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Mathematics, Volume 7, Issue 7 (July 2019)

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Cover Story (view full-size image) We introduce the notion of bi-slant submanifolds of a para Hermitian manifold, which naturally [...] Read more.
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Open AccessFeature PaperArticle
The Regularity of Some Families of Circulant Graphs
Mathematics 2019, 7(7), 657; https://doi.org/10.3390/math7070657
Received: 18 June 2019 / Revised: 17 July 2019 / Accepted: 18 July 2019 / Published: 22 July 2019
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Abstract
We compute the Castelnuovo–Mumford regularity of the edge ideals of two families of circulant graphs, which includes all cubic circulant graphs. A feature of our approach is to combine bounds on the regularity, the projective dimension, and the reduced Euler characteristic to derive [...] Read more.
We compute the Castelnuovo–Mumford regularity of the edge ideals of two families of circulant graphs, which includes all cubic circulant graphs. A feature of our approach is to combine bounds on the regularity, the projective dimension, and the reduced Euler characteristic to derive an exact value for the regularity. Full article
(This article belongs to the Special Issue Current Trends on Monomial and Binomial Ideals)
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Open AccessArticle
Practical Stability with Respect to h-Manifolds for Impulsive Control Functional Differential Equations with Variable Impulsive Perturbations
Mathematics 2019, 7(7), 656; https://doi.org/10.3390/math7070656
Received: 21 May 2019 / Revised: 16 July 2019 / Accepted: 18 July 2019 / Published: 21 July 2019
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Abstract
The present paper is devoted to the problems of practical stability with respect to h-manifolds for impulsive control differential equations with variable impulsive perturbations. We will consider these problems in light of the Lyapunov–Razumikhin method of piecewise continuous functions. The new results [...] Read more.
The present paper is devoted to the problems of practical stability with respect to h-manifolds for impulsive control differential equations with variable impulsive perturbations. We will consider these problems in light of the Lyapunov–Razumikhin method of piecewise continuous functions. The new results are applied to an impulsive control cellular neural network model with variable impulsive perturbations. Full article
(This article belongs to the Special Issue Impulsive Control Systems and Complexity)
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Open AccessFeature PaperArticle
One-Point Optimal Family of Multiple Root Solvers of Second-Order
Mathematics 2019, 7(7), 655; https://doi.org/10.3390/math7070655
Received: 6 June 2019 / Revised: 13 July 2019 / Accepted: 17 July 2019 / Published: 21 July 2019
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Abstract
This manuscript contains the development of a one-point family of iterative functions. The family has optimal convergence of a second-order according to the Kung-Traub conjecture. This family is used to approximate the multiple zeros of nonlinear equations, and is based on the procedure [...] Read more.
This manuscript contains the development of a one-point family of iterative functions. The family has optimal convergence of a second-order according to the Kung-Traub conjecture. This family is used to approximate the multiple zeros of nonlinear equations, and is based on the procedure of weight functions. The convergence behavior is discussed by showing some essential conditions of the weight function. The well-known modified Newton method is a member of the proposed family for particular choices of the weight function. The dynamical nature of different members is presented by using a technique called the “basin of attraction”. Several practical problems are given to compare different methods of the presented family. Full article
(This article belongs to the Special Issue Multivariate Approximation for solving ODE and PDE)
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Open AccessArticle
Existence of Positive Solutions to Singular Boundary Value Problems Involving φ-Laplacian
Mathematics 2019, 7(7), 654; https://doi.org/10.3390/math7070654
Received: 27 May 2019 / Revised: 11 July 2019 / Accepted: 18 July 2019 / Published: 21 July 2019
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Abstract
This paper is concerned with the existence of positive solutions to singular Dirichlet boundary value problems involving φ-Laplacian. For non-negative nonlinearity f=f(t,s) satisfying f(t,0)0, the existence of [...] Read more.
This paper is concerned with the existence of positive solutions to singular Dirichlet boundary value problems involving φ -Laplacian. For non-negative nonlinearity f = f ( t , s ) satisfying f ( t , 0 ) 0 , the existence of an unbounded solution component is shown. By investigating the shape of the component depending on the behavior of f at , the existence, nonexistence and multiplicity of positive solutions are studied. Full article
Open AccessArticle
The Impact of Viscous Dissipation on the Thin Film Unsteady Flow of GO-EG/GO-W Nanofluids
Mathematics 2019, 7(7), 653; https://doi.org/10.3390/math7070653
Received: 17 May 2019 / Revised: 16 July 2019 / Accepted: 17 July 2019 / Published: 20 July 2019
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Abstract
The unsteady flow of nanoliquid film over a flexible surface has been inspected. Water and ethylene glycol are used as the base liquids for the graphene oxide platelets. The comparison of two sorts of nanoliquids has been used for heat transfer enhancement applications. [...] Read more.
