Mathematics

17 pages, 310 KiB

Open AccessArticle

Existence of Solutions for Nonhomogeneous Choquard Equations Involving p-Laplacian

by Xiaoyan Shi, Yulin Zhao and Haibo Chen

Mathematics 2019, 7(9), 871; https://doi.org/10.3390/math7090871 - 19 Sep 2019

Cited by 2 | Viewed by 2508

This paper is devoted to investigating a class of nonhomogeneous Choquard equations with perturbation involving p-Laplacian. Under suitable hypotheses about the perturbation term, the existence of at least two nontrivial solutions for the given problems is obtained using Nehari manifold and minimax methods. [...] Read more.

This paper is devoted to investigating a class of nonhomogeneous Choquard equations with perturbation involving p-Laplacian. Under suitable hypotheses about the perturbation term, the existence of at least two nontrivial solutions for the given problems is obtained using Nehari manifold and minimax methods. Full article

(This article belongs to the Special Issue Nonlinear Functional Analysis and Its Applications)

8 pages, 432 KiB

Open AccessArticle

Classification of the State of Manufacturing Process under Indeterminacy

by Muhammad Aslam and Osama Hasan Arif

Mathematics 2019, 7(9), 870; https://doi.org/10.3390/math7090870 - 19 Sep 2019

Cited by 2 | Viewed by 2293

Abstract

In this paper, the diagnosis of the manufacturing process under the indeterminate environment is presented. The similarity measure index was used to find the probability of the in-control and the out-of-control of the process. The average run length (ARL) was also computed for [...] Read more.

In this paper, the diagnosis of the manufacturing process under the indeterminate environment is presented. The similarity measure index was used to find the probability of the in-control and the out-of-control of the process. The average run length (ARL) was also computed for various values of specified parameters. An example from the Juice Company is considered under the indeterminate environment. From this study, it is concluded that the proposed diagnosis scheme under the neutrosophic statistics is quite simple and effective for the current state of the manufacturing process under uncertainty. The use of the proposed method under the uncertainty environment in the Juice Company may eliminate the non-conforming items and alternatively increase the profit of the company. Full article

(This article belongs to the Special Issue New Challenges in Neutrosophic Theory and Applications)

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18 pages, 291 KiB

Open AccessFeature PaperArticle

Syzygies, Betti Numbers, and Regularity of Cover Ideals of Certain Multipartite Graphs

by A. V. Jayanthan and Neeraj Kumar

Mathematics 2019, 7(9), 869; https://doi.org/10.3390/math7090869 - 19 Sep 2019

Cited by 2 | Viewed by 2454

Abstract

Let G be a finite simple graph on n vertices. Let

J_{G} \subset K [x_{1}, \dots, x_{n}]

be the cover ideal of G. In this article, we obtain syzygies, Betti numbers, and Castelnuovo–Mumford regularity of [...] Read more.

Let G be a finite simple graph on n vertices. Let

J_{G} \subset K [x_{1}, \dots, x_{n}]

be the cover ideal of G. In this article, we obtain syzygies, Betti numbers, and Castelnuovo–Mumford regularity of

J_{G}^{s}

for all

s \geq 1

for certain classes of graphs G. Full article

(This article belongs to the Special Issue Current Trends on Monomial and Binomial Ideals)

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25 pages, 444 KiB

Open AccessArticle

Algebraic Properties of Arbitrage: An Application to Additivity of Discount Functions

by Salvador Cruz Rambaud

Mathematics 2019, 7(9), 868; https://doi.org/10.3390/math7090868 - 19 Sep 2019

Cited by 2 | Viewed by 2558

Abstract

Background: This paper aims to characterize the absence of arbitrage in the context of the Arbitrage Theory proposed by Kreps (1981) and Clark (2000) which involves a certain number of well-known financial markets. More specifically, the framework of this model is a linear [...] Read more.

Background: This paper aims to characterize the absence of arbitrage in the context of the Arbitrage Theory proposed by Kreps (1981) and Clark (2000) which involves a certain number of well-known financial markets. More specifically, the framework of this model is a linear (topological) space X in which a (convex) cone C defines a vector ordering. There exist markets for only some of the contingent claims of X which assign a price

p_{i}

to the marketed claim

m_{i}

. The main purpose of this paper is to provide some novel algebraic characterizations of the no arbitrage condition and specifically to derive the decomposability of discount functions with this approach. Methods: Traditionally, this topic has been focused from a topological or probabilistic point of view. However, in this manuscript the treatment of this topic has been by using purely algebraic tools. Results: We have characterized the absence of arbitrage by only using algebraic concepts, properties and structures. Thus, we have divided these characterizations into those concerning the preference relation and those involving the cone. Conclusion: This paper has provided some novel algebraic properties of the absence of arbitrage by assuming the most general setting. The additivity of discount functions has been derived as a particular case of the general theory. Full article

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21 pages, 823 KiB

Open AccessArticle

A New Global Optimization Algorithm for a Class of Linear Fractional Programming

by X. Liu, Y.L. Gao, B. Zhang and F.P. Tian

Mathematics 2019, 7(9), 867; https://doi.org/10.3390/math7090867 - 19 Sep 2019

Cited by 29 | Viewed by 3031

Abstract

In this paper, we propose a new global optimization algorithm, which can better solve a class of linear fractional programming problems on a large scale. First, the original problem is equivalent to a nonlinear programming problem: It introduces p auxiliary variables. At the [...] Read more.

