incorporated and taken into the models. For obtaining more scientific and accurate ranking results, linguistic terms are adopted to reduce fuzziness and uncertainties of criteria weights in the natural decision-making process. The fuzzy analytic hierarchy process (FAHP) is applied to measure the criteria’s relative significance over the evaluation process. The fuzzy technique for order preference by similarity to an ideal solution (FTOPSIS) is then used to rank the alternatives. The prescribed method was adopted for solving a case study on the 3PRLP selection for an online merchant in Vietnam. As a result, the most compatible 3PRLP was determined. The study also indicated that “lead time,” “customer’s voice,” “cost,” “delivery and service,” and “quality” are the most dominant drivers when selecting 3PLRLs. This study aims to provide a more complete and robust evaluation process to e-commerce businesses and any organization that deals with supply chain management in determining the optimized reverse logistics partners. Full article
(This article belongs to the Special Issue Multiple-Criteria Decision Making)
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Article
Integrating the EBM Model and LTS(A,A,A) Model to Evaluate the Efficiency in the Supply Chain of Packaging Industry in Vietnam
Axioms 2021, 10(1), 33; https://0-doi-org.brum.beds.ac.uk/10.3390/axioms10010033 - 12 Mar 2021
Viewed by 915
Abstract
In recent decades, Vietnamese labeling and packaging has been widely recognized as being one of the fastest developing industries in Vietnam, supported by the tremendous demand of domestic production and the exportation of its packaged goods. The emerging packaging technology trends and the [...] Read more.
In recent decades, Vietnamese labeling and packaging has been widely recognized as being one of the fastest developing industries in Vietnam, supported by the tremendous demand of domestic production and the exportation of its packaged goods. The emerging packaging technology trends and the participation of foreign direct investment (FDI) companies have led to fierce competition between all packaging enterprises in Vietnam. This paper aims to calculate the productivity performance of 10 packaging companies in Vietnam from the past to the future by combining the additive Holt-Winters (LTS(A,A,A)) model to predict key variables in the financial statement for the next 4 years (2020–2023) and an epsilon-based measure of efficiency (EBM) model of data envelopment analysis (DEA) to define the developing trend, efficiency, and ranking of packaging operations. The empirical results will assist packaging enterprises to identify their positions, suggest feasible solutions to overcome shortcomings and catch up with the global trends, and propose superior partnerships for manufacturers, which have packaging service demands and support investment decisions for investors. Overall, all the enterprises in the packaging industry have high productivity. In particular, SIVICO JSC is identified as the most efficient packaging company in Vietnam, as it continuously maintains the first ranking over the observation time, followed by Agriculture Printing & Packing JSC and Bien Hoa Packaging Company. In the past, Tan Dai Hung Plastic JSC was identified as the most unproductive unit, while in the future term, the inefficient decision-making units (DMUs) are Tan Tien Plastic Packaging JSC, Sai Gon Packaging JSC, Dong A JSC, and PetroVietnam Packaging JSC. The suggestion for incompetent enterprises is changing the value of inputs proportionally to optimize for better performance. Full article
(This article belongs to the Special Issue Multiple-Criteria Decision Making)
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Article
A Cellular Potts Model for Analyzing Cell Migration across Constraining Pillar Arrays
Axioms 2021, 10(1), 32; https://0-doi-org.brum.beds.ac.uk/10.3390/axioms10010032 - 12 Mar 2021
Cited by 1 | Viewed by 557
Abstract
Cell migration in highly constrained environments is fundamental in a wide variety of physiological and pathological phenomena. In particular, it has been experimentally shown that the migratory capacity of most cell lines depends on their ability to transmigrate through narrow constrictions, which in [...] Read more.
