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Math. Comput. Appl., Volume 16, Issue 1 (April 2011) – 30 articles , Pages 1-316

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434 KiB  
Article
About Dual Spherical Wrist Motion and Its Trajectory Surface as a Ruled Surface
by Hatice Kuşak and Ali Çalışkan
Math. Comput. Appl. 2011, 16(1), 309-316; https://doi.org/10.3390/mca16010309 - 01 Apr 2011
Viewed by 1258
Abstract
Solid object rotations or rotations of unit real vectors are often used in robotic moves. Yet, due to the complexity of calculations in kinematics analysis, quaternions began to be used in robotic moves. Quaternions help us to calculate rotations in reel space, and [...] Read more.
Solid object rotations or rotations of unit real vectors are often used in robotic moves. Yet, due to the complexity of calculations in kinematics analysis, quaternions began to be used in robotic moves. Quaternions help us to calculate rotations in reel space, and rotation and translation in dual space. Furthermore, we can easily define a screw or an axis through dual vectors. In recent years, there has been efficient studies in mechanics analysis by using dual quaternions and screw moves. In this study, we transferred the well known sequential and modular methods for the rotations being formed in real spherical wrist moves to dual space. Hence, while we rotate the unit vectors only in real space, now we can rotate screws .Hence, while we rotate the unit vectors only in real space, now we can rotate screws or the axis in the dual spherical mechanisms in dual kinematics. Through this study, by being switched to dual spherical mechanism the first time, we will see that we can carry out what we do with unit vectors in real space as well as in dual space. Furthermore, while the orbits drawn by the joint moves are curves in reel spherical wrist moves, the orbits drawn by the joint moves are ruled surfaces in dual spherical wrist moves. We think that this situation would establish a base for different mechanics studies. Full article
181 KiB  
Article
Multiple Time Scales Solution of an Equation with Quadratic and Cubic Nonlinearities Having Fractional- Order Derivative
by Fadime Dal
Math. Comput. Appl. 2011, 16(1), 301-308; https://doi.org/10.3390/mca16010301 - 01 Apr 2011
Cited by 11 | Viewed by 1344
Abstract
Nonlinear vibrations of quadratic and cubic system are considered. The equation of motion includes fractional order term. Multiple time scales (a perturbation method) solution of the system is developed. Effect of fractional order derivative term is discussed. Full article
382 KiB  
Article
Amplitude Noise Reduction in a Nano-Mechanical Oscillator
by Aziz Kolkiran
Math. Comput. Appl. 2011, 16(1), 290-300; https://doi.org/10.3390/mca16010290 - 01 Apr 2011
Cited by 2 | Viewed by 1455 | Correction
Abstract
We study the quantum properties of a nano-mechanical oscillator via the squeezing of the oscillator amplitude. The static longitudinal compressive force 0 F close to a critical value at the Euler buckling instability leads to an anharmonic term in the Hamiltonian and thus [...] Read more.
We study the quantum properties of a nano-mechanical oscillator via the squeezing of the oscillator amplitude. The static longitudinal compressive force 0 F close to a critical value at the Euler buckling instability leads to an anharmonic term in the Hamiltonian and thus the squeezing properties of the nano-mechanical oscillator are to be obtained from the Hamiltonian of the form H = a+a + β(a+ + a) / 4 . This Hamiltonian has no exact solution unlike the other known models of nonlinear interactions of the forms a+2 a2, (a2a)2 and a+4 + a4 - (a+2 a2 + a2 a+2 ) previously employed in quantum optics to study squeezing. Here we solve the Schrodinger equation numerically and show that in-phase quadrature gets squeezed for both vacuum and coherent states. The squeezing can be controlled by bringing F0 close to or far from the critical value Fc. We further study the effect of the transverse driving force on the squeezing in nano-mechanical oscillator. Full article
440 KiB  
Article
An Extended Heuristic Algorithm to Settle Reacting Objects on a Planar Surface
by Gorkem Tokatli, Pinar Dundar, Moharram Challenger and Tufan Turaci
Math. Comput. Appl. 2011, 16(1), 279-289; https://doi.org/10.3390/mca16010279 - 01 Apr 2011
Viewed by 1347
Abstract
Graph theory is a key subject for both mathematics and computer science. It is used for modelling many problems such as maximal independent set, minimum covering and matching. In our study, we have extended the previous work on placing materials that may react [...] Read more.