In this paper, we propose a new global optimization algorithm, which can better solve a class of linear fractional programming problems on a large scale. First, the original problem is equivalent to a nonlinear programming problem: It introduces p auxiliary variables. At the same time, p new nonlinear equality constraints are added to the original problem. By classifying the coefficient symbols of all linear functions in the objective function of the original problem, four sets are obtained, which are

I_{i}^{+}

,

I_{i}^{-}

,

J_{i}^{+}

and

J_{i}^{-}

. Combined with the multiplication rule of real number operation, the objective function and constraint conditions of the equivalent problem are linearized into a lower bound linear relaxation programming problem. Our lower bound determination method only needs

e_{i}^{T} x + f_{i} \neq 0

, and there is no need to convert molecules to non-negative forms in advance for some special problems. A output-space branch and bound algorithm based on solving the linear programming problem is proposed and the convergence of the algorithm is proved. Finally, in order to illustrate the feasibility and effectiveness of the algorithm, we have done a series of numerical experiments, and show the advantages and disadvantages of our algorithm by the numerical results. Full article

(This article belongs to the Special Issue Fixed Point, Optimization, and Applications)

15 pages, 3796 KiB

Open AccessArticle

Nonlinear Operators as Concerns Convex Programming and Applied to Signal Processing

by Anantachai Padcharoen and Pakeeta Sukprasert

Mathematics 2019, 7(9), 866; https://doi.org/10.3390/math7090866 - 19 Sep 2019

Cited by 8 | Viewed by 2694

Abstract

Splitting methods have received a lot of attention lately because many nonlinear problems that arise in the areas used, such as signal processing and image restoration, are modeled in mathematics as a nonlinear equation, and this operator is decomposed as the sum of [...] Read more.

Splitting methods have received a lot of attention lately because many nonlinear problems that arise in the areas used, such as signal processing and image restoration, are modeled in mathematics as a nonlinear equation, and this operator is decomposed as the sum of two nonlinear operators. Most investigations about the methods of separation are carried out in the Hilbert spaces. This work develops an iterative scheme in Banach spaces. We prove the convergence theorem of our iterative scheme, applications in common zeros of accretive operators, convexly constrained least square problem, convex minimization problem and signal processing. Full article

(This article belongs to the Special Issue Iterative Methods for Solving Nonlinear Equations and Systems)

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From top to bottom: Original signal, observation data, recovered signal by Algorithm 2 and SPGA with <math display="inline"><semantics> <mrow> <mi>N</mi> <mo>=</mo> <mn>4096</mn> <mo>,</mo> <mspace width="0.166667em"/> <mi>M</mi> <mo>=</mo> <mn>1024</mn> </mrow> </semantics></math> and 10 spikes, respectively. Full article ">Figure 2
Comparison MSE of two algorithms for recovered signal with <math display="inline"><semantics> <mrow> <mi>N</mi> <mo>=</mo> <mn>4096</mn> <mo>,</mo> <mspace width="0.166667em"/> <mi>M</mi> <mo>=</mo> <mn>1024</mn> </mrow> </semantics></math> and 10 spikes, respectively. Full article ">Figure 3
From top to bottom: Original signal, observation data, recovered signal by Algorithm 2 and SPGA with <math display="inline"><semantics> <mrow> <mi>N</mi> <mo>=</mo> <mn>4096</mn> <mo>,</mo> <mspace width="0.166667em"/> <mi>M</mi> <mo>=</mo> <mn>1024</mn> </mrow> </semantics></math> and 30 spikes, respectively. Full article ">Figure 4
Comparison MSE of two algorithms for recovered signal with <math display="inline"><semantics> <mrow> <mi>N</mi> <mo>=</mo> <mn>4096</mn> <mo>,</mo> <mspace width="0.166667em"/> <mi>M</mi> <mo>=</mo> <mn>1024</mn> </mrow> </semantics></math> and 30 spikes, respectively. Full article ">Figure 5
From top to bottom: Original signal, observation data, recovered signal by Algorithm 2 and SPGA with <math display="inline"><semantics> <mrow> <mi>N</mi> <mo>=</mo> <mn>4096</mn> <mo>,</mo> <mspace width="0.166667em"/> <mi>M</mi> <mo>=</mo> <mn>1024</mn> </mrow> </semantics></math> and 50 spikes, respectively. Full article ">Figure 6
Comparison MSE of two algorithms for recovered signal with <math display="inline"><semantics> <mrow> <mi>N</mi> <mo>=</mo> <mn>4096</mn> <mo>,</mo> <mspace width="0.166667em"/> <mi>M</mi> <mo>=</mo> <mn>1024</mn> </mrow> </semantics></math> and 50 spikes, respectively. Full article ">

