Mathematics doi: 10.3390/math7100884

Authors: Tahair Rasham Giuseppe Marino Abdullah Shoaib

Recently, George et al. (in Georgea, R.; Radenovicb, S.; Reshmac, K.P.; Shuklad, S. Rectangular b-metric space and contraction principles. J. Nonlinear Sci. Appl. 2015, 8, 1005&ndash;1013) furnished the notion of rectangular b-metric pace (RBMS) by taking the place of the binary sum of triangular inequality in the definition of a b-metric space ternary sum and proved some results for Banach and Kannan contractions in such space. In this paper, we achieved fixed-point results for a pair of F-dominated mappings fulfilling a generalized rational F-dominated contractive condition in the better framework of complete rectangular b-metric spaces complete rectangular b-metric spaces. Some new fixed-point results with graphic contractions for a pair of graph-dominated mappings on rectangular b-metric space have been obtained. Some examples are given to illustrate our conclusions. New results in ordered spaces, partial b-metric space, dislocated metric space, dislocated b-metric space, partial metric space, b-metric space, rectangular metric spaces, and metric space can be obtained as corollaries of our results.

]]>Mathematics doi: 10.3390/math7100883

Authors: Shuyu Li Sejun Jang Yunsick Sung

In traditional music composition, the composer has a special knowledge of music and combines emotion and creative experience to create music. As computer technology has evolved, various music-related technologies have been developed. To create new music, a considerable amount of time is required. Therefore, a system is required that can automatically compose music from input music. This study proposes a novel melody composition method that enhanced the original generative adversarial network (GAN) model based on individual bars. Two discriminators were used to form the enhanced GAN model: one was a long short-term memory (LSTM) model that was used to ensure correlation between the bars, and the other was a convolutional neural network (CNN) model that was used to ensure rationality of the bar structure. Experiments were conducted using bar encoding and the enhanced GAN model to compose a new melody and evaluate the quality of the composition melody. In the evaluation method, the TFIDF algorithm was also used to calculate the structural differences between four types of musical instrument digital interface (MIDI) file (i.e., randomly composed melody, melody composed by the original GAN, melody composed by the proposed method, and the real melody). Using the TFIDF algorithm, the structures of the melody composed were compared by the proposed method with the real melody and the structure of the traditional melody was compared with the structure of the real melody. The experimental results showed that the melody composed by the proposed method had more similarity with real melody structure with a difference of only 8% than that of the traditional melody structure.

]]>Mathematics doi: 10.3390/math7100882

Authors: Whan-Hyuk Choi

The purpose of this paper is to classify and enumerate self-dual codes of length 6 over finite field Z p . First, we classify these codes into three cases: decomposable, indecomposable non-MDS and MDS codes. Then, we complete the classification of non-MDS self-dual codes of length 6 over Z p for all primes p in terms of their automorphism group. We obtain all inequivalent classes and find the necessary and sufficient conditions for the existence of each class. Finally, we obtain the number of MDS self-dual codes of length 6.

]]>Mathematics doi: 10.3390/math7100881

Authors: Lu-Chuan Ceng Xiaolong Qin Yekini Shehu Jen-Chih Yao

In a real Hilbert space, let the notation VIP indicate a variational inequality problem for a Lipschitzian, pseudomonotone operator, and let CFPP denote a common fixed-point problem of an asymptotically nonexpansive mapping and finitely many nonexpansive mappings. This paper introduces mildly inertial algorithms with linesearch process for finding a common solution of the VIP and the CFPP by using a subgradient approach. These fully absorb hybrid steepest-descent ideas, viscosity iteration ideas, and composite Mann-type iterative ideas. With suitable conditions on real parameters, it is shown that the sequences generated our algorithms converge to a common solution in norm, which is a unique solution of a hierarchical variational inequality (HVI).

]]>Mathematics doi: 10.3390/math7100879

Authors: Jeong Min Kang Sang-Eon Han Sik Lee

Unlike the study of the fixed point property (FPP, for brevity) of retractable topological spaces, the research of the FPP of non-retractable topological spaces remains. The present paper deals with the issue. Based on order-theoretic foundations and fixed point theory for Khalimsky (K-, for short) topological spaces, the present paper studies the product property of the FPP for K-topological spaces. Furthermore, the paper investigates the FPP of various types of connected K-topological spaces such as non-K-retractable spaces and some points deleted K-topological (finite) planes, and so on. To be specific, after proving that not every one point deleted subspace of a finite K-topological plane X is a K-retract of X, we study the FPP of a non-retractable topological space Y, such as one point deleted space Y ∖ { p } .

]]>Mathematics doi: 10.3390/math7100880

Authors: Yulin Zhao Jiafa Xu Haibo Chen

This paper is devoted to studying the existence of solutions to a class of impulsive fractional differential equations with derivative dependence. The used technical approach is based on variational methods and iterative methods. In addition, an example is given to demonstrate the main results.

]]>Mathematics doi: 10.3390/math7100878

Authors: Alberto Cabada Lucía López-Somoza

In this paper, we prove the existence of solutions of nonlinear boundary value problems of arbitrary even order using the lower and upper solutions method. In particular, we point out the fact that the existence of a pair of lower and upper solutions of a considered problem could imply the existence of solution of another one with different boundary conditions. We consider Neumann, Dirichlet, mixed and periodic boundary conditions.

]]>Mathematics doi: 10.3390/math7100877

Authors: Emad E. Mahmoud M. Higazy Turkiah M. Al-Harthi

In this paper, a chaotic quaternion autonomous nonlinear structure is introduced and intends to be a contribution. It is the first nonlinear dynamical system with quaternion variables to be studied in the literature. With nine dimensions, the new system is a high-dimensional one. Several vital characteristics and features of this model are investigated, such as its Hamiltonian, symmetry, signal flow graph, dissipation, equilibriums and their stability, Lyapunov exponents, Lyapunov dimension, bifurcation diagrams, and chaotic behavior. A circuit implementation is designed to realize the new system, and a scheme is designed to achieve anti-anticipating synchronization (AAS) of two identical chaotic attractors with quaternion variables based on a Lyapunov function and active control. The concept of AAS is yet to be explored in the literature. A simulation experiment is designed and executed to illustrate the effectiveness of the acquired results. After synchronization, numerical outcomes are planned to explain the status variables and errors of these chaotic attractors to prove that AAS is achieved. The secure communication problem is studied based on the obtained events of the AAS of two identical nonlinear Lorenz systems with quaternion variables. AAS connecting the drive and response systems in chaotic systems with quaternion variables is the key to achieving communication. Signal encryption and restoration are simulated numerically.

]]>Mathematics doi: 10.3390/math7100876

Authors: Feng Liu Seongtae Jhang Sung-Kwun Oh Zunwei Fu

We establish one-sided weighted endpoint estimates for the ϱ -variation ( ϱ &gt; 2 ) operators of one-sided singular integrals under certain priori assumption by applying one-sided Calder&oacute;n&ndash;Zygmund argument. Using one-sided sharp maximal estimates, we further prove that the ϱ -variation operators of related commutators are bounded on one-sided weighted Lebesgue and Morrey spaces. In addition, we also show that these operators are bounded from one-sided weighted Morrey spaces to one-sided weighted Campanato spaces. As applications, we obtain some results for the &lambda; -jump operators and the numbers of up-crossings. Our main results represent one-sided extensions of many previously known ones.