Graph theory is a key subject for both mathematics and computer science. It is used for modelling many problems such as maximal independent set, minimum covering and matching. In our study, we have extended the previous work on placing materials that may react with each other on a 2-D warehouse. We have modelled the problem using graph theory. Then, we have developed extensions on the heuristic algorithm which is using Paull-Unger method that finds Maximal Independent Sets. First two of these extensions include finding solutions with gaps for specific graphs, and meanwhile capability of performing replacement in any desired rectangle surface. The last and most effective extension is pruning unnecessary backtracking steps with the help of smarter heuristics in the algorithm. Full article
165 KiB  
Article
Numerical Approach of High-Order Linear Delay Difference Equations with Variable Coefficients in Terms of Laguerre Polynomials
by Burcu Gürbüz, Mustafa Gülsu and Mehmet Sezer
Math. Comput. Appl. 2011, 16(1), 267-278; https://doi.org/10.3390/mca16010267 - 01 Apr 2011
Cited by 7 | Viewed by 1456
Abstract
This paper presents a numerical method for the approximate solution of mthorder linear delay difference equations with variable coefficients under the mixed conditions in terms of Laguerre polynomials. The aim of this article is to present an efficient numerical procedure for solving mth-order [...] Read more.
This paper presents a numerical method for the approximate solution of mthorder linear delay difference equations with variable coefficients under the mixed conditions in terms of Laguerre polynomials. The aim of this article is to present an efficient numerical procedure for solving mth-order linear delay difference equations with variable coefficients. Our method depends mainly on a Laguerre series expansion approach. This method transforms linear delay difference equations and the given conditions into matrix equation which corresponds to a system of linear algebraic equation. The reliability and efficiency of the proposed scheme are demonstrated by some numerical experiments and performed on the computer algebraic system Maple. Full article
125 KiB  
Article
Exp-Function Method for Solving Nonlinear Evolution Equations
by Emine Misirli and Yusuf Gurefe
Math. Comput. Appl. 2011, 16(1), 258-266; https://doi.org/10.3390/mca16010258 - 01 Apr 2011
Cited by 40 | Viewed by 1587
Abstract
In this paper, we applied Exp-function method to some nonlinear evolution equations. The solution procedure of this method, by the help of symbolic computation of Matlab, Mathematica or so on, is of utter simplicity. The obtained results show that Exp-function method is very [...] Read more.
In this paper, we applied Exp-function method to some nonlinear evolution equations. The solution procedure of this method, by the help of symbolic computation of Matlab, Mathematica or so on, is of utter simplicity. The obtained results show that Exp-function method is very powerful and convenient mathematical tool for nonlinear evolution equations in science and engineering. Full article
228 KiB  
Article
Non-Ergodic to Ergodic Regime Transition via Intrusions in a Non-Poisson Renewal System with Power Law Tails
by Osman Çağlar Akin
Math. Comput. Appl. 2011, 16(1), 248-257; https://doi.org/10.3390/mca16010248 - 01 Apr 2011
Viewed by 1169
Abstract
We study the effect of non-linear perturbations in the form of periodic intrusions in the case of a non-Poisson renewal system in the non-ergodic regime. We notice that, intrusions may cause the system to shift the power index and may even cause a [...] Read more.
We study the effect of non-linear perturbations in the form of periodic intrusions in the case of a non-Poisson renewal system in the non-ergodic regime. We notice that, intrusions may cause the system to shift the power index and may even cause a transition from a non-ergodic regime to an ergodic regime. We have made the diffusion entropy analysis (DEA) of the system and notice that the change of the degree of complexity is consistent with the transition as well. Full article
220 KiB  
Article
Studies on Fuzzy Logic Control of Electrical Machines in Turkish Universities: An Overview
by Aykut Kentli
Math. Comput. Appl. 2011, 16(1), 236-247; https://doi.org/10.3390/mca16010236 - 01 Apr 2011
Cited by 4 | Viewed by 1453
Abstract
This study mainly surveys the PhD and Master Theses on fuzzy logic control in Turkey. It is beneficial for researchers to know the previous studies on their subject, in an organized way. From this point of view, it is expected that this study [...] Read more.
This study mainly surveys the PhD and Master Theses on fuzzy logic control in Turkey. It is beneficial for researchers to know the previous studies on their subject, in an organized way. From this point of view, it is expected that this study will help the researchers on fuzzy logic control as there is no similar study on this area. In this study, background information on fuzzy logic is given, and applications on electrical machines are summarized and compared. Lastly, future recommendations are given for new researchers. Full article
200 KiB  
Article
Investigation of Coating Layer to Reduce Thermal Stresses in Steel Fiber Reinforced Aluminum Metal Matrix Composite
by Fuat Okumuş
Math. Comput. Appl. 2011, 16(1), 226-235; https://doi.org/10.3390/mca16010226 - 01 Apr 2011
Cited by 3 | Viewed by 1221
Abstract
In this study, by using coating layers to reduce thermal stresses in the metal matrix composites with a mismatch in coefficients of thermal expansions of fiber and matrix is investigated. The thermoelastic solutions based on a three cylinder model are deformed. It is [...] Read more.
