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Math. Comput. Appl., Volume 22, Issue 1 (March 2017)

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Editorial

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Open AccessEditorial Acknowledgement to Reviewers of MCA in 2016
Math. Comput. Appl. 2017, 22(1), 6; doi:10.3390/mca22010006
Received: 12 January 2017 / Accepted: 12 January 2017 / Published: 12 January 2017
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Abstract The editors of MCA would like to express their sincere gratitude to the following reviewers for assessing manuscripts in 2016.[...] Full article

Research

Jump to: Editorial

Open AccessArticle A Sparse Representation Algorithm for Effective Photograph Retrieval
Math. Comput. Appl. 2017, 22(1), 8; doi:10.3390/mca22010008
Received: 17 July 2016 / Revised: 5 December 2016 / Accepted: 11 January 2017 / Published: 18 January 2017
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Abstract
Searching through information based on a photograph, which may contain graphics and images, has become a popular trend, such as in electronic books, journals, and products. Although many context-based methods have been proposed to retrieve images, most work focuses on selecting appropriate features
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Searching through information based on a photograph, which may contain graphics and images, has become a popular trend, such as in electronic books, journals, and products. Although many context-based methods have been proposed to retrieve images, most work focuses on selecting appropriate features for different objects. In the present study, we apply sparse representation to simultaneously retrieve image and graphics from a photograph. The sparse vector can be regarded as the similarity between the query photograph and dataset. The image with the largest entry (or several largest entries) can be assigned as the retrieved result. In the sparse representation framework, the common image features are used. Experimental results demonstrate that if the similarity vector in photograph retrieval is sparse, feature extraction is no longer critical. Compared with similar works in photograph retrieval, the proposed method has better retrieval accuracy. Full article
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Open AccessArticle Robust Object Tracking in Infrared Video via Adaptive Weighted Patches
Math. Comput. Appl. 2017, 22(1), 3; doi:10.3390/mca22010003
Received: 12 October 2016 / Revised: 7 December 2016 / Accepted: 23 December 2016 / Published: 30 December 2016
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Abstract
With the quick development of computer and electronic techniques, infrared sensor-based object tracking has become a hot research topic in recent years. However, infrared object tracking is still a challenging task due to low resolution, lack of representing information, and occlusion. In this
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With the quick development of computer and electronic techniques, infrared sensor-based object tracking has become a hot research topic in recent years. However, infrared object tracking is still a challenging task due to low resolution, lack of representing information, and occlusion. In this work, we present an adaptive weighted patch-based infrared object tracking scheme. First, the candidate local region is divided into non-overlapping sub regions, and a set of belief weights is set on these patches. After this, a particle filtering-based infrared object tracking system is realized. In the last, the belief weight of each patch is evaluated based on the linear discriminative analysis (LDA) and particle sampling scheme. Experimental results on challenging infrared sequences show that the proposed algorithm can effectively locate the tracking object. Full article
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Open AccessArticle Spatiotemporal Dynamics of a Delayed and Diffusive Viral Infection Model with Logistic Growth
Math. Comput. Appl. 2017, 22(1), 7; doi:10.3390/mca22010007
Received: 28 October 2016 / Revised: 21 December 2016 / Accepted: 21 December 2016 / Published: 14 January 2017
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Abstract
Viruses have important influences on human health: they not only cause some common diseases, but also cause serious illnesses. Moreover, the conventional medicines usually fail to prevent or treat them, and viral infections are hard to treat because viruses live inside the body’s
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Viruses have important influences on human health: they not only cause some common diseases, but also cause serious illnesses. Moreover, the conventional medicines usually fail to prevent or treat them, and viral infections are hard to treat because viruses live inside the body’s cells. However, some mathematical models can help to understand the viral transmission mechanism and control viral diseases. In this paper, a delayed viral infection model with spatial diffusion and logistic growth is presented. The asymptotic stability of nonnegative uniform steady states is investigated by utilizing the linearized method and constructing the proper Lyapunov functional, respectively. The existence of Hopf bifurcation from the positive equilibrium point is established by analyzing the corresponding characteristic equation and the direction of bifurcation, and the properties of bifurcating periodic solutions are derived by the aid of the normal form theory for partial functional differential equations. Then, the cross-diffusion system is introduced. Furthermore, some numerical simulations are carried, out and discussions are given. Full article
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Open AccessArticle Global Modulus-Based Synchronous Multisplitting Multi-Parameters TOR Methods for Linear Complementarity Problems
Math. Comput. Appl. 2017, 22(1), 20; doi:10.3390/mca22010020
Received: 17 October 2016 / Revised: 25 January 2017 / Accepted: 27 January 2017 / Published: 21 February 2017
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Abstract
In 2013, Bai and Zhang constructed modulus-based synchronous multisplitting methods for linear complementarity problems and analyzed the corresponding convergence. In 2014, Zhang and Li studied the weaker convergence results based on linear complementarity problems. In 2008, Zhang et al. presented global relaxed non-stationary
[...] Read more.
