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

Math. Comput. Appl., Volume 4, Issue 3 (December 1999) – 13 articles , Pages 195-314

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4717 KiB  
Article
Building Evolution Friendliness into Cellular Automation Dynamics: The Cytomatrix Neuron Model
by Ahmet Ugur and Michael Conrad
Math. Comput. Appl. 1999, 4(3), 305-314; https://doi.org/10.3390/mca4030305 - 1 Dec 1999
Viewed by 1045
Abstract
The cytomatrix neuron is a softened cellular automaton, roughly motivated by interactions that could occur in a molecular or cellular complex. Subcells exert graded influences on each other and provide a medium for the integration of input signals in space and time. A [...] Read more.
The cytomatrix neuron is a softened cellular automaton, roughly motivated by interactions that could occur in a molecular or cellular complex. Subcells exert graded influences on each other and provide a medium for the integration of input signals in space and time. A readout element located in a suitably activated subcell triggers an output. The neurons are trained through variation-selection learning that acts on multiple dynamical parameters. Extensive experimentation with the model shows that the dynamics can be molded to yield different structures of generalization. Dimensionality can be increased by increasing the number of dynamical parameters open to variation and selection. Learning algorithms that vary the greatest number of parameters were found to have a greater variability in the structures of generalization and to yield higher performance values and learning rates. The focus here is on n-bit exclusive- OR tasks that are known to be hard due to their linear inseparability. The system successfully learned 2-bit and 4-bit exclusive-OR functions. The higher dimensional algorithms exhibited a relatively good performance on the 8-bit exclusive-OR function. Full article
2230 KiB  
Article
Numerical Study of Collision Efficiency of Dust Particles
by Sabit Adanur and Sayavur I. Bakhtiyarov
Math. Comput. Appl. 1999, 4(3), 297-303; https://doi.org/10.3390/mca4030297 - 1 Dec 1999
Viewed by 996
Abstract
The collision efficiency of bound sand particles is studied numerically. The fourth-order Runge - Kutta method was used to solve two ordinary differential equations. Full article
1988 KiB  
Article
Preliminary Group Classification of y" = f(x)y2
by C. Wafo Soh and F. M. Mahhomed
Math. Comput. Appl. 1999, 4(3), 289-295; https://doi.org/10.3390/mca4030289 - 1 Dec 1999
Cited by 2 | Viewed by 1109
Abstract
Direct group classification of y" = f(x)y2 fails because the classifying condition is a third-order non-linear integro-differential equation for which a closed form solution is unknown. This fact prevents a complete group classification. In this paper we [...] Read more.
Direct group classification of y" = f(x)y2 fails because the classifying condition is a third-order non-linear integro-differential equation for which a closed form solution is unknown. This fact prevents a complete group classification. In this paper we resort to the method of preliminary group classification in order to perform a partial group classification of the ordinary differential equation (ode) mentioned above and obtain new classes that admit symmetry. Full article
1255 KiB  
Article
On Statistically Convergent Sequences of Fuzzy Numbers
by Ekrem Savaş
Math. Comput. Appl. 1999, 4(3), 283-287; https://doi.org/10.3390/mca4030283 - 1 Dec 1999
Viewed by 1027
Abstract
In this paper, some equivalent alternative conditions are obtained for a sequence of fuzzy numbers to be statistically Cauchy. Full article
3031 KiB  
Article
A Comparison of Different Versions of the Method of Multiple Scales for an Arbitrary Model of Odd Nonlinearities
by Mehmet Pakdemirli and Hakan Boyacı
Math. Comput. Appl. 1999, 4(3), 273-282; https://doi.org/10.3390/mca4030273 - 1 Dec 1999
Cited by 3 | Viewed by 1061
Abstract
A general model of cubic and fifth order nonlinearities is considered. The linear part as well as the nonlinearities are expressed in terms of arbitrary operators. Two different versions of the method of multiple scales are used in constructing the general transient and [...] Read more.