In this study, by using coating layers to reduce thermal stresses in the metal matrix composites with a mismatch in coefficients of thermal expansions of fiber and matrix is investigated. The thermoelastic solutions based on a three cylinder model are deformed. It is shown that the effectiveness of the layer can be defined by the product of its cofficients of thermal expansions and thickness and that a compensating layer with a sufficiently high coefficient of thermal expansions can reduce the thermal stresses in the metal matrix. . In order to verify the results were compared with the finite element method. In this solution, 224 nodes and 44 nine-node isoparametric elements are used. The study is based on a three cylinder model isolating one steel fiber with a coating layer and a aluminum matrix layer. Only monotonic cooling is studied and the variation of the material properties with temperatures is not considered. The results have been presented in graphics. Full article
150 KiB  
Article
Elasto-Plastic Stress Analysis in Silicon Carbide Fiber Reinforced Magnesium Metal Matrix Composite with a Square Hole
by Fuat Okumuş
Math. Comput. Appl. 2011, 16(1), 216-225; https://doi.org/10.3390/mca16010216 - 01 Apr 2011
Cited by 1 | Viewed by 1230
Abstract
In the present study an elastic-plastic stress analysis is carried out for long silicon carbide fiber reinforced magnesium metal matrix composite with a square hole by using finite element technique. Composite material is manufactured by using molds under a pressure of 35 MPa [...] Read more.
In the present study an elastic-plastic stress analysis is carried out for long silicon carbide fiber reinforced magnesium metal matrix composite with a square hole by using finite element technique. Composite material is manufactured by using molds under a pressure of 35 MPa and heating up to 550 0C by electrical resistance. The laminated plates with square hole consist of four layers and bonded symmetrically. Each layer with constant thickness is meshed into 48 elements and 228 nodes with simply supported. The expansion of plastic zone and residual stress are determined in the symmetric cross-ply and angle-ply laminated plates for small deformations. The load is increased by 0.01 MPa at each step . Iteration numbers are chosen as 150, 300 and 600. The resılts show that the intensity of the residual stresses is maximum near the open square hole and the yield points in symmetric laminates are higher than those in antisymmetric laminates.The plastic regions at the plate edges expand in the direction of the fiber, but at the border of the hole expand toward the diagonal of the hole. Full article
377 KiB  
Article
Non-Linear Transverse Vibrations and 3:1 Internal Resonances of a Tensioned Beam on Multiple Supports
by S.Murat Bağdatlı, H. Rıdvanz Öz and Erdoğan Özkaya
Math. Comput. Appl. 2011, 16(1), 203-215; https://doi.org/10.3390/mca16010203 - 01 Apr 2011
Cited by 8 | Viewed by 1368
Abstract
In this study, nonlinear transverse vibrations of a tensioned Euler-Bernoulli beam resting on multiple supports are investigated. The immovable end conditions due to simple supports cause stretching of neutral axis and introduce cubic nonlinearity to the equations of motion. Forcing and damping effects [...] Read more.
In this study, nonlinear transverse vibrations of a tensioned Euler-Bernoulli beam resting on multiple supports are investigated. The immovable end conditions due to simple supports cause stretching of neutral axis and introduce cubic nonlinearity to the equations of motion. Forcing and damping effects are included in the analysis. The general arbitrary number of support case is investigated and 3, 4, and 5 support cases analyzed in detail. A perturbation technique (the method of multiple scales) is applied to the equations of motion to obtain approximate analytical solutions. 3:1 internal resonance case is also considered. Natural frequencies and mode shapes for the linear problem are found for the tensioned beam. Nonlinear frequencies are calculated; amplitude and phase modulation figures are presented for different forcing and damping cases. Frequency-response and force-response curves are drawn. Different internal resonance cases between modes are investigated. Full article
798 KiB  
Article
Stress Analysis in Al Based Composites Depending on Joining Quality
by N. Sinan Köksal and Mehmet Alkan
Math. Comput. Appl. 2011, 16(1), 194-202; https://doi.org/10.3390/mca16010194 - 01 Apr 2011
Viewed by 1274
Abstract
It is essential that joints in the design of aluminium based materials be safe and at the desired strength. Specific methods are to be used in welding of these materials. Brazing, that assures joining without changing the material properties, is widely used for [...] Read more.
It is essential that joints in the design of aluminium based materials be safe and at the desired strength. Specific methods are to be used in welding of these materials. Brazing, that assures joining without changing the material properties, is widely used for this purpose. In this method, quality joining can be achieved, provided the parameters are set up accurately. In this study, joining characteristics of aluminium based composite materials widely used in automotive industry are investigated in detail. Solid models of the parts manufactured by brazing are created using Solidworks software. Hydrostatic loading similar to the real working conditions is applied to these models and stress analysis is performed using ANSYS software. In the samples, joining regions are 2 mm and 2,83 mm in length; and stress distributions are investigated in three groups assuming full, 70% and 50% joining. Stresses arising from loading in the model are below the damage inducing level, but the shape and the length of the joining region are observed to be significant in stress development. Full article
697 KiB  
Article
Nonlinear Finite Element Analysis of Impact Behavior of Concrete Beam
by Erkan Kantar, R. Tuğrul Erdem and Özgür Anıl
Math. Comput. Appl. 2011, 16(1), 183-193; https://doi.org/10.3390/mca16010183 - 01 Apr 2011
Cited by 20 | Viewed by 1700
Abstract
The least well known loading type is the impact loading that are affecting on to RC structures. Several impact tests have been used to demonstrate the relative brittleness and impact resistance of concrete and similar construction materials. However, none of these tests has [...] Read more.