In 2013, Bai and Zhang constructed modulus-based synchronous multisplitting methods for linear complementarity problems and analyzed the corresponding convergence. In 2014, Zhang and Li studied the weaker convergence results based on linear complementarity problems. In 2008, Zhang et al. presented global relaxed non-stationary multisplitting multi-parameter method by introducing some parameters. In this paper, we extend Bai and Zhang’s algorithms and analyze global modulus-based synchronous multisplitting multi-parameters TOR (two parameters overrelaxation) methods. Moverover, the convergence of the corresponding algorithm in this paper are given when the system matrix is an H + -matrix. Full article
(This article belongs to the Special Issue Information and Computational Science)
Open AccessArticle Design Optimization of the Lines of the Bulbous Bow of a Hull Based on Parametric Modeling and Computational Fluid Dynamics Calculation
Math. Comput. Appl. 2017, 22(1), 4; doi:10.3390/mca22010004
Received: 15 August 2016 / Revised: 17 December 2016 / Accepted: 23 December 2016 / Published: 16 January 2017
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Abstract
To reduce the ship wave-making resistance, the lines of the bulbous bow of a hull are optimized by an automatic optimization platform at the ship design stage. Parametric modeling was applied to the hull by using non-uniform rational basis spline (NURBS). The Rankine-source
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To reduce the ship wave-making resistance, the lines of the bulbous bow of a hull are optimized by an automatic optimization platform at the ship design stage. Parametric modeling was applied to the hull by using non-uniform rational basis spline (NURBS). The Rankine-source panel method was used to calculate the wave-making resistance. A hybrid optimization strategy was applied to achieve the optimization goal. A Ro-Ro ship was taken as an example to illustrate the optimization method adopted, with the objective to minimize the wave-making resistance. The optimization results show that wave-making resistance obviously reduces and the wave-shape of the near bow becomes gentle after the lines of the bulbous bow of the hull are optimized, which demonstrates the validity of the proposed optimization design strategy. Full article
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Open AccessArticle Optimal Hedging with Options and Futures against Price Risk and Background Risk
Math. Comput. Appl. 2017, 22(1), 5; doi:10.3390/mca22010005
Received: 21 October 2016 / Revised: 25 December 2016 / Accepted: 28 December 2016 / Published: 4 January 2017
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Abstract
On the condition that both futures and options exist in the markets for hedging, this paper examines the optimal hedging strategy under price risk and background risk. Compared with the previous research, which has studied options hedging against basis risk and production risk
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On the condition that both futures and options exist in the markets for hedging, this paper examines the optimal hedging strategy under price risk and background risk. Compared with the previous research, which has studied options hedging against basis risk and production risk being extended to options and futures hedging against price risk and background risk, we proposed a model and have taken the budget of buying options into consideration. The model is fairly general and some existing models are special cases of it. We firstly derive the necessary and sufficient conditions that guarantee the optimality of an under-hedge, a full-hedge and an over-hedge of futures for the risk-averse utility. Then, sufficient conditions are stipulated under which an over-hedge is optimal. Furthermore, we propose a program minimizing of tail conditional expectation (TCE), which is inherently equivalent to the risk measure of expected shortfall risk (ES) or the conditional VaR (CVaR) under the continuous-time framework. Finally, we find that ES, in our proposed model, is significantly smaller than the one in the model of options hedging only. Therefore, the results emphasize the need for combining futures hedging and options hedging, and it also shows that imposing background risk, whether it be additive or multiplicative, always has a great impact on the hedging efficiency. We also present some sensitivities of the relevant parameters to provide some suggestions for the investors. Full article
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Open AccessArticle Quasi-Interpolation Operators for Bivariate Quintic Spline Spaces and Their Applications
Math. Comput. Appl. 2017, 22(1), 10; doi:10.3390/mca22010010
Received: 10 October 2016 / Revised: 19 December 2016 / Accepted: 27 December 2016 / Published: 19 January 2017
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Abstract
Splines and quasi-interpolation operators are important both in approximation theory and applications. In this paper, we construct a family of quasi-interpolation operators for the bivariate quintic spline spaces S53(Δmn(2)). Moreover, the properties
