Mathematical and Computational Applications

548 KiB

Open AccessArticle

Numerical Solution of Improper Integrals with Valid Implementation

by Saeid Abbasbandy and Mohammad Ali Fariborzi Araghi

Math. Comput. Appl. 2002, 7(1), 83-91; https://doi.org/10.3390/mca7010083 - 01 Apr 2002

Cited by 16 | Viewed by 2172

In this paper, two theorems are explained which are used in order to find the improper integral I = \({\int_a^\infty}\)f(x)dx numerically. It has been proved in [4], one can use the Trapezoidal and Simpson rules to find the [...] Read more.

In this paper, two theorems are explained which are used in order to find the improper integral I = \({\int_a^\infty}\)f(x)dx numerically. It has been proved in [4], one can use the Trapezoidal and Simpson rules to find the definite integral I_m = \({\int_a^\infty}\)f(x)dx numerically using the CESTAC (Control et Estimation Stochastique des Arrondis de Calculs ) method which is based on the stochastic arithmetic, [5-8,12]. These theorems are developed on the improper integrals. Then, the CESTAC method and stochastic arithmetic are used to validate the results and implement the numerical examples. By using this method, one can find the optimal integer number m ≥ 1 such that I ~ I_m. In the last section two examples are solved. The programs have been provided with Fortran 90. Full article

654 KiB

Open AccessArticle

Transient Dynamic Analysis of Laminated Composite Plate Subjected to Low-Velocity Impact

by Züleyha Aslan and Ramazan Karakuzu

Math. Comput. Appl. 2002, 7(1), 73-82; https://doi.org/10.3390/mca7010073 - 01 Apr 2002

Cited by 8 | Viewed by 1398

Abstract

This paper concerns with the transient response of composite laminates subjected to low-velocity impact. A drop weight impact tower is used for the low velocity impact study and the contact force during impact is measured with a piezoelectric force transducer. Composite laminates, made [...] Read more.

This paper concerns with the transient response of composite laminates subjected to low-velocity impact. A drop weight impact tower is used for the low velocity impact study and the contact force during impact is measured with a piezoelectric force transducer. Composite laminates, made of E-glass/epoxy and having (0/90/0)_s stacking sequence, are considered, Numerical results of E-glass/epoxy cross-ply laminates under three different impact velocities (l m/sec, 2 m/sec and 3 m/sec) and two different impactor masses (135 g and 2600 g) are investigated with 3DIMPACT computer code. Contact force between the impactor and composite laminate, maximum transverse displacement at the center are plotted as functions of time and predicted delamination shapes and sizes are found numerically. The resulting data from the drop-weight tests and computer code provide specific information about the effect of the impactor velocity and impactor mass, all of which have a great influence on the impact response of composite laminates. Full article

642 KiB

Open AccessArticle

Data Envelopment Analysis: An Application to Turkish Banking Industry

by Hasan Bal and Ayhan Gölcükcü

Math. Comput. Appl. 2002, 7(1), 65-72; https://doi.org/10.3390/mca7010065 - 01 Apr 2002

Cited by 4 | Viewed by 1286

Abstract

DEA is a well-known decision making tool and efficiency measurement technique which was proposed by Charnes et al. in : 1978 in EJOR. Since then, the technique had proved itself in many application in many areas like banking, agriculture, transportation and so on [...] Read more.

DEA is a well-known decision making tool and efficiency measurement technique which was proposed by Charnes et al. in : 1978 in EJOR. Since then, the technique had proved itself in many application in many areas like banking, agriculture, transportation and so on and many papers had written in many journals by authors around the worldwide.
DEA is a non-parametric technique and scope of DEA is to determine the efficiency of decision-making units (DMUs). It divides the DMUs into two group named as efficient and inefficient, then derives a piecewise linear frontier with pareto-efficient DMUs and gives an efficiency score of 1(one) to each of them. However, the DMUs below the frontier gets an efficiency score less than 1 (one). Their efficiency score is determined by the distance between the frontier and the coordinates of each of the inefficient DMUs. Furthermore, DEA also determines the source and the amount of inefficiency so that DEA becomes indispensable for decision-makers, named as boss, manager director, owner or others. In this paper, despite of the classical usage, a new area for DEA would be introduced and a new definition would be made for decision-maker. In our work decision-maker is customer. Full article

572 KiB

Open AccessArticle

Analysis of Time-Course of the Recovery from Inactivation of Ionic Currents in Cerebellar Punkinje Cell

by Mahmut Özer

Math. Comput. Appl. 2002, 7(1), 53-63; https://doi.org/10.3390/mca7010053 - 01 Apr 2002

Viewed by 1049

Abstract

In this study, time-course of the recovery from the inactivation of ionic currents which have inactivation in cerebellar Purkinje cell is examined. Kinetics of the ionic currents are expressed with Hodgkin-Huxley equations. Peak value function of the recovering conductance is given explicitly, the [...] Read more.