The least well known loading type is the impact loading that are affecting on to RC structures. Several impact tests have been used to demonstrate the relative brittleness and impact resistance of concrete and similar construction materials. However, none of these tests has been declared to be a Standard test, at least in part due to the lack of statistical data on the variation of the results. In this study; total ten beam specimens at which five of them are manufactured from normal concrete compression strength without reinforcement are manufactured. Remaining five had high concrete compression strength. These specimens are tested under the impacts loading that are applied by dropping constant weight hammer from five different heights. The acceleration arises from the impact loading is measured against time. The change of velocity, displacement and energy is calculated for all specimens. The failure modes of the specimens with normal and high concrete compression strength are observed under the loading of constant weight impact hammer that are dropped from different heights. A finite element model that is made by using ABAQUS software is used for the simulation of experiments and model gave compatible results with experiments. Full article
317 KiB  
Article
Dynamic Response of a Beam Due to an Accelerating Moving Mass Using Moving Finite Element Approximation
by İsmail Esen
Math. Comput. Appl. 2011, 16(1), 171-182; https://doi.org/10.3390/mca16010171 - 01 Apr 2011
Cited by 55 | Viewed by 2011
Abstract
In this study, the dynamic behaviour of a beam carrying accelerating mass is investigated. A MATLAB code was developed for numerical solutions. The accelerating moving mass that is travelling on the beam was modelled as a moving finite element in order to include [...] Read more.
In this study, the dynamic behaviour of a beam carrying accelerating mass is investigated. A MATLAB code was developed for numerical solutions. The accelerating moving mass that is travelling on the beam was modelled as a moving finite element in order to include inertial effects beside gravitation force of mass. Since the mass moves along the deflected curve of the beam, these effects are, respectively, the centripetal force, the inertia force, and the Coriolis force components of the moving mass. The effect of longitudinal force due to acceleration of the moving mass is also included. Dynamic response of the beam was obtained depending on the mass ratio (mass of the load / the mass of the beam) and the acceleration of the mass. Numerical results show the effectiveness of the method. Full article
846 KiB  
Article
An Experimental and Numerical Study on the Effects of Taper Angles and Overlap Length on the Failure and Stress Distribution of Adhesively-Bonded Single-Lap Joints
by Murat Yavuz Solmaz and Aydın Turgut
Math. Comput. Appl. 2011, 16(1), 159-170; https://doi.org/10.3390/mca16010159 - 01 Apr 2011
Cited by 23 | Viewed by 1658
Abstract
This paper examines the failures and strengths of joints bonded by a Neoxil CE92 N8 adhesive at different overlap lengths and different taper angles. The study was carried out both as experimental and numerical. In the experimental stage, lap-shear tests on Single-Lap Joints [...] Read more.
This paper examines the failures and strengths of joints bonded by a Neoxil CE92 N8 adhesive at different overlap lengths and different taper angles. The study was carried out both as experimental and numerical. In the experimental stage, lap-shear tests on Single-Lap Joints (SLJs) with different taper angles and overlap lengths were conducted. The stress analyses in the SLJs were obtained using a linear Finite Element Analysis (FEA) in numerical stage. It is assumed that adhesive and adherend have both geometrical nonlinearity and linear material behaviour. Scrutinising carefully the surfaces of the SLJs, two different failure types, cohesive failures (CF) and special cohesive failures (SCF) were observed. The obtained numerical results were compared with experimental ones. Results indicate that the increasing of both overlap length and taper angle increase the joint strength and, in particular, the highest strength values in all joint geometries are attained by specimens having a taper angle of 15°. Full article
1128 KiB  
Article
Reduction of Stress Concentration at the Corner Bends of the Anti-Roll Bar by Using Parametric Optimisation
by M. Murat Topaç, H. Eren Enginar and N. Sefa Kuralay
Math. Comput. Appl. 2011, 16(1), 148-158; https://doi.org/10.3390/mca16010148 - 01 Apr 2011
Cited by 8 | Viewed by 1545
Abstract
Stress concentration at the corner bends of an anti-roll bar that is designed for an intercity passenger bus is reduced by optimising the shape of the critical regions. In order to do this, parameters which constitute the geometry of the stress concentrated regions [...] Read more.
