Mathematical and Computational Applications

237 KiB

Open AccessArticle

Fixed Order Controller for Schur Stability

by Taner Büyükköroğlu

Math. Comput. Appl. 2016, 21(2), 25; https://doi.org/10.3390/mca21020025 - 20 Jun 2016

Cited by 1 | Viewed by 3390

If the characteristic polynomial of a discrete-time system has all its roots in the open unit disc of the complex plane, the system is called Schur stable. In this paper, the Schur stabilization problem of closed loop discrete-time system by affine compensator is [...] Read more.

If the characteristic polynomial of a discrete-time system has all its roots in the open unit disc of the complex plane, the system is called Schur stable. In this paper, the Schur stabilization problem of closed loop discrete-time system by affine compensator is considered. For this purpose, the distance function between the Schur stability region and the affine controller subset is investigated. Full article

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2001 KiB

Open AccessArticle

A Note on Some Solutions of Copper-Water (Cu-Water) Nanofluids in a Channel with Slowly Expanding or Contracting Walls with Heat Transfer

by Jawad Raza, Azizah Mohd Rohni and Zurni Omar

Math. Comput. Appl. 2016, 21(2), 24; https://doi.org/10.3390/mca21020024 - 16 Jun 2016

Cited by 20 | Viewed by 4433

Abstract

A study has been carried out to examine the occurrence of multiple solutions for Copper-Water nanofluids flows in a porous channel with slowly expanding and contracting walls. The governing equations are first transformed to similarity equations by using similarity transformation. The resulting equations [...] Read more.

A study has been carried out to examine the occurrence of multiple solutions for Copper-Water nanofluids flows in a porous channel with slowly expanding and contracting walls. The governing equations are first transformed to similarity equations by using similarity transformation. The resulting equations are then solved numerically by using the shooting method. The effects of wall expansion ratio and solid volume fraction on velocity and temperature profile have been studied. Numerical results are presented graphically for the variations of different physical parameters. The study reveals that triple solutions exist only for the case of suction. Full article

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751 KiB

Open AccessArticle

A Recommendation System for Execution Plans Using Machine Learning

by Jihad Zahir and Abderrahim El Qadi

Math. Comput. Appl. 2016, 21(2), 23; https://doi.org/10.3390/mca21020023 - 15 Jun 2016

Cited by 12 | Viewed by 5253

Abstract

Generating execution plans is a costly operation for the DataBase Management System (DBMS). An interesting alternative to this operation is to reuse the old execution plans, that were already generated by the optimizer for past queries, to execute new queries. In this paper, [...] Read more.

Generating execution plans is a costly operation for the DataBase Management System (DBMS). An interesting alternative to this operation is to reuse the old execution plans, that were already generated by the optimizer for past queries, to execute new queries. In this paper, we present an approach for execution plan recommendation in two phases. We firstly propose a textual representation of our SQL queries and use it to build a Features Extractor module. Then, we present a straightforward solution to identify query similarity.This solution relies only on the comparison of the SQL statements. Next, we show how to build an improved solution enabled by machine learning techniques. The improved version takes into account the features of the queries’ execution plans. By comparing three machine learning algorithms, we find that the improved solution using Classification Based on Associative Rules (CAR) identifies similarity in

91 %

of the cases. Full article

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4140 KiB

Open AccessArticle

An Improved Interval-Valued Hesitant Fuzzy Multi-Criteria Group Decision-Making Method and Applications

by Zhenhua Ding and Yingyu Wu

Math. Comput. Appl. 2016, 21(2), 22; https://doi.org/10.3390/mca21020022 - 8 Jun 2016

Cited by 10 | Viewed by 3723

Abstract

The Bonferroni mean (BM) can be used in situations where the aggregated arguments are correlated. BM is very useful for solving decision-making problems. For describing fuzziness and vagueness more accurately, the interval-valued hesitant fuzzy set (IVHFS), which is a generalization of the hesitant [...] Read more.

