Mathematical and Computational Applications

410 KiB

Open AccessArticle

On the Semicontinuity Properties of the Attainable Sets of Control Systems with Controls in Lp

by Kh. G. Guseinov, Orhan Ozer and Emrah Akyar

Math. Comput. Appl. 2003, 8(1), 127-134; https://doi.org/10.3390/mca8010127 - 01 Apr 2003

Cited by 1 | Viewed by 1041

In this article the properties of attainable sets of control systems with integral constraints on control are studied. The admissible control functions are chosen from the ball centered at the origin and of radius μ₀ in L_p, p > 1 [...] Read more.

In this article the properties of attainable sets of control systems with integral constraints on control are studied. The admissible control functions are chosen from the ball centered at the origin and of radius μ₀ in L_p, p > 1 It is proved that the attainable sets of the system at the fixed instant of time are left side lower semicontinuous and right side upper semicontinuous with respect to p. Full article

431 KiB

Open AccessArticle

On the Construction of Differential Inclusion with Prescribed Integral Funnel

by Kh. G. Guseinov, O. Özer and S. A. Düzce

Math. Comput. Appl. 2003, 8(1), 119-126; https://doi.org/10.3390/mca8010119 - 01 Apr 2003

Cited by 1 | Viewed by 1075

Abstract

In this article, the inverse problem of the differential inclusion theory is considered. For a given ε > 0 and a given special type set valued map t → V(t), t ∈ [t_*, t^*], it [...] Read more.

In this article, the inverse problem of the differential inclusion theory is considered. For a given ε > 0 and a given special type set valued map t → V(t), t ∈ [t_*, t^*], it is required to define differential inclusion such that the Hausdorff distance between the reachable sets of the differential inclusion with initial set (t_* , V(t_*)) and V(t) would be less than ε for every t ∈ [t_*, t^*]. Full article

478 KiB

Open AccessArticle

An Algorithm for Segment Stability

by V. Dzhafarov and T. Büyükköroğlu

Math. Comput. Appl. 2003, 8(1), 111-118; https://doi.org/10.3390/mca8010111 - 01 Apr 2003

Viewed by 1050

Abstract

In this note an algorithm for testing on stability-unstability of polynomial segments with stable end-points is given. The algorithm is based on well-known segment lemma and on approximate positive real roots of suitable polynomial equation. In this paper an upper bound for absolute [...] Read more.

In this note an algorithm for testing on stability-unstability of polynomial segments with stable end-points is given. The algorithm is based on well-known segment lemma and on approximate positive real roots of suitable polynomial equation. In this paper an upper bound for absolute error of approximate root that guarantees the segment stability or unstability is established. In the case of unstability the algorithm, differs from the existing algorithms, explains the segment behavior in the parameter space. Some illustrative examples also are given. Full article

528 KiB

Open AccessArticle

On the Buckling Analysis of Plates Reinforced with Stiff Ribs

by Harnit Akbulut and Ömer Gündoğdu

Math. Comput. Appl. 2003, 8(1), 103-110; https://doi.org/10.3390/mca8010103 - 01 Apr 2003

Cited by 2 | Viewed by 1118

Abstract

This paper deals with analytical buckling analysis of the rectangular orthotropic simply supported plates reinforced with longitudinal stiff ribs. It was considered that the ribs with rectangular and circular cross-sections were parallel and equivalent to each other. It was further assumed that the [...] Read more.

This paper deals with analytical buckling analysis of the rectangular orthotropic simply supported plates reinforced with longitudinal stiff ribs. It was considered that the ribs with rectangular and circular cross-sections were parallel and equivalent to each other. It was further assumed that the ribs were rigidly fastened to the plate and that their cross sections were perpendicular to the undeformed middle surface of the plate. These reinforced plates were subjected to the uniaxial uniform distributed compressive loads. In the study, the effect of the numbers and the cross-sections of the ribs on the buckling load were investigated. The results are striking in that how the ribs effect the isotropic plates with low strength. Full article

559 KiB

Open AccessArticle

Recovering Images from Traveltime Data

by Dursun Üstündağ and Ersen Özbaşaran

Math. Comput. Appl. 2003, 8(1), 95-102; https://doi.org/10.3390/mca8010095 - 01 Apr 2003