The unsteady flow of nanoliquid film over a flexible surface has been inspected. Water and ethylene glycol are used as the base liquids for the graphene oxide platelets. The comparison of two sorts of nanoliquids has been used for heat transfer enhancement applications. The thickness of the nanoliquid film is kept as a variable. The governing equations for the flow problem have been altered into the set of nonlinear differential equations. The BVP 2.0 package has been used for the solution of the problem. The sum of the square residual error has been calculated up to the 10th order approximations. It has been observed that the graphene oxide ethylene glycol based nanofluid (GO-EG) is more efficient for heat transfer enhancement as compared to the graphene oxide water based nanofluid (GO-W). The impact of the physical parameters has been plotted and discussed. Full article
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Open AccessArticle
On Extended Adjacency Index with Respect to Acyclic, Unicyclic and Bicyclic Graphs
Mathematics 2019, 7(7), 652; https://doi.org/10.3390/math7070652
Received: 9 June 2019 / Revised: 14 July 2019 / Accepted: 18 July 2019 / Published: 20 July 2019
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Abstract
For a (molecular) graph G, the extended adjacency index EA(G) is defined as Equation (1). In this paper we introduce some graph transformations which increase or decrease the extended adjacency (EA) index. Also, we obtain [...] Read more.
For a (molecular) graph G, the extended adjacency index E A ( G ) is defined as Equation (1). In this paper we introduce some graph transformations which increase or decrease the extended adjacency ( E A ) index. Also, we obtain the extremal acyclic, unicyclic and bicyclic graphs with minimum and maximum of the E A index by a unified method, respectively. Full article
(This article belongs to the Special Issue Advances and Novel Approaches in Discrete Optimization)
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Open AccessFeature PaperArticle
Functions of Minimal Norm with the Given Set of Fourier Coefficients
Mathematics 2019, 7(7), 651; https://doi.org/10.3390/math7070651
Received: 17 June 2019 / Revised: 13 July 2019 / Accepted: 19 July 2019 / Published: 20 July 2019
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Abstract
We prove the existence and uniqueness of the solution of the problem of the minimum norm function · with a given set of initial coefficients of the trigonometric Fourier series cj, j=0,1, [...] Read more.
We prove the existence and uniqueness of the solution of the problem of the minimum norm function · with a given set of initial coefficients of the trigonometric Fourier series c j , j = 0 , 1 , , 2 n . Then, we prove the existence and uniqueness of the solution of the nonnegative function problem with a given set of coefficients of the trigonometric Fourier series c j , j = 1 , , 2 n for the norm · 1 . Full article
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Open AccessArticle
A Novel Integral Equation for the Riemann Zeta Function and Large t-Asymptotics
Mathematics 2019, 7(7), 650; https://doi.org/10.3390/math7070650
Received: 7 June 2019 / Revised: 17 July 2019 / Accepted: 18 July 2019 / Published: 20 July 2019
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Abstract
Based on the new approach to Lindelöf hypothesis recently introduced by one of the authors, we first derive a novel integral equation for the square of the absolute value of the Riemann zeta function. Then, we introduce the machinery needed to obtain an [...] Read more.
Based on the new approach to Lindelöf hypothesis recently introduced by one of the authors, we first derive a novel integral equation for the square of the absolute value of the Riemann zeta function. Then, we introduce the machinery needed to obtain an estimate for the solution of this equation. This approach suggests a substantial improvement of the current large t - asymptotics estimate for ζ 1 2 + i t . Full article
(This article belongs to the Special Issue Mathematical Analysis and Analytic Number Theory 2019)
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Open AccessArticle
Measures of Probabilistic Neutrosophic Hesitant Fuzzy Sets and the Application in Reducing Unnecessary Evaluation Processes
Mathematics 2019, 7(7), 649; https://doi.org/10.3390/math7070649
Received: 20 June 2019 / Revised: 15 July 2019 / Accepted: 16 July 2019 / Published: 19 July 2019
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Abstract
Distance measure and similarity measure have been applied to various multi-criteria decision-making environments, like talent selections, fault diagnoses and so on. Some improved distance and similarity measures have been proposed by some researchers. However, hesitancy is reflected in all aspects of life, thus [...] Read more.
