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Math. Comput. Appl., Volume 23, Issue 1 (March 2018)

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Open AccessArticle Numerical Solution for Fuzzy Enzyme Kinetic Equations by the Runge–Kutta Method
Math. Comput. Appl. 2018, 23(1), 16; https://doi.org/10.3390/mca23010016
Received: 8 February 2018 / Revised: 11 March 2018 / Accepted: 14 March 2018 / Published: 18 March 2018
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Abstract
One of the most important biochemical reactions is catalyzed by enzymes. A numerical method to solve nonlinear equations of enzyme kinetics, known as the Michaelis and Menten equations, together with fuzzy initial values is introduced. The numerical method is based on the fourth
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One of the most important biochemical reactions is catalyzed by enzymes. A numerical method to solve nonlinear equations of enzyme kinetics, known as the Michaelis and Menten equations, together with fuzzy initial values is introduced. The numerical method is based on the fourth order Runge–Kutta method, which is generalized for a fuzzy system of differential equations. The convergence and stability of the method are also presented. The capability of the method in fuzzy enzyme kinetics is demonstrated by some numerical examples. Full article
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Open AccessArticle Explicit Solutions for the (2 + 1)-Dimensional Jaulent–Miodek Equation Using the Integrating Factors Method in an Unbounded Domain
Math. Comput. Appl. 2018, 23(1), 15; https://doi.org/10.3390/mca23010015
Received: 28 February 2018 / Revised: 15 March 2018 / Accepted: 16 March 2018 / Published: 16 March 2018
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Abstract
In this work, we prove that the integrating factors can be used as a reduction method. Analytical solutions of the Jaulent–Miodek (JM) equation are obtained using integrating factors as an extension of a recent work where, through hidden symmetries, the JM was reduced
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In this work, we prove that the integrating factors can be used as a reduction method. Analytical solutions of the Jaulent–Miodek (JM) equation are obtained using integrating factors as an extension of a recent work where, through hidden symmetries, the JM was reduced to ordinary differential equations (ODEs). Some of these ODEs had no quadrature. We here derive several new solutions for these non-solvable ODEs. Full article
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Open AccessArticle A New Hybrid Whale Optimizer Algorithm with Mean Strategy of Grey Wolf Optimizer for Global Optimization
Math. Comput. Appl. 2018, 23(1), 14; https://doi.org/10.3390/mca23010014
Received: 16 February 2018 / Revised: 6 March 2018 / Accepted: 8 March 2018 / Published: 12 March 2018
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Abstract
The quest for an efficient nature-inspired optimization technique has continued over the last few decades. In this paper, a hybrid nature-inspired optimization technique has been proposed. The hybrid algorithm has been constructed using Mean Grey Wolf Optimizer (MGWO) and Whale Optimizer Algorithm (WOA).
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The quest for an efficient nature-inspired optimization technique has continued over the last few decades. In this paper, a hybrid nature-inspired optimization technique has been proposed. The hybrid algorithm has been constructed using Mean Grey Wolf Optimizer (MGWO) and Whale Optimizer Algorithm (WOA). We have utilized the spiral equation of Whale Optimizer Algorithm for two procedures in the Hybrid Approach GWO (HAGWO) algorithm: (i) firstly, we used the spiral equation in Grey Wolf Optimizer algorithm for balance between the exploitation and the exploration process in the new hybrid approach; and (ii) secondly, we also applied this equation in the whole population in order to refrain from the premature convergence and trapping in local minima. The feasibility and effectiveness of the hybrid algorithm have been tested by solving some standard benchmarks, XOR, Baloon, Iris, Breast Cancer, Welded Beam Design, Pressure Vessel Design problems and comparing the results with those obtained through other metaheuristics. The solutions prove that the newly existing hybrid variant has higher stronger stability, faster convergence rate and computational accuracy than other nature-inspired metaheuristics on the maximum number of problems and can successfully resolve the function of constrained nonlinear optimization in reality. Full article
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Open AccessArticle Impact Evaluation of Electric Vehicle Parking on Solving Security-Constrained Unit Commitment Problem
Math. Comput. Appl. 2018, 23(1), 13; https://doi.org/10.3390/mca23010013
Received: 23 January 2018 / Revised: 21 February 2018 / Accepted: 1 March 2018 / Published: 7 March 2018
