Mathematical and Computational Applications

492 KiB

Open AccessArticle

Cylindrical Magneto-Hydrodynamic Model of Shock Waves with Radiation Heat Flux in Non-Uniform Rotating Atmosphere

by Ashok Ganguly and Shilpa Shinde

Math. Comput. Appl. 2002, 7(3), 287-296; https://doi.org/10.3390/mca7030287 - 01 Dec 2002

Viewed by 942

A self similar, theoretical model of cylindrical magneto-hydrodynamics shock wave with radiation heat flux in non-uniform rotating atmosphere, in the rotating medium, in the presence of magnetic field, radiation and gravitation, has been developed. Subsequently, its comparison with the hydro dynamic case has [...] Read more.

A self similar, theoretical model of cylindrical magneto-hydrodynamics shock wave with radiation heat flux in non-uniform rotating atmosphere, in the rotating medium, in the presence of magnetic field, radiation and gravitation, has been developed. Subsequently, its comparison with the hydro dynamic case has been shown with the help of variations of flow variables with distance graphically. In case of density and radiation flux and mass a significant variation has been observed. Full article

675 KiB

Open AccessArticle

Two Strips Problem Resting on an Elastic Foundation

by Ahmet Birinci, Mehmet Çakıroğlu and Ragıp Erdöl

Math. Comput. Appl. 2002, 7(3), 275-286; https://doi.org/10.3390/mca7030275 - 01 Dec 2002

Viewed by 1022

Abstract

In this paper, a layered composite made of two materials with different elastic constants and heights resting on an elastic foundation is studied according to theory of Elasticity. Symmetrical distributed load whose length is 2a is applied to the upper elastic layer. Gravity [...] Read more.

In this paper, a layered composite made of two materials with different elastic constants and heights resting on an elastic foundation is studied according to theory of Elasticity. Symmetrical distributed load whose length is 2a is applied to the upper elastic layer. Gravity forces of the layered composite are neglected. The components of the stresses and displacements at a point located in the layered composite are obtained by using Integral Transform technique. Singular terms are subtracted from expressions of the stresses and their closed integral forms are added. The stresses and the displacements in any point of the layered composite are investigated and their graphics are plotted. Full article

777 KiB

Open AccessArticle

Response of a Parametrically Excited System with Quadratic and Cubic Non-Linearities

by M. Eissa, S. A. EI-Serafi, M. M. Kamel, M. Z. Rageb and Y. A. Amer

Math. Comput. Appl. 2002, 7(3), 263-274; https://doi.org/10.3390/mca7030263 - 01 Dec 2002

Cited by 1 | Viewed by 1075

Abstract

An investigation is presented of the response of a three-degree-of-freedom system with quadratic and cubic non-linearities under parametric excitations. The problem of suppressing the vibration of a structure that is subjected to combination parametric excitation is considered, where the vibration amplitudes resulting from [...] Read more.

An investigation is presented of the response of a three-degree-of-freedom system with quadratic and cubic non-linearities under parametric excitations. The problem of suppressing the vibration of a structure that is subjected to combination parametric excitation is considered, where the vibration amplitudes resulting from such resonance can not be controlled. The fixed points of the three equations are obtained and their stability are determined. Numerical solutions are conducted to obtain the response of the three modes and their stability. Effects of the different parameters on both response and stability of the system are also investigated. Full article

790 KiB

Open AccessArticle

A Template Based Graph Reduction System Based on Combinators

by Abdullah Çavuşoğlu, H. Haldun Göktaş and Necla Vardal

Math. Comput. Appl. 2002, 7(3), 253-262; https://doi.org/10.3390/mca7030253 - 01 Dec 2002

Viewed by 1115

Abstract

Graph reduction is one of the important evaluation strategy for lazy functional Programming. A combinator is a function that contains no free variables. The idea is based on the fact that, all of the variables in a program can be removed by transforming [...] Read more.

Graph reduction is one of the important evaluation strategy for lazy functional Programming. A combinator is a function that contains no free variables. The idea is based on the fact that, all of the variables in a program can be removed by transforming it into a sequence of combinators which would be drawn from a small pre-defined (fixed) set of combinators (SKI), or which would be drawn from an unlimited number of non-pre- defined set of dynamic super-combinators (SC). We are suggesting a template based algorithm which reduces the stored graph structure of the super-combinators. We can define any produced super-combinators by using templates and use them to perform reduction on the graph. The template based algorithrn could be extended and any produced super-combinators can be defined with a predefined template list. The test results show that our approach increases the efficiency of super-combinators algorithms. Full article

463 KiB

Open AccessArticle

Kinetic Equations for Ultrasonic Scission of Polymers

by M. Can

Math. Comput. Appl. 2002, 7(3), 241-252; https://doi.org/10.3390/mca7030241 - 01 Dec 2002

Viewed by 1244

Abstract

When a long chain of polymer is sonicated it is known that it preferentially breaks at the middle and long chain radicals result. The termination step is especially important to control the degree of polymerisation P_n. In this paper, in the [...] Read more.