Distance measure and similarity measure have been applied to various multi-criteria decision-making environments, like talent selections, fault diagnoses and so on. Some improved distance and similarity measures have been proposed by some researchers. However, hesitancy is reflected in all aspects of life, thus the hesitant information needs to be considered in measures. Then, it can effectively avoid the loss of fuzzy information. However, regarding fuzzy information, it only reflects the subjective factor. Obviously, this is a shortcoming that will result in an inaccurate decision conclusion. Thus, based on the definition of a probabilistic neutrosophic hesitant fuzzy set (PNHFS), as an extended theory of fuzzy set, the basic definition of distance, similarity and entropy measures of PNHFS are established. Next, the interconnection among the distance, similarity and entropy measures are studied. Simultaneously, a novel measure model is established based on the PNHFSs. In addition, the new measure model is compared by some existed measures. Finally, we display their applicability concerning the investment problems, which can be utilized to avoid redundant evaluation processes. Full article
(This article belongs to the Special Issue New Challenges in Neutrosophic Theory and Applications)
Open AccessFeature PaperArticle
Statistical Tests for Extreme Precipitation Volumes
Mathematics 2019, 7(7), 648; https://doi.org/10.3390/math7070648
Received: 24 June 2019 / Revised: 15 July 2019 / Accepted: 17 July 2019 / Published: 19 July 2019
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Abstract
The analysis of the real observations of precipitation based on the novel statistical approach using the negative binomial distribution as a model for describing the random duration of a wet period is considered and discussed. The study shows that this distribution fits very [...] Read more.
The analysis of the real observations of precipitation based on the novel statistical approach using the negative binomial distribution as a model for describing the random duration of a wet period is considered and discussed. The study shows that this distribution fits very well to the real observations and generalized standard methods used in meteorology to detect an extreme volume of precipitation. It also provides a theoretical base for the determination of asymptotic approximations to the distributions of the maximum daily precipitation volume within a wet period, as well as the total precipitation volume over a wet period. The paper demonstrates that the relation of the unique precipitation volume, having the gamma distribution, divided by the total precipitation volume taken over the wet period is given by the Snedecor–Fisher or beta distributions. It allows us to construct statistical tests to determine the extreme precipitations. Within this approach, it is possible to introduce the notions of relatively and absolutely extreme precipitation volumes. An alternative method to determine an extreme daily precipitation volume based on a certain quantile of the tempered Snedecor–Fisher distribution is also suggested. The results of the application of these methods to real data are presented. Full article
(This article belongs to the Special Issue Stochastic Processes: Theory and Applications)
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Open AccessArticle
Dynamic Parallel Mining Algorithm of Association Rules Based on Interval Concept Lattice
Mathematics 2019, 7(7), 647; https://doi.org/10.3390/math7070647
Received: 19 May 2019 / Revised: 11 July 2019 / Accepted: 17 July 2019 / Published: 19 July 2019
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Abstract
An interval concept lattice is an expansion form of a classical concept lattice and a rough concept lattice. It is a conceptual hierarchy consisting of a set of objects with a certain number or proportion of intent attributes. Interval concept lattices refine the [...] Read more.
An interval concept lattice is an expansion form of a classical concept lattice and a rough concept lattice. It is a conceptual hierarchy consisting of a set of objects with a certain number or proportion of intent attributes. Interval concept lattices refine the proportion of intent containing extent to get a certain degree of object set, and then mine association rules, so as to achieve minimal cost and maximal return. Faced with massive data, the structure of an interval concept lattice is more complex. Even if the lattice structures have been united first, the time complexity of mining interval association rules is higher. In this paper, the principle of mining association rules with parameters is studied, and the principle of a vertical union algorithm of interval association rules is proposed. On this basis, a dynamic mining algorithm of interval association rules is designed to achieve rule aggregation and maintain the diversity of interval association rules. Finally, the rationality and efficiency of the algorithm are verified by a case study. Full article
(This article belongs to the Special Issue Evolutionary Algorithms in Intelligent Systems)
Open AccessFeature PaperArticle
Parameter Estimation of Lindley Distribution Based on Progressive Type-II Censored Competing Risks Data with Binomial Removals
Mathematics 2019, 7(7), 646; https://doi.org/10.3390/math7070646
Received: 12 June 2019 / Revised: 15 July 2019 / Accepted: 15 July 2019 / Published: 19 July 2019
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Abstract
The competing risk model based on Lindley distribution is discussed under the progressive type-II censored sample data with binomial removals. The maximum likelihood estimation of the unknown parameters of the distribution is established. Using the Lindley approximation method, we also obtain the Bayesian [...] Read more.