Viewed by 986

Abstract

We study here a mathematical problem of retrieving slowness (reciprocal of velocity) distribution of a medium from a set of the measured first arrivals traveltimes data between source?sand receivers within the medium. Full article

262 KiB

Open AccessArticle

Potential Symmetry Generators of Some Perturbed Nonlinear Evolution Related Equations

by A. H. Kara

Math. Comput. Appl. 2003, 8(1), 89-94; https://doi.org/10.3390/mca8010089 - 01 Apr 2003

Cited by 3 | Viewed by 958

Abstract

Some recent results on approximate Lie group methods and previously developed concepts on potential symmetries are extended and applied to nonlinear systems perturbed to some order by a small parameter. The potential (or auxiliary) form of the perturbed . system necessarily requires knowledge [...] Read more.

Some recent results on approximate Lie group methods and previously developed concepts on potential symmetries are extended and applied to nonlinear systems perturbed to some order by a small parameter. The potential (or auxiliary) form of the perturbed . system necessarily requires knowledge of an "approximate" conservation law of the system. We make an analysis on a perturbed Burgers equation and discuss other nonlinear equations where the results are applicable. Full article

632 KiB

Open AccessArticle

Stress Intensity Factors for a Ring-Shaped Crack in a Transversely Isotropic Thick Layer

by Necati Ataberk, Mesut Uyaner and Ahmet Avci

Math. Comput. Appl. 2003, 8(1), 79-88; https://doi.org/10.3390/mca8010079 - 01 Apr 2003

Cited by 2 | Viewed by 1219

Abstract

The problem of a ring-shaped crack in an infinitely long thick layer was considered in this study. The problem was formulated for a transversely isotropic material by using integral transform technique under uniform load. Due to the geometry of the configuration, Hankel integral [...] Read more.

The problem of a ring-shaped crack in an infinitely long thick layer was considered in this study. The problem was formulated for a transversely isotropic material by using integral transform technique under uniform load. Due to the geometry of the configuration, Hankel integral transform technique was chosen and the problem was reduced to a singular integral equation. This integral equation was solved numerically by using Gaussian Quadrature Formulae and the values were evaluated for discrete points. Stress intensity factors were obtained by using these values. They were tabulated for various ring−haped crack sizes and transversely isotropic materials. Full article

442 KiB

Open AccessArticle

Phase-Plane Analysis for a Simplified Model of Purkinje Cell Dendrite

by Mahmut Ozer

Math. Comput. Appl. 2003, 8(1), 71-78; https://doi.org/10.3390/mca8010071 - 01 Apr 2003

Viewed by 1035

Abstract

In this study, phase-plane analysis is carried out for a simplified model of Purkinje cell dendrite in term.s of voltage-gated ionic channels involved. State variables, nuliclines and equilibrium points of the model are determined, and effects of ionic channel conductance and injected current [...] Read more.

In this study, phase-plane analysis is carried out for a simplified model of Purkinje cell dendrite in term.s of voltage-gated ionic channels involved. State variables, nuliclines and equilibrium points of the model are determined, and effects of ionic channel conductance and injected current on the shape of nuliclines and the equilibrium points are investigated. Full article

391 KiB

Open AccessArticle

Invariant Solutions and Conservation Laws of the Black-Scholes Equation

by C. A. Pooe, F. M. Mahomed and C. Wafo Soh

Math. Comput. Appl. 2003, 8(1), 63-70; https://doi.org/10.3390/mca8010063 - 01 Apr 2003

Cited by 1 | Viewed by 1232

Abstract

As the Black-Scholes equation can be transformed into the one-dimensional linear heat equation via two sets of transformations, an optimal system of one-dimensional subalgebras for the one-dimensional heat equation is exploited to obtain two classes of optimal systems of one-dimensional subalgebras for the [...] Read more.