Stress concentration at the corner bends of an anti-roll bar that is designed for an intercity passenger bus is reduced by optimising the shape of the critical regions. In order to do this, parameters which constitute the geometry of the stress concentrated regions are determined. The effect of these parameters on stress concentration is evaluated by using Design of Experiments (DoE) approach. Possible design options and their corresponding mass and maximum equivalent stress values are obtained by using finite element analysis. The results are assessed by means of response surfaces generated by FEA software. Transition form that gives optimum stress concentration is determined. Full article
446 KiB  
Article
A Model for the Calculation of Mechanical Properties of Hydroxyapatite Coatings on Ti6Al4V Substrate Using Finite Element Methods
by Ahmet Pasinli, Osman Culha, Erdal Celik and Mustafa Toparli
Math. Comput. Appl. 2011, 16(1), 136-147; https://doi.org/10.3390/mca16010136 - 01 Apr 2011
Viewed by 1286
Abstract
The scope of this study is to find out yield curve on the coating-substrate system of hydroxyapatite (HA) by finite element modeling. With this regard, Hydroxyapatite (HA) coatings were successfully formed on Ti6Al4V substrates by using biomimetic technique. Experimental indentation tests were conducted [...] Read more.
The scope of this study is to find out yield curve on the coating-substrate system of hydroxyapatite (HA) by finite element modeling. With this regard, Hydroxyapatite (HA) coatings were successfully formed on Ti6Al4V substrates by using biomimetic technique. Experimental indentation tests were conducted on Dynamic Ultra-micro Hardness test machine. In finite element modeling (FEM), mechanical properties of coatings were determined by using ABAQUS software package. This numerical study was carried out using an axisymmetric FEM model. To calculate the mechanical properties of coating, the resulting load–unload test data of the samples obtained from the experimental indentation tests were analyzed and curvefitted in Kick’s and Meyer’s law for the loading and the unloading part of the loadunload curve respectively. Then, a set of analytical functions that take the pile-up and sink-in effects into account during instrumented sharp indentation were solved using numerical methods These analytical functions were defined within an identified representative plastic strain, εr, for the Vickers indenter geometry as a strain level that allows for the description of the indentation loading response independent of strain hardening exponent, n. Full article
730 KiB  
Article
Numerical Investigation of Residual Stresses in YBCO/CeO2/YSZ/CeO2/Ni Architextured Materials for Coated Conductors
by Mustafa Toparli, Onur Sayman and Erdal Celik
Math. Comput. Appl. 2011, 16(1), 125-135; https://doi.org/10.3390/mca16010125 - 01 Apr 2011
Cited by 3 | Viewed by 1212
Abstract
In this study, the stress analysis of YBCO/CeO2/YSZ/CeO2/Ni architextured materials under cryogenic conditions was carried out for coated conductor applications. YBCO/CeO2/YSZ/CeO2 multilayer films were fabricated on Ni tape substrate using reel-to-reel sol-gel and Pulse Laser Deposition [...] Read more.
In this study, the stress analysis of YBCO/CeO2/YSZ/CeO2/Ni architextured materials under cryogenic conditions was carried out for coated conductor applications. YBCO/CeO2/YSZ/CeO2 multilayer films were fabricated on Ni tape substrate using reel-to-reel sol-gel and Pulse Laser Deposition (PLD) systems. The microstructural evolution of high temperature superconducting YBCO film and buffer layers with CeO2/YSZ/CeO2 configuration grown on textured Ni tape substrates were investigated by a Scanning Electron Microscope (SEM). SEM observations revealed that crack-free, pinhole-free, continuous superconducting film and buffer layers were obtained by solgel and PLD systems. The thermal distribution in the each layer was calculated using the classical lamination theory in the temperature range of 25 to -270°C in liquid helium media. The residual stresses occurred during the manufacturing are neglected therefore, all the residual stresses are assumed to be zero at 25°C. Different thermal expansion coefficients and modulus of elasticity bring about the thermal stresses in the layers. Full article
2466 KiB  
Article
Calculation of the Mechanical Properties of FeB Layer's by Finite Element Method
by Osman Culha, Mustafa Toparli, Tevfik Aksoy and Mustafa Akdag
Math. Comput. Appl. 2011, 16(1), 113-124; https://doi.org/10.3390/mca16010113 - 01 Apr 2011
Cited by 5 | Viewed by 1215
Abstract
Surface treatments of engineering materials are important for serviceable engineering components. One of the thermo-chemical surface treatments of steel based materials is the boriding process. In this study, low alloy steel substrates were borided by pack boriding process at 900 °C. Experimental indentation [...] Read more.
Surface treatments of engineering materials are important for serviceable engineering components. One of the thermo-chemical surface treatments of steel based materials is the boriding process. In this study, low alloy steel substrates were borided by pack boriding process at 900 °C. Experimental indentation tests were conducted on Dynamic Ultra-micro Hardness test machine, under applied peak loads of 800 mN, 1000 mN, 1200 mN and 1400 mN. To get the mechanical properties of FeB layers, the resulting load–unload test data of the samples obtained from the experimental indentation tests were analyzed and curve-fitted in Kick’s and Meyer’s law for the loading and the unloading part of the load-unload curve respectively. Then, a set of analytical functions that take the pile-up and sink-in effects into account during instrumented sharp indentation were solved using numerical methods. These analytical functions were defined within an identified representative plastic strain, εr, for the Vickers indenter geometry as a strain level that allows for the description of the indentation loading response independent of strain hardening exponent, n. The mechanical characterization of samples, finite element modeling was applied to simulate the mechanical response of FeB layer on low alloy steel substrate by using ABAQUS software package program. Full article
439 KiB  
Article
Three Dimensional Cutting Problem: An Integer Programming Approach
by Bayram Kahraman
Math. Comput. Appl. 2011, 16(1), 105-112; https://doi.org/10.3390/mca16010105 - 01 Apr 2011
Cited by 2 | Viewed by 1162
Abstract
Cutting problem is one of the major problems faced in marble factories. Huge marble blocks coming from marble quarries are first cut into planes according to their depths. Then these planes are sized according to the length and width of the demanded products. [...] Read more.
