Mathematical and Computational Applications

225 KiB

Open AccessArticle

Similarity Solutions for Boundary Layer Equations of a Powel-Eyring Fluid

by Tasawar Hayat, Mehmet Pakdemirli and Yiğit Aksoy

Math. Comput. Appl. 2013, 18(1), 62-70; https://doi.org/10.3390/mca18010062 - 01 Apr 2013

Cited by 8 | Viewed by 1350

Boundary layer equations are derived for the first time for the Powel-Eyring fluid model, a non-Newtonian model proposed for pseudoplastic behavior. Using a scaling symmetry of the equations, partial differential system is transferred to an ordinary differential system. Resulting equations are numerically solved [...] Read more.

Boundary layer equations are derived for the first time for the Powel-Eyring fluid model, a non-Newtonian model proposed for pseudoplastic behavior. Using a scaling symmetry of the equations, partial differential system is transferred to an ordinary differential system. Resulting equations are numerically solved using a finite difference algorithm. Effects of non-Newtonian parameters on the solutions are discussed. Full article

325 KiB

Open AccessArticle

Anti-Periodic Solutions for Neural Networks with Delays and Impulses

by Peilin Shi and Lingzhen Dong

Math. Comput. Appl. 2013, 18(1), 50-61; https://doi.org/10.3390/mca18010050 - 01 Apr 2013

Cited by 2 | Viewed by 1040

Abstract

In this paper we investigate a class of artificial neural networks with delays subject to periodic impulses. By exploiting Lyapunov functions, we analyze the global exponential stability of an arbitrary solution with initial value being bounded by _Υ . Further, we discuss the [...] Read more.

In this paper we investigate a class of artificial neural networks with delays subject to periodic impulses. By exploiting Lyapunov functions, we analyze the global exponential stability of an arbitrary solution with initial value being bounded by _Υ . Further, we discuss the existence of anti-periodic solutions by constructing fundamental function sequences based on a solution with initial value being bounded by γ . We also establish sufficient conditions to ensure the existence, uniqueness and exponential stability of anti-periodic solutions, which are new and easily verifiable. At last, we present a network with its time-series and phase graphics to demonstrate our results. Full article

382 KiB

Open AccessArticle

Elasto-Plastic Stress Analysis in Laminated Thermoplastic Composite Plates with an Elliptic Hole

by Gurbet Örçen and Mustafa Gür

Math. Comput. Appl. 2013, 18(1), 38-49; https://doi.org/10.3390/mca18010038 - 01 Apr 2013

Viewed by 1387

Abstract

In this paper, elasto-plastic stress analysis in laminated thermoplastic composite plates having an elliptic hole in the middle is examined by using finite element method. Composite plates consist of four orthotropic laminations and bonded symmetrically \([\theta^{0}/-\theta^{0}]\). Uniform loadings in vertical direction are applied [...] Read more.

In this paper, elasto-plastic stress analysis in laminated thermoplastic composite plates having an elliptic hole in the middle is examined by using finite element method. Composite plates consist of four orthotropic laminations and bonded symmetrically \([\theta^{0}/-\theta^{0}]\). Uniform loadings in vertical direction are applied to the selected composite plates. The loading and reinforcement angle are gradually increased from the yield point of the plate. The load steps increased as 0.0001 MPa at each iteration. Iteration numbers are chosen 25, 50, 75 and 100. A quarter of the plate is taken into consideration due to symmetry. Elasto-plastic stresses are obtained according to load steps and orientation angles. Full article

293 KiB

Open AccessArticle

Analysis of a Modified Logistic Model for Describing the Growth of Durable Customer Goods in China

by Li-Qun Ji

Math. Comput. Appl. 2013, 18(1), 30-37; https://doi.org/10.3390/mca18010030 - 01 Apr 2013

Cited by 4 | Viewed by 1254

Abstract

The ability of a modified logistic model for forecasting the growth of durable consumer goods in China was investigated. The fitting of the modified logistic model to the historical data uses a pattern search technique to establish the optimum parameter values. Two data [...] Read more.