The Bonferroni mean (BM) can be used in situations where the aggregated arguments are correlated. BM is very useful for solving decision-making problems. For describing fuzziness and vagueness more accurately, the interval-valued hesitant fuzzy set (IVHFS), which is a generalization of the hesitant fuzzy set (HFS), can be used to describe the membership degrees with interval numbers. The aim of this paper is to propose the interval-valued hesitant fuzzy Bonferroni mean (IVHFBM) for aggregating interval-valued hesitant fuzzy information. Furthermore, the weighted form of IVHFBM (IVHFWBM) is forwarded and, hereby, a multi-criteria group decision-making (MCGDM) method is established. A case study on the problem of evaluating research funding applications in China is analyzed. A comparison between the proposed method and existing ones demonstrates its practicability. Full article

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670 KiB

Open AccessArticle

Holographic Tachyon in Fractal Geometry

by Mustafa Salti and Oktay Aydogdu

Math. Comput. Appl. 2016, 21(2), 21; https://doi.org/10.3390/mca21020021 - 31 May 2016

Cited by 2 | Viewed by 4064

Abstract

The search of a logical quantum gravity theory is one of the noteworthy issues in modern theoretical physics. It is known that most of the quantum gravity theories describe our universe as a dimensional flow. From this point of view, one can investigate [...] Read more.

The search of a logical quantum gravity theory is one of the noteworthy issues in modern theoretical physics. It is known that most of the quantum gravity theories describe our universe as a dimensional flow. From this point of view, one can investigate whether and how these attractive properties are related with the ultraviolet-divergence problem. These important points motivated us to discuss the reconstruction of a scalar field problem in the fractal theory which is a well-known quantum theory of gravity. Making use of time-like fractal model and considering the holographic description of galactic dark energy, we implement a correspondence between the tachyon model of galactic dark energy effect and holographic energy. Such a connection gives us an opportunity to redefine the fractal dynamics of selected scalar field representation by considering the time-evolution of holographic energy. Full article

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901 KiB

Open AccessArticle

Predictive Abilities of Bayesian Regularization and Levenberg–Marquardt Algorithms in Artificial Neural Networks: A Comparative Empirical Study on Social Data

by Murat Kayri

Math. Comput. Appl. 2016, 21(2), 20; https://doi.org/10.3390/mca21020020 - 24 May 2016

Cited by 353 | Viewed by 14081

Abstract

The objective of this study is to compare the predictive ability of Bayesian regularization with Levenberg–Marquardt Artificial Neural Networks. To examine the best architecture of neural networks, the model was tested with one-, two-, three-, four-, and five-neuron architectures, respectively. MATLAB (2011a) was [...] Read more.

The objective of this study is to compare the predictive ability of Bayesian regularization with Levenberg–Marquardt Artificial Neural Networks. To examine the best architecture of neural networks, the model was tested with one-, two-, three-, four-, and five-neuron architectures, respectively. MATLAB (2011a) was used for analyzing the Bayesian regularization and Levenberg–Marquardt learning algorithms. It is concluded that the Bayesian regularization training algorithm shows better performance than the Levenberg–Marquardt algorithm. The advantage of a Bayesian regularization artificial neural network is its ability to reveal potentially complex relationships, meaning it can be used in quantitative studies to provide a robust model. Full article

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206 KiB

Open AccessArticle

A Multiple Attribute Decision-Making Method Based on Exponential Fuzzy Numbers

by Sha Fu and Guo-bing Fan

Math. Comput. Appl. 2016, 21(2), 19; https://doi.org/10.3390/mca21020019 - 21 May 2016

Cited by 2 | Viewed by 3438

Abstract

Regarding the multi-attribute decision-making problem where both the attribute value and attribute weight of a scheme are exponential fuzzy numbers, this paper proposes a fuzzy multiple attribute decision-making method based on exponential fuzzy numbers. The expected value and variance of the exponential fuzzy [...] Read more.