13 pages, 270 KiB

Open AccessArticle

Fourier Truncation Regularization Method for a Time-Fractional Backward Diffusion Problem with a Nonlinear Source

by Fan Yang, Ping Fan, Xiao-Xiao Li and Xin-Yi Ma

Mathematics 2019, 7(9), 865; https://doi.org/10.3390/math7090865 - 19 Sep 2019

Cited by 22 | Viewed by 2564

Abstract

In present paper, we deal with a backward diffusion problem for a time-fractional diffusion problem with a nonlinear source in a strip domain. We all know this nonlinear problem is severely ill-posed, i.e., the solution does not depend continuously on the measurable data. [...] Read more.

In present paper, we deal with a backward diffusion problem for a time-fractional diffusion problem with a nonlinear source in a strip domain. We all know this nonlinear problem is severely ill-posed, i.e., the solution does not depend continuously on the measurable data. Therefore, we use the Fourier truncation regularization method to solve this problem. Under an a priori hypothesis and an a priori regularization parameter selection rule, we obtain the convergence error estimates between the regular solution and the exact solution at

0 \leq x < 1

. Full article

21 pages, 327 KiB

Open AccessArticle

The Distribution Function of a Probability Measure on a Linearly Ordered Topological Space

by José Fulgencio Gálvez-Rodríguez and Miguel Ángel Sánchez-Granero

Mathematics 2019, 7(9), 864; https://doi.org/10.3390/math7090864 - 18 Sep 2019

Cited by 4 | Viewed by 2374

Abstract

In this paper, we describe a theory of a cumulative distribution function on a space with an order from a probability measure defined in this space. This distribution function plays a similar role to that played in the classical case. Moreover, we define [...] Read more.

In this paper, we describe a theory of a cumulative distribution function on a space with an order from a probability measure defined in this space. This distribution function plays a similar role to that played in the classical case. Moreover, we define its pseudo-inverse and study its properties. Those properties will allow us to generate samples of a distribution and give us the chance to calculate integrals with respect to the related probability measure. Full article

12 pages, 742 KiB

Open AccessArticle

New Inequalities of Weaving K-Frames in Subspaces

by Zhong-Qi Xiang

Mathematics 2019, 7(9), 863; https://doi.org/10.3390/math7090863 - 18 Sep 2019

Viewed by 2091

Abstract

In the present paper, we obtain some new inequalities for weaving K-frames in subspaces based on the operator methods. The inequalities are associated with a sequence of bounded complex numbers and a parameter

λ \in R

. We also give a double [...] Read more.

In the present paper, we obtain some new inequalities for weaving K-frames in subspaces based on the operator methods. The inequalities are associated with a sequence of bounded complex numbers and a parameter

λ \in R

. We also give a double inequality for weaving K-frames with the help of two bounded linear operators induced by K-dual. Facts prove that our results cover those recently obtained on weaving frames due to Li and Leng, and Xiang. Full article

(This article belongs to the Special Issue Inequalities)

8 pages, 239 KiB

Open AccessArticle

On a New Generalization of Banach Contraction Principle with Application

by Hüseyin Işık, Babak Mohammadi, Mohammad Reza Haddadi and Vahid Parvaneh

Mathematics 2019, 7(9), 862; https://doi.org/10.3390/math7090862 - 18 Sep 2019

Cited by 9 | Viewed by 2821

Abstract

The main purpose of the current work is to present firstly a new generalization of Caristi’s fixed point result and secondly the Banach contraction principle. An example and an application is given to show the usability of our results. Full article

(This article belongs to the Special Issue Fixed Point, Optimization, and Applications)

31 pages, 1512 KiB

Open AccessFeature PaperArticle

Variational Partitioned Runge–Kutta Methods for Lagrangians Linear in Velocities

by Tomasz M. Tyranowski and Mathieu Desbrun

Mathematics 2019, 7(9), 861; https://doi.org/10.3390/math7090861 - 18 Sep 2019

Cited by 5 | Viewed by 3351

Abstract

In this paper, we construct higher-order variational integrators for a class of degenerate systems described by Lagrangians that are linear in velocities. We analyze the geometry underlying such systems and develop the appropriate theory for variational integration. Our main observation is that the [...] Read more.

