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Math. Comput. Appl., Volume 18, Issue 3 (December 2013) – 38 articles , Pages 139-557

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391 KiB  
Article
On the Thermal Buckling Behavior of Laminated Hybrid Composite Plates Due to Square/Circular Cut-Outs
by Ahmet Erkliğ and Eyüp Yeter
Math. Comput. Appl. 2013, 18(3), 548-557; https://doi.org/10.3390/mca18030548 - 1 Dec 2013
Cited by 2 | Viewed by 1453
Abstract
Cut-outs like circular, rectangular, elliptical, triangular are generally used in composite structures due to access ports for mechanical and electrical systems, damage inspection, to serve as doors and windows, and sometimes to reduce the overall weight of the structure. In this paper the [...] Read more.
Cut-outs like circular, rectangular, elliptical, triangular are generally used in composite structures due to access ports for mechanical and electrical systems, damage inspection, to serve as doors and windows, and sometimes to reduce the overall weight of the structure. In this paper the effects of cut-outs on the thermal buckling behavior of hybrid composite plates in cross-ply and angle-ply laminate are presented. The effects of eccentric cut-out size in different plate aspect ratios and boundary conditions on the thermal buckling behavior of the cross-ply and angle-ply laminated hybrid composite plates are also investigated. Finite element analysis is also performed to calculate thermal buckling temperatures for Kevlar/Epoxy, Boron/Epoxy and E-glass/Epoxy. Several outcomes and behavioral characteristics are discussed. These outcomes include the effects of cut-out size, shape, plate aspect ratio and boundary conditions. Full article
1245 KiB  
Article
Exact Solution and Buckling Configuration of Nanotubes Containing Internal Flowing Fluid
by B. Gültekin Sınır, F. Esra Uz and Sefa Ergun
Math. Comput. Appl. 2013, 18(3), 539-547; https://doi.org/10.3390/mca18030539 - 1 Dec 2013
Cited by 1 | Viewed by 1429
Abstract
In this study, the post-divergence behaviour of nanotubes of conveying internal moving fluid with both inner and outer surface layers are analyzed in nonlinear theorical model. The governing equation has the cubic nonlinearity. The source of this nonlinearity is the surface effect and [...] Read more.
In this study, the post-divergence behaviour of nanotubes of conveying internal moving fluid with both inner and outer surface layers are analyzed in nonlinear theorical model. The governing equation has the cubic nonlinearity. The source of this nonlinearity is the surface effect and mid-plane stretching in the nanobeam theory. Exact solutions for the post buckling configurations of nanotubes with clamped-hinged with torsionally spring and hybrid boundary conditions is found. The critical flow velocity at which the nanotube is buckled is shown. The effects of various non-dimensional system parameters on the post-buckling behaviour are investigated. Full article
669 KiB  
Article
Multi Response Optimization Application on a Manufacturing Factory
by Hakan Akçay and A. Sermet Anagün
Math. Comput. Appl. 2013, 18(3), 531-538; https://doi.org/10.3390/mca18030531 - 1 Dec 2013
Cited by 35 | Viewed by 1765
Abstract
The purpose of real-life problems is often to be able to find less expensive and more effective ways of production without compromising product quality because companies must provide competitive advantage to maintain existence. In order to improve quality, design of experiment techniques is [...] Read more.
The purpose of real-life problems is often to be able to find less expensive and more effective ways of production without compromising product quality because companies must provide competitive advantage to maintain existence. In order to improve quality, design of experiment techniques is employed. RSM is a widely used technique thanks to its minimum number of experiment requirement. Hence it is used especially with continuous solution spaces and high-cost experimentations. Moreover, in most cases there is more than one response that firms must optimize simultaneously. For instance companies want to reduce the costs while improving product quality. Decision making is more difficult when conflicting objectives exist. For this reason multi response optimization is an important field to study. In this study, optimization of a manufacturing problem with two responses was carried out by the application of response surface methodology (RSM) and desirability function. Full article
446 KiB  
Article
Legendre Collocation Method for Solving Nonlinear Differential Equations
by Aysun Güner and Salih Yalçınbaş
Math. Comput. Appl. 2013, 18(3), 521-530; https://doi.org/10.3390/mca18030521 - 1 Dec 2013
Cited by 5 | Viewed by 2001
Abstract
In this study, a matrix method based on Legendre collocation points on interval [-1,1] is proposed for the approximate solution of the some first order nonlinear ordinary differential equations with the mixed conditions in terms of Legendre polynomials. The method by means of [...] Read more.