Regarding the multi-attribute decision-making problem where both the attribute value and attribute weight of a scheme are exponential fuzzy numbers, this paper proposes a fuzzy multiple attribute decision-making method based on exponential fuzzy numbers. The expected value and variance of the exponential fuzzy number were calculated according to the definitions of expectation and variance in probability theory. By comprehensively considering factors such as expected value, variance, and attitude preference of the decision-maker, this paper gave the score function of the exponential fuzzy number, based on which the accurate attribute weight can be determined. Subsequently, based on the distance measure between exponential fuzzy numbers, the distance was calculated between each scheme and the positive/negative ideal scheme, respectively, and the relative closeness of each scheme was solved; based on this, sorting and prioritizing were conducted. Finally, the feasibility and effectiveness of the proposed method were verified through case analysis. Full article

1193 KiB

Open AccessArticle

A Class of Cubic Trigonometric Automatic Interpolation Curves and Surfaces with Parameters

by Juncheng Li

Math. Comput. Appl. 2016, 21(2), 18; https://doi.org/10.3390/mca21020018 - 20 May 2016

Cited by 6 | Viewed by 3918

Abstract

This paper presents the cubic trigonometric interpolation curves with two parameters generated over the space {1, sint, cost, sin²t, sin³t, cos³t}. The new curves can not only automatically interpolate the [...] Read more.

This paper presents the cubic trigonometric interpolation curves with two parameters generated over the space {1, sint, cost, sin²t, sin³t, cos³t}. The new curves can not only automatically interpolate the given data points without solving equation systems, but are also C² and adjust their shape by altering values of the two parameters. The optimal interpolation curves can be determined by an energy optimization model. The corresponding interpolation surfaces have characteristics similar to the new curves. Full article

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214 KiB

Open AccessArticle

Three-Parameter Interval Grey Number Multi-Attribute Decision Making Method Based on Information Entropy

by Sha Fu

Math. Comput. Appl. 2016, 21(2), 17; https://doi.org/10.3390/mca21020017 - 11 May 2016

Cited by 9 | Viewed by 3503

Abstract

Aimed at the situation that the plan attribute value is a three-parameter interval grey number and that attribute weight is uncertain, a three-parameter interval grey number multi-attribute decision making method based on information entropy is proposed. In this study, we combine the three-parameter [...] Read more.

Aimed at the situation that the plan attribute value is a three-parameter interval grey number and that attribute weight is uncertain, a three-parameter interval grey number multi-attribute decision making method based on information entropy is proposed. In this study, we combine the three-parameter interval grey number decision-making problem with information entropy, build the distance entropy model of the three-parameter interval grey number, and provide a solution to the empowerment problem of the three-parameter interval grey number in grey decision-making problems. On this basis, we build the uncertainty decision making framework based on Technique for Order Preference by Similarity to Ideal Solution (TOPSIS) thinking and obtain the comprehensive distances of plans from positive and negative ideal solutions through calculation. We thus determine the closeness, and, based on this value, organize these plans. Finally, we verify the feasibility and effectiveness of the proposed methods through case analysis. Full article

515 KiB

Open AccessArticle

Finite Volume Method for the Relativistic Burgers Model on a (1+1)-Dimensional de Sitter Spacetime

by Tuba Ceylan and Baver Okutmustur

Math. Comput. Appl. 2016, 21(2), 16; https://doi.org/10.3390/mca21020016 - 10 May 2016

Cited by 2 | Viewed by 3561

Abstract

Several generalizations of the relativistic models of Burgers equations have recently been established and developed on different spacetime geometries. In this work, we take into account the de Sitter spacetime geometry, introduce our relativistic model by a technique based on the vanishing pressure [...] Read more.

