Mathematical and Computational Applications

4717 KiB

Open AccessArticle

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 - 01 Dec 1999

Viewed by 950

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

Open AccessArticle

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 - 01 Dec 1999

Viewed by 929

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

Open AccessArticle

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 - 01 Dec 1999

Cited by 2 | Viewed by 1022

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

Open AccessArticle

On Statistically Convergent Sequences of Fuzzy Numbers

by Ekrem Savaş

Math. Comput. Appl. 1999, 4(3), 283-287; https://doi.org/10.3390/mca4030283 - 01 Dec 1999

Viewed by 945

Abstract

In this paper, some equivalent alternative conditions are obtained for a sequence of fuzzy numbers to be statistically Cauchy. Full article

3031 KiB

Open AccessArticle

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 - 01 Dec 1999

Cited by 3 | Viewed by 975

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

Open AccessArticle

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 - 01 Dec 1999

Cited by 13 | Viewed by 1050

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

Open AccessArticle

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 - 01 Dec 1999

Viewed by 1076

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

Open AccessArticle

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 - 01 Dec 1999

Cited by 1 | Viewed by 1012

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

Open AccessArticle

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 - 01 Dec 1999

Viewed by 1007

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

Open AccessArticle

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 - 01 Dec 1999

Viewed by 993

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

Open AccessArticle

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 - 01 Dec 1999

Viewed by 962

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

Open AccessArticle

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 - 01 Dec 1999

Viewed by 978

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

Open AccessArticle

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 - 01 Dec 1999

Cited by 3 | Viewed by 1155

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

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