As the Black-Scholes equation can be transformed into the one-dimensional linear heat equation via two sets of transformations, an optimal system of one-dimensional subalgebras for the one-dimensional heat equation is exploited to obtain two classes of optimal systems of one-dimensional subalgebras for the well-known Black-Scholes equation of the mathematics of finance. Two methods for the derivation of the two classes of optimal systems of group-invariant solutions for this model are available. We present the simpler approach Full article

298 KiB

Open AccessArticle

Goursat Problem for the Factorizable Hyperbolic Equation in Two Independent Variables

by I K. Johnpillai and F M. Mahomed

Math. Comput. Appl. 2003, 8(1), 55-62; https://doi.org/10.3390/mca8010055 - 01 Apr 2003

Cited by 2 | Viewed by 1077

Abstract

For the scalar linear hyperbolic partial differential equations (PDEs) in two independent variables to be factorizable, the Laplace invariants h or k must be zero. In this paper, we find the Riemann function for the Goursat problem using the Lie group theoretical method [...] Read more.

For the scalar linear hyperbolic partial differential equations (PDEs) in two independent variables to be factorizable, the Laplace invariants h or k must be zero. In this paper, we find the Riemann function for the Goursat problem using the Lie group theoretical method where the hyperbolic . equation involved is factorized. What emerges is that the ordinary differential equation (ODE) whose solution gives the Riemann function for the Goursat problem is factorizable. Finally, an example is given as application of the methods Full article

354 KiB

Open AccessArticle

Modelling Tractive Performance for Drive Wheel

by Kazim Çarman and Fariz Dünyamalioğlu

Math. Comput. Appl. 2003, 8(1), 49-54; https://doi.org/10.3390/mca8010049 - 01 Apr 2003

Cited by 3 | Viewed by 1095

Abstract

A model was developed by regression analysis to predict the tractive performance of 7.00-18 radial ply tire for agricultural tractors. Different parameters that affect the cone index of soil and wheel slip were considered for the analysis. To obtain experiments values belonging to [...] Read more.

A model was developed by regression analysis to predict the tractive performance of 7.00-18 radial ply tire for agricultural tractors. Different parameters that affect the cone index of soil and wheel slip were considered for the analysis. To obtain experiments values belonging to tractive performance of tire, a study was conducted in the soil bin by using a single wheel agricultural tire test machine. Performance of this model was compared with model developed by Wismer and Luth (1974) to predicted tractive performance. Mathematical and statistical methods were used to fitting and analysing of models. Results showed that M₁ model outputs were closer to experimental values than M₂ model outputs for prediction of traction performance Full article

869 KiB

Open AccessArticle

Design-Optimization of Mechanical Components Using the “Multiple Objective Tabu Search” Method

by Adil Baykasoğlu

Math. Comput. Appl. 2003, 8(1), 35-47; https://doi.org/10.3390/mca8010035 - 01 Apr 2003

Viewed by 1189

Abstract

The multiple objective version of the tabu search (TS algorithm was initially developed by Baykasoglu et al [1-3]. The idea of applying tabu search to multiple objective optimization, inspired from its solution structure, in which tabu search works with more than one solution [...] Read more.

The multiple objective version of the tabu search (TS algorithm was initially developed by Baykasoglu et al [1-3]. The idea of applying tabu search to multiple objective optimization, inspired from its solution structure, in which tabu search works with more than one solution (neighborhood solutions) at a time. This situation creates the opportunity to evaluate multiple objectives simultaneously in one run. To enable the original tabu search algorithm to work with more than one objective the selection and updating stages were redefined. Other stages are identical to the original tabu search algorithm. In this paper, mutiple objective tabu search algorithm is used to solve mechanical component design problems) with multiple objectives. Although there exists a number of classical techniques, meta-heuristic algorithms including TS have an edge over the classical methods in that they can find multiple Pareto-optimal solutions in one single run. In the paper four mechanical component design problems borrowed from the literature are solved. The results are compared with several other solution techniques including multiple objective genetic algorithms. It is observed that in many of the cases the multiple objective tabu search algorithm can find better and much wider spread of solutions than the compared algorithms. Full article

390 KiB

Open AccessArticle

On Complexity of a Global Optimization Problem

by Urfat G. Nuriyev

Math. Comput. Appl. 2003, 8(1), 27-34; https://doi.org/10.3390/mca8010027 - 01 Apr 2003

Cited by 1 | Viewed by 1070

Abstract

The Solution of the Subproblem of the Cutting Angle Method of Global Optimization for problems of minimizing increasing Positively Homogeneous of degree one functions is proved to be NP-Complete. For the proof of this fact we formulate another problem which we call "Dominating [...] Read more.