Several generalizations of the relativistic models of Burgers equations have recently been established and developed on different spacetime geometries. In this work, we take into account the de Sitter spacetime geometry, introduce our relativistic model by a technique based on the vanishing pressure Euler equations of relativistic compressible fluids on a (1+1)-dimensional background and construct a second order Godunov type finite volume scheme to examine numerical experiments within an analysis of the cosmological constant. Numerical results demonstrate the efficiency of the method for solutions containing shock and rarefaction waves. Full article

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1283 KiB

Open AccessArticle

A New Algorithm for the Numerical Solution of Telegraph Equations by Using Fibonacci Polynomials

by Ayşe Kurt Bahşı and Salih Yalçınbaş

Math. Comput. Appl. 2016, 21(2), 15; https://doi.org/10.3390/mca21020015 - 10 May 2016

Cited by 6 | Viewed by 4374

Abstract

In this study, we present a numerical scheme to solve the telegraph equation by using Fibonacci polynomials. This method is based on the Fibonacci collocation method which transforms the equation into a matrix equation, and the unknown of this equation is a Fibonacci [...] Read more.

In this study, we present a numerical scheme to solve the telegraph equation by using Fibonacci polynomials. This method is based on the Fibonacci collocation method which transforms the equation into a matrix equation, and the unknown of this equation is a Fibonacci coefficients matrix. Some numerical examples with comparisons are included to demonstrate the validity and applicability of the proposed method. The results show the efficiency and accuracy of this paper. Full article

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216 KiB

Open AccessArticle

Geometric Properties of Normalized Wright Functions

by Nizami Mustafa

Math. Comput. Appl. 2016, 21(2), 14; https://doi.org/10.3390/mca21020014 - 4 May 2016

Cited by 12 | Viewed by 3541

Abstract

The purpose of the present paper is to investigate some characterizations for the Wright functions to be in the subclasses [...] Read more.

The purpose of the present paper is to investigate some characterizations for the Wright functions to be in the subclasses

S^{*} (α, β)

and

C (α, β) (α, β \in [0, 1))

. Several sufficient conditions are obtained for the normalized Wright functions to be in these classes. Results obtained in this paper are new and their usefulness is put forth by several corollaries. Full article

1884 KiB

Open AccessArticle

Design of a Parameter-Dependent Optimal Vibration Control of a Non-Linear Vehicle Suspension System

by Hakan Yazici

Math. Comput. Appl. 2016, 21(2), 13; https://doi.org/10.3390/mca21020013 - 27 Apr 2016

Cited by 9 | Viewed by 5157

Abstract

This paper is concerned with the design of a parameter-dependent optimal controller for an active vibration attenuation problem of a non-linear vehicle system. A five degree-of-freedom vertical vibration model having an integrated vehicle seat, a non-linear vehicle suspension system, and a seated human [...] Read more.

This paper is concerned with the design of a parameter-dependent optimal controller for an active vibration attenuation problem of a non-linear vehicle system. A five degree-of-freedom vertical vibration model having an integrated vehicle seat, a non-linear vehicle suspension system, and a seated human body is presented to analyze ride comfort and safety requirements under different types of road disturbances. In the suspension system, the non-linear parts of spring and damper dynamics are considered as scheduling parameters, which are measurable and available for feedback. Then, a parameter-dependent optimal state-feedback controller design that minimizes L₂ gain from disturbance to performance output for a linear parameter-varying (LPV) system is presented with linear matrix inequality (LMI) constraints. Finally, numerical simulations are conducted to demonstrate the effectiveness of the proposed controller. Full article

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411 KiB

Open AccessArticle

Direct Solution of Second-Order Ordinary Differential Equation Using a Single-Step Hybrid Block Method of Order Five

by Ra’ft Abdelrahim and Zurni Omar

Math. Comput. Appl. 2016, 21(2), 12; https://doi.org/10.3390/mca21020012 - 12 Apr 2016

Cited by 16 | Viewed by 3938

Abstract

This paper proposes a new hybrid block method of order five for solving second-order ordinary differential equations directly. The method is developed using interpolation and collocation techniques. The use of the power series approximate solution as an interpolation polynomial and its second derivative [...] Read more.