In this study, a matrix method based on Legendre collocation points on interval [-1,1] is proposed for the approximate solution of the some first order nonlinear ordinary differential equations with the mixed conditions in terms of Legendre polynomials. The method by means of Legendre collocation points, transforms the differential equation to a matrix equation which corresponds to a system of nonlinear algebraic equations with unknown Legendre coefficients. Also, the method can be used for solving Riccati equation. The numerical results show the effectuality of the method for this type of equations. Comparisons are made between the obtained solution and the exact solution. Full article
811 KiB  
Article
Performance Analysis of Distance Transform Based Inter-Slice Similarity Information on Segmentation of Medical Image Series
by Eşref Selvi, Merve Özdemir and M. Alper Selver
Math. Comput. Appl. 2013, 18(3), 511-520; https://doi.org/10.3390/mca18030511 - 1 Dec 2013
Cited by 2 | Viewed by 1393
Abstract
Segmentation of organs from CT and MR image series is a challenging research area in all fields of medical imaging. Although, organs of interest are three-dimensional in nature, slice-by-slice approaches are widely used in clinical applications because of their ease of integration with [...] Read more.
Segmentation of organs from CT and MR image series is a challenging research area in all fields of medical imaging. Although, organs of interest are three-dimensional in nature, slice-by-slice approaches are widely used in clinical applications because of their ease of integration with the current manual segmentation scheme (i.e. gold standard). Moreover, the high anisotropy of CT and MR data makes intra-slice information more reliable than inter-slice features. Nevertheless, slice-by-slice techniques should be supported with adjacent slice information since it is shown that features using the similarity of adjacent image slices outperform measures based on single-slice features in all cases. One of this similarity features is the distance transform which is shown to be effective on providing inter-slice similarity of abdominal organs. A parameter that control the vicinity of search area using the distance transform is α, which determines the order of the power of distance transforms applied to the image. Since there is no study discussing the effect of α on segmentation performance, the aim of this study is to analyze how changes on α affects performance in terms of accuracy, computation and time requirements. The simulations performed on several medical image series and for four different abdominal organs show the importance of parameter analysis for distance transformation. Full article
626 KiB  
Article
Determination of the Impact Behavior of Concrete and Reinforced Concrete Beams
by Engin Gücüyen, R. Tuğrul Erdem, Erkan Kantar and Muhiddin Bağcı
Math. Comput. Appl. 2013, 18(3), 502-510; https://doi.org/10.3390/mca18030502 - 1 Dec 2013
Cited by 1 | Viewed by 1547
Abstract
Behavior types of structural members under various loads have been a main field of interest in engineering sciences. There have been several studies performed about determining the behavior of members under tensile, compression, bending and torsion loads until today. However, terrorist attacks and [...] Read more.
Behavior types of structural members under various loads have been a main field of interest in engineering sciences. There have been several studies performed about determining the behavior of members under tensile, compression, bending and torsion loads until today. However, terrorist attacks and destructive earthquakes have aroused interests of scientists and engineers about solutions of impact problems. In this study, behavior of concrete and reinforced concrete beams under impact loads is investigated. For this purpose, a testing apparatus has been created. Data obtained from experimental study are compared with the analysis results of ABAQUS finite elements program. Full article
363 KiB  
Article
A New Heuristic Algorithm to Solve the Maximum Independent Set Problem
by Onur Ugurlu
Math. Comput. Appl. 2013, 18(3), 495-501; https://doi.org/10.3390/mca18030495 - 1 Dec 2013
Viewed by 1503
Abstract
The Maximum Independent Set Problem is a classic graph optimization NPhard problem. Given a graph G=(V,E), the independent set problem is that of finding a maximum-cardinality subset S of V such that no two vertices in S are adjacent. In this paper, the [...] Read more.