In this paper, we construct higher-order variational integrators for a class of degenerate systems described by Lagrangians that are linear in velocities. We analyze the geometry underlying such systems and develop the appropriate theory for variational integration. Our main observation is that the evolution takes place on the primary constraint and the “Hamiltonian” equations of motion can be formulated as an index-1 differential-algebraic system. We also construct variational Runge–Kutta methods and analyze their properties. The general properties of Runge–Kutta methods depend on the “velocity” part of the Lagrangian. If the “velocity” part is also linear in the position coordinate, then we show that non-partitioned variational Runge–Kutta methods are equivalent to integration of the corresponding first-order Euler–Lagrange equations, which have the form of a Poisson system with a constant structure matrix, and the classical properties of the Runge–Kutta method are retained. If the “velocity” part is nonlinear in the position coordinate, we observe a reduction of the order of convergence, which is typical of numerical integration of DAEs. We verified our results through numerical experiments for various dynamical systems. Full article

(This article belongs to the Special Issue Geometric Numerical Integration)

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19 pages, 323 KiB

Open AccessFeature PaperArticle

Inertial-Like Subgradient Extragradient Methods for Variational Inequalities and Fixed Points of Asymptotically Nonexpansive and Strictly Pseudocontractive Mappings

by Lu-Chuan Ceng, Adrian Petruşel, Ching-Feng Wen and Jen-Chih Yao

Mathematics 2019, 7(9), 860; https://doi.org/10.3390/math7090860 - 17 Sep 2019

Cited by 15 | Viewed by 2328

Abstract

Let VIP indicate the variational inequality problem with Lipschitzian and pseudomonotone operator and let CFPP denote the common fixed-point problem of an asymptotically nonexpansive mapping and a strictly pseudocontractive mapping in a real Hilbert space. Our object in this article is to establish [...] Read more.

Let VIP indicate the variational inequality problem with Lipschitzian and pseudomonotone operator and let CFPP denote the common fixed-point problem of an asymptotically nonexpansive mapping and a strictly pseudocontractive mapping in a real Hilbert space. Our object in this article is to establish strong convergence results for solving the VIP and CFPP by utilizing an inertial-like gradient-like extragradient method with line-search process. Via suitable assumptions, it is shown that the sequences generated by such a method converge strongly to a common solution of the VIP and CFPP, which also solves a hierarchical variational inequality (HVI). Full article

(This article belongs to the Special Issue Applied Functional Analysis and Its Applications)

18 pages, 324 KiB

Open AccessArticle

Algebraic Algorithms for Even Circuits in Graphs

by Huy Tài Hà and Susan Morey

Mathematics 2019, 7(9), 859; https://doi.org/10.3390/math7090859 - 17 Sep 2019

Cited by 1 | Viewed by 2342

Abstract

We present an algebraic algorithm to detect the existence of and to list all indecomposable even circuits in a given graph. We also discuss an application of our work to the study of directed cycles in digraphs. Full article

(This article belongs to the Special Issue Current Trends on Monomial and Binomial Ideals)

31 pages, 2071 KiB

Open AccessReview

Applications of Game Theory in Project Management: A Structured Review and Analysis

by Mahendra Piraveenan

Mathematics 2019, 7(9), 858; https://doi.org/10.3390/math7090858 - 17 Sep 2019

Cited by 23 | Viewed by 15170

Abstract

This paper provides a structured literature review and analysis of using game theory to model project management scenarios. We select and review thirty-two papers from Scopus, present a complex three-dimensional classification of the selected papers, and analyse the resultant citation network. According to [...] Read more.

This paper provides a structured literature review and analysis of using game theory to model project management scenarios. We select and review thirty-two papers from Scopus, present a complex three-dimensional classification of the selected papers, and analyse the resultant citation network. According to the industry-based classification, the surveyed literature can be classified in terms of construction industry, ICT industry or unspecified industry. Based on the types of players, the literature can be classified into papers that use government-contractor games, contractor–contractor games, contractor-subcontractor games, subcontractor–subcontractor games or games involving other types of players. Based on the type of games used, papers using normal-form non-cooperative games, normal-form cooperative games, extensive-form non-cooperative games or extensive-form cooperative games are present. Also, we show that each of the above classifications plays a role in influencing which papers are likely to cite a particular paper, though the strongest influence is exerted by the type-of-game classification. Overall, the citation network in this field is sparse, implying that the awareness of authors in this field about studies by other academics is suboptimal. Our review suggests that game theory is a very useful tool for modelling project management scenarios, and that more work needs to be done focusing on project management in ICT domain, as well as by using extensive-form cooperative games where relevant. Full article

(This article belongs to the Special Issue Game Theory)

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25 pages, 413 KiB

Open AccessArticle

Time-Consistent Investment-Reinsurance Strategies for the Insurer and the Reinsurer under the Generalized Mean-Variance Criteria

by Helu Xiao, Tiantian Ren, Yanfei Bai and Zhongbao Zhou

Mathematics 2019, 7(9), 857; https://doi.org/10.3390/math7090857 - 17 Sep 2019

Cited by 4 | Viewed by 2424

Abstract

Most of the existing literature on optimal investment-reinsurance only studies from the perspective of insurers and also treats the investment-reinsurance decision as a continuous process. However, in practice, the benefits of reinsurers cannot be ignored, nor can decision-makers engage in continuous trading. Under [...] Read more.