In this study, time-course of the recovery from the inactivation of ionic currents which have inactivation in cerebellar Purkinje cell is examined. Kinetics of the ionic currents are expressed with Hodgkin-Huxley equations. Peak value function of the recovering conductance is given explicitly, the curve of recovery and its approximation are obtained. It's shown that recovering conductance of ionic currents which are studied is asymptotically exponential. Full article

574 KiB

Open AccessArticle

Numerical Solution of Fuzzy Differential Equation

by S. Abbasbandy and T. Allah Viranloo

Math. Comput. Appl. 2002, 7(1), 41-52; https://doi.org/10.3390/mca7010041 - 01 Apr 2002

Cited by 46 | Viewed by 2783

Abstract

In this paper numerical algorithms for solving fuzzy ordinary differential equations are considered. A scheme based on the 2nd Taylor method in detail is discussed and this is followed by a complete error analysis. The algorithm is illustrated by solving some linear and [...] Read more.

In this paper numerical algorithms for solving fuzzy ordinary differential equations are considered. A scheme based on the 2nd Taylor method in detail is discussed and this is followed by a complete error analysis. The algorithm is illustrated by solving some linear and nonlinear fuzzy cauchy problems. Full article

341 KiB

Open AccessArticle

Some Solutions for an Equation of Order of 4p

by Abdullah Altın and Ayşegül Erençin

Math. Comput. Appl. 2002, 7(1), 33-40; https://doi.org/10.3390/mca7010033 - 01 Apr 2002

Viewed by 1068

Abstract

We obtain all solutions which depend only on r for a singular partial differential equation of order 4p. Here, the operator includes Laplacian and GASPT (Generalized Axially Symmetric Potential Theory) operator. Full article

747 KiB

Open AccessArticle

Elastic-Plastic Stress Analysis and Residual Stresses in Metal Matrix Laminated Plates under In-Plane Loading

by Mahmut Özbay

Math. Comput. Appl. 2002, 7(1), 23-32; https://doi.org/10.3390/mca7010023 - 01 Apr 2002

Viewed by 1013

Abstract

Metal matrix composites reinforoed by give high strengths, specific stiffness, ductility, yield point and a good temperature performance. They provide a relatively new way of strengthening metals. In this study, continuous steel fiber reinforced aluminum matrix composite manufactured die casting process has been [...] Read more.

Metal matrix composites reinforoed by give high strengths, specific stiffness, ductility, yield point and a good temperature performance. They provide a relatively new way of strengthening metals. In this study, continuous steel fiber reinforced aluminum matrix composite manufactured die casting process has been used as a simply supported Symmetric and antisymmetric laminated plate loaded by in- plane forces. An elastic- plastic numerical solution has been carried out by finite element technique for several load numbers. Residual stresses have been given in tables. Full article

440 KiB

Open AccessArticle

Pressure Distribution in a Slider Bearing Lubricated with Second and Third Grade Fluids

by M. Yürüsoy

Math. Comput. Appl. 2002, 7(1), 15-22; https://doi.org/10.3390/mca7010015 - 01 Apr 2002

Cited by 8 | Viewed by 1080

Abstract

A Slider bearing with second and third grade fluids as lubricant is analysed in the present study. The analysis is based on perturbation technique. Choosing second and third grade effects to be smaller than the viscous effects, a perturbation solution is constructed. Under [...] Read more.

A Slider bearing with second and third grade fluids as lubricant is analysed in the present study. The analysis is based on perturbation technique. Choosing second and third grade effects to be smaller than the viscous effects, a perturbation solution is constructed. Under the thin film assumption, inertia terms are negligible compared to the viscous, second and third grade terms. The pressure distributions in the bearing are calculated approximately. Full article

4164 KiB

Open AccessArticle

Possibilistic Data Envelopment Analysis

by Ihsan Alp

Math. Comput. Appl. 2002, 7(1), 5-14; https://doi.org/10.3390/mca7010005 - 01 Apr 2002

Cited by 3 | Viewed by 1322

Abstract

Data of problems in real world, fuzziness/impreciseness/absence appears due to various reasons very often. In such cases, difficulty in model building can be overcome by using fuzzy set theory and concepts. In this study, only situation of data lacking will be considered, Data [...] Read more.

Data of problems in real world, fuzziness/impreciseness/absence appears due to various reasons very often. In such cases, difficulty in model building can be overcome by using fuzzy set theory and concepts. In this study, only situation of data lacking will be considered, Data envelopment analysis cannotbe used in the absence of one or more data in: model. If those absent datum or data can be supplied with possibilistic membership function, the problem is solved. In this study, a suggestion will be given about how to apply data envelopment analysis with the assistance of possibilistic membership function in real world problem with lacking data. Model problem has been chosen in the banking sector, which is a very popular area. Full article

223 KiB

Open AccessArticle

Group Classification and Some Similarity Solutions for a Nonlinear Filtration Equation

by Mehmet Pakdemirli

Math. Comput. Appl. 2002, 7(1), 1-4; https://doi.org/10.3390/mca7010001 - 01 Apr 2002

Viewed by 1022

Abstract

A nonlinear filtration equation in which the filter coefficient is an arbitrary function of the specific deposit is considered. Lie Group theory is applied to the coupled system of partial differential equations. Group classification is performed with respect to the arbitrary filter coefficient. [...] Read more.

A nonlinear filtration equation in which the filter coefficient is an arbitrary function of the specific deposit is considered. Lie Group theory is applied to the coupled system of partial differential equations. Group classification is performed with respect to the arbitrary filter coefficient. Some similarity solutions are constructed using the symmetries. Full article

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Math. Comput. Appl., Volume 7, Issue 1 (April 2002) – 10 articles , Pages 1-91

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