The Maximum Independent Set Problem is a classic graph optimization NPhard problem. Given a graph G=(V,E), the independent set problem is that of finding a maximum-cardinality subset S of V such that no two vertices in S are adjacent. In this paper, the maximum independent set problem is discussed and a new heuristic algorithm is proposed to solve this problem. The performance of the algorithm has been tested on DIMACS benchmark instances and compared with the literature works. The experimental results show that the proposed approach can yield good solutions. Full article
236 KiB  
Article
A Genetic Algorithm to Solve the Multidimensional Knapsack Problem
by Murat Ersen Berberler, Asli Guler and Urfat G. Nurıyev
Math. Comput. Appl. 2013, 18(3), 486-494; https://doi.org/10.3390/mca18030486 - 1 Dec 2013
Cited by 9 | Viewed by 2426
Abstract
In this paper, The Multidimensional Knapsack Problem (MKP) which occurs in many different applications is studied and a genetic algorithm to solve the MKP is proposed. Unlike the technique of the classical genetic algorithm, initial population is not randomly generated in the proposed [...] Read more.
In this paper, The Multidimensional Knapsack Problem (MKP) which occurs in many different applications is studied and a genetic algorithm to solve the MKP is proposed. Unlike the technique of the classical genetic algorithm, initial population is not randomly generated in the proposed algorithm, thus the solution space is scanned more efficiently. Moreover, the algorithm is written in C programming language and is tested on randomly generated instances. It is seen that the algorithm yields optimal solutions for all instances. Full article
340 KiB  
Article
Müntz-Legendre Polynomial Solutions of Linear Delay Fredholm Integro-Differential Equations and Residual Correction
by Şuayip Yüzbaşı, Emrah Gök and Mehmet Sezer
Math. Comput. Appl. 2013, 18(3), 476-485; https://doi.org/10.3390/mca18030476 - 1 Dec 2013
Cited by 6 | Viewed by 1627
Abstract
In this paper, we consider the Müntz-Legendre polynomial solutions of the linear delay Fredholm integro-differential equations and residual correction. Firstly, the linear delay Fredholm integro-differential equations are transformed into a system of linear algebraic equations by using by the matrix operations of the [...] Read more.
In this paper, we consider the Müntz-Legendre polynomial solutions of the linear delay Fredholm integro-differential equations and residual correction. Firstly, the linear delay Fredholm integro-differential equations are transformed into a system of linear algebraic equations by using by the matrix operations of the Müntz-Legendre polynomials and the collocation points. When this system is solved, the Müntz- Legendre polynomial solution is obtained. Then, an error estimation is presented by means of the residual function and the Müntz-Legendre polynomial solutions are improved by the residual correction method. The technique is illustrated by studying the problem for an example. The obtained results show that error estimation and the residual correction method is very effective. Full article
297 KiB  
Article
Taylor Matrix Solution of the Mathematical Model of the RLC Circuits
by M. Mustafa Bahşı and Mehmet Çevik
Math. Comput. Appl. 2013, 18(3), 467-475; https://doi.org/10.3390/mca18030467 - 1 Dec 2013
Cited by 4 | Viewed by 1579
Abstract
The RLC circuit is a basic building block of the more complicated electrical circuits and networks. The present study introduces a novel and simple numerical method for the solution this problem in terms of Taylor polynomials in the matrix form. Particular and general [...] Read more.
The RLC circuit is a basic building block of the more complicated electrical circuits and networks. The present study introduces a novel and simple numerical method for the solution this problem in terms of Taylor polynomials in the matrix form. Particular and general solutions of the related differential equation can be determined by this method. The method is illustrated by a numerical application and a quite good agreement is observed between the results of the present method and those of the exact method. Full article
244 KiB  
Article
A Parametric Hybrid Method for the Traveling Salesman Problem
by Gözde Kızılates and Fidan Nuriyeva
Math. Comput. Appl. 2013, 18(3), 459-466; https://doi.org/10.3390/mca18030459 - 1 Dec 2013
Viewed by 1531
Abstract
The traveling salesman problem (TSP) is one of the typical NP–Hard problems of combinatorial optimization area. This paper proposes a new hyper heuristic algorithm named Parametric Hybrid Method (PHM) based on The Farthest Vertex (FV) and Greedy heuristics for solving the traveling salesman [...] Read more.