]]>Mathematics doi: 10.3390/math7100875

Authors: Rezk Ali Abdalla Younis Gomaa Hashim

For an efficient energy harvesting by the PV/thermoelectric system, the maximum power point tracking (MPPT) principle is targeted, aiming to operate the system close to peak power point. Under a uniform distribution of the solar irradiance, there is only one maximum power point (MPP), which easily can be efficiently determined by any traditional MPPT method, such as the incremental conductance (INC). A different situation will occur for the non-uniform distribution of solar irradiance, where more than one MPP will exist on the power versus voltage plot of the PV/thermoelectric system. The determination of the global MPP cannot be achieved by conventional methods. To deal with this issue the application of soft computing techniques based on optimization algorithms is used. However, MPPT based on optimization algorithms is very tedious and time consuming, especially under normal conditions. To solve this dilemma, this research examines a hybrid MPPT method, consisting of an incremental conductance (INC) approach and a moth-flame optimizer (MFO), referred to as (INC-MFO) procedure, to reach high adaptability at different environmental conditions. In this way, the combination of the two different algorithms facilitates the utilization of the advantages of the two methods, thereby resulting in a faster speed tracking with uniform radiation distribution and a high accuracy in the case of a non-uniform distribution. It is very important to mention that the INC method is used to track the maximum power point under normal conditions, whereas the MFO optimizer is most relevant for the global search under partial shading. The obtained results revealed that the proposed strategy performed best in both of the dynamic and the steady-state conditions at uniform and non-uniform radiation.

]]>Mathematics doi: 10.3390/math7100874

Authors: Chang Lo Chen Liou

Failure mode and effects analysis (FMEA) is a risk assessment method that effectively diagnoses a product&rsquo;s potential failure modes. It is based on expert experience and investigation to determine the potential failure modes of the system or product to develop improvement strategies to reduce the risk of failures. However, the traditional FMEA has many shortcomings that were proposed by many studies. This study proposes a hybrid FMEA and multi-attribute decision-making (MADM) model to establish an evaluation framework, combining the rough best worst method (R-BWM) and rough technique for order preference by similarity to an ideal solution technique (R-TOPSIS) to determine the improvement order of failure modes. In addition, this study adds the concept of aspiration level to R-TOPSIS technology (called R-TOPSIS-AL), which not only optimizes the reliability of the TOPSIS calculation program, but also obtains more potential information. This study then demonstrates the effectiveness and robustness of the proposed model through a multinational audio equipment manufacturing company. The results show that the proposed model can overcome many shortcomings of traditional FMEA, and effectively assist decision-makers and research and development (R&amp;D) departments in improving the reliability of products.

]]>Mathematics doi: 10.3390/math7100873

Authors: Nichaphat Patanarapeelert Thanin Sitthiwirattham

In this paper, we study fractional symmetric Hahn difference calculus. The new idea of the symmetric Hahn difference operator, the fractional symmetric Hahn integral, and the fractional symmetric Hahn operators of Riemann&ndash;Liouville and Caputo types are presented. In addition, we formulate some fundamental properties based on these fractional symmetric Hahn operators.

]]>Mathematics doi: 10.3390/math7100872

Authors: . Xiang Liu

This paper aims to present a Clenshaw&ndash;Curtis&ndash;Filon quadrature to approximate thesolution of various cases of Cauchy-type singular integral equations (CSIEs) of the second kind witha highly oscillatory kernel function. We adduce that the zero case oscillation (k = 0) proposed methodgives more accurate results than the scheme introduced in Dezhbord at el. (2016) and Eshkuvatovat el. (2009) for small values of N. Finally, this paper illustrates some error analyses and numericalresults for CSIEs.

]]>Mathematics doi: 10.3390/math7090871

Authors: Shi Zhao Chen

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.

]]>Mathematics doi: 10.3390/math7090870

Authors: Muhammad Aslam Osama Hasan Arif

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.

]]>Mathematics doi: 10.3390/math7090869

Authors: A. V. Jayanthan Neeraj Kumar

Let G be a finite simple graph on n vertices. Let J G &sub; K [ x 1 , &hellip; , x n ] be the cover ideal of G. In this article, we obtain syzygies, Betti numbers, and Castelnuovo&ndash;Mumford regularity of J G s for all s &ge; 1 for certain classes of graphs G.

]]>Mathematics doi: 10.3390/math7090868

Authors: Salvador Cruz Rambaud

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.

]]>Mathematics doi: 10.3390/math7090867

Authors: X. Liu Y.L. Gao B. Zhang F.P. Tian

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 ≠ 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.

]]>Mathematics doi: 10.3390/math7090866

Authors: Anantachai Padcharoen Pakeeta Sukprasert

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.

]]>Mathematics doi: 10.3390/math7090865

Authors: Fan Yang Ping Fan Xiao-Xiao Li Xin-Yi Ma

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 &le; x &lt; 1 .

]]>Mathematics doi: 10.3390/math7090864

Authors: José Fulgencio Gálvez-Rodríguez Miguel Ángel Sánchez-Granero

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.

]]>Mathematics doi: 10.3390/math7090863

Authors: Zhong-Qi Xiang

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 &lambda; &isin; 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.

]]>Mathematics doi: 10.3390/math7090862

Authors: Hüseyin Işık Babak Mohammadi Mohammad Reza Haddadi Vahid Parvaneh

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

]]>Mathematics doi: 10.3390/math7090861

Authors: Tomasz M. Tyranowski Mathieu Desbrun

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 &ldquo;Hamiltonian&rdquo; equations of motion can be formulated as an index-1 differential-algebraic system. We also construct variational Runge&ndash;Kutta methods and analyze their properties. The general properties of Runge&ndash;Kutta methods depend on the &ldquo;velocity&rdquo; part of the Lagrangian. If the &ldquo;velocity&rdquo; part is also linear in the position coordinate, then we show that non-partitioned variational Runge&ndash;Kutta methods are equivalent to integration of the corresponding first-order Euler&ndash;Lagrange equations, which have the form of a Poisson system with a constant structure matrix, and the classical properties of the Runge&ndash;Kutta method are retained. If the &ldquo;velocity&rdquo; 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.

]]>Mathematics doi: 10.3390/math7090860

Authors: Lu-Chuan Ceng Adrian Petruşel Ching-Feng Wen Jen-Chih Yao

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).

]]>Mathematics doi: 10.3390/math7090858

Authors: Mahendra Piraveenan

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&ndash;contractor games, contractor-subcontractor games, subcontractor&ndash;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.

]]>Mathematics doi: 10.3390/math7090857

Authors: Helu Xiao Tiantian Ren Yanfei Bai Zhongbao Zhou

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&rsquo;s and the reinsurer&rsquo;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.

]]>Mathematics doi: 10.3390/math7090859

Authors: Huy Tài Hà Susan Morey

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.

]]>Mathematics doi: 10.3390/math7090856

Authors: Hind Hashem Ahmed El-Sayed Dumitru Baleanu

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.

]]>Mathematics doi: 10.3390/math7090855

Authors: Ramandeep Behl Ioannis K. Argyros Ali Saleh Alshomrani

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.

]]>Mathematics doi: 10.3390/math7090854

Authors: Jing Zhang Jin Xu Kai Jia Yimin Yin Zhengming Wang

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.

]]>Mathematics doi: 10.3390/math7090853

Authors: M. Consuelo Casabán Rafael Company Lucas Jódar

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.

]]>Mathematics doi: 10.3390/math7090852

Authors: Hasanen A. Hammad Manuel De la Sen

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.