When a long chain of polymer is sonicated it is known that it preferentially breaks at the middle and long chain radicals result. The termination step is especially important to control the degree of polymerisation P_n. In this paper, in the absence of the radical traps the nature of the phenomenological kinetic equations derived in [4] are studied. It has been found that for all possible values of the parameters, the only equilibrium point is linearly stable. But because of the nonlinear effects, stability of the equilibrium point depends on the parameter space. For some set of parameters and initial conditions, it has been observed that the solutions are asymptotically periodic. But large time behaviour of all these solutions are not realistic in the sense that functions representing nonnegative physical quantities assume negative values. A modified version of the kinetic equations whose solutions remain nonnegative in the time course is also proposed. Full article

230 KiB

Open AccessArticle

Some Properties of Ruled Surfaces under Homothety in E3

by Emin Kasap, Salim Yüce and Nuri Kuruoğlu

Math. Comput. Appl. 2002, 7(3), 235-239; https://doi.org/10.3390/mca7030235 - 01 Dec 2002

Viewed by 1181

Abstract

It is clearly that, If f : E³→E³ is a homothety and \(\varphi\) is a surface in three dimensional Euclidean space E³, \(f(\varphi) = \overline{\varphi}\) is also a surface in E³. In this paper, the [...] Read more.

It is clearly that, If f : E³→E³ is a homothety and \(\varphi\) is a surface in three dimensional Euclidean space E³, \(f(\varphi) = \overline{\varphi}\) is also a surface in E³. In this paper, the surface \(\varphi\) has been taken a ruled surface, specially. It was shown that image surface \(f(\varphi) = \overline{\varphi}\) has been a ruled surface, too. Furthermore, It was investigated whether some properties related with ruled surfaces on \(\varphi\) have been invariant under the homothety f or not. Full article

309 KiB

Open AccessArticle

The Harnack Inequalities for Nonnegative Solutions of an Elliptic and Ultra-Hyperbolic Equation

by Nuri Özalp and Fatma Taşdelen

Math. Comput. Appl. 2002, 7(3), 229-234; https://doi.org/10.3390/mca7030229 - 01 Dec 2002

Viewed by 1144

Abstract

In this study, in means of the Harnack inequalities of the harmonic functions, some Harnack type inequalities are given for the solutions of GASPT equation with singular coefficients and for two expanded equations of it. Full article

547 KiB

Open AccessArticle

Robust Control of a Spatial Robot Using Sliding Modes

by Nurkan Yagiz

Math. Comput. Appl. 2002, 7(3), 219-228; https://doi.org/10.3390/mca7030219 - 01 Dec 2002

Cited by 4 | Viewed by 1071

Abstract

In this work the control of a spatial robot by sliding mode control is studied. The robot model has three degrees of freedom. These robots are usually used in material handling in remote dangerous environments and production line. First, the mathematical model of [...] Read more.

In this work the control of a spatial robot by sliding mode control is studied. The robot model has three degrees of freedom. These robots are usually used in material handling in remote dangerous environments and production line. First, the mathematical model of the system is formulated. The equations of motion are driven by employing Lagrangian formulation based on the energy equations. Then the sliding mode control theory is applied. Special care is given to the chattering problem. The chattering may have serious damaging effect on gear systems as well as motor drive systems. Hence, the chattering character of classical sliding mode control is overcome and a new version of the control method is applied on robot. The simulation results are presented in graphical form and the robust character of the selected control method is shown to be capable of controlling the robots successfully against the disturbances as well as having the robot follow the desired trajectory. Full article

370 KiB

Open AccessArticle

Some Bounds on \(\ell_p\) Matrix and \(\ell_p\) Operator Norms of Almost Circulant, Cauchy-Toeplitz and Cauchy-Hankel Matrices

by Süleyman Solak and Durmuş Bozkurt

Math. Comput. Appl. 2002, 7(3), 211-218; https://doi.org/10.3390/mca7030211 - 01 Dec 2002

Cited by 4 | Viewed by 1061

Abstract

Let C_n, T_n and H_n denote almost circulant, Cauchy-ToeplitZ and Cauchy-Hankel matrices, respectively. We find some upper bounds for \(\ell_p\) matrix norm and \(\ell_p\) operator norm of this matrices. Moreover, we give some results for Kronecker products C_n\(\otimes\)T_n and C_n\(\otimes\)H_n. Full article

268 KiB

Open AccessArticle

On the Norms of GCD Matrices

by Durmuş Bozkurt and Süleyman Solak

Math. Comput. Appl. 2002, 7(3), 205-210; https://doi.org/10.3390/mca7030205 - 01 Dec 2002

Cited by 5 | Viewed by 1282

Abstract

In this study, we have established the bounds for the \(\ell_p \) norms and the Euclidean norm of almost GCD Cauchy-Toeplitz, almost GCD Cauchy-Hankel and GCD matrices, respectively. Full article

1213 KiB

Open AccessArticle

A Method to Increase the Size of Healty Subcubes Set in a Hypercube System with Node or Link Failures

by Novruz Allahverdi

Math. Comput. Appl. 2002, 7(3), 189-203; https://doi.org/10.3390/mca7030189 - 01 Dec 2002

Viewed by 1225

Abstract

In this study we considered and analyzed the different cases of node- and link-faults in a hypercube multiprocessor. We revealed that, the direct use of sharp product operation is not sufficient to discard only computational part (processor and memory), when only this part [...] Read more.

In this study we considered and analyzed the different cases of node- and link-faults in a hypercube multiprocessor. We revealed that, the direct use of sharp product operation is not sufficient to discard only computational part (processor and memory), when only this part of node is faulty. We also showed that in case when some links in communication part (router) incident to a healthy node are faulty, the sharp product operation does not allow to leave the healthy links and the node incident to these links in the set of healthy subcubes. In order to remove this lack we propose in this study the formal procedures with aid of which we can subtract first only the faulty node, excluding the healthy links incident to this node and second only the faulty links, excluding also the healthy nodes incident to these links of such systems. Full article

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Math. Comput. Appl., Volume 7, Issue 3 (December 2002) – 11 articles , Pages 189-296

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