The traveling salesman problem (TSP) is one of the typical NP–Hard problems of combinatorial optimization area. This paper proposes a new hyper heuristic algorithm named Parametric Hybrid Method (PHM) based on The Farthest Vertex (FV) and Greedy heuristics for solving the traveling salesman problem. In addition, many problem instances from TSPLIB (traveling salesman problem library) were solved with NN, Greedy and PHM algorithms. The experimental results show that the new hybrid algorithm is more effective and efficient than both Greedy and Nearest Neighbor algorithms. Full article
363 KiB  
Article
Fibonacci Collocation Method for Solving Linear Differential - Difference Equations
by Ayşe Kurt, Salih Yalçınbaş and Mehmet Sezer
Math. Comput. Appl. 2013, 18(3), 448-458; https://doi.org/10.3390/mca18030448 - 1 Dec 2013
Cited by 7 | Viewed by 1426
Abstract
This study presents a new method for the solution of mth-order linear differential-difference equations with variable coefficients under the mixed conditions. We introduce a Fibonacci collocation method based on the Fibonacci polynomials for the approximate solution. Numerical examples are included to demonstrate the [...] Read more.
This study presents a new method for the solution of mth-order linear differential-difference equations with variable coefficients under the mixed conditions. We introduce a Fibonacci collocation method based on the Fibonacci polynomials for the approximate solution. Numerical examples are included to demonstrate the applicability of the technique. The obtained results are compared by the known results. Full article
863 KiB  
Article
Novel Bracing Type Against Seismic Loading: KX Type
by M. Akif Kutuk and Ibrahim Gov
Math. Comput. Appl. 2013, 18(3), 438-447; https://doi.org/10.3390/mca18030438 - 1 Dec 2013
Cited by 1 | Viewed by 1346
Abstract
In this study, a new bracing system is proposed which is named as KX type. Element removal method is used to obtain this new bracing. KX type optimized bracing is compared with V, and K type bracings under seismic loading. Maximum deformation value [...] Read more.
In this study, a new bracing system is proposed which is named as KX type. Element removal method is used to obtain this new bracing. KX type optimized bracing is compared with V, and K type bracings under seismic loading. Maximum deformation value is used as performance indicator to compare effectiveness of V, K, and proposed KX type bracings to resist seismic loads. The proposed KX type bracing, yielded 99.72%, 93% and 88% reduced deformation with respect to unbraced, K type, and V type bracings respectively. Full article
761 KiB  
Article
Numerical Investigation of Impinging Jets with Nanofluids on a Moving Plate
by Erdem Ersayın and Fatih Selimefendigil
Math. Comput. Appl. 2013, 18(3), 428-437; https://doi.org/10.3390/mca18030428 - 1 Dec 2013
Cited by 11 | Viewed by 1563
Abstract
In this study a numerical investigation of an impinging jet flow, on a heated moving plate, is presented. The purpose of this study is to numerically investigate the effects of various parameters such as nanoparticle volume fraction, pulsating frequency, plate velocity, Reynolds number [...] Read more.
In this study a numerical investigation of an impinging jet flow, on a heated moving plate, is presented. The purpose of this study is to numerically investigate the effects of various parameters such as nanoparticle volume fraction, pulsating frequency, plate velocity, Reynolds number on the heat transfer characteristics. Navier-Stokes equations and energy equations are solved with a commercial finite volume based code. It is observed that adding nanoparticles increases the peak value of Nusselt number. It is also observed that the value of Nusselt number at the stagnation point is higher at the low velocities of impingement surface. In the unsteady case, heat transfer enhancement is seen at low frequencies. Full article
474 KiB  
Article
The Time Scale Calculus Approach to the Geodesic Problem in 3D Dynamic Data Sets
by Sibel Paşalı Atmaca and Ömer Akgüller
Math. Comput. Appl. 2013, 18(3), 421-427; https://doi.org/10.3390/mca18030421 - 1 Dec 2013
Viewed by 1252
Abstract
Geodesics have a fundamental role in the geometry of curved surfaces, as well as in discrete geometry. We present the time scale analogy of the dynamic data sets parameterized by a tensor product of two times scales. The goal of our study is [...] Read more.
Geodesics have a fundamental role in the geometry of curved surfaces, as well as in discrete geometry. We present the time scale analogy of the dynamic data sets parameterized by a tensor product of two times scales. The goal of our study is the find the shortest and straightest path between two points on a point cloud like data sets which also involves continuous data. Full article
1188 KiB  
Article
Modeling and Control of a Variable Speed Variable Pitch Angle Prototype Wind Turbine
by Sanem Evren, Mustafa Ünel and Mahmut F. Akşit
Math. Comput. Appl. 2013, 18(3), 408-420; https://doi.org/10.3390/mca18030408 - 1 Dec 2013
Cited by 7 | Viewed by 1524
Abstract
This paper focuses on modeling, control and simulation of a 500 KW horizontal axis prototype wind turbine that is being developed in the context of the MILRES (National Wind Energy Systems) Project in Turkey. The prototype turbine is designed as variable speed variable [...] Read more.