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Splines and quasi-interpolation operators are important both in approximation theory and applications. In this paper, we construct a family of quasi-interpolation operators for the bivariate quintic spline spaces S 5 3 ( Δ m n ( 2 ) ) . Moreover, the properties of the proposed quasi-interpolation operators are studied, as well as its applications for solving the two-dimensional Burgers’ equation and image reconstruction. Some numerical examples show that these methods, which are easy to implement, provide accurate results. Full article
(This article belongs to the Special Issue Information and Computational Science)
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Open AccessArticle Analysis of Inflection and Singular Points on a Parametric Curve with a Shape Factor
Math. Comput. Appl. 2017, 22(1), 9; doi:10.3390/mca22010009
Received: 19 September 2016 / Revised: 25 December 2016 / Accepted: 11 January 2017 / Published: 19 January 2017
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Abstract
The features of a class of cubic curves with a shape factor are analyzed by means of the theory of envelope and topological mapping. The effects of the shape factor on the cubic curves are made clear. Necessary and sufficient conditions are derived
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The features of a class of cubic curves with a shape factor are analyzed by means of the theory of envelope and topological mapping. The effects of the shape factor on the cubic curves are made clear. Necessary and sufficient conditions are derived for the curve to have one or two inflection points, a loop or a cusp, or to be locally or globally convex. Those conditions are completely characterized by the relative position of the edge vectors of the control polygon and the shape factor. The results are summarized in a shape diagram, which is useful when the cubic parametric curves are used for geometric modeling. Furthermore, we discuss the influences of the shape factor on the shape diagram and the ability for adjusting the shape of the curve. Full article
(This article belongs to the Special Issue Information and Computational Science)
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Open AccessArticle Optimization of Setting Take-Profit Levels for Derivative Trading
Math. Comput. Appl. 2017, 22(1), 1; doi:10.3390/mca22010001
Received: 11 September 2016 / Revised: 29 November 2016 / Accepted: 9 December 2016 / Published: 22 December 2016
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Abstract
This paper develops an optimal stopping rule by characterizing the take-profit level. The optimization problem is modeled by geometric Brownian motion with two switchable regimes and solved by stochastic calculation. A closed-form profitability function for the trading strategies is given, and based on
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This paper develops an optimal stopping rule by characterizing the take-profit level. The optimization problem is modeled by geometric Brownian motion with two switchable regimes and solved by stochastic calculation. A closed-form profitability function for the trading strategies is given, and based on which the optimal take-profit level is numerically achievable with small cost of computational complexity. Full article
Open AccessArticle A Novel, Energy-Aware Task Duplication-Based Scheduling Algorithm of Parallel Tasks on Clusters
Math. Comput. Appl. 2017, 22(1), 2; doi:10.3390/mca22010002
Received: 21 September 2016 / Revised: 9 December 2016 / Accepted: 19 December 2016 / Published: 27 December 2016
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Abstract
Increasing energy has become an important issue in high performance clusters. To balance the energy and performance, we proposed a novel, energy-aware duplication-based scheduling (NEADS). An existing energy-aware duplication-based algorithm replicates all qualified predecessor tasks in a bottom-up manner. Some tasks without direct
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Increasing energy has become an important issue in high performance clusters. To balance the energy and performance, we proposed a novel, energy-aware duplication-based scheduling (NEADS). An existing energy-aware duplication-based algorithm replicates all qualified predecessor tasks in a bottom-up manner. Some tasks without direct relation may be replicated to the same processor, which cannot reduce the communication energy. Instead, the computation overhead may be increased. In contrast, the proposed algorithm only replicates the directly correlated predecessor tasks in the energy threshold range without lengthening the schedule length. The proposed algorithm is compared with the non-duplication algorithm and existing duplicated-based algorithm. Extensive experimental results show that the proposed algorithm can effectively reduce energy consumption in various applications. It has advantages over other algorithms on computation-intensive applications. Full article
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Open AccessArticle An Initial Condition Optimization Approach for Improving the Prediction Precision of a GM(1,1) Model
Math. Comput. Appl. 2017, 22(1), 21; doi:10.3390/mca22010021
Received: 28 December 2016 / Revised: 8 February 2017 / Accepted: 8 February 2017 / Published: 22 February 2017