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Abstract
In this paper, the employment of a vehicle-to-grid (V2G) system in the security-constrained unit commitment (SCUC) problem is considered. SCUC has gained remarkable attention from researchers in the field of electric power systems, aiming to determine the generation schedule in which the system
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In this paper, the employment of a vehicle-to-grid (V2G) system in the security-constrained unit commitment (SCUC) problem is considered. SCUC has gained remarkable attention from researchers in the field of electric power systems, aiming to determine the generation schedule in which the system operator maximizes the system security and minimizes the generation costs, while satisfying the system and units’ constraints. Tremendous technological advances in recent years have attracted the attention of system operators to utilize novel sources of electricity, accompanied with thermal units. To this end, V2G technology recently drew remarkable consideration as a new energy resource. V2G reduces the dependence of electricity production procedures on small-scale and costly thermal units, and subsequently has a strong impact on the operation costs and ameliorates the management of load vacillations. This paper presents the use of V2G in scheduling and operating power systems. A successful technique for investigating the impacts of V2G on a real power system is running SCUC on power systems in which electric vehicle parking is installed on different buses. In order to assess its applicability, the proposed method has been applied in two case studies: the IEEE 6-bus system and the extended IEEE 30-bus system. This study presents two simulation scenarios: the SCUC problem was first evaluated separately, and then in the presence of some electrical vehicles connected to the grid. The results demonstrate the reduction of the total operation cost. In addition, by using the proposed method, the operator can specify the optimal number of vehicles needed in the parking each hour. The results can help the system operators and designers in designing, planning, and operating such power systems. Full article
(This article belongs to the Section Engineering)
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Open AccessArticle Nonlinear Multi-Frequency Dynamics of Wind Turbine Components with a Single-Mesh Helical Gear Train
Math. Comput. Appl. 2018, 23(1), 12; https://doi.org/10.3390/mca23010012
Received: 12 January 2018 / Revised: 13 February 2018 / Accepted: 24 February 2018 / Published: 1 March 2018
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Abstract
A complex nonlinear model for a single-mesh helical gear train is developed by including a time-varying mesh stiffness, axial vibrations, torsional vibrations, shaft and bearing damping, generator back EMF (Electromotive Force) and gear backlashes. With the help of a time series and Fast
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A complex nonlinear model for a single-mesh helical gear train is developed by including a time-varying mesh stiffness, axial vibrations, torsional vibrations, shaft and bearing damping, generator back EMF (Electromotive Force) and gear backlashes. With the help of a time series and Fast Fourier Transform (FFT) frequency spectrum, the effects of these nonlinear terms on the wind turbine and generator rotational speeds are studied under different excitation conditions by numerically integrating the associated equations using the RK4 algorithm. Results show that for lightly damped oscillations, an extra harmonic is induced in the generator dynamics due to contributions from internal excitations. However, this extra vibration can be suppressed at higher damping. Big helical angles will generally induce heavy nonlinear vibrations in the turbine and generator; a smaller mesh frequency will induce extra noise in the generator; and the external excitation due to wind gust has a greater influence on the nonlinearity of the wind turbine dynamics as compared to the internal excitations due to static transmission errors, time-varying mesh stiffness and the generator back EMF. Full article
(This article belongs to the Section Engineering)
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Open AccessArticle Machine Learning-Based Sentiment Analysis for Twitter Accounts
Math. Comput. Appl. 2018, 23(1), 11; https://doi.org/10.3390/mca23010011
Received: 16 January 2018 / Revised: 23 February 2018 / Accepted: 24 February 2018 / Published: 27 February 2018
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Abstract
Growth in the area of opinion mining and sentiment analysis has been rapid and aims to explore the opinions or text present on different platforms of social media through machine-learning techniques with sentiment, subjectivity analysis or polarity calculations. Despite the use of various