Most of the existing literature on optimal investment-reinsurance only studies from the perspective of insurers and also treats the investment-reinsurance decision as a continuous process. However, in practice, the benefits of reinsurers cannot be ignored, nor can decision-makers engage in continuous trading. Under the discrete-time framework, we first propose a multi-period investment-reinsurance optimization problem considering the joint interests of the insurer and the reinsurer, among which their performance is measured by two generalized mean-variance criteria. We derive the time-consistent investment-reinsurance strategies for the proposed model by maximizing the weighted sum of the insurer’s and the reinsurer’s mean-variance objectives. We discuss the time-consistent investment-reinsurance strategies under two special premium principles. Finally, we provide some numerical simulations to show the impact of the intertemporal restrictions on the time-consistent investment-reinsurance strategies. These results indicate that the intertemporal restrictions will urge the insurer and the reinsurer to shrink the position invested in the risky asset; however, for the time-consistent reinsurance strategy, the impact of the intertemporal restrictions depends on who is the leader in the proposed model. Full article

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9 pages, 231 KiB

Open AccessArticle

Existence Results for Block Matrix Operator of Fractional Orders in Banach Algebras

by Hind Hashem, Ahmed El-Sayed and Dumitru Baleanu

Mathematics 2019, 7(9), 856; https://doi.org/10.3390/math7090856 - 17 Sep 2019

Cited by 4 | Viewed by 2011

Abstract

This paper is concerned with proving the existence of solutions for a coupled system of quadratic integral equations of fractional order in Banach algebras. This result is a direct application of a fixed point theorem of Banach algebras. Some particular cases, examples and [...] Read more.

This paper is concerned with proving the existence of solutions for a coupled system of quadratic integral equations of fractional order in Banach algebras. This result is a direct application of a fixed point theorem of Banach algebras. Some particular cases, examples and remarks are illustrated. Finally, the stability of solutions for that coupled system are studied. Full article

(This article belongs to the Section Mathematics and Computer Science)

12 pages, 769 KiB

Open AccessFeature PaperArticle

High Convergence Order Iterative Procedures for Solving Equations Originating from Real Life Problems

by Ramandeep Behl, Ioannis K. Argyros and Ali Saleh Alshomrani

Mathematics 2019, 7(9), 855; https://doi.org/10.3390/math7090855 - 17 Sep 2019

Cited by 2 | Viewed by 2108

Abstract

The foremost aim of this paper is to suggest a local study for high order iterative procedures for solving nonlinear problems involving Banach space valued operators. We only deploy suppositions on the first-order derivative of the operator. Our conditions involve the Lipschitz or [...] Read more.

The foremost aim of this paper is to suggest a local study for high order iterative procedures for solving nonlinear problems involving Banach space valued operators. We only deploy suppositions on the first-order derivative of the operator. Our conditions involve the Lipschitz or Hölder case as compared to the earlier ones. Moreover, when we specialize to these cases, they provide us: larger radius of convergence, higher bounds on the distances, more precise information on the solution and smaller Lipschitz or Hölder constants. Hence, we extend the suitability of them. Our new technique can also be used to broaden the usage of existing iterative procedures too. Finally, we check our results on a good number of numerical examples, which demonstrate that they are capable of solving such problems where earlier studies cannot apply. Full article

(This article belongs to the Special Issue Difference Equations and Discrete Dynamical Systems: Theory and Applications)

16 pages, 429 KiB

Open AccessFeature PaperArticle

Optimal Sliced Latin Hypercube Designs with Slices of Arbitrary Run Sizes

by Jing Zhang, Jin Xu, Kai Jia, Yimin Yin and Zhengming Wang

Mathematics 2019, 7(9), 854; https://doi.org/10.3390/math7090854 - 16 Sep 2019

Cited by 5 | Viewed by 3053

Abstract

Sliced Latin hypercube designs (SLHDs) are widely used in computer experiments with both quantitative and qualitative factors and in batches. Optimal SLHDs achieve better space-filling property on the whole experimental region. However, most existing methods for constructing optimal SLHDs have restriction on the [...] Read more.