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Abstract
Grey model GM(1,1) has attained excellent prediction accuracy with restricted data and has been broadly utilized in a range of areas. However, the GM(1,1) forecasting model sometimes yields large forecasting errors which directlyaffect the simulation and prediction precision directly. Therefore, the improvement of
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Grey model GM(1,1) has attained excellent prediction accuracy with restricted data and has been broadly utilized in a range of areas. However, the GM(1,1) forecasting model sometimes yields large forecasting errors which directlyaffect the simulation and prediction precision directly. Therefore, the improvement of the GM(1,1) model is an essential issue, and the current study aims to enhance the prediction precision of the GM(1,1) model. Specifically, in order to improve the prediction precision of GM(1,1) model, it is necessary to consider improving the initial condition in the response function of the model. Consequently, the purpose of this paper is to put forward a new method to enhance the performance of the GM(1,1) model by optimizing its initial condition. The minimum sum of squared error was used to optimize the new initial condition of the model. The numerical outcomes show that the improved GM(1,1) model provides considerably better performance than traditional grey model GM(1,1) . The result demonstrates that the improved grey model GM(1,1) achieves the objective of minimizing the forecast errors. Full article
Open AccessArticle A New Approximation Method with High Order Accuracy
Math. Comput. Appl. 2017, 22(1), 11; doi:10.3390/mca22010011
Received: 12 October 2016 / Revised: 2 January 2017 / Accepted: 5 January 2017 / Published: 19 January 2017
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Abstract
In this paper, we propose a new multilevel univariate approximation method with high order accuracy using radial basis function interpolation and cubic B-spline quasi-interpolation. The proposed approach includes two schemes, which are based on radial basis function interpolation with less center points, and
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In this paper, we propose a new multilevel univariate approximation method with high order accuracy using radial basis function interpolation and cubic B-spline quasi-interpolation. The proposed approach includes two schemes, which are based on radial basis function interpolation with less center points, and cubic B-spline quasi-interpolation operator. Error analysis shows that our method produces higher accuracy compared with other approaches. Numerical examples demonstrate that the proposed scheme is effective. Full article
(This article belongs to the Special Issue Information and Computational Science)
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Open AccessArticle Game Analysis of Low Carbonization for Urban Logistics Service Systems
Math. Comput. Appl. 2017, 22(1), 12; doi:10.3390/mca22010012
Received: 24 September 2016 / Revised: 15 January 2017 / Accepted: 16 January 2017 / Published: 22 January 2017
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Abstract
To improve carbon efficiency for an urban logistics service system composed of a third-party logistics service provider (3PL) and an e-business enterprise, a low-carbon operation game between them was studied. Considering low carbon technology investment cost and sales expansion effect of low carbon
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To improve carbon efficiency for an urban logistics service system composed of a third-party logistics service provider (3PL) and an e-business enterprise, a low-carbon operation game between them was studied. Considering low carbon technology investment cost and sales expansion effect of low carbon level, profit functions for both players were constituted. Based on their different bargaining capabilities, in total, five types of game scenarios were designed. Through analytical solution, Nash Equilibria under different scenarios were obtained. By analyzing these equilibria, four major propositions were given, in which some key variables and the system performance indexes were compared. Results show that the best system yields could only be achieved under the fully cooperative situation. Limited cooperation only for carbon emission reduction does not benefit the system performance improvement. E-business enterprise-leading game’s performance overtook 3PL-leading ones. Full article
Open AccessArticle A Five-Point Subdivision Scheme with Two Parameters and a Four-Point Shape-Preserving Scheme
Math. Comput. Appl. 2017, 22(1), 22; doi:10.3390/mca22010022
Received: 9 October 2016 / Revised: 10 January 2017 / Accepted: 13 February 2017 / Published: 24 February 2017
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Abstract
In order to improve the flexibility of curves, a new five-point binary approximating subdivision scheme with two parameters is presented. The generating polynomial method is used to investigate the uniform convergence and Ck-continuity of this scheme. In a special case, the