The ability of a modified logistic model for forecasting the growth of durable consumer goods in China was investigated. The fitting of the modified logistic model to the historical data uses a pattern search technique to establish the optimum parameter values. Two data sets on the quantity of air conditioner owned per 100 urban households at year-end and color TV set owned per 100 rural households at year-end were analyzed in this work. Additionally, the logistic model was applied to the same data. Both two models were compared using their goodness of fit to the historical data. The comparison has revealed that the modified logistic model is more appropriate for describing the growth of durable consumer goods in China. Full article

483 KiB

Open AccessArticle

Approximate Solutions of Linear Fredholm Integral Equations System with Variable Coefficients

by Salih Yalçınbaş

Math. Comput. Appl. 2013, 18(1), 19-29; https://doi.org/10.3390/mca18010019 - 01 Apr 2013

Cited by 1 | Viewed by 988

Abstract

In this paper, a new approximate method has been presented to solve the linear Fredholm integral equations system (FIEs). The technique is based on, first, differentiating both sides of integral equations n times and then substituting the Taylor series the unknown functions in [...] Read more.

In this paper, a new approximate method has been presented to solve the linear Fredholm integral equations system (FIEs). The technique is based on, first, differentiating both sides of integral equations n times and then substituting the Taylor series the unknown functions in the resulting equation and later, transforming to a matrix equation. By merging these results, a new system which corresponds to a system of linear algebraic equations is obtained. The solution of this system yields the Taylor coefficients of the solution function. Also, this method gives the analytic solution when the exact solutions are polynomials. So as to Show this capability and robustness, some systems of FIEs are solved by the presented method in order to obtain their approximate solutions. Full article

176 KiB

Open AccessArticle

A New Method for Solving Matrix Equation AXB + CXT D = E

by Minghui Wang

Math. Comput. Appl. 2013, 18(1), 12-18; https://doi.org/10.3390/mca18010012 - 01 Apr 2013

Viewed by 1106

Abstract

In this paper, we propose a new iterative algorithm to solve the matrix equation AXB + CX^T D = E. The algorithm can obtain the minimal Frobenius norm solution or the least-squares solution with minimal Frobenius norm. Our algorithm is better [...] Read more.

In this paper, we propose a new iterative algorithm to solve the matrix equation AXB + CX^T D = E. The algorithm can obtain the minimal Frobenius norm solution or the least-squares solution with minimal Frobenius norm. Our algorithm is better than Algorithm II of the paper [M. Wang, etc., Iterative algorithms for solving the matrix equation AXB + CX^T D = E, Appl. Math. Comput. 187, 622-629, 2007] Full article

320 KiB

Open AccessArticle

On Helices and Bertrand Curves in Euclidean 3-Space

by Murat Babaarslan and Yusuf Yayli

Math. Comput. Appl. 2013, 18(1), 1-11; https://doi.org/10.3390/mca18010001 - 01 Apr 2013

Cited by 6 | Viewed by 1366

Abstract

In this article, we investigate Bertrand curves corresponding to the spherical images of the tangent, binormal, principal normal and Darboux indicatrices of a space curve in Euclidean 3-space. As a result, in case of a space curve is a general helix, we show [...] Read more.

In this article, we investigate Bertrand curves corresponding to the spherical images of the tangent, binormal, principal normal and Darboux indicatrices of a space curve in Euclidean 3-space. As a result, in case of a space curve is a general helix, we show that the curves corresponding to the spherical images of its the tangent indicatrix and binormal indicatrix are both Bertrand curves and circular helices. Similarly, in case of a space curve is a slant helix, we demonstrate that the curve corresponding to the spherical image of its the principal normal indicatrix is both a Bertrand curve and a circular helix. Full article

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Math. Comput. Appl., Volume 18, Issue 1 (April 2013) – 7 articles , Pages 1-70

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