Sliced Latin hypercube designs (SLHDs) are widely used in computer experiments with both quantitative and qualitative factors and in batches. Optimal SLHDs achieve better space-filling property on the whole experimental region. However, most existing methods for constructing optimal SLHDs have restriction on the run sizes. In this paper, we propose a new method for constructing SLHDs with arbitrary run sizes, and a new combined space-filling measurement describing the space-filling property for both the whole design and its slices. Furthermore, we develop general algorithms to search for the optimal SLHD with arbitrary run sizes under the proposed measurement. Examples are presented to illustrate that effectiveness of the proposed methods. Full article

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21 pages, 1121 KiB

Open AccessFeature PaperArticle

Numerical Integral Transform Methods for Random Hyperbolic Models with a Finite Degree of Randomness

by M. Consuelo Casabán, Rafael Company and Lucas Jódar

Mathematics 2019, 7(9), 853; https://doi.org/10.3390/math7090853 - 16 Sep 2019

Cited by 3 | Viewed by 2324

Abstract

This paper deals with the construction of numerical solutions of random hyperbolic models with a finite degree of randomness that make manageable the computation of its expectation and variance. The approach is based on the combination of the random Fourier transforms, the random [...] Read more.

This paper deals with the construction of numerical solutions of random hyperbolic models with a finite degree of randomness that make manageable the computation of its expectation and variance. The approach is based on the combination of the random Fourier transforms, the random Gaussian quadratures and the Monte Carlo method. The recovery of the solution of the original random partial differential problem throughout the inverse integral transform allows its numerical approximation using Gaussian quadratures involving the evaluation of the solution of the random ordinary differential problem at certain concrete values, which are approximated using Monte Carlo method. Numerical experiments illustrating the numerical convergence of the method are included. Full article

(This article belongs to the Special Issue Stochastic Differential Equations and Their Applications)

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9 pages, 267 KiB

Open AccessArticle

Analytical Solution of Urysohn Integral Equations by Fixed Point Technique in Complex Valued Metric Spaces

by Hasanen A. Hammad and Manuel De la Sen

Mathematics 2019, 7(9), 852; https://doi.org/10.3390/math7090852 - 15 Sep 2019

Cited by 24 | Viewed by 2994

Abstract

The purpose of this article is to introduce a fixed point result for a general contractive condition in the context of complex valued metric spaces. Also, some important corollaries under this contractive condition are obtained. As an application, we find a unique solution [...] Read more.

The purpose of this article is to introduce a fixed point result for a general contractive condition in the context of complex valued metric spaces. Also, some important corollaries under this contractive condition are obtained. As an application, we find a unique solution for Urysohn integral equations, and some illustrative examples are given to support our obtaining results. Our results extend and generalize the results of Azam et al. Previous known related results in the literarure and some other known results in the literature. Full article

(This article belongs to the Special Issue Fixed Point Theory and Related Nonlinear Problems with Applications)

6 pages, 215 KiB

Open AccessFeature PaperArticle

Faces of 2-Dimensional Simplex of Order and Chain Polytopes

by Aki Mori

Mathematics 2019, 7(9), 851; https://doi.org/10.3390/math7090851 - 14 Sep 2019

Viewed by 2138

Abstract

Each of the descriptions of vertices, edges, and facets of the order and chain polytope of a finite partially ordered set are well known. In this paper, we give an explicit description of faces of 2-dimensional simplex in terms of vertices. Namely, it [...] Read more.

Each of the descriptions of vertices, edges, and facets of the order and chain polytope of a finite partially ordered set are well known. In this paper, we give an explicit description of faces of 2-dimensional simplex in terms of vertices. Namely, it will be proved that an arbitrary triangle in 1-skeleton of the order or chain polytope forms the face of 2-dimensional simplex of each polytope. These results mean a generalization in the case of 2-faces of the characterization known in the case of edges. Full article

(This article belongs to the Special Issue Current Trends on Monomial and Binomial Ideals)

10 pages, 270 KiB

Open AccessArticle

A Lyapunov-Type Inequality for a Laplacian System on a Rectangular Domain with Zero Dirichlet Boundary Conditions

by Mohamed Jleli and Bessem Samet

Mathematics 2019, 7(9), 850; https://doi.org/10.3390/math7090850 - 14 Sep 2019

Cited by 2 | Viewed by 2329

Abstract

We consider a coupled system of partial differential equations involving Laplacian operator, on a rectangular domain with zero Dirichlet boundary conditions. A Lyapunov-type inequality related to this problem is derived. This inequality provides a necessary condition for the existence of nontrivial positive solutions. [...] Read more.