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In order to improve the flexibility of curves, a new five-point binary approximating subdivision scheme with two parameters is presented. The generating polynomial method is used to investigate the uniform convergence and C k -continuity of this scheme. In a special case, the five-point scheme changes into a four-point scheme, which can generate C 3 limit curves. The shape-preserving properties of the four-point scheme are analyzed, and a few examples are given to illustrate the efficiency and the shape-preserving effect of this special case. Full article
(This article belongs to the Special Issue Information and Computational Science)
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Open AccessArticle Laplace Transform Homotopy Perturbation Method for the Two Dimensional Black Scholes Model with European Call Option
Math. Comput. Appl. 2017, 22(1), 23; doi:10.3390/mca22010023
Received: 24 December 2016 / Revised: 7 February 2017 / Accepted: 20 February 2017 / Published: 27 February 2017
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Abstract
The Black Scholes model is a well-known and useful mathematical model in financial markets. In this paper, the two-dimensional Black Scholes equation with European call option is studied. The explicit solution of this problem is carried out in the form of a Mellin–Ross
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The Black Scholes model is a well-known and useful mathematical model in financial markets. In this paper, the two-dimensional Black Scholes equation with European call option is studied. The explicit solution of this problem is carried out in the form of a Mellin–Ross function by using Laplace transform homotopy perturbation method. The solution example demonstrates that the proposed scheme is effective. Full article
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Open AccessArticle New Unidimensional Indexes for China
Math. Comput. Appl. 2017, 22(1), 13; doi:10.3390/mca22010013
Received: 18 December 2016 / Revised: 4 January 2017 / Accepted: 4 January 2017 / Published: 24 January 2017
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Abstract
A first principal component combines several indicators so as to maximize their internal consistency for measuring a construct. First principal components are extracted here from Swiss Economic Institute and World Bank datasets containing yearly societal indicators for China. These indicators are input to
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A first principal component combines several indicators so as to maximize their internal consistency for measuring a construct. First principal components are extracted here from Swiss Economic Institute and World Bank datasets containing yearly societal indicators for China. These indicators are input to population-weighted regressions without recourse to survey sampling or probabilistic inference. The results demonstrate Chomskyan globalization and domestic credit as strong exogenous and endogenous predictors of Chinese per capita GDP. These encouraging findings, easily extendable to other nations, are brought by two new societal indexes with assured unidimensionality. Full article
Open AccessArticle Safeguarding against Inactivation Temperatures during Plasma Treatment of Skin: Multiphysics Model and Phase Field Method
Math. Comput. Appl. 2017, 22(1), 24; doi:10.3390/mca22010024
Received: 6 January 2017 / Revised: 20 February 2017 / Accepted: 20 February 2017 / Published: 2 March 2017
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Abstract
One of the most appealing applications of cold plasmas is medical treatment of the skin. An important concern is the capability to safeguard the non-targeted cells against inactivation temperatures during the plasma treatment. Unfortunately, it is problematic to experimentally determine the highest transient
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One of the most appealing applications of cold plasmas is medical treatment of the skin. An important concern is the capability to safeguard the non-targeted cells against inactivation temperatures during the plasma treatment. Unfortunately, it is problematic to experimentally determine the highest transient temperatures in these cells during the plasma treatment. In the present work, a complete multiphysics model was built based on finite element analysis using phase field method coupled with heat transfer and fluid dynamics to study the discharge phenomenon of cold plasma with helium carrier gas ejected out of a tube for skin treatment. In such plasmas with carrier gas, the fractions of plasma constituents are small compared to the carrier gas, so thermofluid analysis is needed for the carrier gas as the major contributor to the fluid and heat flow. The phase field method has been used to capture the moving helium gas in air, which has enabled us to compute fluid dynamics parameters for each phase individually. In addition to computational fluid dynamic analyses, we have also considered heat transfer in the fluids and to the skin using the Fourier law of heat conduction, which led to a multiphysics system. In the present paper, various flow velocities and tube-to-target distances (TTDs) have been considered to reveal the dependence of the fluid discharge output parameters on the flow and efficiency of heat transfer to the skin and the surrounding environment. The built model is a useful tool for future development of plasma treatment devices and to safeguard the non-targeted cells against inactivation temperatures. Full article