The Solution of the Subproblem of the Cutting Angle Method of Global Optimization for problems of minimizing increasing Positively Homogeneous of degree one functions is proved to be NP-Complete. For the proof of this fact we formulate another problem which we call "Dominating Subset with Minimal Weight". The solution of this problem is also NP-Complete. Full article

345 KiB

Open AccessArticle

Thermodynamic Effects at Interaction between Laser Beam and Heavy - Viscous Liquids

by Hikmet Gafaroglu Hassanov

Math. Comput. Appl. 2003, 8(1), 21-26; https://doi.org/10.3390/mca8010021 - 01 Apr 2003

Viewed by 935

Abstract

Influence of laser radiation on thermodynamic properties of heavy - viscous liquids is investigated. Mathematical model taking into account liquids viscosity and their thermal specifications is firstly developed. Inverse problem for acoustic pressure is Solved. Formula for determining thermodynamic parameters of liquid is [...] Read more.

Influence of laser radiation on thermodynamic properties of heavy - viscous liquids is investigated. Mathematical model taking into account liquids viscosity and their thermal specifications is firstly developed. Inverse problem for acoustic pressure is Solved. Formula for determining thermodynamic parameters of liquid is obtained. Effect of main laser beam characteristics (radiation duration and intensity) on generation of non - stationary states in liquid is estimated. Full article

442 KiB

Open AccessArticle

A Mathematical Model for The Separation of Viscous Liquid Flow by Magnetic Field

by Hikmet Gafaroglu Hassanov

Math. Comput. Appl. 2003, 8(1), 13-19; https://doi.org/10.3390/mca8010013 - 01 Apr 2003

Cited by 1 | Viewed by 1124

Abstract

Inverse problem of the two - phase liquid flow separation on components under magnetic field action is firstly resolved at given law of the moving boundary alteration. Automodel solution is established, which may be approximated till various areas of dimensionless variable O. It [...] Read more.

Inverse problem of the two - phase liquid flow separation on components under magnetic field action is firstly resolved at given law of the moving boundary alteration. Automodel solution is established, which may be approximated till various areas of dimensionless variable O. It is found the relationship between the phase radius r o and magnetic properties of the liquid involved. The dependence of velocity function on rheological parameters of the liquid is estimated. The changes of the liquid flow separation due to effect of the alternating magnetic field are shown. It is established, what liquids should be combined in total flow in order to acquire the best effect of separation. Full article

690 KiB

Open AccessArticle

Effect of Shaft Elasticity on the Performance of Slip Energy Recovery Drives

by Salva Saleh Basurrah and Mehmet Akbaba

Math. Comput. Appl. 2003, 8(1), 1-11; https://doi.org/10.3390/mca8010001 - 01 Apr 2003

Viewed by 1036

Abstract

All rotating shafts, even in the absence of external load, deflect during rotation. The magnitude of the deflection depends upon the stiffness of the shaft, its supports and also upon the load level. In this paper, a complete study of the effect of [...] Read more.

All rotating shafts, even in the absence of external load, deflect during rotation. The magnitude of the deflection depends upon the stiffness of the shaft, its supports and also upon the load level. In this paper, a complete study of the effect of shaft elasticity or stiffness coefficient on the performance of a slip energy recovery drive (SERD) has been presented. The elastic shaft model is derived through the use of Lagrange formulation and it is incorporated into the slip SERD model. A computer program is developed to analyze the complete performance of the drive including the effect of shaft elasticity. A load torque that is a quadratic function of the shaft speed is assumed throughout the analysis. Numerous computer simulations were carried out to illustrate the performance of the SERD with elastic transmission for different stiffness coefficients of the shaft material, taking into account the effects of changing the modulus of elasticity and shaft dimensions. Full article

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Math. Comput. Appl., Volume 8, Issue 1 (April 2003) – 16 articles , Pages 1-134

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