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Volume 7, August
Mathematical and Computational Applications is published by MDPI from Volume 21 Issue 1 (2016). Articles in this Issue were published by another publisher in Open Access under a CC-BY (or CC-BY-NC-ND) licence. Articles are hosted by MDPI on mdpi.com as a courtesy and upon agreement with the previous journal publisher.

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

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Open AccessArticle
Cylindrical Magneto-Hydrodynamic Model of Shock Waves with Radiation Heat Flux in Non-Uniform Rotating Atmosphere
Math. Comput. Appl. 2002, 7(3), 287-296; https://doi.org/10.3390/mca7030287 - 01 Dec 2002
Viewed by 539
Abstract
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
Open AccessArticle
Two Strips Problem Resting on an Elastic Foundation
Math. Comput. Appl. 2002, 7(3), 275-286; https://doi.org/10.3390/mca7030275 - 01 Dec 2002
Viewed by 591
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
Open AccessArticle
Response of a Parametrically Excited System with Quadratic and Cubic Non-Linearities
Math. Comput. Appl. 2002, 7(3), 263-274; https://doi.org/10.3390/mca7030263 - 01 Dec 2002
Cited by 1 | Viewed by 599
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
Open AccessArticle
A Template Based Graph Reduction System Based on Combinators
Math. Comput. Appl. 2002, 7(3), 253-262; https://doi.org/10.3390/mca7030253 - 01 Dec 2002
Viewed by 631
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
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 800
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 Pn. 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 Pn. 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
Open AccessArticle
Some Properties of Ruled Surfaces under Homothety in E3
Math. Comput. Appl. 2002, 7(3), 235-239; https://doi.org/10.3390/mca7030235 - 01 Dec 2002
Viewed by 647
Abstract
It is clearly that, If f : E3E3 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 : E3E3 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
Open AccessArticle
The Harnack Inequalities for Nonnegative Solutions of an Elliptic and Ultra-Hyperbolic Equation
Math. Comput. Appl. 2002, 7(3), 229-234; https://doi.org/10.3390/mca7030229 - 01 Dec 2002
Viewed by 702
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
Open AccessArticle
Robust Control of a Spatial Robot Using Sliding Modes
Math. Comput. Appl. 2002, 7(3), 219-228; https://doi.org/10.3390/mca7030219 - 01 Dec 2002
Cited by 3 | Viewed by 559
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
Open AccessArticle
Some Bounds on \(\ell_p\) Matrix and \(\ell_p\) Operator Norms of Almost Circulant, Cauchy-Toeplitz and Cauchy-Hankel Matrices
Math. Comput. Appl. 2002, 7(3), 211-218; https://doi.org/10.3390/mca7030211 - 01 Dec 2002
Cited by 3 | Viewed by 579
Abstract
Let Cn, Tn and Hn 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 Cn\(\otimes\)Tn and Cn\(\otimes\)Hn. Full article
Open AccessArticle
On the Norms of GCD Matrices
Math. Comput. Appl. 2002, 7(3), 205-210; https://doi.org/10.3390/mca7030205 - 01 Dec 2002
Cited by 5 | Viewed by 757
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
Open AccessArticle
A Method to Increase the Size of Healty Subcubes Set in a Hypercube System with Node or Link Failures
Math. Comput. Appl. 2002, 7(3), 189-203; https://doi.org/10.3390/mca7030189 - 01 Dec 2002
Viewed by 677
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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