]]>Mathematics doi: 10.3390/math7090851

Authors: Aki Mori

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.

]]>Mathematics doi: 10.3390/math7090850

Authors: Mohamed Jleli Bessem Samet

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.

]]>Mathematics doi: 10.3390/math7090849

Authors: Pradip Debnath Manuel de La Sen

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&ndash;Rogers-type and the other one is for set-valued Reich&ndash;Rus&ndash;Ćirić-type contractions. Examples are provided to validate the results.

]]>Mathematics doi: 10.3390/math7090848

Authors: Hari M. Srivastava Qazi Zahoor Ahmad Maslina Darus Nazar Khan Bilal Khan Naveed Zaman Hasrat Hussain Shah

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.

]]>Mathematics doi: 10.3390/math7090847

Authors: Sheikh Imran Ishrat Zahid Akhtar Khan Arshad Noor Siddiquee Irfan Anjum Badruddin Ali Algahtani Shakeel Javaid Rajan Gupta

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&rsquo;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 &deg;F of temperature), a reasonably streamlined pod manufacturing process can be achieved for sustainable operations.

]]>Mathematics doi: 10.3390/math7090846

Authors: Yingkang Xie Zhen Wang Bo Meng

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.

]]>Mathematics doi: 10.3390/math7090845

Authors: Xia Wu JinRong Wang Jialu Zhang

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&ndash;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.

]]>Mathematics doi: 10.3390/math7090844

Authors: Yaqin Wang Xiaoli Fang Tae-Hwa Kim

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.

]]>Mathematics doi: 10.3390/math7090843

Authors: Xiaodi Li A. Vinodkumar T. Senthilkumar

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.

]]>Mathematics doi: 10.3390/math7090842

Authors: Idris Ahmed Poom Kumam Gafurjan Ibragimov Jewaidu Rilwan Wiyada Kumam

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.

]]>Mathematics doi: 10.3390/math7090839

Authors: Young Hee Geum Young Ik Kim

This paper is devoted to an analysis on locating and counting satellite components born along the stability circle in the parameter space for a family of Jarratt-like iterative methods. An elementary theory of plane geometric curves is pursued to locate bifurcation points of such satellite components. In addition, the theory of Farey sequence is adopted to count the number of the satellite components as well as to characterize relationships between the bifurcation points. A linear stability theory on local bifurcations is developed based upon a small perturbation about the fixed point of the iterative map with a control parameter. Some properties of fixed and critical points under the M&ouml;bius conjugacy map are investigated. Theories and examples on locating and counting bifurcation points of satellite components in the parameter space are presented to analyze the bifurcation behavior underlying the dynamics behind the iterative map.

]]>Mathematics doi: 10.3390/math7090841

Authors: Seifu Endris Yimer Poom Kumam Anteneh Getachew Gebrie Rabian Wangkeeree

In this paper, we introduce an iterative scheme with inertial effect using Mann iterative scheme and gradient-projection for solving the bilevel variational inequality problem over the intersection of the set of common fixed points of a finite number of nonexpansive mappings and the set of solution points of the constrained optimization problem. Under some mild conditions we obtain strong convergence of the proposed algorithm. Two examples of the proposed bilevel variational inequality problem are also shown through numerical results.

]]>Mathematics doi: 10.3390/math7090840

Authors: Namhoon Kim

By considering a contour integral of a cotangent sum, we give a simple derivation of a transformation formula of the series A ( &tau; , s ) = &sum; n = 1 &infin; &sigma; s &minus; 1 ( n ) e 2 &pi; i n &tau; for complex s under the action of the modular group on &tau; in the upper half plane. Some special cases directly give expressions of generalized Dedekind sums as cotangent sums.

]]>Mathematics doi: 10.3390/math7090838

Authors: Boris Ryabko

An infinite sequence x 1 x 2 … of letters from some alphabet { 0 , 1 , … , b − 1 } , b ≥ 2 , is called k-distributed ( k ≥ 1 ) if any k-letter block of successive digits appears with the frequency b − k in the long run. The sequence is called normal (or ∞-distributed) if it is k-distributed for any k ≥ 1 . We describe two classes of low-entropy processes that with probability 1 generate either k-distributed sequences or ∞-distributed sequences. Then, we show how those processes can be used for building random number generators whose outputs are either k-distributed or ∞-distributed. Thus, these generators have statistical properties that are mathematically proven.

]]>Mathematics doi: 10.3390/math7090837

Authors: Ahmed M. Elaiw Safiya F. Alshehaiween Aatef D. Hobiny

In this paper, we construct an Human immunodeficiency virus (HIV) dynamics model with impairment of B-cell functions and the general incidence rate. We incorporate three types of infected cells, (i) latently-infected cells, which contain the virus, but do not generate HIV particles, (ii) short-lived productively-infected cells, which live for a short time and generate large numbers of HIV particles, and (iii) long-lived productively-infected cells, which live for a long time and generate small numbers of HIV particles. The model considers five distributed time delays to characterize the time between the HIV contact of an uninfected CD4 + T-cell and the creation of mature HIV. The nonnegativity and boundedness of the solutions are proven. The model admits two equilibria, infection-free equilibrium E P 0 and endemic equilibrium E P 1 . We derive the basic reproduction number R 0 , which determines the existence and stability of the two equilibria. The global stability of each equilibrium is proven by utilizing the Lyapunov function and LaSalle&rsquo;s invariance principle. We prove that if R 0 &lt; 1 , then E P 0 is globally asymptotically stable, and if R 0 &gt; 1 , then E P 1 is globally asymptotically stable. These theoretical results are illustrated by numerical simulations. The effect of impairment of B-cell functions, time delays, and antiviral treatment on the HIV dynamics are studied. We show that if the functions of B-cells are impaired, then the concentration of HIV is increased in the plasma. Moreover, we observe that the time delay has a similar effect to drug efficacy. This gives some impression for developing a new class of treatments to increase the delay period and then suppress the HIV replication.

]]>Mathematics doi: 10.3390/math7090836

Authors: Parbati Saha Tapas K. Samanta Nabin C. Kayal Binayak S. Choudhury Manuel de la Sen

In this paper, we establish Hyers&ndash;Ulam&ndash;Rassias stability results belonging to two different set valued functional equations in several variables, namely additive and cubic. The results are obtained in the contexts of Banach spaces. The work is in the domain of set valued analysis.

]]>Mathematics doi: 10.3390/math7090835

Authors: Wenguang Yu Yaodi Yong Guofeng Guan Yujuan Huang Wen Su Chaoran Cui

Recently, the valuation of variable annuity products has become a hot topic in actuarial science. In this paper, we use the Fourier cosine series expansion (COS) method to value the guaranteed minimum death benefit (GMDB) products. We first express the value of GMDB by the discounted density function approach, then we use the COS method to approximate the valuation Equations. When the distribution of the time-until-death random variable is approximated by a combination of exponential distributions and the price of the fund is modeled by an exponential L&eacute;vy process, explicit equations for the cosine coefficients are given. Some numerical experiments are also made to illustrate the efficiency of our method.

]]>Mathematics doi: 10.3390/math7090834

Authors: Jin Yang Li Liu

Compressed sensing theory is widely used in the field of fault signal diagnosis and image processing. Sparse recovery is one of the core concepts of this theory. In this paper, we proposed a sparse recovery algorithm using a smoothed l0 norm and a randomized coordinate descent (RCD), then applied it to sparse signal recovery and image denoising. We adopted a new strategy to express the (P0) problem approximately and put forward a sparse recovery algorithm using RCD. In the computer simulation experiments, we compared the performance of this algorithm to other typical methods. The results show that our algorithm possesses higher precision in sparse signal recovery. Moreover, it achieves higher signal to noise ratio (SNR) and faster convergence speed in image denoising.