Cell migration in highly constrained environments is fundamental in a wide variety of physiological and pathological phenomena. In particular, it has been experimentally shown that the migratory capacity of most cell lines depends on their ability to transmigrate through narrow constrictions, which in turn relies on their deformation capacity. In this respect, the nucleus, which occupies a large fraction of the cell volume and is substantially stiffer than the surrounding cytoplasm, imposes a major obstacle. This aspect has also been investigated with the use of microfluidic devices formed by dozens of arrays of aligned polymeric pillars that limit the available space for cell movement. Such experimental systems, in particular, in the designs developed by the groups of Denais and of Davidson, were here reproduced with a tailored version of the Cellular Potts model, a grid-based stochastic approach where cell dynamics are established by a Metropolis algorithm for energy minimization. The proposed model allowed quantitatively analyzing selected cell migratory determinants (e.g., the cell and nuclear speed and deformation, and forces acting at the nuclear membrane) in the case of different experimental setups. Most of the numerical results show a remarkable agreement with the corresponding empirical data. Full article
(This article belongs to the Special Issue Differential Models, Numerical Simulations and Applications)
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Article
Fixed-Point Study of Generalized Rational Type Multivalued Contractive Mappings on Metric Spaces with a Graph
Axioms 2021, 10(1), 31; https://0-doi-org.brum.beds.ac.uk/10.3390/axioms10010031 - 11 Mar 2021
Viewed by 576
Abstract
The main result of this paper is a fixed-point theorem for multivalued contractions obtained through an inequality with rational terms. The contraction is an F-type contraction. The results are obtained in a metric space endowed with a graph. The main theorem is [...] Read more.
The main result of this paper is a fixed-point theorem for multivalued contractions obtained through an inequality with rational terms. The contraction is an F-type contraction. The results are obtained in a metric space endowed with a graph. The main theorem is supported by illustrative examples. Several results as special cases are obtained by specific choices of the control functions involved in the inequality. The study is broadly in the domain of setvalued analysis. The methodology of the paper is a blending of both graph theoretic and analytic methods. Full article
(This article belongs to the Special Issue Theory and Application of Fixed Point)
Article
An Efficient Chicken Search Optimization Algorithm for the Optimal Design of Fuzzy Controllers
Axioms 2021, 10(1), 30; https://0-doi-org.brum.beds.ac.uk/10.3390/axioms10010030 - 09 Mar 2021
Cited by 3 | Viewed by 761
Abstract
A proposed architecture to design the optimal parameters of Membership Functions (MFs) of Type-1 Fuzzy Logic Systems (T1FLSs) using the Chicken Search Optimization (CSO) is applied to three Fuzzy Logic Controllers (FLCs) in this paper. Two types of MFs are considered in the [...] Read more.
A proposed architecture to design the optimal parameters of Membership Functions (MFs) of Type-1 Fuzzy Logic Systems (T1FLSs) using the Chicken Search Optimization (CSO) is applied to three Fuzzy Logic Controllers (FLCs) in this paper. Two types of MFs are considered in the study: triangular and trapezoidal ones. The performance and efficiency of the CSO algorithm are particularly good when perturbations are added during the execution in each control problem. Two benchmark control problems: Water Tank Controller and Inverted Pendulum Controller are considered for testing the proposed approach. Also, the optimal design of a fuzzy controller for trajectory tracking of an Autonomous Mobile Robot (AMR) is considered to test the CSO. The main goal is to highlight the efficiency of CSO algorithm in finding optimal fuzzy controllers of non-linear plants. Two types of perturbations are considered in each control problem. Results show that the CSO algorithm presents excellent results in the field of Fuzzy Logic Controllers. Two types of Fuzzy Inference Systems: Takagi-Sugeno and Mamdani FLSs, are implemented in this paper. The most important metrics usually applied in control are used in this paper, such as: Integral Time Absolute Error (ITAE), Integral Time Squared Error (ITSE), Integral Absolute Error (IAE), Integral Square Error (ISE), Mean Square Error (MSE), and Root Mean Square Error (RMSE). Full article
(This article belongs to the Special Issue Fuzzy Control Systems: Theory and Applications)
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Article
Bell-Based Bernoulli Polynomials with Applications
Axioms 2021, 10(1), 29; https://0-doi-org.brum.beds.ac.uk/10.3390/axioms10010029 - 02 Mar 2021
Cited by 1 | Viewed by 842
Abstract
In this paper, we consider Bell-based Stirling polynomials of the second kind and derive some useful relations and properties including some summation formulas related to the Bell polynomials and Stirling numbers of the second kind. Then, we introduce Bell-based Bernoulli polynomials of order [...] Read more.