Cutting problem is one of the major problems faced in marble factories. Huge marble blocks coming from marble quarries are first cut into planes according to their depths. Then these planes are sized according to the length and width of the demanded products. In this study, cutting problem of a marble factory is handled. The two problems, which are cutting marble blocks into planes and sizing these planes, are integrated together. An integer programming model is built for the integrated problem. The objective of the model is to minimize total waste of marble while finding the cutting design of the marble block and marble planes. The model is used to solve the cutting problem of a real life marble processing factory. It is shown that the mathematical model decreases wasted amount of marble considerably compared to the industry average. Full article
260 KiB  
Article
A Facility Layout Problem in a Marble Factory via Simulation
by Rahime Sancar Edis, Bayram Kahraman, Özlem Uzun Araz and M. Kemal Özfırat
Math. Comput. Appl. 2011, 16(1), 97-104; https://doi.org/10.3390/mca16010097 - 01 Apr 2011
Cited by 13 | Viewed by 1774
Abstract
The marble factory in this study is a typical instance of a flow shop based production system. Adding new machines to the plant and/or introducing a new product may convert the actual layout to an inefficient one. Such cases may cause a significant [...] Read more.
The marble factory in this study is a typical instance of a flow shop based production system. Adding new machines to the plant and/or introducing a new product may convert the actual layout to an inefficient one. Such cases may cause a significant increase in transportation of materials between machines that decreases the utilization rates of machines and operators as well as overall productivity. Therefore, facility planning is a key issue in marble plants in terms of total cost and customer satisfaction. Another important property of these plants is its dynamic and stochastic behavior in terms of scrap rates, demands and processing times. The aim of this study is to develop an efficient plant layout for such dynamic systems. At first, the simulation model of the current system is built on ARENA 10.0. Then, an alternative layout is generated after some analysis and then, it is evaluated via simulation model. The proposed layout provides reduction in total transportation time as well as an increase in productivity. Full article
166 KiB  
Article
Performance of an Ensemble Clustering Algorithm on Biological Data Sets
by Harun Pirim, Dilip Gautam, Tanmay Bhowmik, Andy D. Perkins, Burak Ekşioglu and Ahmet Alkan
Math. Comput. Appl. 2011, 16(1), 87-96; https://doi.org/10.3390/mca16010087 - 01 Apr 2011
Cited by 5 | Viewed by 1326
Abstract
Ensemble clustering is a promising approach that combines the results of multiple clustering algorithms to obtain a consensus partition by merging different partitions based upon well-defined rules. In this study, we use an ensemble clustering approach for merging the results of five different [...] Read more.
Ensemble clustering is a promising approach that combines the results of multiple clustering algorithms to obtain a consensus partition by merging different partitions based upon well-defined rules. In this study, we use an ensemble clustering approach for merging the results of five different clustering algorithms that are sometimes used in bioinformatics applications. The ensemble clustering result is tested on microarray data sets and compared with the results of the individual algorithms. An external cluster validation index, adjusted rand index (C-rand), and two internal cluster validation indices; silhouette, and modularity are used for comparison purposes. Full article
355 KiB  
Article
Optimization of Open Canal Cross Sections by Differential Evolution Algorithm
by Mustafa Erkan Turan and Mehmet Ali Yurdusev
Math. Comput. Appl. 2011, 16(1), 77-86; https://doi.org/10.3390/mca16010077 - 01 Apr 2011
Cited by 12 | Viewed by 1356
Abstract
Open canals are important water transfer structures used in water resources systems. As such, they may require substantial amount of investment depending on its length and cross section. Therefore, cross section design should be carried out on an optimization basis. Traditionally, optimal sizing [...] Read more.