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Open AccessArticle Event Triggered Multi-Agent Consensus of DC Motors to Regulate Speed by LQR Scheme
Math. Comput. Appl. 2017, 22(1), 14; doi:10.3390/mca22010014
Received: 21 November 2016 / Accepted: 19 January 2017 / Published: 26 January 2017
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Abstract
In the presented paper, the leader-following consensus algorithm of a multi-agent system (MAS) is used along with the centralized event-triggering scheme to make the speed of the network-coupled multiple-motors synchronizable. In the proposed method, the updates for the controller are event-driven based on
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In the presented paper, the leader-following consensus algorithm of a multi-agent system (MAS) is used along with the centralized event-triggering scheme to make the speed of the network-coupled multiple-motors synchronizable. In the proposed method, the updates for the controller are event-driven based on local information. Moreover, the basic consensus protocol is also revised such that the speed information of the motors is used in order to reach identical speed. The main benefit of the planned event-triggered methodology is the energy saving by avoiding the continuous control of the system. As far as stability analysis of the system is concerned, a common Lyapunov function is incorporated to validate stability. The acquired results endorse the success of the proposed methodology. Full article
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Open AccessArticle A Weakly Pareto Compliant Quality Indicator
Math. Comput. Appl. 2017, 22(1), 25; doi:10.3390/mca22010025
Received: 15 December 2016 / Revised: 22 February 2017 / Accepted: 27 February 2017 / Published: 6 March 2017
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Abstract
In multi‐ and many‐objective optimization problems, the optimization target is to obtain a set of non‐dominated solutions close to the Pareto‐optimal front, well‐distributed, maximally extended and fully filled. Comparing solution sets is crucial in evaluating the performance of different optimization algorithms. The use
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In multi‐ and many‐objective optimization problems, the optimization target is to obtain a set of non‐dominated solutions close to the Pareto‐optimal front, well‐distributed, maximally extended and fully filled. Comparing solution sets is crucial in evaluating the performance of different optimization algorithms. The use of performance indicators is common in comparing those sets and, subsequently, optimization algorithms. Therefore, an effective performance indicator must encompass these features as a whole and, above all, it must be Pareto dominance compliant. Unfortunately, some of the known indicators often fail to properly reflect the quality of a solution set or cost a lot to compute. This paper demonstrates that the Degree of Approximation (DOA) quality indicator is a weakly Pareto compliant unary indicator that gives a good estimation of the match between the approximated front and the Pareto‐optimal front. Full article
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Open AccessArticle An M/G/1 Retrial G-Queue with General Retrial Times and Working Breakdowns
Math. Comput. Appl. 2017, 22(1), 15; doi:10.3390/mca22010015
Received: 4 October 2016 / Revised: 2 January 2017 / Accepted: 24 January 2017 / Published: 2 February 2017
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Abstract
This paper considers an M/G/1 retrial G-queue with general retrial times, in which the server is subject to working breakdowns and repairs. If the system is not empty during a normal service period, the arrival of a negative customer can cause the server
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This paper considers an M/G/1 retrial G-queue with general retrial times, in which the server is subject to working breakdowns and repairs. If the system is not empty during a normal service period, the arrival of a negative customer can cause the server breakdown, and the failed server still works at a lower service rate rather than stopping the service completely. Applying the embedded Markov chain, we obtain the necessary and sufficient condition for the stability of the system. Using the supplementary variable method, we deal with the generating functions of the number of customers in the orbit. Various system performance measures are also developed. Finally, some numerical examples and a cost optimization analysis are presented. Full article
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Open AccessArticle On Existence and Uniqueness of Solutions to the Fuzzy Dynamic Equations on Time Scales
Math. Comput. Appl. 2017, 22(1), 16; doi:10.3390/mca22010016
Received: 12 December 2016 / Revised: 1 February 2017 / Accepted: 1 February 2017 / Published: 8 February 2017
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Abstract
In this paper, we introduce a new metric on the space of fuzzy continuous functions on time scales by using the exponential function, eγ(t,t0), where γ>0 is a constant. Then, we provide some