In this paper, we consider Bell-based Stirling polynomials of the second kind and derive some useful relations and properties including some summation formulas related to the Bell polynomials and Stirling numbers of the second kind. Then, we introduce Bell-based Bernoulli polynomials of order α and investigate multifarious correlations and formulas including some summation formulas and derivative properties. Also, we acquire diverse implicit summation formulas and symmetric identities for Bell-based Bernoulli polynomials of order α. Moreover, we attain several interesting formulas of Bell-based Bernoulli polynomials of order α arising from umbral calculus. Full article
(This article belongs to the Special Issue p-adic Analysis and q-Calculus with Their Applications)
Article
Note on Common Fixed Point Theorems in Convex Metric Spaces
Axioms 2021, 10(1), 28; https://0-doi-org.brum.beds.ac.uk/10.3390/axioms10010028 - 27 Feb 2021
Viewed by 546
Abstract
In the present paper, we pointed out that there is a gap in the proof of the main result of Rouzkard et al. (The Bulletin of the Belgian Mathematical Society 2012). Then after, utilizing the concept of (E.A.) property in convex metric space, [...] Read more.
In the present paper, we pointed out that there is a gap in the proof of the main result of Rouzkard et al. (The Bulletin of the Belgian Mathematical Society 2012). Then after, utilizing the concept of (E.A.) property in convex metric space, we obtained an alternative and correct version of this result. Finally, it is clarified that in the theory of common fixed point, the notion of (E.A.) property in the set up of convex metric space develops some new dimensions in comparison to the hypothesis that a range set of one map is contained in the range set of another map. Full article
(This article belongs to the Special Issue Theory and Application of Fixed Point)
Article
Coefficients of a Comprehensive Subclass of Meromorphic Bi-Univalent Functions Associated with the Faber Polynomial Expansion
Axioms 2021, 10(1), 27; https://0-doi-org.brum.beds.ac.uk/10.3390/axioms10010027 - 27 Feb 2021
Cited by 2 | Viewed by 650
Abstract
In this paper, we introduce a new comprehensive subclass ΣB(λ,μ,β) of meromorphic bi-univalent functions in the open unit disk U. We also find the upper bounds for the initial Taylor-Maclaurin coefficients [...] Read more.
In this paper, we introduce a new comprehensive subclass ΣB(λ,μ,β) of meromorphic bi-univalent functions in the open unit disk U. We also find the upper bounds for the initial Taylor-Maclaurin coefficients |b0|, |b1| and |b2| for functions in this comprehensive subclass. Moreover, we obtain estimates for the general coefficients |bn|(n1) for functions in the subclass ΣB(λ,μ,β) by making use of the Faber polynomial expansion method. The results presented in this paper would generalize and improve several recent works on the subject. Full article
(This article belongs to the Collection Mathematical Analysis and Applications)
Article
Approximation of the Fixed Point for Unified Three-Step Iterative Algorithm with Convergence Analysis in Busemann Spaces
Axioms 2021, 10(1), 26; https://0-doi-org.brum.beds.ac.uk/10.3390/axioms10010026 - 27 Feb 2021
Cited by 1 | Viewed by 568
Abstract
In this manuscript, a new three-step iterative scheme to approximate fixed points in the setting of Busemann spaces is introduced. The proposed algorithms unify and extend most of the existing iterative schemes. Thereafter, by making consequent use of this method, strong and Δ [...] Read more.
In this manuscript, a new three-step iterative scheme to approximate fixed points in the setting of Busemann spaces is introduced. The proposed algorithms unify and extend most of the existing iterative schemes. Thereafter, by making consequent use of this method, strong and Δ-convergence results of mappings that satisfy the condition (Eμ) in the framework of uniformly convex Busemann space are obtained. Our results generalize several existing results in the same direction. Full article
(This article belongs to the Special Issue Theory and Application of Fixed Point)
Article
A New Inverted Topp-Leone Distribution: Applications to the COVID-19 Mortality Rate in Two Different Countries
Axioms 2021, 10(1), 25; https://0-doi-org.brum.beds.ac.uk/10.3390/axioms10010025 - 26 Feb 2021
Cited by 6 | Viewed by 802
Abstract
This paper aims to find a statistical model for the COVID-19 spread in the United Kingdom and Canada. We used an efficient and superior model for fitting the COVID 19 mortality rates in these countries by specifying an optimal statistical model. A new [...] Read more.