The competing risk model based on Lindley distribution is discussed under the progressive type-II censored sample data with binomial removals. The maximum likelihood estimation of the unknown parameters of the distribution is established. Using the Lindley approximation method, we also obtain the Bayesian estimation of the unknown parameters of the distribution under different loss functions. The performance of different estimates is studied in this article. A real practical dataset is analyzed for illustration. Full article
(This article belongs to the Section Mathematics and Computers Science)
Open AccessArticle
Properties of Fluctuating States in Loop Quantum Cosmology
Mathematics 2019, 7(7), 645; https://doi.org/10.3390/math7070645
Received: 7 June 2019 / Revised: 15 July 2019 / Accepted: 16 July 2019 / Published: 19 July 2019
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Abstract
In loop quantum cosmology, the values of volume fluctuations and correlations determine whether the dynamics of an evolving state exhibits a bounce. Of particular interest are states that are supported only on either the positive or the negative part of the spectrum of [...] Read more.
In loop quantum cosmology, the values of volume fluctuations and correlations determine whether the dynamics of an evolving state exhibits a bounce. Of particular interest are states that are supported only on either the positive or the negative part of the spectrum of the Hamiltonian that generates this evolution. It is shown here that the restricted support on the spectrum does not significantly limit the possible values of volume fluctuations. Full article
(This article belongs to the Special Issue Mathematical and Computational Cosmology)
Open AccessArticle
Linear Convergence of an Iterative Algorithm for Solving the Multiple-Sets Split Feasibility Problem
Mathematics 2019, 7(7), 644; https://doi.org/10.3390/math7070644
Received: 4 June 2019 / Revised: 13 July 2019 / Accepted: 15 July 2019 / Published: 18 July 2019
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Abstract
In this paper, we propose the simultaneous sub-gradient projection algorithm with the dynamic step size (SSPA for short) for solving the multiple-sets split feasibility problem (MSSFP for short) and investigate its linear convergence. We involve a notion of bounded linear regularity for the [...] Read more.
In this paper, we propose the simultaneous sub-gradient projection algorithm with the dynamic step size (SSPA for short) for solving the multiple-sets split feasibility problem (MSSFP for short) and investigate its linear convergence. We involve a notion of bounded linear regularity for the MSSFP and construct several sufficient conditions to prove the linear convergence for the SSPA. In particular, the SSPA is an easily calculated algorithm that uses orthogonal projection onto half-spaces. Furthermore, some numerical results are provided to verify the effectiveness of our proposed algorithm. Full article
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Open AccessArticle
Some New Observations on Geraghty and Ćirić Type Results in b-Metric Spaces
Mathematics 2019, 7(7), 643; https://doi.org/10.3390/math7070643
Received: 10 June 2019 / Revised: 13 July 2019 / Accepted: 15 July 2019 / Published: 18 July 2019
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Abstract
We discuss recent fixed point results in b-metric spaces given by Pant and Panicker (2016). Our results are with shorter proofs. In addition, for ε(1,3], our results are genuine generalizations of ones from Pant and [...] Read more.
We discuss recent fixed point results in b-metric spaces given by Pant and Panicker (2016). Our results are with shorter proofs. In addition, for ε ( 1 , 3 ] , our results are genuine generalizations of ones from Pant and Panicker. Full article
(This article belongs to the Special Issue Fixed Point Theory and Dynamical Systems with Applications)
Open AccessArticle
R-Adaptive Multisymplectic and Variational Integrators
Mathematics 2019, 7(7), 642; https://doi.org/10.3390/math7070642
Received: 30 May 2019 / Revised: 3 July 2019 / Accepted: 9 July 2019 / Published: 18 July 2019
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Abstract
Moving mesh methods (also called r-adaptive methods) are space-adaptive strategies used for the numerical simulation of time-dependent partial differential equations. These methods keep the total number of mesh points fixed during the simulation but redistribute them over time to follow the areas [...] Read more.