]]>Mathematics doi: 10.3390/math7090833

Authors: Anthony Sofo Amrik Singh Nimbran

In this paper, we present some Euler-like sums involving partial sums of the harmonic and odd harmonic series. First, we give a brief historical account of Euler&rsquo;s work on the subject followed by notations used in the body of the paper. After discussing some alternating Euler sums, we investigate the connection of integrals of inverse trigonometric and hyperbolic type functions to generate many new Euler sum identities. We also give some new identities for Catalan&rsquo;s constant, Apery&rsquo;s constant and a fast converging identity for the famous &zeta; ( 2 ) constant.

]]>Mathematics doi: 10.3390/math7090832

Authors: Xin Yang Shigang Wen Zhifeng Liu Cai Li Chuangxia Huang

The foreign exchange (FX) market, one of the important components of the financial market, is a typical complex system. In this paper, by resorting to the complex network method, we use the daily closing prices of 41 FX markets to build the dynamical networks and their minimum spanning tree (MST) maps by virtue of a moving window correlation coefficient. The properties of FX networks are characterized by the normalized tree length, node degree distributions, centrality measures and edge survival ratios. Empirical results show that: (i) the normalized tree length plays a role in identifying crises and is negatively correlated with the market return and volatility; (ii) 83% of FX networks follow power-law node degree distribution, which means that the FX market is a typical heterogeneous market, and a few hub nodes play key roles in the market; (iii) the highest centrality measures reveal that the USD, EUR and CNY are the three most powerful currencies in FX markets; and (iv) the edge survival ratio analysis implies that the FX structure is relatively stable.

]]>Mathematics doi: 10.3390/math7090831

Authors: Ali Yousef Hosny Hamdy

This paper considers sequentially two main problems. First, we estimate both the mean and the variance of the normal distribution under a unified one decision framework using Hall&rsquo;s three-stage procedure. We consider a minimum risk point estimation problem for the variance considering a squared-error loss function with linear sampling cost. Then we construct a confidence interval for the mean with a preassigned width and coverage probability. Second, as an application, we develop Fortran codes that tackle both the point estimation and confidence interval problems for the inverse coefficient of variation using a Monte Carlo simulation. The simulation results show negative regret in the estimation of the inverse coefficient of variation, which indicates that the three-stage procedure provides better estimation than the optimal.

]]>Mathematics doi: 10.3390/math7090830

Authors: Dumitru Baleanu Arran Fernandez

Fractional calculus dates its inception to a correspondence between Leibniz and L&rsquo;Hopital in 1695, when Leibniz described &ldquo;paradoxes&rdquo; and predicted that &ldquo;one day useful consequences will be drawn&rdquo; from them. In today&rsquo;s world, the study of non-integer orders of differentiation has become a thriving field of research, not only in mathematics but also in other parts of science such as physics, biology, and engineering: many of the &ldquo;useful consequences&rdquo; predicted by Leibniz have been discovered. However, the field has grown so far that researchers cannot yet agree on what a &ldquo;fractional derivative&rdquo; can be. In this manuscript, we suggest and justify the idea of classification of fractional calculus into distinct classes of operators.

]]>Mathematics doi: 10.3390/math7090829

Authors: Savin Treanţă

In this paper, optimality conditions are studied for a new class of PDE and PDI-constrained scalar variational control problems governed by path-independent curvilinear integral functionals. More precisely, we formulate and prove a minimal criterion for a local optimal solution of the considered PDE and PDI-constrained variational control problem to be its global optimal solution. The effectiveness of the main result is validated by a two-dimensional non-convex scalar variational control problem.

]]>Mathematics doi: 10.3390/math7090828

Authors: Jiamin Wei YangQuan Chen Yongguang Yu Yuquan Chen

L&eacute;vy flights is a random walk where the step-lengths have a probability distribution that is heavy-tailed. It has been shown that L&eacute;vy flights can maximize the efficiency of resource searching in uncertain environments and also the movements of many foragers and wandering animals have been shown to follow a L&eacute;vy distribution. The reason mainly comes from the fact that the L&eacute;vy distribution has an infinite second moment and hence is more likely to generate an offspring that is farther away from its parent. However, the investigation into the efficiency of other different heavy-tailed probability distributions in swarm-based searches is still insufficient up to now. For swarm-based search algorithms, randomness plays a significant role in both exploration and exploitation or diversification and intensification. Therefore, it is necessary to discuss the optimal randomness in swarm-based search algorithms. In this study, cuckoo search (CS) is taken as a representative method of swarm-based optimization algorithms, and the results can be generalized to other swarm-based search algorithms. In this paper, four different types of commonly used heavy-tailed distributions, including Mittag-Leffler distribution, Pareto distribution, Cauchy distribution, and Weibull distribution, are considered to enhance the searching ability of CS. Then four novel CS algorithms are proposed and experiments are carried out on 20 benchmark functions to compare their searching performances. Finally, the proposed methods are used to system identification to demonstrate the effectiveness.

]]>Mathematics doi: 10.3390/math7090827

Authors: Zhongbao Zhou Qianying Jin Jian Peng Helu Xiao Shijian Wu

The super-efficiency data envelopment analysis model is innovative in evaluating the performance of crude oil prices&rsquo; volatility forecasting models. This multidimensional ranking, which takes account of multiple criteria, gives rise to a unified decision as to which model performs best. However, the rankings are unreliable because some efficiency scores are infeasible solutions in nature. What&rsquo;s more, the desirability of indexes is worth discussing so as to avoid incorrect rankings. Hence, herein we introduce four models, which address the issue of undesirable characteristics of indexes and infeasibility of the super efficiency models. The empirical results reveal that the new rankings are more robust and quite different from the existing results.

]]>Mathematics doi: 10.3390/math7090826

Authors: Maria P. Beccar-Varela Md Al Masum Bhuiyan Maria C. Mariani Osei K. Tweneboah

In this work, an analytic approach for solving higher order ordinary differential equations (ODEs) is developed. The techniques offer analytic flexibility in many research areas such as physics, engineering, and applied sciences and are effective for solving complex ODEs.

]]>Mathematics doi: 10.3390/math7090825

Authors: Chesoong Kim Sergei Dudin Olga Dudina

We consider a queueing network with a finite number of nodes and servers moving between the nodes as a model of car sharing. The arrival process of customers to various nodes is defined by a marked Markovian arrival process. The customer that arrives at a certain node when there is no idle server (car) is lost. Otherwise, he/she is able to start the service. With known probability, which depends on the node and the number of available cars, this customer can balk the service and leave the system. The service time of a customer has an exponential distribution. Location of the server in the network after service completion is random with the known probability distribution. The behaviour of the network is described by a multi-dimensional continuous-time Markov chain. The generator of this chain is derived which allows us to compute the stationary distribution of the network states. The formulas for computing the key performance indicators of the system are given. Numerical results are presented. They characterize the dependence of some performance measures of the network and the nodes on the total number of cars (fleet size of the car sharing system) and correlation in the arrival process.