This paper aims to find a statistical model for the COVID-19 spread in the United Kingdom and Canada. We used an efficient and superior model for fitting the COVID 19 mortality rates in these countries by specifying an optimal statistical model. A new lifetime distribution with two-parameter is introduced by a combination of inverted Topp-Leone distribution and modified Kies family to produce the modified Kies inverted Topp-Leone (MKITL) distribution, which covers a lot of application that both the traditional inverted Topp-Leone and the modified Kies provide poor fitting for them. This new distribution has many valuable properties as simple linear representation, hazard rate function, and moment function. We made several methods of estimations as maximum likelihood estimation, least squares estimators, weighted least-squares estimators, maximum product spacing, Crame´r-von Mises estimators, and Anderson-Darling estimators methods are applied to estimate the unknown parameters of MKITL distribution. A numerical result of the Monte Carlo simulation is obtained to assess the use of estimation methods. also, we applied different data sets to the new distribution to assess its performance in modeling data. Full article
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Article
Fixed Points of Some Asymptotically Regular Multivalued Mappings Satisfying a Kannan-Type Condition
Axioms 2021, 10(1), 24; https://0-doi-org.brum.beds.ac.uk/10.3390/axioms10010024 - 25 Feb 2021
Cited by 1 | Viewed by 795
Abstract
In this paper, we establish some existence of fixed-point results for some asymptotically regular multivalued mappings satisfying Kannan-type contractive condition without assuming compactness of the underlying metric space or continuity of the mapping. Full article
(This article belongs to the Collection Mathematical Analysis and Applications)
Article
Analysis of the Transient Behaviour in the Numerical Solution of Volterra Integral Equations
Axioms 2021, 10(1), 23; https://0-doi-org.brum.beds.ac.uk/10.3390/axioms10010023 - 23 Feb 2021
Viewed by 605
Abstract
In this paper, the asymptotic behaviour of the numerical solution to the Volterra integral equations is studied. In particular, a technique based on an appropriate splitting of the kernel is introduced, which allows one to obtain vanishing asymptotic (transient) behaviour in the numerical [...] Read more.
In this paper, the asymptotic behaviour of the numerical solution to the Volterra integral equations is studied. In particular, a technique based on an appropriate splitting of the kernel is introduced, which allows one to obtain vanishing asymptotic (transient) behaviour in the numerical solution, consistently with the properties of the analytical solution, without having to operate restrictions on the integration steplength. Full article
(This article belongs to the Special Issue Differential Models, Numerical Simulations and Applications)
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Article
On Λ-Fractional Viscoelastic Models
Axioms 2021, 10(1), 22; https://0-doi-org.brum.beds.ac.uk/10.3390/axioms10010022 - 20 Feb 2021
Cited by 1 | Viewed by 575
Abstract
Λ-Fractional Derivative (Λ-FD) is a new groundbreaking Fractional Derivative (FD) introduced recently in mechanics. This derivative, along with Λ-Transform (Λ-T), provides a reliable alternative to fractional differential equations’ current solving. To put it straightforwardly, Λ-Fractional Derivative might be the only authentic non-local derivative [...] Read more.
Λ-Fractional Derivative (Λ-FD) is a new groundbreaking Fractional Derivative (FD) introduced recently in mechanics. This derivative, along with Λ-Transform (Λ-T), provides a reliable alternative to fractional differential equations’ current solving. To put it straightforwardly, Λ-Fractional Derivative might be the only authentic non-local derivative that exists. In the present article, Λ-Fractional Derivative is used to describe the phenomenon of viscoelasticity, while the whole methodology is demonstrated meticulously. The fractional viscoelastic Zener model is studied, for relaxation as well as for creep. Interesting results are extracted and compared to other methodologies showing the value of the pre-mentioned method. Full article
(This article belongs to the Special Issue Axioms on Advanced Differential Equations for Mathematical Modeling)
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Article
On Almost Projective Modules
Axioms 2021, 10(1), 21; https://0-doi-org.brum.beds.ac.uk/10.3390/axioms10010021 - 16 Feb 2021
Viewed by 509
Abstract
In this note, we investigate the relationship between almost projective modules and generalized projective modules. These concepts are useful for the study on the finite direct sum of lifting modules. It is proved that; if M is generalized N-projective for any modules [...] Read more.
In this note, we investigate the relationship between almost projective modules and generalized projective modules. These concepts are useful for the study on the finite direct sum of lifting modules. It is proved that; if M is generalized N-projective for any modules M and N, then M is almost N-projective. We also show that if M is almost N-projective and N is lifting, then M is im-small N-projective. We also discuss the question of when the finite direct sum of lifting modules is again lifting. Full article
Article
Cascading Operators in CAT(0) Spaces
Axioms 2021, 10(1), 20; https://0-doi-org.brum.beds.ac.uk/10.3390/axioms10010020 - 09 Feb 2021
Viewed by 603
Abstract
In this work, we introduce the notion of cascading non-expansive mappings in the setting of CAT(0) spaces. This family of mappings properly contains the non-expansive maps, but it differs from other generalizations of this class of maps. Considering the concept [...] Read more.