Open canals are important water transfer structures used in water resources systems. As such, they may require substantial amount of investment depending on its length and cross section. Therefore, cross section design should be carried out on an optimization basis. Traditionally, optimal sizing of open canal cross sections are undertaken by nonlinear optimization techniques such as Lagrange Multipliers. In this study, optimum cross sections of different canal geometries are obtained using differential evolution algorithm and the findings of these exercises are compared with those of given in related literature. It is observed that differential evolution algorithm can be well applicable to the problem and capable of giving the global optima. Full article
236 KiB  
Article
Technical Efficiency and Total Factor Productivity Growth in the Hazelnut Agricultural Sales Cooperatives Unions in Turkey
by Mehmet Candemir, Mümin Özcan, Mustafa Güneş and Ertuğrul Deliktaş
Math. Comput. Appl. 2011, 16(1), 66-76; https://doi.org/10.3390/mca16010066 - 01 Apr 2011
Cited by 15 | Viewed by 1759
Abstract
This study measures the production efficiencies and total factor productivity changes of Hazelnut Agricultural Sales Cooperatives Unions (HASCUs) in Turkey over the period 2004-2008. Turkey produces %78.2 hazelnut production of world and gives service to 233,820 farmers in the Black Sea Region of [...] Read more.
This study measures the production efficiencies and total factor productivity changes of Hazelnut Agricultural Sales Cooperatives Unions (HASCUs) in Turkey over the period 2004-2008. Turkey produces %78.2 hazelnut production of world and gives service to 233,820 farmers in the Black Sea Region of Turkey. To measure production efficiencies of these units, Data Envelopment Analysis (DEA) Approach and Malmquist Productivity Indexes are used. In the our efficiency analysis, the data of 50 HASCUs is considered but only the data of 37 cooperative units is found appropriate for the DEA. The findings of our study show that the average annual technical efficiency scores of HASCUs change between 0.841 and 0.938. It has also been observed that there are average annual %1.3 improvements in technical efficiency, 3% regress in technical change, and %1.7 decreases in the total factor productivity of the HASCUs over the period 2004-2008. Full article
404 KiB  
Article
Searching for the Shortest Path Through Group Processing for TSP
by İbrahim Meşecan, İhsan Ömür Bucak and Özcan Asilkan
Math. Comput. Appl. 2011, 16(1), 53-65; https://doi.org/10.3390/mca16010053 - 01 Apr 2011
Cited by 1 | Viewed by 1244
Abstract
Thanks to its complexity, Traveling Salesman Problem (TSP) has been one of the most intensively studied problems in computational mathematics. Although many solutions have been offered so far, all of them have yielded some disadvantages and none has been able to claim for [...] Read more.
Thanks to its complexity, Traveling Salesman Problem (TSP) has been one of the most intensively studied problems in computational mathematics. Although many solutions have been offered so far, all of them have yielded some disadvantages and none has been able to claim for the best solution. We believe that better solution could be obtained through iterative evaluations, until a certain number of islands are reached, if we could develop an algorithm which grows geometrically. Some algorithms have suggested random solutions and many suggested using the closest neighbors. In many cases islands exist in groups or chains in any length. Therefore they can be connected to any other island rather than the closest one. This can be better identified when we spot out the patterns and island chains. In this paper, we have searched for the identification of patterns and chains. We propose an iterative Group Processing (GP) approach which finds better paths in the 90% of the cases overall as we compare it to Random Logic (RL) programs and most up-to-date Artificial Neural Network based TSP programs. Full article
1508 KiB  
Article
Entropy in Dichotic Listening EEEG Recordings
by Alper Vahaplar, C. Cengiz Çelikoğlu and Murat Özgören
Math. Comput. Appl. 2011, 16(1), 43-52; https://doi.org/10.3390/mca16010043 - 01 Apr 2011
Cited by 4 | Viewed by 1300
Abstract
The dichotic listening (DL) paradigm has an important role in brain asymmetry studies at the behavioral level. In dichotic listening, the subjects are alerted by diotic or dichotic stimuli which are meaningless, consonant vowel syllables on both ears. The subjects then presented the [...] Read more.
The dichotic listening (DL) paradigm has an important role in brain asymmetry studies at the behavioral level. In dichotic listening, the subjects are alerted by diotic or dichotic stimuli which are meaningless, consonant vowel syllables on both ears. The subjects then presented the syllable they heard through a 6 button keypad. During this procedure, the EEG signals of the subjects were recorded by a 64 channel cap. Entropy is a measure of complexity or disorder in a signal. In other words, it is a measure of uncertainty of information in a statistical description of a system. The Shannon entropy gives a useful criterion for analyzing and comparing probability distribution, it provides a measure of the information of any distribution. In this study, the EEG recordings are examined by their entropy values. Different entropy measures are compared for different time intervals. EEG data and dichotic listening paradigm are evaluated in terms of entropy changes. The effects of ear advantage and auditory stimuli are investigated on entropy. Full article
261 KiB  
Article
Sensor Fault Detection and Diagnosis of a Process Using Unknown Input Observer
by Jafar Zarei and Javad Poshtan
Math. Comput. Appl. 2011, 16(1), 31-42; https://doi.org/10.3390/mca16010031 - 01 Apr 2011
Cited by 47 | Viewed by 1795
Abstract
In this paper, a robust sensor fault detection and isolation (FDI) method based on the unknown input observer (UIO) approach is presented. The basic principle of unknown input observers is to decouple disturbances from the state estimation error. A single full-order observer is [...] Read more.