]]>Mathematics doi: 10.3390/math7090824

Authors: Matej Črepinšek Miha Ravber Marjan Mernik Tomaž Kosar

Multi-Objective Evolutionary Algorithms (MOEAs) have been applied successfully for solving real-world multi-objective problems. Their success can depend highly on the configuration of their control parameters. Different tuning methods have been proposed in order to solve this problem. Tuning can be performed on a set of problem instances in order to obtain robust control parameters. However, for real-world problems, the set of problem instances at our disposal usually are not very plentiful. This raises the question: What is a sufficient number of problems used in the tuning process to obtain robust enough parameters? To answer this question, a novel method called MOCRS-Tuning was applied on different sized problem sets for the real-world integration and test order problem. The configurations obtained by the tuning process were compared on all the used problem instances. The results show that tuning greatly improves the algorithms&rsquo; performance and that a bigger subset used for tuning does not guarantee better results. This indicates that it is possible to obtain robust control parameters with a small subset of problem instances, which also substantially reduces the time required for tuning.

]]>Mathematics doi: 10.3390/math7090823

Authors: Jianming Xue Xingkai Hu

The main purpose of this paper is to present some weighted arithmetic-geometric operator mean inequalities. These inequalities are refinements and generalizations of the corresponding results. An example is provided to confirm the effectiveness of the results.

]]>Mathematics doi: 10.3390/math7090822

Authors: Wolf-Dieter Richter Vincent Wenzel

This paper aims to introduce a mathematical-philosophical type of question from the fascinating world of generalized circle numbers to the widest possible readership. We start with recalling well-known (in part from school) properties of the polygonal approximation of the common circle when approximating the famous circle number &pi; by convergent sequences of upper and lower bounds being based upon the lengths of polygons. Next, we shortly refer to some results from the literature where suitably defined generalized circle numbers of l p - and l p , q -circles, &pi; p and &pi; p , q , respectively, are considered and turn afterwards over to the approximation of an l p -circle by a family of l p , q -circles with q converging to p, q &rarr; p . Then we ask whether or not there holds the continuity property &pi; p , q &rarr; &pi; p as q &rarr; p . The answer to this question leads us to the answer of the question stated in the paper&rsquo;s title. Presenting here for illustration true paintings instead of strong technical or mathematical drawings intends both to stimulate opening heart and senses of the reader for recognizing generalized circles in his real life and to suggest the philosophical challenge of the consequences coming out from the demonstrated non-continuity property.

]]>Mathematics doi: 10.3390/math7090821

Authors: Mutti-Ur Rehman Muhammad Tayyab Muhammad Fazeel Anwar

In various modern linear control systems, a common practice is to make use of control in the feedback loops which act as an important tool for linear feedback systems. Stability and instability analysis of a linear feedback system give the measure of perturbed system to be singular and non-singular. The main objective of this article is to discuss numerical computation of the &mu; -values bounds by using low ranked ordinary differential equations based technique. Numerical computations illustrate the behavior of the method and the spectrum of operators are then numerically analyzed.

]]>Mathematics doi: 10.3390/math7090820

Authors: Pu Wu Huiqin Jiang Sakineh Nazari-Moghaddam Seyed Mahmoud Sheikholeslami Zehui Shao Lutz Volkmann

A set S &sube; V ( G ) in a graph G is a dominating set if S dominates all vertices in G, where we say a vertex dominates each vertex in its closed neighbourhood. A set is independent if it is pairwise non-adjacent. The minimum cardinality of an independent dominating set on a graph G is called the independent domination number i ( G ) . A graph G is ID-stable if the independent domination number of G is not changed when any vertex is removed. In this paper, we study basic properties of ID-stable graphs and we characterize all ID-stable trees and unicyclic graphs. In addition, we establish bounds on the order of ID-stable trees.

]]>Mathematics doi: 10.3390/math7090819

Authors: Hongjun Wei Jinjiang Yuan Yuan Gao

We consider the coordination of transportation and batching scheduling with one single vehicle for minimizing total weighted completion time. The computational complexity of the problem with batch capacity of at least 2 was posed as open in the literature. For this problem, we show the unary NP-hardness for every batch capacity at least 3 and present a polynomial-time 3-approximation algorithm when the batch capacity is at least 2.

]]>Mathematics doi: 10.3390/math7090818

Authors: Alejandro Arceo Luis E. Garza Gerardo Romero

In this contribution, we consider sequences of orthogonal polynomials associated with a perturbation of some classical weights consisting of the introduction of a parameter t, and deduce some algebraic properties related to their zeros, such as their equations of motion with respect to t. These sequences are later used to explicitly construct families of polynomials that are stable for all values of t, i.e., robust stability on these families is guaranteed. Some illustrative examples are presented.

]]>Mathematics doi: 10.3390/math7090817

Authors: Fernando Sánchez Lasheras Manuel José Fernández Gutiérrez Juan Cereijo Viña

In level tests carried out in recent years to evaluate the competence acquired by calculus students enrolled in the Computer Software Engineering degree at the University of Oviedo, it has been observed that a significant percentage of students make very similar conceptual errors. This article describes the research undertaken by a working group of teachers called BACUNIMAT, currently made up of two university professors and five high school professors. The name BACUNIMAT is the acronym in Spanish for the High School and University Teachers Working Group. The aim of this research group was to analyze the main deficiencies in mathematical knowledge that students possess upon arrival at university. The analysis was performed in order to propose solutions to alleviate these deficiencies. The research proposes how to focus mathematical teaching in secondary schools in order to better prepare students for university.

]]>Mathematics doi: 10.3390/math7090816

Authors: A. Martín del Rey R. Casado Vara D. Hernández Serrano

The aim of this work is to completely solve the reversibility problem for symmetric linear cellular automata with radius r = 3 and null boundary conditions. The main result obtained is the explicit computation of the local transition functions of the inverse cellular automata. This allows introduction of possible and interesting applications in digital image encryption.

]]>Mathematics doi: 10.3390/math7090815

Authors: Abdolreza Amiri Mohammad Taghi Darvishi Alicia Cordero Juan Ramón Torregrosa

In this paper, an iterative method for solving large, sparse systems of weakly nonlinear equations is presented. This method is based on Hermitian/skew-Hermitian splitting (HSS) scheme. Under suitable assumptions, we establish the convergence theorem for this method. In addition, it is shown that any faster and less time-consuming two-stage splitting method that satisfies the convergence theorem can be replaced instead of the HSS inner iterations. Numerical results, such as CPU time, show the robustness of our new method. This method is easy, fast and convenient with an accurate solution.

]]>Mathematics doi: 10.3390/math7090814

Authors: Xiuyan Ma

In this paper, we consider a manufacturer who produces and sells a kind of innovative product in the monopoly market environment. Because the life cycle of an innovative product is usually shorter than its procurement lead time, one unique demand quantity (scenario) will occur in the selling season; thus, there is only one chance for the manufacturer to determine both optimal production quantity and optimal sale price. Considering this one-time feature of such a decision problem, a price-setting newsvendor model for innovative products is proposed. Different to the existing price-setting newsvendor models, the proposed models determine the optimal production quantity and sale price based on some specific state (scenario) which is most applicable for the manufacturer. The theoretical analysis provides managerial insights into the manufacturers&rsquo; behaviors in a monopoly market of an innovative product, and several phenomena in the luxury goods market are well explained.