In this work, we introduce the notion of cascading non-expansive mappings in the setting of CAT(0) spaces. This family of mappings properly contains the non-expansive maps, but it differs from other generalizations of this class of maps. Considering the concept of Δ-convergence in metric spaces, we prove a principle of demiclosedness for this type of mappings and a Δ-convergence theorem for a Mann iteration process defined using cascading operators. Full article
(This article belongs to the Special Issue Fixed Point Theory and Its Related Topics II)
Article
Comparison of the Sub-Tour Elimination Methods for the Asymmetric Traveling Salesman Problem Applying the SECA Method
Axioms 2021, 10(1), 19; https://0-doi-org.brum.beds.ac.uk/10.3390/axioms10010019 - 08 Feb 2021
Cited by 2 | Viewed by 864
Abstract
There are many sub-tour elimination constraint (SEC) formulations for the traveling salesman problem (TSP). Among the different methods found in articles, usually three apply more than others. This study examines the Danzig–Fulkerson–Johnson (DFJ), Miller–Tucker–Zemlin (MTZ), and Gavish–Graves (GG) formulations to select the best [...] Read more.
There are many sub-tour elimination constraint (SEC) formulations for the traveling salesman problem (TSP). Among the different methods found in articles, usually three apply more than others. This study examines the Danzig–Fulkerson–Johnson (DFJ), Miller–Tucker–Zemlin (MTZ), and Gavish–Graves (GG) formulations to select the best asymmetric traveling salesman problem (ATSP) formulation. The study introduces five criteria as the number of constraints, number of variables, type of variables, time of solving, and differences between the optimum and the relaxed value for comparing these constraints. The reason for selecting these criteria is that they have the most significant impact on the mathematical problem-solving complexity. A new and well-known multiple-criteria decision making (MCDM) method, the simultaneous evaluation of the criteria and alternatives (SECA) method was applied to analyze these criteria. To use the SECA method for ranking the alternatives and extracting information about the criteria from constraints needs computational computing. In this research, we use CPLEX 12.8 software to compute the criteria value and LINGO 11 software to solve the SECA method. Finally, we conclude that the Gavish–Graves (GG) formulation is the best. The new web-based software was used for testing the results. Full article
(This article belongs to the Special Issue Multiple-Criteria Decision Making)
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Article
Modeling and Forecasting of COVID-19 Spreading by Delayed Stochastic Differential Equations
Axioms 2021, 10(1), 18; https://0-doi-org.brum.beds.ac.uk/10.3390/axioms10010018 - 07 Feb 2021
Cited by 4 | Viewed by 1174
Abstract
The novel coronavirus disease (COVID-19) pneumonia has posed a great threat to the world recent months by causing many deaths and enormous economic damage worldwide. The first case of COVID-19 in Morocco was reported on 2 March 2020, and the number of reported [...] Read more.
The novel coronavirus disease (COVID-19) pneumonia has posed a great threat to the world recent months by causing many deaths and enormous economic damage worldwide. The first case of COVID-19 in Morocco was reported on 2 March 2020, and the number of reported cases has increased day by day. In this work, we extend the well-known SIR compartmental model to deterministic and stochastic time-delayed models in order to predict the epidemiological trend of COVID-19 in Morocco and to assess the potential role of multiple preventive measures and strategies imposed by Moroccan authorities. The main features of the work include the well-posedness of the models and conditions under which the COVID-19 may become extinct or persist in the population. Parameter values have been estimated from real data and numerical simulations are presented for forecasting the COVID-19 spreading as well as verification of theoretical results. Full article
(This article belongs to the Special Issue Axioms on Advanced Differential Equations for Mathematical Modeling)
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Article
A Three-Phase Fundamental Diagram from Three-Dimensional Traffic Data
Axioms 2021, 10(1), 17; https://0-doi-org.brum.beds.ac.uk/10.3390/axioms10010017 - 07 Feb 2021
Cited by 1 | Viewed by 822
Abstract
This paper uses empirical traffic data collected from three locations in Europe and the US to reveal a three-phase fundamental diagram with two phases located in the uncongested regime. Model-based clustering, hypothesis testing and regression analyses are applied to the speed–flow–occupancy relationship represented [...] Read more.