Moving mesh methods (also called r-adaptive methods) are space-adaptive strategies used for the numerical simulation of time-dependent partial differential equations. These methods keep the total number of mesh points fixed during the simulation but redistribute them over time to follow the areas where a higher mesh point density is required. There are a very limited number of moving mesh methods designed for solving field-theoretic partial differential equations, and the numerical analysis of the resulting schemes is challenging. In this paper, we present two ways to construct r-adaptive variational and multisymplectic integrators for (1+1)-dimensional Lagrangian field theories. The first method uses a variational discretization of the physical equations, and the mesh equations are then coupled in a way typical of the existing r-adaptive schemes. The second method treats the mesh points as pseudo-particles and incorporates their dynamics directly into the variational principle. A user-specified adaptation strategy is then enforced through Lagrange multipliers as a constraint on the dynamics of both the physical field and the mesh points. We discuss the advantages and limitations of our methods. Numerical results for the Sine–Gordon equation are also presented. Full article
(This article belongs to the Special Issue Geometric Numerical Integration)
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Open AccessArticle
Traveling Waves in a Nonlocal Dispersal SIR Model with Standard Incidence Rate and Nonlocal Delayed Transmission
Mathematics 2019, 7(7), 641; https://doi.org/10.3390/math7070641
Received: 15 April 2019 / Revised: 6 July 2019 / Accepted: 17 July 2019 / Published: 18 July 2019
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Abstract
In this paper, we study the traveling wave solutions for a nonlocal dispersal SIR epidemic model with standard incidence rate and nonlocal delayed transmission. The existence and nonexistence of traveling wave solutions are determined by the basic reproduction number of the corresponding reaction [...] Read more.
In this paper, we study the traveling wave solutions for a nonlocal dispersal SIR epidemic model with standard incidence rate and nonlocal delayed transmission. The existence and nonexistence of traveling wave solutions are determined by the basic reproduction number of the corresponding reaction system and the minimal wave speed. To prove these results, we apply the Schauder’s fixed point theorem and two-sided Laplace transform. The main difficulties are that the complexity of the incidence rate in the epidemic model and the lack of regularity for nonlocal dispersal operator. Full article
Open AccessFeature PaperArticle
Directionally Correlated Movement Can Drive Qualitative Changes in Emergent Population Distribution Patterns
Mathematics 2019, 7(7), 640; https://doi.org/10.3390/math7070640
Received: 26 June 2019 / Revised: 12 July 2019 / Accepted: 16 July 2019 / Published: 18 July 2019
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Abstract
A fundamental goal of ecology is to understand the spatial distribution of species. For moving animals, their location is crucially dependent on the movement mechanisms they employ to navigate the landscape. Animals across many taxa are known to exhibit directional correlation in their [...] Read more.
A fundamental goal of ecology is to understand the spatial distribution of species. For moving animals, their location is crucially dependent on the movement mechanisms they employ to navigate the landscape. Animals across many taxa are known to exhibit directional correlation in their movement. This work explores the effect of such directional correlation on spatial pattern formation in a model of between-population taxis (i.e., movement of each population in response to the presence of the others). A telegrapher-taxis formalism is used, which generalises a previously studied diffusion-taxis system by incorporating a parameter T, measuring the characteristic time for directional persistence. The results give general criteria for determining when changes in T will drive qualitative changes in the predictions of linear pattern formation analysis for N 2 populations. As a specific example, the N = 2 case is explored in detail, showing that directional correlation can cause one population to ‘chase’ the other across the landscape while maintaining a non-constant spatial distribution. Overall, this study demonstrates the importance of accounting for directional correlation in movement for understanding both quantitative and qualitative aspects of species distributions. Full article
(This article belongs to the Special Issue Partial Differential Equations in Ecology: 80 Years and Counting)
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Open AccessArticle
A New Class of 2q-Point Nonstationary Subdivision Schemes and Their Applications
Mathematics 2019, 7(7), 639; https://doi.org/10.3390/math7070639
Received: 1 May 2019 / Revised: 1 July 2019 / Accepted: 15 July 2019 / Published: 18 July 2019
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Abstract
The main objective of this study is to introduce a new class of 2q-point approximating nonstationary subdivision schemes (ANSSs) by applying Lagrange-like interpolant. The theory of asymptotic equivalence is applied to find the continuity of the ANSSs. These schemes can be [...] Read more.