]]>Mathematics doi: 10.3390/math7090813

Authors: Thanon Korkiatsakul Sanoe Koonprasert Khomsan Neamprem

The generalized time fractional Kolmogorov-Petrovsky-Piskunov equation (FKPP), D t &alpha; &omega; ( x , t ) = a ( x , t ) D x x &omega; ( x , t ) + F ( &omega; ( x , t ) ) , which plays an important role in engineering, chemical reaction problem is proposed by Caputo fractional order derivative sense. In this paper, we develop a framework wavelet, including shift Chebyshev polynomial of the first kind as a mother wavelet, and also construct some operational matrices that represent Caputo fractional derivative to obtain analytical solutions for FKPP equation with three different types of Initial Boundary conditions (Dirichlet, Dirichlet-Neumann, and Neumann-Robin). Our results shown that the Chebyshev wavelet is a powerful method, due to its simplicity, efficiency in analytical approximations, and its fast convergence. The comparison of the Chebyshev wavelet results indicates that the proposed method not only gives satisfactory results but also do not need large amount of CPU times.

]]>Mathematics doi: 10.3390/math7090812

Authors: Remigiusz Wisniewski Grzegorz Bazydło Paweł Szcześniak Iwona Grobelna Marcin Wojnakowski

The paper proposes a novel design technique of cyber-physical systems (CPSs). The system is specified by a Petri net, and further modelled in a hardware description language (HDL) towards final implementation in a programmable device. Contrary to the traditional design methods, the proposed solution is highly focused on the verification aspects. The system is checked three times before the final implementation in hardware. Initially, the Petri-net based specification is formally verified by the application of the model-checking technique. Secondly, software verification of the modelled system is performed. Finally, the hardware verification of the already implemented system is executed. The proposed method is explained by an example of a direct matrix converter (MC) with transistor commutation and space vector modulation (SVM). The main benefits, as well as the limitations, of the proposed solution are discussed and analysed.

]]>Mathematics doi: 10.3390/math7090811

Authors: Elena-Corina Cipu

In this paper, we formulate and prove weak, strong and converse duality results in variational control problems involving ( &rho; , b ) -quasiinvex path-independent curvilinear integral cost functionals.

]]>Mathematics doi: 10.3390/math7090810

Authors: Gia-Shie Liu

This paper combines computer-based monitoring technologies and Internet of things (IoT) technology to develop IoT condition-based group replacement decision support system for a production/service system with numerous parallel independent operating servers. This proposed IoT conditioned-based group replacement decision support system first develops the discounted cost model for a service/production system with numerous independent working servers. The original discounted cost model is further revised into an equivalent model to stimulate the proof procedure by applying the uniformization approach. Several significant theoretical properties are proved and many numerical examples are conducted for two kinds of group replacement policies, respectively. The first class of group replacement policy is developed and proved theoretically that there is a threshold of amount of customers existed to activate the group replacement depending on various amount of operating servers; numerical examples conducted in this study can also illustrate the above theoretical outcomes already derived for the first class of group replacement policy. Besides, for the second class of group replacement policy, the results of numerical examples definitely demonstrate that there is a threshold of the amount of operating servers needed to start the group replacement according to distinct amount of customers in the system. This proposed IoT condition-based group replacement decision support system derives the structure and detailed procedure flow to actually conduct the group replacement operations for many practical service or production systems.

]]>Mathematics doi: 10.3390/math7090809

Authors: Wei-Shih Du

In this paper, we introduce the new concepts of K-adjustability convexity and strictly K-adjustability convexity which respectively generalize and extend the concepts of K-convexity and strictly K-convexity. We establish some new existence and uniqueness theorems of zeros for vector-valued functions with K-adjustability convexity. As their applications, we obtain existence theorems for the minimization problem and fixed point problem which are original and quite different from the known results in the existing literature.

]]>Mathematics doi: 10.3390/math7090808

Authors: Hamed H Al-Sulami Jamshaid Ahmad Nawab Hussain Abdul Latif

The aim of this study is to investigate the existence of solutions for the following Fredholm integral inclusion &phi; ( t ) &isin; f ( t ) + &int; 0 1 K ( t , s , &phi; ( s ) ) ϱ s for t &isin; [ 0 , 1 ] , where f &isin; C [ 0 , 1 ] is a given real-valued function and K : [ 0 , 1 ] &times; [ 0 , 1 ] &times; R &rarr; K c v ( R ) a given multivalued operator, where K c v represents the family of non-empty compact and convex subsets of R , &phi; &isin; C [ 0 , 1 ] is the unknown function and ϱ is a metric defined on C [ 0 , 1 ] . To attain this target, we take advantage of fixed point theorems for &alpha; -fuzzy mappings satisfying a new class of contractive conditions in the context of complete metric spaces. We derive new fixed point results which extend and improve the well-known results of Banach, Kannan, Chatterjea, Reich, Hardy-Rogers, Berinde and Ćirić by means of this new class of contractions. We also give a significantly non-trivial example to support our new results.

]]>Mathematics doi: 10.3390/math7090807

Authors: Saima Rashid Thabet Abdeljawad Fahd Jarad Muhammad Aslam Noor

In the present paper, we investigate some Hermite-Hadamard ( HH ) inequalities related to generalized Riemann-Liouville fractional integral ( GRLFI ) via exponentially convex functions. We also show the fundamental identity for GRLFI having the first order derivative of a given exponentially convex function. Monotonicity and exponentially convexity of functions are used with some traditional and forthright inequalities. In the application part, we give examples and new inequalities for the special means.

]]>Mathematics doi: 10.3390/math7090806

Authors: Ginkyu Choi Soon-Mo Jung Jaiok Roh

In this paper, we will consider the Hyers-Ulam stability for the second order inhomogeneous linear differential equation, u &Prime; ( x ) + &alpha; u &prime; ( x ) + &beta; u ( x ) = r ( x ) , with constant coefficients. More precisely, we study the properties of the approximate solutions of the above differential equation in the class of twice continuously differentiable functions with suitable conditions and compare them with the solutions of the homogeneous differential equation u &Prime; ( x ) + &alpha; u &prime; ( x ) + &beta; u ( x ) = 0 . Several mathematicians have studied the approximate solutions of such differential equation and they obtained good results. In this paper, we use the classical integral method, via the Wronskian, to establish the stability of the second order inhomogeneous linear differential equation with constant coefficients and we will compare our result with previous ones. Specially, for any desired point c &isin; R we can have a good approximate solution near c with very small error estimation.

]]>Mathematics doi: 10.3390/math7090805

Authors: Monther Rashed Alfuraidan Ibrahim Nabeel Joudah

In this work, we obtain a new formula for Fibonacci&rsquo;s family m-step sequences. We use our formula to find the nth term with less time complexity than the matrix multiplication method. Then, we extend our results for all linear homogeneous recurrence m-step relations with constant coefficients by using the last few terms of its corresponding Fibonacci&rsquo;s family m-step sequence. As a computational number theory application, we develop a method to estimate the square roots.

]]>Mathematics doi: 10.3390/math7090804

Authors: Ioannis K. Argyros Neha Gupta J. P. Jaiswal

The semi-local convergence analysis of a well defined and efficient two-step Chord-type method in Banach spaces is presented in this study. The recurrence relation technique is used under some weak assumptions. The pertinency of the assumed method is extended for nonlinear non-differentiable operators. The convergence theorem is also established to show the existence and uniqueness of the approximate solution. A numerical illustration is quoted to certify the theoretical part which shows that earlier studies fail if the function is non-differentiable.