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Growth in the area of opinion mining and sentiment analysis has been rapid and aims to explore the opinions or text present on different platforms of social media through machine-learning techniques with sentiment, subjectivity analysis or polarity calculations. Despite the use of various machine-learning techniques and tools for sentiment analysis during elections, there is a dire need for a state-of-the-art approach. To deal with these challenges, the contribution of this paper includes the adoption of a hybrid approach that involves a sentiment analyzer that includes machine learning. Moreover, this paper also provides a comparison of techniques of sentiment analysis in the analysis of political views by applying supervised machine-learning algorithms such as Naïve Bayes and support vector machines (SVM). Full article
(This article belongs to the Special Issue Applied Modern Mathematics in Complex Networks)
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Open AccessArticle Heavy Ball Restarted CMRH Methods for Linear Systems
Math. Comput. Appl. 2018, 23(1), 10; https://doi.org/10.3390/mca23010010
Received: 1 February 2018 / Revised: 17 February 2018 / Accepted: 23 February 2018 / Published: 25 February 2018
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Abstract
The restarted CMRH method (changing minimal residual method based on the Hessenberg process) using fewer operations and storage is an alternative method to the restarted generalized minimal residual method (GMRES) method for linear systems. However, the traditional restarted CMRH method, which completely ignores
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The restarted CMRH method (changing minimal residual method based on the Hessenberg process) using fewer operations and storage is an alternative method to the restarted generalized minimal residual method (GMRES) method for linear systems. However, the traditional restarted CMRH method, which completely ignores the history information in the previous cycles, presents a slow speed of convergence. In this paper, we propose a heavy ball restarted CMRH method to remedy the slow convergence by bringing the previous approximation into the current search subspace. Numerical examples illustrate the effectiveness of the heavy ball restarted CMRH method. Full article
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Open AccessArticle Estimation Parameter of R = P(Y < X) for Length-Biased Weighted Lomax Distributions in the Presence of Outliers
Math. Comput. Appl. 2018, 23(1), 9; https://doi.org/10.3390/mca23010009
Received: 22 November 2017 / Revised: 13 February 2018 / Accepted: 14 February 2018 / Published: 16 February 2018
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Abstract
The concept of length-biased distribution is applied in expending proper models for lifetime data. The length-biased distribution is a special case of well-known weighted distribution. In this article, we introduce a length-biased weighted Lomax distribution (LBWLD) with k presence of outliers and estimate
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The concept of length-biased distribution is applied in expending proper models for lifetime data. The length-biased distribution is a special case of well-known weighted distribution. In this article, we introduce a length-biased weighted Lomax distribution (LBWLD) with k presence of outliers and estimate the parameter of R = P(Y < X) when the random variables X and Y are independent and have LBWLD in presence of outliers and without outliers, respectively. The bias and mean square error (MSE) of the estimator are examined with simulations of numerical and bootstrap resampling. Analysis of a real data set is considered for illustrative purposes. Full article
Open AccessFeature PaperArticle An Algorithmic Comparison of the Hyper-Reduction and the Discrete Empirical Interpolation Method for a Nonlinear Thermal Problem
Math. Comput. Appl. 2018, 23(1), 8; https://doi.org/10.3390/mca23010008
Received: 19 December 2017 / Revised: 2 February 2018 / Accepted: 7 February 2018 / Published: 13 February 2018
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Abstract
A novel algorithmic discussion of the methodological and numerical differences of competing parametric model reduction techniques for nonlinear problems is presented. First, the Galerkin reduced basis (RB) formulation is presented, which fails at providing significant gains with respect to the computational efficiency for
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A novel algorithmic discussion of the methodological and numerical differences of competing parametric model reduction techniques for nonlinear problems is presented. First, the Galerkin reduced basis (RB) formulation is presented, which fails at providing significant gains with respect to the computational efficiency for nonlinear problems. Renowned methods for the reduction of the computing time of nonlinear reduced order models are the Hyper-Reduction and the (Discrete) Empirical Interpolation Method (EIM, DEIM). An algorithmic description and a methodological comparison of both methods are provided. The accuracy of the predictions of the hyper-reduced model and the (D)EIM in comparison to the Galerkin RB is investigated. All three approaches are applied to a simple uncertainty quantification of a planar nonlinear thermal conduction problem. The results are compared to computationally intense finite element simulations. Full article