This paper focuses on modeling, control and simulation of a 500 KW horizontal axis prototype wind turbine that is being developed in the context of the MILRES (National Wind Energy Systems) Project in Turkey. The prototype turbine is designed as variable speed variable pitch angle wind turbine due to its advantages in efficiency and the structure. Aerodynamic, mechanical and electrical subsystems along with pitch and torque controllers are designed in both Matlab/Simulink and S4WT simulation environments. The main control purpose is to generate a power curve that is close to the ideal power curve where the power is limited to the nomial value above the nominal wind speed. Turbism is integrated with both environments to generate a realistic wind profile of Kaimal turbulence model. The performance analysis of the prototype turbine is done under the power production scenario in both environments, Start up, emergency stop, shut down and parked scenarios are also implemented in S4WT. Full article
541 KiB  
Article
Numerical Solution of the Multigroup Neutron Diffusion Equation by the Meshless RBF Collocation Method
by Tayfun Tanbay and Bilge Ozgener
Math. Comput. Appl. 2013, 18(3), 399-407; https://doi.org/10.3390/mca18030399 - 1 Dec 2013
Cited by 8 | Viewed by 1315
Abstract
The multigroup neutron diffusion criticality problem is studied by the radial basis function collocation method. The multiquadric is chosen as the radial basis function. To investigate the effectiveness of the method, one, two and three-group problems are considered. It is found that the [...] Read more.
The multigroup neutron diffusion criticality problem is studied by the radial basis function collocation method. The multiquadric is chosen as the radial basis function. To investigate the effectiveness of the method, one, two and three-group problems are considered. It is found that the radial basis function collocation method produces highly accurate multiplication factors and it is also efficient in the calculation of group fluxes. Full article
493 KiB  
Article
A Comparative Study of Artificial Neural Networks and Logistic Regression for Classification of Marketing Campaign Results
by Ali Aydın Koç and Özgür Yeniay
Math. Comput. Appl. 2013, 18(3), 392-398; https://doi.org/10.3390/mca18030392 - 1 Dec 2013
Cited by 10 | Viewed by 1870
Abstract
In this study, we focus on Artificial Neural Networks which are popularly used as universal non-linear inference models and Logistic Regression, which is a well known classification method in the field of statistical learning; there are many classification algorithms in the literature, though. [...] Read more.
In this study, we focus on Artificial Neural Networks which are popularly used as universal non-linear inference models and Logistic Regression, which is a well known classification method in the field of statistical learning; there are many classification algorithms in the literature, though. We briefly introduce the techniques and discuss the advantages and disadvantages of these two methods through an application with real-world data set related with direct marketing campaigns of a Portuguese banking institution. The classification goal is to predict if the client will subscribe a term deposit or not after campaigns. Full article
256 KiB  
Article
Taylor Collocation Method for Solving a Class of the First Order Nonlinear Differential Equations
by Dilek Taştekin, Salih Yalçınbaş and Mehmet Sezer
Math. Comput. Appl. 2013, 18(3), 383-391; https://doi.org/10.3390/mca18030383 - 1 Dec 2013
Cited by 2 | Viewed by 1589
Abstract
In this study, we present a reliable numerical approximation of the some first order nonlinear ordinary differential equations with the mixed condition by the using a new Taylor collocation method. The solution is obtained in the form of a truncated Taylor series with [...] Read more.
In this study, we present a reliable numerical approximation of the some first order nonlinear ordinary differential equations with the mixed condition by the using a new Taylor collocation method. The solution is obtained in the form of a truncated Taylor series with easily determined components. Also, the method can be used to solve Riccati equation. The numerical results show the effectuality of the method for this type of equations. Comparing the methodology with some known techniques shows that the existing approximation is relatively easy and highly accurate. Full article
996 KiB  
Article
Real-Time Multiple Object Tracking Using Virtual Shells
by Taygun Kekec, Mustafa Unel and Hakan Erdogan
Math. Comput. Appl. 2013, 18(3), 373-382; https://doi.org/10.3390/mca18030373 - 1 Dec 2013
Viewed by 1476
Abstract
This paper presents a new multiple object tracking framework where arbitrarily shaped complex objects having severe occlusions are successfully tracked in real-time using stationary cameras. The proposed method utilizes the concept of a virtual shell that encloses each moving object in the scene [...] Read more.