A general model of cubic and fifth order nonlinearities is considered. The linear part as well as the nonlinearities are expressed in terms of arbitrary operators. Two different versions of the method of multiple scales are used in constructing the general transient and steady-state solutions of the model: Modified Rahman-Burton method and the Reconstitution method. It is found that the usual ordering of reconstitution can be used, if at higher orders of approximation, the time scale corresponding to that order is considered and all other time derivatives are ignored. Results are applied to an example and steady-state solutions are compared numerically for both methods. Full article
4030 KiB  
Article
Frictionless Contact between a Rigid Stamp and an Elastic Layered Composite Resting on Simple Supports
by Ahmet Birinci and Ragıp Erdöl
Math. Comput. Appl. 1999, 4(3), 261-272; https://doi.org/10.3390/mca4030261 - 1 Dec 1999
Cited by 13 | Viewed by 1140
Abstract
The frictionless contact between a rounded or flat-ended rigid stamp and an elastic layered composite is considered according to theory of Elasticity. The elastic layered composite consisted of two materials with different elastic constants and heights is rested on simple supports. It is [...] Read more.
The frictionless contact between a rounded or flat-ended rigid stamp and an elastic layered composite is considered according to theory of Elasticity. The elastic layered composite consisted of two materials with different elastic constants and heights is rested on simple supports. It is assumed that the layered composite is subjected to a concentrated load with a magnitude of 2P by means of a rigid stamp on its top surface and the effect of gravity is neglected. Stresses and displacements are expressed depending on the contact pressure using Fourier transforms technique and the problem is formulated in terms of a singular integral equation for the contact pressure. The singular integral equation is solved numerically by using appropriate Gauss- Chebyshev integration. Numerical results obtained for various dimensionless quantities for the contact pressure are presented in graphical form. Full article
2885 KiB  
Article
Assessing Enviromental Consequences of Water Projects Based on a Pseudo Expert System Approach
by Mehmet Ali Yurdusev
Math. Comput. Appl. 1999, 4(3), 251-259; https://doi.org/10.3390/mca4030251 - 1 Dec 1999
Viewed by 1167
Abstract
Environmental Impact Assessment (EIA) of any development project is now a part of the project analysis today. This is not only required by national and/or international legislation, but also the growing environmental awareness of societies has forced project implementers to consider any environmental [...] Read more.
Environmental Impact Assessment (EIA) of any development project is now a part of the project analysis today. This is not only required by national and/or international legislation, but also the growing environmental awareness of societies has forced project implementers to consider any environmental consequences beforehand and take the necessary measures to mitigate adverse effects. As a protect cycle may include several steps, the consideration of environmental impacts at each level is now something inevitable. Although large numbers of environmental impact assessment procedures are available, an appropriate. EIA procedure that is compatible with the level must be adopted. To this end, a tailor-made procedure for water resources planning process is devised, which is a computer model for the environmental assessment of planning components such as reservoirs and abstraction schemes etc. The model provides all the necessary facilities and knowledge thereby assisting the user to evaluate a particular impact by means of generic knowledge in relation to the impact and the site characteristics. As such, the model lakes a form of expert system without a proper shell being used. The intention is to use the outcomes of this model including environmental impacts along with the economical considerations in large-scale water resources planning process. Full article
2333 KiB  
Article
Plane Wave Diffraction by an Open Parallel Plate Waveguide with Dielectric Loading
by Bahattin Türetken and Ali Alkumru
Math. Comput. Appl. 1999, 4(3), 241-249; https://doi.org/10.3390/mca4030241 - 1 Dec 1999
Cited by 1 | Viewed by 1120
Abstract
The diffraction of plane electromagnetic waves by an open parallel plate waveguide with dielectric loading is investigated rigorously by using the Fourier transform technique. This method of formulation gives rise to Wiener- Hopf equations. The solution of each Wiener-Hopf equation contains a set [...] Read more.
The diffraction of plane electromagnetic waves by an open parallel plate waveguide with dielectric loading is investigated rigorously by using the Fourier transform technique. This method of formulation gives rise to Wiener- Hopf equations. The solution of each Wiener-Hopf equation contains a set of infinitely many constants satisfying an infinite system of linear algebraic equations. A numerical solution of this systems is obtained for various values of the distances between the plates, plate thickness, the number of wave in the dielectric region. Full article
2133 KiB  
Article
Stress Analysis in Adhesive-Butt Joints of Cylindrical Pressure Vessels
by Durmuş Günay and Alpay Aydemir
Math. Comput. Appl. 1999, 4(3), 233-239; https://doi.org/10.3390/mca4030233 - 1 Dec 1999
Viewed by 1089
Abstract
In this study, the stress distributions in adhesive butt joints of cylindrical pressure vessels are analyzed by the finite element method using eight-node-quadrilateral axisymmetric finite elements. The structure consists of two cylindrical adherends bonded by an adhesive arid the joint is subjected to [...] Read more.