The main objective of this study is to introduce a new class of 2 q -point approximating nonstationary subdivision schemes (ANSSs) by applying Lagrange-like interpolant. The theory of asymptotic equivalence is applied to find the continuity of the ANSSs. These schemes can be nicely generalized to contain local shape parameters that allow the user to locally adjust the shape of the limit curve/surface. Moreover, many existing approximating stationary subdivision schemes (ASSSs) can be obtained as nonstationary counterparts of the proposed ANSSs. Full article
(This article belongs to the Special Issue Discrete and Computational Geometry)
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Open AccessFeature PaperArticle
On the Sum of Reciprocal of Polynomial Applied to Higher Order Recurrences
Mathematics 2019, 7(7), 638; https://doi.org/10.3390/math7070638
Received: 24 June 2019 / Revised: 12 July 2019 / Accepted: 15 July 2019 / Published: 18 July 2019
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Abstract
Recently a lot of papers have been devoted to partial infinite reciprocal sums of a higher-order linear recursive sequence. In this paper, we continue this program by finding a sequence which is asymptotically equivalent to partial infinite sums, including a reciprocal of polynomial [...] Read more.
Recently a lot of papers have been devoted to partial infinite reciprocal sums of a higher-order linear recursive sequence. In this paper, we continue this program by finding a sequence which is asymptotically equivalent to partial infinite sums, including a reciprocal of polynomial applied to linear higher order recurrences. Full article
(This article belongs to the Section Mathematics and Computers Science)
Open AccessArticle
A Fast Derivative-Free Iteration Scheme for Nonlinear Systems and Integral Equations
Mathematics 2019, 7(7), 637; https://doi.org/10.3390/math7070637
Received: 23 June 2019 / Revised: 11 July 2019 / Accepted: 11 July 2019 / Published: 18 July 2019
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Abstract
Derivative-free schemes are a class of competitive methods since they are one remedy in cases at which the computation of the Jacobian or higher order derivatives of multi-dimensional functions is difficult. This article studies a variant of Steffensen’s method with memory for tackling [...] Read more.
Derivative-free schemes are a class of competitive methods since they are one remedy in cases at which the computation of the Jacobian or higher order derivatives of multi-dimensional functions is difficult. This article studies a variant of Steffensen’s method with memory for tackling a nonlinear system of equations, to not only be independent of the Jacobian calculation but also to improve the computational efficiency. The analytical parts of the work are supported by several tests, including an application in mixed integral equations. Full article
(This article belongs to the Special Issue Iterative Methods for Solving Nonlinear Equations and Systems)
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Open AccessArticle
A Comparative Analysis of Simulated Annealing and Variable Neighborhood Search in the ATCo Work-Shift Scheduling Problem
Mathematics 2019, 7(7), 636; https://doi.org/10.3390/math7070636
Received: 25 June 2019 / Revised: 15 July 2019 / Accepted: 16 July 2019 / Published: 17 July 2019
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Abstract
This paper deals with the air traffic controller (ATCo) work shift scheduling problem. This is a multi-objective optimization problem, as it involves identifying the best possible distribution of ATCo work and rest periods and positions, ATCo workload and control center changes in order [...] Read more.
This paper deals with the air traffic controller (ATCo) work shift scheduling problem. This is a multi-objective optimization problem, as it involves identifying the best possible distribution of ATCo work and rest periods and positions, ATCo workload and control center changes in order to cover an airspace sector configuration, while, at the same time, complying with ATCo working conditions. We propose a three-phase problem-solving methodology based on the variable neighborhood search (VNS) to tackle this problem. The solution structure should resemble the previous template-based solution. Initial infeasible solutions are built using a template-based heuristic in Phase 1. Then, VNS is conducted in Phase 2 in order to arrive at a feasible solution. This constitutes the starting point of a new search process carried out in Phase 3 to derive an optimal solution based on a weighted sum fitness function. We analyzed the performance in the proposed methodology of VNS against simulated annealing, as well as the use of regular expressions compared with the implementation in the code to verify the feasibility of the analyzed solutions, taking into account four representative and complex instances of the problem corresponding to different airspace sectorings. Full article
(This article belongs to the Special Issue Optimization for Decision Making)
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Open AccessArticle
On the Efficacy of Ensemble of Constraint Handling Techniques in Self-Adaptive Differential Evolution
Mathematics 2019, 7(7), 635; https://doi.org/10.3390/math7070635
Received: 9 June 2019 / Revised: 8 July 2019 / Accepted: 10 July 2019 / Published: 17 July 2019
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Abstract
Self-adaptive variants of evolutionary algorithms (EAs) tune their parameters on the go by learning from the search history. Adaptive differential evolution with optional external archive (JADE) and self-adaptive differential evolution (SaDE) are two well-known self-adaptive versions of differential evolution (DE). They are both [...] Read more.