This paper presents a new multiple object tracking framework where arbitrarily shaped complex objects having severe occlusions are successfully tracked in real-time using stationary cameras. The proposed method utilizes the concept of a virtual shell that encloses each moving object in the scene and simplifies analysis of object interactions. Object’s state transitions are handled by an event resolution analysis. Such a regional analysis boosts the tracking process. Finally, a pixel level evaluation is employed for all objects to establish successful pixel memberships. The proposed tracking algorithm is experimentally tested on some public databases and our own challenging aquarium setup that contains many different fish interactions. Full article
621 KiB  
Article
Performance Improvement in Vslam Using Stabilized Feature Points
by Caner Şahin and Mustafa Ünel
Math. Comput. Appl. 2013, 18(3), 361-372; https://doi.org/10.3390/mca18030361 - 1 Dec 2013
Cited by 1 | Viewed by 1429
Abstract
Simultaneous localization and mapping (SLAM) is the main prerequisite for the autonomy of a mobile robot. In this paper, we present a novel method that enhances the consistency of the map using stabilized corner features. The proposed method integrates template matching based video [...] Read more.
Simultaneous localization and mapping (SLAM) is the main prerequisite for the autonomy of a mobile robot. In this paper, we present a novel method that enhances the consistency of the map using stabilized corner features. The proposed method integrates template matching based video stabilization and Harris corner detector. Extracting Harris corner features from stabilized video consistently increases the accuracy of the localization. Data coming from a video camera and odometry are fused in an Extended Kalman Filter (EKF) to determine the pose of the robot and build the map of the environment. Simulation results validate the performance improvement obtained by the proposed technique. Full article
556 KiB  
Article
Vibration Analysis of Functionally Graded Sandwich Beam with Variable Cross-Section
by Hasan Çallıoğlu, Ersin Demir, Yasin Yılmaz and Metin Sayer
Math. Comput. Appl. 2013, 18(3), 351-360; https://doi.org/10.3390/mca18030351 - 1 Dec 2013
Cited by 4 | Viewed by 1958
Abstract
In this study, free vibration behavior of a multilayered symmetric sandwich beam made of Functionally Graded Material (FGM) with variable cross-section is investigated. The elasticity and density of the Functionally Graded (FG) sandwich beam vary through the thickness according to the power and [...] Read more.
In this study, free vibration behavior of a multilayered symmetric sandwich beam made of Functionally Graded Material (FGM) with variable cross-section is investigated. The elasticity and density of the Functionally Graded (FG) sandwich beam vary through the thickness according to the power and exponential laws by using mixture rules and laminate theory. In order to provide this, fifty layered beam is considered. Each layer is isotropic and homogeneous although the volume fractions of the constituents of the layers are different. Furthermore, the width of the beam varies exponentially along the length of the beam with rectangular cross-section. The natural frequencies are computed for conventional boundary conditions of the FG sandwich beam using theoretical procedure. The effects of material index, geometric index and slenderness ratio are also discussed. Finally, the obtained results are compared with those in literature and a finite element based commercial program ANSYS® and found to be consistent with each other. Full article
584 KiB  
Article
Numerical Study of Heat Transfer Due to Twinjets Impingement onto an Isothermal Moving Plate
by Anıl Başaran and Fatih Selimefendigil
Math. Comput. Appl. 2013, 18(3), 340-350; https://doi.org/10.3390/mca18030340 - 1 Dec 2013
Cited by 10 | Viewed by 1645
Abstract
In this study, heat transfer from a moving isothermal hot plate due to double impinging vertical slot jets was investigated for a laminar flow. The rectangular geometry consists of a confining adiabatic wall placed parallel to the moving impingement. The jets are located [...] Read more.