In this paper, a robust sensor fault detection and isolation (FDI) method based on the unknown input observer (UIO) approach is presented. The basic principle of unknown input observers is to decouple disturbances from the state estimation error. A single full-order observer is designed to detect sensor faults in the presence of unknown inputs (disturbances). By doing so, we generate a residual, a weighted output of the state estimation error, decoupled from disturbances. The resulting robust (in the sense of disturbances) residual can be used for fault detection. Although this scheme has successful fault detection, using one observer is not successful in fault isolation. Therefore, a robust sensor fault isolation observer scheme is proposed. In order to evaluate its ability, the presented method is adopted to detect and isolate sensor faults of a highly nonlinear dynamic system. The faulty behavior of output sensors in a jacketed continuous stirred tank reactor (CSTR), around operating point, is investigated. Simulation results show that model uncertainties and disturbances can be distinguished from a response to a sensor fault. Full article
591 KiB  
Article
A Mineral Classification System with Multiple Artificial Neural Network Using K-Fold Cross Validation
by Nurdan Akhan Baykan and Nihat Yılmaz
Math. Comput. Appl. 2011, 16(1), 22-30; https://doi.org/10.3390/mca16010022 - 01 Apr 2011
Cited by 17 | Viewed by 2016
Abstract
The aim of this study is to show the artificial neural network (ANN) on classification of mineral based on color values of pixels. Twenty two images were taken from the thin sections using a digital camera mounted on the microscope and transmitted to [...] Read more.
The aim of this study is to show the artificial neural network (ANN) on classification of mineral based on color values of pixels. Twenty two images were taken from the thin sections using a digital camera mounted on the microscope and transmitted to a computer. Images, under both plane-polarized and cross-polarized light, contain maximum intensity. To select training and test data, 5-fold-cross validation method was involved and multi layer perceptron neural network (MLPNN) with one hidden layer was employed for classification. The classification of mineral using ANN proved %93.86 accuracy for 400 data. In second study, for each of the 5 different mineral considered, 5 different network models were implemented. Size of data set was same with previous data. Each network model was differed from each other. Also 5-fold-cross validation method was involved to select data and MLPNN with one hidden layer was used. The classification accuracy of mineral using different ANN is %90.67; %96.16; %93.91; %92; %97.62 for quartz, muscovite, biotite, chlorite and opaque respectively. Full article
209 KiB  
Article
Automated Extraction of Semantic Word Relations in Turkish Lexicon
by Zeynep Orhan, İlknur Pehlivan, Volkan Uslan and Pınar Önder
Math. Comput. Appl. 2011, 16(1), 13-21; https://doi.org/10.3390/mca16010013 - 01 Apr 2011
Cited by 8 | Viewed by 1257
Abstract
This paper studies the extraction of semantic word relations found in Turkish lexicon. Main goal of the study is to build an effective lexical-conceptual database and contribute to natural language processing (NLP) studies in Turkish. Fundamental word relations to be studied are meronymy [...] Read more.
This paper studies the extraction of semantic word relations found in Turkish lexicon. Main goal of the study is to build an effective lexical-conceptual database and contribute to natural language processing (NLP) studies in Turkish. Fundamental word relations to be studied are meronymy (part-whole), synonymy, antonymy and hypernymy (hierarchical). This study is an improvement of an earlier work [1] on semantic relations of Turkish lexicon. It was inspired by well known projects such as Rose [2], ThinkMap [3], and WordNet [4]. An online dictionary provided by Turkish Language Foundation (TDK) [5] is used as the corpus in this study. The dictionary contains more than 63K lexemes. Morphological analysis are done by using a tool called Zemberek [6]. The results are presented by means of obtained noun-pairs and their accuracy. Full article
164 KiB  
Article
Symbolic Computation of Recursion Operators for Nonlinear Differential-Difference Equations
by Ünal Göktaş and Willy Hereman
Math. Comput. Appl. 2011, 16(1), 1-12; https://doi.org/10.3390/mca16010001 - 01 Apr 2011
Cited by 1 | Viewed by 1165
Abstract
An algorithm for the symbolic computation of recursion operators for systems of nonlinear differential-difference equations (DDEs) is presented. Recursion operators allow one to generate an infinite sequence of generalized symmetries. The existence of a recursion operator therefore guarantees the complete integrability of the [...] Read more.
An algorithm for the symbolic computation of recursion operators for systems of nonlinear differential-difference equations (DDEs) is presented. Recursion operators allow one to generate an infinite sequence of generalized symmetries. The existence of a recursion operator therefore guarantees the complete integrability of the DDE. The algorithm is based in part on the concept of dilation invariance and uses our earlier algorithms for the symbolic computation of conservation laws and generalized symmetries. The algorithm has been applied to a number of well-known DDEs, including the Kacvan Moerbeke (Volterra), Toda, and Ablowitz-Ladik lattices, for which recursion operators are shown. The algorithm has been implemented in Mathematica, a leading computer algebra system. The package DDERecursionOperator.m is briefly discussed. Full article
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