Self-adaptive variants of evolutionary algorithms (EAs) tune their parameters on the go by learning from the search history. Adaptive differential evolution with optional external archive (JADE) and self-adaptive differential evolution (SaDE) are two well-known self-adaptive versions of differential evolution (DE). They are both unconstrained search and optimization algorithms. However, if some constraint handling techniques (CHTs) are incorporated in their frameworks, then they can be used to solve constrained optimization problems (COPs). In an early work, an ensemble of constraint handling techniques (ECHT) is probabilistically hybridized with the basic version of DE. The ECHT consists of four different CHTs: superiority of feasible solutions, self-adaptive penalty, ε -constraint handling technique and stochastic ranking. This paper employs ECHT in the selection schemes, where offspring competes with their parents for survival to the next generation, of JADE and SaDE. As a result, JADE-ECHT and SaDE-ECHT are developed, which are the constrained variants of JADE and SaDE. Both algorithms are tested on 24 COPs and the experimental results are collected and compared according to algorithms’ evaluation criteria of CEC’06. Their comparison, in terms of feasibility rate (FR) and success rate (SR), shows that SaDE-ECHT surpasses JADE-ECHT in terms of FR, while JADE-ECHT outperforms SaDE-ECHT in terms of SR. Full article
(This article belongs to the Special Issue Evolutionary Algorithms in Intelligent Systems)
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Open AccessArticle
A Coupled Fixed Point Technique for Solving Coupled Systems of Functional and Nonlinear Integral Equations
Mathematics 2019, 7(7), 634; https://doi.org/10.3390/math7070634
Received: 25 June 2019 / Revised: 13 July 2019 / Accepted: 14 July 2019 / Published: 17 July 2019
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Abstract
In this paper, we obtain coupled fixed point results for F-contraction mapping satisfying a nonlinear contraction condition in the framework of complete metric space without and with a directed graph. As applications of our results, we study a problem of existence and [...] Read more.
In this paper, we obtain coupled fixed point results for F-contraction mapping satisfying a nonlinear contraction condition in the framework of complete metric space without and with a directed graph. As applications of our results, we study a problem of existence and uniqueness of solutions for a class of systems of functional equations that appears in dynamic programming and nonlinear integral equations. Finally, illustrative examples to support some our results are discussed. Full article
(This article belongs to the Special Issue Applications in Theoretical and Computational Fixed Point Problems)
Open AccessArticle
Analytical Solution for Multi-Energy Groups of Neutron Diffusion Equations by a Residual Power Series Method
Mathematics 2019, 7(7), 633; https://doi.org/10.3390/math7070633
Received: 1 July 2019 / Revised: 15 July 2019 / Accepted: 15 July 2019 / Published: 17 July 2019
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Abstract
In this paper, a multi-energy groups of a neutron diffusion equations system is analytically solved by a residual power series method. The solution is generalized to consider three different geometries: slab, cylinder and sphere. Diffusion of two and four energy groups of neutrons [...] Read more.
In this paper, a multi-energy groups of a neutron diffusion equations system is analytically solved by a residual power series method. The solution is generalized to consider three different geometries: slab, cylinder and sphere. Diffusion of two and four energy groups of neutrons is specifically analyzed through numerical calculation at certain boundary conditions. This study revels sufficient analytical description for radial flux distribution of multi-energy groups of neutron diffusion theory as well as determination of each nuclear reactor dimension in criticality case. The generated results are compatible with other different methods data. The generated results are practically efficient for neutron reactors dimension. Full article
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Open AccessArticle
On q-Hermite-Hadamard Inequalities for Differentiable Convex Functions
Mathematics 2019, 7(7), 632; https://doi.org/10.3390/math7070632
Received: 12 June 2019 / Revised: 10 July 2019 / Accepted: 15 July 2019 / Published: 17 July 2019
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Abstract
In this paper, we establish some new results on the left-hand side of the q-Hermite–Hadamard inequality for differentiable convex functions with a critical point. Our work extends the results of Alp et. al (q-Hermite Hadamard inequalities and quantum estimates for [...] Read more.