In this study, heat transfer from a moving isothermal hot plate due to double impinging vertical slot jets was investigated for a laminar flow. The rectangular geometry consists of a confining adiabatic wall placed parallel to the moving impingement. The jets are located symmetrically at mid point of upper wall. Water and Al2O3 nanoparticles mixture with different volumetric fraction was used as working medium. In considered jet impingement problem, the effects of the jet exit Reynolds numbers, ranging from 50 to 200, the normalized plate velocity, ranging from 0 to 2, and volumetric fractions of nanofluid, ranging from 0% to 6% were investigated. The commercial software package based on finite volume method FLUENT (version 6.3.26) is used in this study for the computations. It has been observed that increasing normalized plate velocity increases the heat transfer from bottom surface. Similarly, increasing Reynolds number of slot jets leads to enhancement of heat transfer. Besides, increasing volumetric fraction of nanofluid conributes to heat transfer enhancement. Full article
302 KiB  
Article
A Full Factorial Design Based Desirability Function Approach for Optimization of Properties of C 40/50 Concrete Class
by Barış Şimşek, Y. Tansel İç and Emir H.Şimşek
Math. Comput. Appl. 2013, 18(3), 330-339; https://doi.org/10.3390/mca18030330 - 1 Dec 2013
Cited by 14 | Viewed by 1851
Abstract
In this study a full factorial design (FFD) based desirability function approach (DFA) was used to the modeling of determined quality criteria of C 40/50 (C50). A FFD based DFA was also applied to determine optimal mixture proportions of C50. The mixture proportion [...] Read more.
In this study a full factorial design (FFD) based desirability function approach (DFA) was used to the modeling of determined quality criteria of C 40/50 (C50). A FFD based DFA was also applied to determine optimal mixture proportions of C50. The mixture proportion modeled by using FFD was determined as the function of variables such as water to binder materials ratio, coarse aggregate (II) to total aggregate ratio, the percentage of superplasticizer content and fly ash amount. The properties of C50 were identified as that the slump flow and 28th day compressive strength. The model results were tested with experimental runs. The results showed that the determined regression meta-models were useful for prediction of properties of C50 with the mixture parameters. The results also showed that the FFD based DFA are effective in solving the mixture proportions optimization problem. Full article
553 KiB  
Article
Some Relations on Hermite Matrix Polynomials
by Levent Kargin and Veli Kurt
Math. Comput. Appl. 2013, 18(3), 323-329; https://doi.org/10.3390/mca18030323 - 1 Dec 2013
Cited by 10 | Viewed by 1548
Abstract
In this study we give addition theorem, multiplication theorem and summation formula for Hermite matrix polynomials. We write Hermite matrix polynomials as hypergeometric matrix functions. We also obtain a new generating function for Hermite matrix polynomials and using this function, we prove some [...] Read more.
In this study we give addition theorem, multiplication theorem and summation formula for Hermite matrix polynomials. We write Hermite matrix polynomials as hypergeometric matrix functions. We also obtain a new generating function for Hermite matrix polynomials and using this function, we prove some new results and relations. Full article
634 KiB  
Article
A New Simulated Annealing Approach for Travelling Salesman Problem
by Hüsamettin Bayram and Ramazan Şahin
Math. Comput. Appl. 2013, 18(3), 313-322; https://doi.org/10.3390/mca18030313 - 1 Dec 2013
Cited by 18 | Viewed by 2217
Abstract
The aim of this study is to improve searching capability of simulated annealing (SA) heuristic through integration of two new neighborhood mechanisms. Due to its ease of formulation, difficulty to solve and various real life applications several Travelling Salesman Problems (TSP) were selected [...] Read more.
The aim of this study is to improve searching capability of simulated annealing (SA) heuristic through integration of two new neighborhood mechanisms. Due to its ease of formulation, difficulty to solve and various real life applications several Travelling Salesman Problems (TSP) were selected from the literature for the testing of the proposed methods. The proposed methods were also compared to conventional SA with swap neighborhood. The results have shown that the proposed techniques are more effective than conventional SA, both in terms of solution quality and time. Full article
694 KiB  
Article
Cropped Quad-Tree Based Solid Object Colouring with Cuda
by Abdullah Çavuşoğlu, Baha Şen, Caner Özcan and Salih Görgünoğlu
Math. Comput. Appl. 2013, 18(3), 301-312; https://doi.org/10.3390/mca18030301 - 1 Dec 2013
Viewed by 1863
Abstract
In this study, surfaces of solid objects are coloured with Cropped Quad-Tree method utilizing GPU computing optimization. There are numerous methods used in solid object colouring. When the studies carried out in different fields are taken into consideration, it is seen that quad-tree [...] Read more.