(This article belongs to the Section Engineering)
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Open AccessArticle Bifurcation and Chaos in Real Dynamics of a Two-Parameter Family Arising from Generating Function of Generalized Apostol-Type Polynomials
Math. Comput. Appl. 2018, 23(1), 7; https://doi.org/10.3390/mca23010007
Received: 13 January 2018 / Revised: 30 January 2018 / Accepted: 1 February 2018 / Published: 3 February 2018
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Abstract
The aim of this paper is to investigate the bifurcation and chaotic behaviour in the two-parameter family of transcendental functions fλ,n(x)=λx(ex+1)n, λ>0, x
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The aim of this paper is to investigate the bifurcation and chaotic behaviour in the two-parameter family of transcendental functions f λ , n ( x ) = λ x ( e x + 1 ) n , λ > 0 , x R , n N \ { 1 } which arises from the generating function of the generalized Apostol-type polynomials. The existence of the real fixed points of f λ , n ( x ) and their stability are studied analytically and the periodic points of f λ , n ( x ) are computed numerically. The bifurcation diagrams and Lyapunov exponents are simulated; these demonstrate chaotic behaviour in the dynamical system of the function f λ , n ( x ) for certain ranges of parameter λ . Full article
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Open AccessArticle Novel Spreadsheet Direct Method for Optimal Control Problems
Math. Comput. Appl. 2018, 23(1), 6; https://doi.org/10.3390/mca23010006
Received: 26 December 2017 / Revised: 22 January 2018 / Accepted: 23 January 2018 / Published: 25 January 2018
Cited by 3 | PDF Full-text (5706 KB) | HTML Full-text | XML Full-text | Supplementary Files
Abstract
We devise a simple yet highly effective technique for solving general optimal control problems in Excel spreadsheets. The technique exploits Excel’s native nonlinear programming (NLP) Solver Command, in conjunction with two calculus worksheet functions, namely, an initial value problem solver and a discrete
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We devise a simple yet highly effective technique for solving general optimal control problems in Excel spreadsheets. The technique exploits Excel’s native nonlinear programming (NLP) Solver Command, in conjunction with two calculus worksheet functions, namely, an initial value problem solver and a discrete data integrator, in a direct solution paradigm adapted to the spreadsheet. The technique is tested on several highly nonlinear constrained multivariable control problems with remarkable results in terms of reliability, consistency with pseudo-spectral reported answers, and computing times in the order of seconds. The technique requires no more than defining a few analogous formulas to the problem mathematical equations using basic spreadsheet operations, and no programming skills are needed. It introduces an alternative, simpler tool for solving optimal control problems in social and natural science disciplines. Full article
(This article belongs to the Special Issue Optimization in Control Applications)
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Open AccessArticle Solution of Fuzzy Differential Equations Using Fuzzy Sumudu Transforms
Math. Comput. Appl. 2018, 23(1), 5; https://doi.org/10.3390/mca23010005
Received: 15 December 2017 / Revised: 16 January 2018 / Accepted: 16 January 2018 / Published: 17 January 2018
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Abstract
The uncertain nonlinear systems can be modeled with fuzzy differential equations (FDEs) and the solutions of these equations are applied to analyze many engineering problems. However, it is very difficult to obtain solutions of FDEs. In this paper, the solutions of FDEs are
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The uncertain nonlinear systems can be modeled with fuzzy differential equations (FDEs) and the solutions of these equations are applied to analyze many engineering problems. However, it is very difficult to obtain solutions of FDEs. In this paper, the solutions of FDEs are approximated by utilizing the fuzzy Sumudu transform (FST) method. Significant theorems are suggested in order to explain the properties of FST. The proposed method is validated with three real examples. Full article
(This article belongs to the Special Issue Optimization in Control Applications)
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Open AccessArticle Logic Operators on Delta-Sigma Bit-Streams