We consider a coupled system of partial differential equations involving Laplacian operator, on a rectangular domain with zero Dirichlet boundary conditions. A Lyapunov-type inequality related to this problem is derived. This inequality provides a necessary condition for the existence of nontrivial positive solutions. Full article

(This article belongs to the Special Issue Mathematical Analysis and Boundary Value Problems)

7 pages, 258 KiB

Open AccessArticle

Set-Valued Interpolative Hardy–Rogers and Set-Valued Reich–Rus–Ćirić-Type Contractions in b-Metric Spaces

by Pradip Debnath and Manuel de La Sen

Mathematics 2019, 7(9), 849; https://doi.org/10.3390/math7090849 - 14 Sep 2019

Cited by 29 | Viewed by 3208

Abstract

In this paper, using an interpolative approach, we investigate two fixed point theorems in the framework of a b-metric space whose all closed and bounded subsets are compact. One of the theorems is for set-valued Hardy–Rogers-type and the other one is for [...] Read more.

In this paper, using an interpolative approach, we investigate two fixed point theorems in the framework of a b-metric space whose all closed and bounded subsets are compact. One of the theorems is for set-valued Hardy–Rogers-type and the other one is for set-valued Reich–Rus–Ćirić-type contractions. Examples are provided to validate the results. Full article

(This article belongs to the Special Issue Fixed Point Theory and Related Nonlinear Problems with Applications)

10 pages, 271 KiB

Open AccessArticle

Upper Bound of the Third Hankel Determinant for a Subclass of Close-to-Convex Functions Associated with the Lemniscate of Bernoulli

by Hari M. Srivastava, Qazi Zahoor Ahmad, Maslina Darus, Nazar Khan, Bilal Khan, Naveed Zaman and Hasrat Hussain Shah

Mathematics 2019, 7(9), 848; https://doi.org/10.3390/math7090848 - 14 Sep 2019

Cited by 32 | Viewed by 2903

Abstract

In this paper, our aim is to define a new subclass of close-to-convex functions in the open unit disk

U

that are related with the right half of the lemniscate of Bernoulli. For this function class, we obtain the upper bound of the [...] Read more.

In this paper, our aim is to define a new subclass of close-to-convex functions in the open unit disk

U

that are related with the right half of the lemniscate of Bernoulli. For this function class, we obtain the upper bound of the third Hankel determinant. Various other related results are also considered. Full article

(This article belongs to the Special Issue Mathematical Analysis and Analytic Number Theory 2019)

17 pages, 6213 KiB

Open AccessArticle

Optimising Parameters for Expanded Polystyrene Based Pod Production Using Taguchi Method

by Sheikh Imran Ishrat, Zahid Akhtar Khan, Arshad Noor Siddiquee, Irfan Anjum Badruddin, Ali Algahtani, Shakeel Javaid and Rajan Gupta

Mathematics 2019, 7(9), 847; https://doi.org/10.3390/math7090847 - 14 Sep 2019

Cited by 14 | Viewed by 4761

Abstract

Expanded polystyrene (EPS) is used in the building and construction industry for insulation and under flooring purposes. The objective of the study is to investigate the impact of the application of the total quality management (TQM) technique on the significant parameters of the [...] Read more.

Expanded polystyrene (EPS) is used in the building and construction industry for insulation and under flooring purposes. The objective of the study is to investigate the impact of the application of the total quality management (TQM) technique on the significant parameters of the pod production process in a New Zealand based EPS manufacturing facility. In this work, Taguchi’s L₂₇ orthogonal array (OA) is considered for conducting experiments through three input parameters i.e., weight of untreated beads, batch duration, and temperature is investigated. Based on the results, the analyses are carried out while using statistical approaches, such as analysis of the means (ANOM) and analysis of variance (ANOVA). The results from confirmatory experiment indicate that, at optimal parameters setting (17 kg of untreated bead, 130 s of batch duration and 155 °F of temperature), a reasonably streamlined pod manufacturing process can be achieved for sustainable operations. Full article

(This article belongs to the Special Issue Applied Mathematical Methods in Mechanical Engineering)

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10 pages, 910 KiB

Open AccessArticle

Stability and Bifurcation of a Delayed Time-Fractional Order Business Cycle Model with a General Liquidity Preference Function and Investment Function

by Yingkang Xie, Zhen Wang and Bo Meng

Mathematics 2019, 7(9), 846; https://doi.org/10.3390/math7090846 - 13 Sep 2019

Cited by 14 | Viewed by 3267

Abstract

In this paper, the business cycle (BC) is described by a delayed time-fractional-order model (DTFOM) with a general liquidity preference function and an investment function. Firstly, the existence and uniqueness of the DTFOM solution are proven. Then, some conditions are presented to guarantee [...] Read more.