This paper proposes a new hybrid block method of order five for solving second-order ordinary differential equations directly. The method is developed using interpolation and collocation techniques. The use of the power series approximate solution as an interpolation polynomial and its second derivative as a collocation equation is considered in deriving the method. Properties of the method such as zero stability, order, consistency, convergence and region of absolute stability are investigated. The new method is then applied to solve the system of second-order ordinary differential equations and the accuracy is better when compared with the existing methods in terms of error. Full article

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1702 KiB

Open AccessArticle

New Exact Solutions of the System of Equations for the Ion Sound and Langmuir Waves by ETEM

by Seyma Tuluce Demiray and Hasan Bulut

Math. Comput. Appl. 2016, 21(2), 11; https://doi.org/10.3390/mca21020011 - 2 Apr 2016

Cited by 18 | Viewed by 3414

Abstract

This manuscript focuses attention on new exact solutions of the system of equations for the ion sound wave under the action of the ponderomotive force due to high-frequency field and for the Langmuir wave. The extended trial equation method (ETEM), which is one [...] Read more.

This manuscript focuses attention on new exact solutions of the system of equations for the ion sound wave under the action of the ponderomotive force due to high-frequency field and for the Langmuir wave. The extended trial equation method (ETEM), which is one of the analytical methods, has been handled for finding exact solutions of the system of equations for the ion sound wave and the Langmuir wave. By using this method, exact solutions including the rational function solution, traveling wave solution, soliton solution, Jacobi elliptic function solution, hyperbolic function solution and periodic wave solution of this system of equations have been obtained. In addition, by using Mathematica Release 9, some graphical simulations were done to see the behavior of these solutions. Full article

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300 KiB

Open AccessArticle

Positive Almost Periodic Solutions for a Delayed Predator–Prey Model with Hassell-Varley Type Functional Response

by Tianwei Zhang, Liyan Pang and Yongzhi Liao

Math. Comput. Appl. 2016, 21(2), 10; https://doi.org/10.3390/mca21020010 - 1 Apr 2016

Cited by 1 | Viewed by 4126

Abstract

By means of a fixed point theorem of coincidence degree theory, sufficient conditions are established for the existence of a positive almost periodic solution to a kind of delayed predator–prey model with Hassell-Varley type functional response. The method used in this paper offers [...] Read more.

By means of a fixed point theorem of coincidence degree theory, sufficient conditions are established for the existence of a positive almost periodic solution to a kind of delayed predator–prey model with Hassell-Varley type functional response. The method used in this paper offers a possible means to study the existence of positive almost periodic solutions to the models in biological populations. Finally, an example as well as numerical simulations are given to illustrate the feasibility and effectiveness of our results. Full article

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227 KiB

Open AccessArticle

The Regularization-Homotopy Method for the Two-Dimensional Fredholm Integral Equations of the First Kind

by Ahmet Altürk

Math. Comput. Appl. 2016, 21(2), 9; https://doi.org/10.3390/mca21020009 - 30 Mar 2016

Cited by 13 | Viewed by 3122

Abstract

In this work, we consider two-dimensional linear and nonlinear Fredholm integral equations of the first kind. The combination of the regularization method and the homotopy perturbation method, or shortly, the regularization-homotopy method is used to find a solution to the equation. The application [...] Read more.

In this work, we consider two-dimensional linear and nonlinear Fredholm integral equations of the first kind. The combination of the regularization method and the homotopy perturbation method, or shortly, the regularization-homotopy method is used to find a solution to the equation. The application of this method is based upon converting the first kind of equation to the second kind by applying the regularization method. Then the homotopy perturbation method is employed to the resulting second kind of equation to obtain a solution. A few examples including linear and nonlinear equations are provided to show the validity and applicability of this approach. Full article

1718 KiB

Open AccessArticle

New Analytic Solutions for the (N + 1)-Dimensional Generalized Boussinesq Equation

by Baojian Hong and Dianchen Lu

Math. Comput. Appl. 2016, 21(2), 8; https://doi.org/10.3390/mca21020008 - 25 Mar 2016

Viewed by 3024

Abstract

In this paper, the generalized Jacobi elliptic functions expansion method with computerized symbolic computation are employed to investigate explicitly analytic solutions of the (N + 1)-dimensional generalized Boussinesq equation. The exact solutions to the equation are constructed analytically under certain circumstances, some [...] Read more.