In this study, surfaces of solid objects are coloured with Cropped Quad-Tree method utilizing GPU computing optimization. There are numerous methods used in solid object colouring. When the studies carried out in different fields are taken into consideration, it is seen that quad-tree method displays a prominent position in terms of speed and performance. Cropped quad-tree is obtained as a result of the developments seen with the frequent use of this method in the field of computer sciences. Two different versions of algorithm which operate recursively on CPU and at the same time which use GPU computing optimization are used in this study. Besides, OpenGL is used for graphics drawing process. Within the setting of the study, results are obtained via CPU and GPU’s, at first using Quad-Tree method and then Cropped Quad-Tree method. It is observed that GPU computing is obviously faster than CPU computing and Cropped Quad-Tree method produces rapid results compared to Quad-Tree method as a result of performance. GPU computing method boosted approximately performance by up to 20 times compared to only CPU usage; furthermore, cropped quad-tree method boosted approximately performance of algorithm by up to 25 times on average dependent on screen and object size. Full article
430 KiB  
Article
Bernstein Collocation Method for Solving Nonlinear Differential Equations
by Aysegul Akyuz Dascioglu and Nese Isler
Math. Comput. Appl. 2013, 18(3), 293-300; https://doi.org/10.3390/mca18030293 - 1 Dec 2013
Cited by 8 | Viewed by 2089
Abstract
In this study, a collocation method based on Bernstein polynomials is developed for solution of the nonlinear ordinary differential equations with variable coefficients, under the mixed conditions. These equations are expressed as linear ordinary differential equations via quasilinearization method iteratively. By using the [...] Read more.
In this study, a collocation method based on Bernstein polynomials is developed for solution of the nonlinear ordinary differential equations with variable coefficients, under the mixed conditions. These equations are expressed as linear ordinary differential equations via quasilinearization method iteratively. By using the Bernstein collocation method, solutions of these linear equations are approximated. Combining the quasilinearization and the Bernstein collocation methods, the approximation solution of nonlinear differential equations is obtained. Moreover, some numerical solutions are given to illustrate the accuracy and implementation of the method. Full article
277 KiB  
Article
Error Estimates for Differential Difference Schemes to Pseudo-Parabolic Initial-Boundary Value Problem with Delay
by Pinar Okcu and Gabil M. Amiraliyev
Math. Comput. Appl. 2013, 18(3), 283-292; https://doi.org/10.3390/mca18030283 - 1 Dec 2013
Cited by 8 | Viewed by 1504
Abstract
We consider the one dimensional initial-boundary Sobolev problem with delay. For solving this problem numerically, we construct fourth order differential- difference scheme and obtain the error estimate for its solution. Further we use the appropriate Runge-Kutta method for the realization of our differential-difference [...] Read more.
We consider the one dimensional initial-boundary Sobolev problem with delay. For solving this problem numerically, we construct fourth order differential- difference scheme and obtain the error estimate for its solution. Further we use the appropriate Runge-Kutta method for the realization of our differential-difference problem. Full article
698 KiB  
Article
A Mathematical Model for Two Dimensional Loading Problem in Cross-Docking Network Design
by İlker Küükoğlu, Aslı Aksoy, Seval Ene and Nursel Öztürk
Math. Comput. Appl. 2013, 18(3), 273-282; https://doi.org/10.3390/mca18030273 - 1 Dec 2013
Cited by 1 | Viewed by 1499
Abstract
In this paper, the transportation problem of cross-docking network is taken into account. Cross-docking centers differ from distribution centers or warehouses in that the loads are transported from origins to destinations through cross-docking centers without storing them for a long time. Goods are [...] Read more.
In this paper, the transportation problem of cross-docking network is taken into account. Cross-docking centers differ from distribution centers or warehouses in that the loads are transported from origins to destinations through cross-docking centers without storing them for a long time. Goods are unloaded from incoming trucks and reloaded immediately onto outgoing trucks in these cross-docking centers. This problem is formulated using a mixed integer programming with two-dimensional loading constraints. The two-dimensional shapes are applied for both trucks and loads in order to find exact capacity of each truck in basis of each product. The illustrative problems are solved and results show that the proposed model finds practical solutions with two- dimensional loading constraints. Full article
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