]]>Mathematics doi: 10.3390/math7090803

Authors: Ramandeep Behl Waleed M. Al-Hamdan

We present a new optimal class of Ostrowski&rsquo;s method for obtaining multiple zeros of univariate nonlinear functions. Several researchers tried to construct an optimal family of Ostrowski&rsquo;s method for multiple zeros, but they did not have success in this direction. The new strategy adopts a weight function approach. The design structure of new families of Ostrowski&rsquo;s technique is simpler than the existing classical families of the same order for multiple zeros. The classical Ostrowski&rsquo;s method of fourth-order can obtain a particular form for the simple root. Their efficiency is checked on a good number of relevant numerical examples. These results demonstrate the performance of our methods. We find that the new methods are just as competent as other existing robust techniques available in the literature.

]]>Mathematics doi: 10.3390/math7090800

Authors: Panuwat Luangchaisri Thawhat Changphas

Let P 2 &sub; P 1 be a pair of weakly semiprime ideals of an ordered semigroup ( S , &middot; , &le; ) . Then, the pair P 2 &sub; P 1 is called a weakly semiprime segment of S if ⋂ n &isin; N I n &sube; P 2 for all ideals I of S such that P 2 &sub; I &sub; P 1 . In this paper, we classify weakly semiprime segments of an ordered semigroup into four types; those that are simple, exceptional, Archimedean, and decomposable.

]]>Mathematics doi: 10.3390/math7090801

Authors: Josef Mikeš Irena Hinterleitner Nadezda Guseva

In the present paper, we study conformal mappings between a connected n-dimension pseudo-Riemannian Einstein manifolds. Let g be a pseudo-Riemannian Einstein metric of indefinite signature on a connected n-dimensional manifold M. Further assume that there is a point at which not all sectional curvatures are equal and through which in linearly independent directions pass n complete null (light-like) geodesics. If, for the function &psi; the metric &psi; &minus; 2 g is also Einstein, then &psi; is a constant, and conformal mapping is homothetic. Note that Kiosak and Matveev previously assumed that all light-lines were complete. If the Einstein manifold is closed, the completeness assumption can be omitted (the latter result is due to Mike&scaron; and K&uuml;hnel).

]]>Mathematics doi: 10.3390/math7090802

Authors: Mohsen Rostamian Delavar Manuel De La Sen

Two mappings L w and P w , in connection with Fej&eacute;r&rsquo;s inequality, are considered for the convex and nonsymmetric monotone functions. Some basic properties and results along with some refinements for Fej&eacute;r&rsquo;s inequality according to these new settings are obtained. As applications, some special means type inequalities are given.

]]>Mathematics doi: 10.3390/math7090799

Authors: Valeriy A. Naumov Yuliya V. Gaidamaka Konstantin E. Samouylov

In this paper, we study a Markovian queuing system consisting of two subsystems of an arbitrary structure. Each subsystem generates a multi-class Markovian arrival process of customers arriving to the other subsystem. We derive the necessary and sufficient conditions for the stationary distribution to be of product form and consider some particular cases of the subsystem interaction for which these conditions can be easily verified.

]]>Mathematics doi: 10.3390/math7090798

Authors: Valeriy A. Naumov Yuliya V. Gaidamaka Konstantin E. Samouylov

In this paper, we study queueing systems with an infinite and finite number of waiting places that can be modeled by a Quasi-Birth-and-Death process. We derive the conditions under which the stationary distribution for a loss system is a truncation of the stationary distribution of the Quasi-Birth-and-Death process and obtain the stationary distributions of both processes. We apply the obtained results to the analysis of a semi-open network in which a customer from an external queue replaces a customer leaving the system at the node from which the latter departed.

]]>Mathematics doi: 10.3390/math7090797

Authors: Aliya Naaz Siddiqui Bang-Yen Chen Oguzhan Bahadir

Warped products play crucial roles in differential geometry, as well as in mathematical physics, especially in general relativity. In this article, first we define and study statistical solitons on Ricci-symmetric statistical warped products R &times; f N 2 and N 1 &times; f R . Second, we study statistical warped products as submanifolds of statistical manifolds. For statistical warped products statistically immersed in a statistical manifold of constant curvature, we prove Chen&rsquo;s inequality involving scalar curvature, the squared mean curvature, and the Laplacian of warping function (with respect to the Levi&ndash;Civita connection). At the end, we establish a relationship between the scalar curvature and the Casorati curvatures in terms of the Laplacian of the warping function for statistical warped product submanifolds in the same ambient space.

]]>Mathematics doi: 10.3390/math7090796

Authors: Jean-Philippe Aguilar Jan Korbel Yuri Luchko

In this article, we first provide a survey of the exponential option pricing models and show that in the framework of the risk-neutral approach, they are governed by the space-fractional diffusion equation. Then, we introduce a more general class of models based on the space-time-fractional diffusion equation and recall some recent results in this field concerning the European option pricing and the risk-neutral parameter. We proceed with an extension of these results to the class of exotic options. In particular, we show that the call and put prices can be expressed in the form of simple power series in terms of the log-forward moneyness and the risk-neutral parameter. Finally, we provide the closed-form formulas for the first and second order risk sensitivities and study the dependencies of the portfolio hedging and profit-and-loss calculations upon the model parameters.

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Authors: Aled Morris Luca Börger Elaine Crooks

We model the growth, dispersal and mutation of two phenotypes of a species using reaction&ndash;diffusion equations, focusing on the biologically realistic case of small mutation rates. Having verified that the addition of a small linear mutation term to a Lotka&ndash;Volterra system limits it to only two steady states in the case of weak competition, an unstable extinction state and a stable coexistence state, we exploit the fact that the spreading speed of the system is known to be linearly determinate to show that the spreading speed is a nonincreasing function of the mutation rate, so that greater mixing between phenotypes leads to slower propagation. We also find the ratio at which the phenotypes occur at the leading edge in the limit of vanishing mutation.

]]>Mathematics doi: 10.3390/math7090794

Authors: Jessie Marie Byrnes Yu-Jau Lin Tzong-Ru Tsai Yuhlong Lio

Let X and Y follow two independent Burr type XII distributions and &delta; = P ( X &lt; Y ) . If X is the stress that is applied to a certain component and Y is the strength to sustain the stress, then &delta; is called the stress&ndash;strength parameter. In this study, The Bayes estimator of &delta; is investigated based on a progressively first failure-censored sample. Because of computation complexity and no closed form for the estimator as well as posterior distributions, the Markov Chain Monte Carlo procedure using the Metropolis&ndash;Hastings algorithm via Gibbs sampling is built to collect a random sample of &delta; via the joint distribution of the progressively first failure-censored sample and random parameters and the empirical distribution of this collected sample is used to estimate the posterior distribution of &delta; . Then, the Bayes estimates of &delta; using the square error, absolute error, and linear exponential error loss functions are obtained and the credible interval of &delta; is constructed using the empirical distribution. An intensive simulation study is conducted to investigate the performance of these three types of Bayes estimates and the coverage probabilities and average lengths of the credible interval of &delta; . Moreover, the performance of the Bayes estimates is compared with the maximum likelihood estimates. The Internet of Things and a numerical example about the miles-to-failure of vehicle components for reliability evaluation are provided for application purposes.