In this paper, the generalized Jacobi elliptic functions expansion method with computerized symbolic computation are employed to investigate explicitly analytic solutions of the (N + 1)-dimensional generalized Boussinesq equation. The exact solutions to the equation are constructed analytically under certain circumstances, some of these solutions are degenerated to soliton-like solutions and trigonometric function solutions in the limit cases when the modulus of the Jacobi elliptic function solutions tends to 0 and 1, which shows that the applied method is more powerful and will be used in further works to establish more entirely new exact solutions for other kinds of higher-dimensional nonlinear partial differential equations in mathematical physics. Full article

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984 KiB

Open AccessArticle

Estimating Variances in Weighted Least-Squares Estimation of Distributional Parameters

by Yeliz Mert Kantar

Math. Comput. Appl. 2016, 21(2), 7; https://doi.org/10.3390/mca21020007 - 25 Mar 2016

Cited by 6 | Viewed by 4386

Abstract

Many estimation methods have been proposed for the parameters of statistical distribution. The least squares estimation method, based on a regression model or probability plot, is frequently used by practitioners since its implementation procedure is extremely simple in complete and censoring data cases. [...] Read more.

Many estimation methods have been proposed for the parameters of statistical distribution. The least squares estimation method, based on a regression model or probability plot, is frequently used by practitioners since its implementation procedure is extremely simple in complete and censoring data cases. However, in the procedure, heteroscedasticity is present in the used regression model and, thus, the weighted least squares estimation or alternative methods should be used. This study proposes an alternative method for the estimation of variance, based on a dependent variable generated via simulation, in order to estimate distributional parameters using the weighted least squares method. In the estimation procedure, the variances or weights are expressed as a function of the rank of the data point in the sample. The considered weighted estimation method is evaluated for the shape parameter of the log-logistic and Weibull distributions via a simulation study. It is found that the considered weighted estimation method shows better performance than the maximum likelihood, least-squares, and certain other alternative estimation approaches in terms of mean square error for most of the considered sample sizes. In addition, a real-life example from hydrology is provided to demonstrate the performance of the considered method. Full article

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9526 KiB

Open AccessArticle

New Complex Hyperbolic Function Solutions for the (2+1)-Dimensional Dispersive Long Water–Wave System

by Hasan Bulut and Haci Mehmet Baskonus

Math. Comput. Appl. 2016, 21(2), 6; https://doi.org/10.3390/mca21020006 - 24 Mar 2016

Cited by 32 | Viewed by 3873

Abstract

In this paper, new algorithms called the “Modified exp(−Ω)-expansion function method” and “Improved Bernoulli sub-equation function method” have been proposed. The first algorithm is based on the exp(−Ω(ξ))-expansion method; the latter is based on the Bernoulli sub-Ordinary Differential Equation method. The methods proposed [...] Read more.

In this paper, new algorithms called the “Modified exp(−Ω)-expansion function method” and “Improved Bernoulli sub-equation function method” have been proposed. The first algorithm is based on the exp(−Ω(ξ))-expansion method; the latter is based on the Bernoulli sub-Ordinary Differential Equation method. The methods proposed have been expressed comprehensively in this manuscript. The analytical solutions and application results are presented by drawing the two- and three-dimensional surfaces of solutions such as hyperbolic, complex, trigonometric and exponential solutions for the (2+1)-dimensional dispersive long water–wave system. Finally, a conclusion has been presented by mentioning the important discoveries in this manuscript. Full article

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Math. Comput. Appl., Volume 21, Issue 2 (June 2016) – 20 articles

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