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In this paper, we introduce a new metric on the space of fuzzy continuous functions on time scales by using the exponential function, e γ ( t , t 0 ) , where γ > 0 is a constant. Then, we provide some conditions to prove an existence and uniqueness theorem for solutions to nonlinear fuzzy dynamic equations. Furthermore, we present three different examples including a practical example to illustrate the main results. Full article
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Open AccessArticle Modeling Sound Propagation Using the Corrective Smoothed Particle Method with an Acoustic Boundary Treatment Technique
Math. Comput. Appl. 2017, 22(1), 26; doi:10.3390/mca22010026
Received: 5 January 2017 / Revised: 6 March 2017 / Accepted: 6 March 2017 / Published: 15 March 2017
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Abstract
The development of computational acoustics allows the simulation of sound generation and propagation in a complex environment. In particular, meshfree methods are widely used to solve acoustics problems through arbitrarily distributed field points and approximation smoothness flexibility. As a Lagrangian meshfree method, the
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The development of computational acoustics allows the simulation of sound generation and propagation in a complex environment. In particular, meshfree methods are widely used to solve acoustics problems through arbitrarily distributed field points and approximation smoothness flexibility. As a Lagrangian meshfree method, the smoothed particle hydrodynamics (SPH) method reduces the difficulty in solving problems with deformable boundaries, complex topologies, or multiphase medium. The traditional SPH method has been applied in acoustic simulation. This study presents the corrective smoothed particle method (CSPM), which is a combination of the SPH kernel estimate and Taylor series expansion. The CSPM is introduced as a Lagrangian approach to improve the accuracy when solving acoustic wave equations in the time domain. Moreover, a boundary treatment technique based on the hybrid meshfree and finite difference time domain (FDTD) method is proposed, to represent different acoustic boundaries with particles. To model sound propagation in pipes with different boundaries, soft, rigid, and absorbing boundary conditions are built with this technique. Numerical results show that the CSPM algorithm is consistent and demonstrates convergence with exact solutions. The main computational parameters are discussed, and different boundary conditions are validated as being effective for benchmark problems in computational acoustics. Full article
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Open AccessArticle New Scientific Contribution on the 2-D Subdomain Technique in Cartesian Coordinates: Taking into Account of Iron Parts
Math. Comput. Appl. 2017, 22(1), 17; doi:10.3390/mca22010017
Received: 17 January 2017 / Revised: 27 January 2017 / Accepted: 1 February 2017 / Published: 10 February 2017
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Abstract
The most significant assumptions in the subdomain technique (i.e., based on the formal resolution of Maxwell’s equations applied in subdomain) is defined by: Theiron parts(i.e.,theteeth and the back-iron are considered to be infinitely permeable, i.e., µiron → +∞, so that the saturation effect
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The most significant assumptions in the subdomain technique (i.e., based on the formal resolution of Maxwell’s equations applied in subdomain) is defined by: Theiron parts(i.e.,theteeth and the back-iron are considered to be infinitely permeable, i.e., µiron → +∞, so that the saturation effect is neglected. In this paper, the authors present a new scientific contribution on improving of this method in two-dimensional (2-D) and in Cartesian coordinates by focusing on the consideration of iron. The subdomains connection is carried out in the two directions (i.e., x-andy-edges). Forexample,the improvement was performed by solving magnetostatic Maxwell’s equations for an air- or iron-cored coil supplied by a direct current. To evaluate the efficacy of the proposed technique, the magnetic flux density distributions have been compared with those obtained by the 2-D finite-element analysis (FEA). The semi-analytical results are in quite satisfying agreement with those obtained by the 2-D FEA, considering both amplitude and waveform. Full article
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Open AccessArticle Damping Characteristics of Viscoelastic Damping Structure under Coupled Condition
Math. Comput. Appl. 2017, 22(1), 27; doi:10.3390/mca22010027
Received: 18 November 2016 / Revised: 24 February 2017 / Accepted: 3 March 2017 / Published: 15 March 2017
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Abstract
Temperature has an influence on damping characteristics of the viscoelastic damping structure. The change of the damping characteristics of the structure under the cycle load is a dynamic and coupled process. The hyperelastic-viscoelastic model was used to describe nonlinear deformation and viscoelasticity simultaneously.