]]>Mathematics doi: 10.3390/math7090793

Authors: Zepeng Li Naoki Matsumoto Enqiang Zhu Jin Xu Tommy Jensen

A graph G is uniquely k-colorable if the chromatic number of G is k and G has only one k-coloring up to the permutation of the colors. For a plane graph G, two faces f 1 and f 2 of G are adjacent ( i , j )-faces if d ( f 1 ) = i, d ( f 2 ) = j, and f 1 and f 2 have a common edge, where d ( f ) is the degree of a face f. In this paper, we prove that every uniquely three-colorable plane graph has adjacent ( 3 , k )-faces, where k &le; 5. The bound of five for k is the best possible. Furthermore, we prove that there exists a class of uniquely three-colorable plane graphs having neither adjacent ( 3 , i )-faces nor adjacent ( 3 , j )-faces, where i , j are fixed in { 3 , 4 , 5 } and i &ne; j. One of our constructions implies that there exists an infinite family of edge-critical uniquely three-colorable plane graphs with n vertices and 7 3 n - 14 3 edges, where n ( &ge; 11 ) is odd and n &equiv; 2 ( mod 3 ).

]]>Mathematics doi: 10.3390/math7090792

Authors: Pierluigi Colli Gianni Gilardi Jürgen Sprekels

In this paper, we study the distributed optimal control of a system of three evolutionary equations involving fractional powers of three self-adjoint, monotone, unbounded linear operators having compact resolvents. The system is a generalization of a Cahn&ndash;Hilliard type phase field system modeling tumor growth that has been proposed by Hawkins&ndash;Daarud, van der Zee and Oden. The aim of the control process, which could be realized by either administering a drug or monitoring the nutrition, is to keep the tumor cell fraction under control while avoiding possible harm for the patient. In contrast to previous studies, in which the occurring unbounded operators governing the diffusional regimes were all given by the Laplacian with zero Neumann boundary conditions, the operators may in our case be different; more generally, we consider systems with fractional powers of the type that were studied in a recent work by the present authors. In our analysis, we show the Fr&eacute;chet differentiability of the associated control-to-state operator, establish the existence of solutions to the associated adjoint system, and derive the first-order necessary conditions of optimality for a cost functional of tracking type.

]]>Mathematics doi: 10.3390/math7090791

Authors: Mingchang Chih

Batching is a well-known method used to estimate the variance of the sample mean in steady-state simulation. Dynamic batching is a novel technique employed to implement traditional batch means estimators without the knowledge of the simulation run length a priori. In this study, we reinvestigated the dynamic batch means (DBM) algorithm with binary tree hierarchy and further proposed a binary coding idea to construct the corresponding data structure. We also present a closed-form expression for the DBM estimator with binary tree coding idea. This closed-form expression implies a mathematical expression that clearly defines itself in an algebraic binary relation. Given that the sample size and storage space are known in advance, we can show that the computation complexity in the closed-form expression for obtaining the indexes c j ( k ) , i.e., the batch mean shifts s , is less than the effort in recursive expression.

]]>Mathematics doi: 10.3390/math7090790

Authors: Tarek F. Ibrahim Zehra Nurkanović

By using the Kolmogorov-Arnold-Moser (KAM) theory, we investigate the stability of two elliptic equilibrium points (zero equilibrium and negative equilibrium) of the difference equation t n + 1 = &alpha; t n + &beta; t n 2 &minus; t n &minus; 1 , n = 0 , 1 , 2 , &hellip; , where are t &minus; 1 , t 0 , &alpha; &isin; R , &alpha; &ne; 0 , &beta; &gt; 0 . By using the symmetries we find the periodic solutions with some periods. Finally, some numerical examples are given to verify our theoretical results.

]]>Mathematics doi: 10.3390/math7090789

Authors: Suthep Suantai Suparat Kesornprom Prasit Cholamjiak

In this paper, we focus on studying the split feasibility problem (SFP), which has many applications in signal processing and image reconstruction. A popular technique is to employ the iterative method which is so called the relaxed CQ algorithm. However, the speed of convergence usually depends on the way of selecting the step size of such algorithms. We aim to suggest a new hybrid CQ algorithm for the SFP by using the self adaptive and the line-search techniques. There is no computation on the inverse and the spectral radius of a matrix. We then prove the weak convergence theorem under mild conditions. Numerical experiments are included to illustrate its performance in compressed sensing. Some comparisons are also given to show the efficiency with other CQ methods in the literature.

]]>Mathematics doi: 10.3390/math7090788

Authors: Weizhang Liang Bing Dai Guoyan Zhao Hao Wu

Due to various environmental issues caused by resource exploitation, establishing green mines is an essential measure to realize sustainable growth for mining companies. This research aimed to develop a novel methodology to evaluate the performance of green mines within hesitant fuzzy conditions. First, hesitant fuzzy sets (HFSs) were used to express original fuzzy assessment values. Then, the extended expert grading approach and the modified maximum deviation method with HFNs were combined to determine comprehensive importance degrees of criteria. Afterward, the traditional qualitative flexible (QUALIFLEX) method was integrated with the Organ&iacute;sation, rangement et synth&egrave;se de donn&eacute;es relationnelles (ORESTE) model to achieve the rankings of mines. Finally, the proposed hesitant fuzzy ORESTE&ndash;QUALIFLEX approach was utilized to evaluate the performance of green mines. In addition, the robustness of the method was verified by a sensitivity analysis, while the effectiveness and strengths were certified by a comparison analysis. The results indicate that the proposed methodology has great robustness and advantages and that it is feasible and effective for the performance evaluation of green mines under hesitant fuzzy environment.

]]>Mathematics doi: 10.3390/math7090787

Authors: Li-Na Cao Guofeng Yao

A differential equation of panel vibration in supersonic flow is established on the basis of the thin-plate large deflection theory under the assumption of a quasi-steady temperature field. The equation is dimensionless, and the derivation of its second-order Galerkin discretization yields a four-dimensional system. The algebraic criterion of the Hopf bifurcation is applied to study the motion stability of heated panels in supersonic flow. We provide a supplementary explanation for the proof process of a theorem, and analytical expressions of flutter dynamic pressure and panel vibration frequencies are derived. The conclusion is that the algebraic criterion of Hopf bifurcation can be applied in high-dimensional problems with many parameters. Moreover, the computational intensity of the method established in this work is less than that of conventional eigenvalue computation methods using parameter variation.

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Authors: Huiping Chen Guiqiong Xu Pingle Yang

Combining the ideas and advantages of intuitionistic fuzzy set (IFS) and hesitant fuzzy set (HFS), dual hesitant fuzzy set (DHFS) could express uncertain and complex information given by decision makers (DMs) in a more flexible manner. By virtue of the existing measure methods, elements in DHFSs should be of equal length and thus some values must be added into the shorter elements according to the risk preference of DMs. The extension of values will increase the subjectivity of decision-making to some extent, and different extension methods may produce different results. In order to address this issue, we first propose several new forms of distance and similarity measures without adding values. Subsequently, according to the proposed distance and similarity measures, two entropy measures are presented from the viewpoints of complementary set and the fuzziest set, respectively. Furthermore, based on the new distance and entropy measures, an extended technique for order preference by similarity to an ideal solution (TOPSIS) method is proposed for dealing with multi-attribute decision-making problems in the context of DHFS. Finally, two practical examples are analyzed to show the validity and applicability of the proposed method.

]]>Mathematics doi: 10.3390/math7090785

Authors: Jae Hee Kim Hee Sik Kim Joseph Neggers

In this paper, we define the notion of a probability function on a poset which is similar to the probability function discussed on d-algebras, and obtain three probability functions on posets. Moreover, we define a probability realizer of a poset, and we provide some examples to describe its role for the standard probability function. We apply the notion of a probability function to the ordered plane and obtain three probability functions on it.

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