In this paper, we establish some new results on the left-hand side of the q-Hermite–Hadamard inequality for differentiable convex functions with a critical point. Our work extends the results of Alp et. al (q-Hermite Hadamard inequalities and quantum estimates for midpoint type inequalities via convex and quasi-convex functions, J. King Saud Univ. Sci., 2018, 30, 193-203), by considering the critical point-type inequalities. Full article
Open AccessArticle
Inspection Plan Based on the Process Capability Index Using the Neutrosophic Statistical Method
Mathematics 2019, 7(7), 631; https://doi.org/10.3390/math7070631
Received: 25 June 2019 / Revised: 11 July 2019 / Accepted: 11 July 2019 / Published: 16 July 2019
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Abstract
The Process Capability Index (PCI) has been widely used in industry to advance the quality of a product. Neutrosophic statistics is the more generalized form of classical statistics and is applied when the data from the production process or a product lot is [...] Read more.
The Process Capability Index (PCI) has been widely used in industry to advance the quality of a product. Neutrosophic statistics is the more generalized form of classical statistics and is applied when the data from the production process or a product lot is incomplete, incredible, and indeterminate. In this paper, we will originally propose a variable sampling plan for the PCI using neutrosophic statistics. The neutrosophic operating function will be given. The neutrosophic plan parameters will be determined using the neutrosophic optimization solution. A comparison between plans based on neutrosophic statistics and classical statistics is given. The application of the proposed neutrosophic sampling plan will be given using company data. Full article
(This article belongs to the Special Issue New Challenges in Neutrosophic Theory and Applications)
Open AccessArticle
Existence of Solutions for Anti-Periodic Fractional Differential Inclusions Involving ψ-Riesz-Caputo Fractional Derivative
Mathematics 2019, 7(7), 630; https://doi.org/10.3390/math7070630
Received: 9 June 2019 / Revised: 7 July 2019 / Accepted: 12 July 2019 / Published: 15 July 2019
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Abstract
In this paper, we investigate the existence of solutions for a class of anti-periodic fractional differential inclusions with ψ-Riesz-Caputo fractional derivative. A new definition of ψ-Riesz-Caputo fractional derivative of order α is proposed. By means of Contractive map theorem and nonlinear [...] Read more.
In this paper, we investigate the existence of solutions for a class of anti-periodic fractional differential inclusions with ψ -Riesz-Caputo fractional derivative. A new definition of ψ -Riesz-Caputo fractional derivative of order α is proposed. By means of Contractive map theorem and nonlinear alternative for Kakutani maps, sufficient conditions for the existence of solutions to the fractional differential inclusions are given. We present two examples to illustrate our main results. Full article
Open AccessArticle
Modeling and Efficiency Optimization of Steam Boilers by Employing Neural Networks and Response-Surface Method (RSM)
Mathematics 2019, 7(7), 629; https://doi.org/10.3390/math7070629
Received: 6 June 2019 / Revised: 24 June 2019 / Accepted: 3 July 2019 / Published: 15 July 2019
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Abstract
Boiler efficiency is called to some extent of total thermal energy which can be recovered from the fuel. Boiler efficiency losses are due to four major factors: Dry gas flux, the latent heat of steam in the flue gas, the combustion loss or [...] Read more.
Boiler efficiency is called to some extent of total thermal energy which can be recovered from the fuel. Boiler efficiency losses are due to four major factors: Dry gas flux, the latent heat of steam in the flue gas, the combustion loss or the loss of unburned fuel, and radiation and convection losses. In this research, the thermal behavior of boilers in gas refinery facilities is studied and their efficiency and their losses are calculated. The main part of this research is comprised of analyzing the effect of various parameters on efficiency such as excess air, fuel moisture, air humidity, fuel and air temperature, the temperature of combustion gases, and thermal value of the fuel. Based on the obtained results, it is possible to analyze and make recommendations for optimizing boilers in the gas refinery complex using response-surface method (RSM). Full article
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Open AccessArticle
Cantor Paradoxes, Possible Worlds and Set Theory
Mathematics 2019, 7(7), 628; https://doi.org/10.3390/math7070628
Received: 24 May 2019 / Revised: 1 July 2019 / Accepted: 11 July 2019 / Published: 15 July 2019
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Abstract
In this paper, we illustrate the paradox concerning maximally consistent sets of propositions, which is contrary to set theory. It has been shown that Cantor paradoxes do not offer particular advantages for any modal theories. The paradox is therefore not a specific difficulty [...] Read more.
In this paper, we illustrate the paradox concerning maximally consistent sets of propositions, which is contrary to set theory. It has been shown that Cantor paradoxes do not offer particular advantages for any modal theories. The paradox is therefore not a specific difficulty for modal concepts, and it also neither grants advantages nor disadvantages for any modal theory. The underlying problem is quite general, and affects anyone who intends to use the notion of “world” in its ontology. Full article
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