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Temperature has an influence on damping characteristics of the viscoelastic damping structure. The change of the damping characteristics of the structure under the cycle load is a dynamic and coupled process. The hyperelastic-viscoelastic model was used to describe nonlinear deformation and viscoelasticity simultaneously. The temperature distribution and change of the damping characteristics under the coupled condition was analyzed by finite element method (FEM). The maximum value of the simulation results was in agreement with the one calculated by the formula in the literature. Dynamic stiffness and dissipated energy were obtained based on the hysteresis loop. Dynamic stiffness and dissipated energy gradually decreased with the increase of the temperature. Full article
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Open AccessArticle Rape Plant Disease Recognition Method of Multi-Feature Fusion Based on D-S Evidence Theory
Math. Comput. Appl. 2017, 22(1), 18; doi:10.3390/mca22010018
Received: 19 October 2016 / Revised: 14 December 2016 / Accepted: 20 January 2017 / Published: 15 February 2017
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Abstract
In view of the low accuracy and uncertainty of the traditional rape plant disease recognition relying on a single feature, this paper puts forward a rape plant disease recognition method based on Dempster-Shafer (D-S) evidence theory and multi-feature fusion. Firstly, color matrix and
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In view of the low accuracy and uncertainty of the traditional rape plant disease recognition relying on a single feature, this paper puts forward a rape plant disease recognition method based on Dempster-Shafer (D-S) evidence theory and multi-feature fusion. Firstly, color matrix and gray-level co-occurrence matrix are extracted as two kinds of features from rape plant images after processing. Then by calculating the Euclidean distance between the test samples and training samples, the basic probability assignment function can be constructed. Finally, the D-S combination rule of evidence is used to achieve fusion, and final recognition results are given by using the variance. This method is used to collect rape plant images for disease recognition, and recognition rate arrives at 97.09%. Compared with other methods, experimental results show that the method is more effective and with lower computational complexity. Full article
(This article belongs to the Special Issue Information and Computational Science)
Open AccessArticle On the Bias of the Maximum Likelihood Estimators of Parameters of the Weibull Distribution
Math. Comput. Appl. 2017, 22(1), 19; doi:10.3390/mca22010019
Received: 18 September 2016 / Accepted: 20 January 2017 / Published: 15 February 2017
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Abstract
Usually, the parameters of a Weibull distribution are estimated by maximum likelihood estimation. To reduce the biases of the maximum likelihood estimators (MLEs) of two-parameter Weibull distributions, we propose analytic bias-corrected MLEs. Two other common estimators of Weibull distributions, least-squares estimators and percentiles
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Usually, the parameters of a Weibull distribution are estimated by maximum likelihood estimation. To reduce the biases of the maximum likelihood estimators (MLEs) of two-parameter Weibull distributions, we propose analytic bias-corrected MLEs. Two other common estimators of Weibull distributions, least-squares estimators and percentiles estimators, are also introduced. Based on a comparison of their performances in the simulation study, we strongly recommend the analytic bias-corrected MLEs for the parameters of Weibull distributions, especially when the sample size is small. Full article
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