This paper uses empirical traffic data collected from three locations in Europe and the US to reveal a three-phase fundamental diagram with two phases located in the uncongested regime. Model-based clustering, hypothesis testing and regression analyses are applied to the speed–flow–occupancy relationship represented in the three-dimensional space to rigorously validate the three phases and identify their gaps. The finding is consistent across the aforementioned different geographical locations. Accordingly, we propose a three-phase macroscopic traffic flow model and a characterization of solutions to the Riemann problems. This work identifies critical structures in the fundamental diagram that are typically ignored in first- and higher-order models and could significantly impact travel time estimation on highways. Full article
(This article belongs to the Special Issue Differential Models, Numerical Simulations and Applications)
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Article
A Strong Convergence Theorem for Split Null Point Problem and Generalized Mixed Equilibrium Problem in Real Hilbert Spaces
Axioms 2021, 10(1), 16; https://0-doi-org.brum.beds.ac.uk/10.3390/axioms10010016 - 05 Feb 2021
Viewed by 526
Abstract
In this paper, we study a schematic approximation of solutions of a split null point problem for a finite family of maximal monotone operators in real Hilbert spaces. We propose an iterative algorithm that does not depend on the operator norm which solves [...] Read more.
In this paper, we study a schematic approximation of solutions of a split null point problem for a finite family of maximal monotone operators in real Hilbert spaces. We propose an iterative algorithm that does not depend on the operator norm which solves the split null point problem and also solves a generalized mixed equilibrium problem. We prove a strong convergence of the proposed algorithm to a common solution of the two problems. We display some numerical examples to illustrate our method. Our result improves some existing results in the literature. Full article
(This article belongs to the Special Issue Theory and Application of Fixed Point)
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Article
Iterative Sequences for a Finite Number of Resolvent Operators on Complete Geodesic Spaces
Axioms 2021, 10(1), 15; https://0-doi-org.brum.beds.ac.uk/10.3390/axioms10010015 - 26 Jan 2021
Viewed by 690
Abstract
We consider Halpern’s and Mann’s types of iterative schemes to find a common minimizer of a finite number of proper lower semicontinuous convex functions defined on a complete geodesic space with curvature bounded above. Full article
(This article belongs to the Special Issue Theory and Application of Fixed Point)
Article
Stability of Weak Solutions to Parabolic Problems with Nonstandard Growth and Cross–Diffusion
Axioms 2021, 10(1), 14; https://0-doi-org.brum.beds.ac.uk/10.3390/axioms10010014 - 22 Jan 2021
Viewed by 585
Abstract
We study the stability of a unique weak solution to certain parabolic systems with nonstandard growth condition, which are additionally dependent on a cross-diffusion term. More precisely, we show that two unique weak solutions of the considered system with different initial values are [...] Read more.
We study the stability of a unique weak solution to certain parabolic systems with nonstandard growth condition, which are additionally dependent on a cross-diffusion term. More precisely, we show that two unique weak solutions of the considered system with different initial values are controlled by their initial values. Full article
Editorial
Acknowledgment to Reviewers of Axioms in 2020
Axioms 2021, 10(1), 13; https://0-doi-org.brum.beds.ac.uk/10.3390/axioms10010013 - 21 Jan 2021
Viewed by 651
Abstract
Peer review is the driving force of journal development, and reviewers are gatekeepers who ensure that Axioms maintains its standards for the high quality of its published papers [...] Full article
Article
Input-to-State Stability of a Scalar Conservation Law with Nonlocal Velocity
Axioms 2021, 10(1), 12; https://0-doi-org.brum.beds.ac.uk/10.3390/axioms10010012 - 21 Jan 2021
Viewed by 671
Abstract
In this paper, we study input-to-state stability (ISS) of an equilibrium for a scalar conservation law with nonlocal velocity and measurement error arising in a highly re-entrant manufacturing system. By using a suitable Lyapunov function, we prove sufficient and necessary conditions on ISS. [...] Read more.
In this paper, we study input-to-state stability (ISS) of an equilibrium for a scalar conservation law with nonlocal velocity and measurement error arising in a highly re-entrant manufacturing system. By using a suitable Lyapunov function, we prove sufficient and necessary conditions on ISS. We propose a numerical discretization of the scalar conservation law with nonlocal velocity and measurement error. A suitable discrete Lyapunov function is analyzed to provide ISS of a discrete equilibrium for the proposed numerical approximation. Finally, we show computational results to validate the theoretical findings. Full article
(This article belongs to the Special Issue Differential Models, Numerical Simulations and Applications)
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