In this study, the stress distributions in adhesive butt joints of cylindrical pressure vessels are analyzed by the finite element method using eight-node-quadrilateral axisymmetric finite elements. The structure consists of two cylindrical adherends bonded by an adhesive arid the joint is subjected to an internal pressure. Stress distributions and the effects of the adhesive thickness on the stress distributions in the joint are studied. Full article
2030 KiB  
Article
Invariant Solutions for Soil Water Equations
by V. A. Baikov and C. M. Khalique
Math. Comput. Appl. 1999, 4(3), 217-223; https://doi.org/10.3390/mca4030217 - 1 Dec 1999
Viewed by 1070
Abstract
We obtain exact solutions for a class of nonlinear partial differential equations which models soil water infiltration and redistribution in a bedded soil profile irrigated by a drip irrigation system. The solutions obtained are invariant under two parameter symmetry groups. Full article
2401 KiB  
Article
Assessment and Comparison of Discrete Optimal Multirate and Conventional Analogue Controller Design Applied to a Hydrogenerator System
by Anastasios K. Boglou and Demetrios P. Papadopoulos
Math. Comput. Appl. 1999, 4(3), 209-215; https://doi.org/10.3390/mca4030209 - 1 Dec 1999
Viewed by 1039
Abstract
In the present work an algebraic and an optimal control method (in connection with linear continuous systems as well as a new optimal multirate control method (in connection with linear discrete systems) are presented and applied, in order to design a suitable excitation [...] Read more.
In the present work an algebraic and an optimal control method (in connection with linear continuous systems as well as a new optimal multirate control method (in connection with linear discrete systems) are presented and applied, in order to design a suitable excitation controller (analogue and digital type respectively) and thus obtain a pertinent closed-loop system with enhanced dynamic stability characteristics. The obtained computer simulation results, based on a practical power system of the Greek national grid, show clearly the validity-suitability-effectiveness and implementabilitv of the excitation controllers designed using these control procedures. Full article
957 KiB  
Article
The IBM-1 Study for Some Ce Isotopes
by Sait İnan, Abdülkadir Yörük and Atalay Küçükbursa
Math. Comput. Appl. 1999, 4(3), 205-207; https://doi.org/10.3390/mca4030205 - 1 Dec 1999
Viewed by 1058
Abstract
The structure of even-even Ce isotopes with neutron number 72≤N≤76 are studied within the framework of the Interacting Boson Modei (IBM-l). The excitation energies and the B(E2) values of the above nuclei are calculated. It is found that the agreements between the calculated [...] Read more.
The structure of even-even Ce isotopes with neutron number 72≤N≤76 are studied within the framework of the Interacting Boson Modei (IBM-l). The excitation energies and the B(E2) values of the above nuclei are calculated. It is found that the agreements between the calculated and observed data are much better in the model of the effective boson consideration. Full article
2480 KiB  
Article
Three Dimensional Stress Analysis in Adhesively Bonded Joints with Rivets
by Ali Kaya, Mehmet Tekelioğlu and Muhammet Cerit
Math. Comput. Appl. 1999, 4(3), 195-203; https://doi.org/10.3390/mca4030195 - 1 Dec 1999
Cited by 3 | Viewed by 1249
Abstract
Stress and strain distributions in the adhesively bonded joints subjected to distributed forces are investigated using finite element method. The bonded materials reinforced with rivets are the same. The investigations are conducted on a three dimensional model. The finite element model of the [...] Read more.
Stress and strain distributions in the adhesively bonded joints subjected to distributed forces are investigated using finite element method. The bonded materials reinforced with rivets are the same. The investigations are conducted on a three dimensional model. The finite element model of the joint is obtained using isoparametric three dimensional elements having eight nodes with three degrees of freedom each. The stress components and their distributions both on adhesive surface and on metallic elements are given in dimensionless from using three dimensional graphics. Full article
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