In this paper, the business cycle (BC) is described by a delayed time-fractional-order model (DTFOM) with a general liquidity preference function and an investment function. Firstly, the existence and uniqueness of the DTFOM solution are proven. Then, some conditions are presented to guarantee that the positive equilibrium point of DTFOM is locally stable. In addition, Hopf bifurcation is obtained by a new method, where the time delay is regarded as the bifurcation parameter. Finally, a numerical example of DTFOM is given to verify the effectiveness of the proposed model and methods. Full article

(This article belongs to the Special Issue Mathematical Economics: Application of Fractional Calculus)

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12 pages, 268 KiB

Open AccessFeature PaperArticle

Hermite–Hadamard-Type Inequalities for Convex Functions via the Fractional Integrals with Exponential Kernel

by Xia Wu, JinRong Wang and Jialu Zhang

Mathematics 2019, 7(9), 845; https://doi.org/10.3390/math7090845 - 12 Sep 2019

Cited by 24 | Viewed by 3230

Abstract

In this paper, we establish three fundamental integral identities by the first- and second-order derivatives for a given function via the fractional integrals with exponential kernel. With the help of these new fractional integral identities, we introduce a few interesting Hermite–Hadamard-type inequalities involving [...] Read more.

In this paper, we establish three fundamental integral identities by the first- and second-order derivatives for a given function via the fractional integrals with exponential kernel. With the help of these new fractional integral identities, we introduce a few interesting Hermite–Hadamard-type inequalities involving left-sided and right-sided fractional integrals with exponential kernels for convex functions. Finally, some applications to special means of real number are presented. Full article

(This article belongs to the Special Issue Fractional Differential Equations, Inclusions and Inequalities with Applications)

10 pages, 750 KiB

Open AccessArticle

Viscosity Methods and Split Common Fixed Point Problems for Demicontractive Mappings

by Yaqin Wang, Xiaoli Fang and Tae-Hwa Kim

Mathematics 2019, 7(9), 844; https://doi.org/10.3390/math7090844 - 12 Sep 2019

Cited by 5 | Viewed by 2386

Abstract

We, first, propose a new method for solving split common fixed point problems for demicontractive mappings in Hilbert spaces, and then establish the strong convergence of such an algorithm, which extends the Halpern type algorithm studied by Wang and Xu to a viscosity [...] Read more.

We, first, propose a new method for solving split common fixed point problems for demicontractive mappings in Hilbert spaces, and then establish the strong convergence of such an algorithm, which extends the Halpern type algorithm studied by Wang and Xu to a viscosity iteration. Above all, the step sizes in this algorithm are chosen without a priori knowledge of the operator norms. Full article

(This article belongs to the Special Issue Fixed Point Theory and Related Nonlinear Problems with Applications)

22 pages, 638 KiB

Open AccessArticle

Exponential Stability Results on Random and Fixed Time Impulsive Differential Systems with Infinite Delay

by Xiaodi Li, A. Vinodkumar and T. Senthilkumar

Mathematics 2019, 7(9), 843; https://doi.org/10.3390/math7090843 - 12 Sep 2019

Cited by 8 | Viewed by 2353

Abstract

In this paper, we investigated the stability criteria like an exponential and weakly exponential stable for random impulsive infinite delay differential systems (RIIDDS). Furthermore, we proved some extended exponential and weakly exponential stability results for RIIDDS by using the Lyapunov function and Razumikhin [...] Read more.

In this paper, we investigated the stability criteria like an exponential and weakly exponential stable for random impulsive infinite delay differential systems (RIIDDS). Furthermore, we proved some extended exponential and weakly exponential stability results for RIIDDS by using the Lyapunov function and Razumikhin technique. Unlike other studies, we show that the stability behavior of the random time impulses is faster than the fixed time impulses. Finally, two examples were studied for comparative results of fixed and random time impulses it shows by simulation. Full article

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11 pages, 245 KiB

Open AccessArticle

An Optimal Pursuit Differential Game Problem with One Evader and Many Pursuers

by Idris Ahmed, Poom Kumam, Gafurjan Ibragimov, Jewaidu Rilwan and Wiyada Kumam

Mathematics 2019, 7(9), 842; https://doi.org/10.3390/math7090842 - 11 Sep 2019

Cited by 6 | Viewed by 3390

Abstract

The objective of this paper is to study a pursuit differential game with finite or countably number of pursuers and one evader. The game is described by differential equations in

l_{2}

-space, and integral constraints are imposed on the control function of [...] Read more.

The objective of this paper is to study a pursuit differential game with finite or countably number of pursuers and one evader. The game is described by differential equations in

l_{2}

-space, and integral constraints are imposed on the control function of the players. The duration of the game is fixed and the payoff functional is the greatest lower bound of distances between the pursuers and evader when the game is terminated. However, we discuss the condition for finding the value of the game and construct the optimal strategies of the players which ensure the completion of the game. An important fact to note is that we relaxed the usual conditions on the energy resources of the players. Finally, some examples are provided to illustrate our result. Full article

(This article belongs to the Special Issue Game Theory)

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Mathematics, Volume 7, Issue 9 (September 2019) – 106 articles

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