Math. Comput. Appl. 2018, 23(1), 4; https://doi.org/10.3390/mca23010004
Received: 12 December 2017 / Revised: 11 January 2018 / Accepted: 15 January 2018 / Published: 17 January 2018
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Abstract
The fundamental logic operations NOT, OR, AND, and XOR processing bit-streams of ΔΣ-modulators are discussed herein. The resulting bit-streams are evaluated on the basis of their mean values and their standard deviations. Mathematical expressions are presented for their mean values; i.e.,
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The fundamental logic operations NOT, OR, AND, and XOR processing bit-streams of Δ Σ -modulators are discussed herein. The resulting bit-streams are evaluated on the basis of their mean values and their standard deviations. Mathematical expressions are presented for their mean values; i.e., the logic function XOR results in the negative multiplication of two bipolar bit-streams, and the logic function AND results in the multiplication of two unipolar bit-streams. As the results are valid for bit-streams with independent high-frequency components, the normed cross-product is utilized for evaluation of the independence of the high-frequency components. In order to achieve a high independence between the input bit-streams, representing the same value, the quantization noise is affected. Multiple strategies are examined and Δ Σ -modulators with different designs are chosen as the best-suited solution. The operations are evaluated on a testbench. Full article
(This article belongs to the Section Engineering)
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Open AccessEditorial Acknowledgement to Reviewers of MCA in 2017
Math. Comput. Appl. 2018, 23(1), 3; https://doi.org/10.3390/mca23010003
Received: 16 January 2018 / Revised: 16 January 2018 / Accepted: 16 January 2018 / Published: 16 January 2018
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Abstract
Peer review is an essential part in the publication process, ensuring that MCA (Mathematical and Computational Applications) maintains high quality standards for its published papers.[...] Full article
Open AccessArticle Mathematical Modeling of Drag Coefficient Reduction in Circular Cylinder Using Two Passive Controls at Re = 1000
Math. Comput. Appl. 2018, 23(1), 2; https://doi.org/10.3390/mca23010002
Received: 2 December 2017 / Revised: 20 December 2017 / Accepted: 11 January 2018 / Published: 16 January 2018
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Abstract
One of the many ways to reduce drag force is by adding a small object called passive control. Two passive controls will be placed in front and at the rear of the main object. The main object used is a circular cylinder, and
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One of the many ways to reduce drag force is by adding a small object called passive control. Two passive controls will be placed in front and at the rear of the main object. The main object used is a circular cylinder, and the passive controls used are the Type-I cylinder in the front and an elliptical cylinder at the rear of the main object. The distances between the main object and the passive controls are varied. The Reynolds number used is 1000. The effective distance between the main object and the passive controls is analyzed by using the mathematical model so that the drag coefficient on the main object is compared with the simulated one. Full article
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Open AccessFeature PaperArticle A Fast Recommender System for Cold User Using Categorized Items
Math. Comput. Appl. 2018, 23(1), 1; https://doi.org/10.3390/mca23010001
Received: 17 December 2017 / Revised: 8 January 2018 / Accepted: 14 January 2018 / Published: 15 January 2018
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Abstract
In recent years, recommender systems (RS) provide a considerable progress to users. RSs reduce the cost of a user’s time in order to reach to desired results faster. The main issue of RSs is the presence of cold users which are less active
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In recent years, recommender systems (RS) provide a considerable progress to users. RSs reduce the cost of a user’s time in order to reach to desired results faster. The main issue of RSs is the presence of cold users which are less active and their preferences are more difficult to detect. The aim of this study is to provide a new way to improve recall and precision in recommender systems for cold users. According to the available categories of items, prioritization of the proposed items is improved and then presented to the cold user. The obtained results show that in addition to increased speed of processing, recall and precision have an acceptable improvement. Full article
(This article belongs to the Special Issue Applied Modern Mathematics in Complex Networks)
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