Mathematical and Computational Applications

335 KiB

Open AccessArticle

by M. Anaç Kiliç, M. Pakdemirli and B. Solmaz

Math. Comput. Appl. 2004, 9(1), 117-123; https://doi.org/10.3390/mca9010117 - 01 Apr 2004

Viewed by 1202

Long wave equations propagating along an open channel with bottom friction are considered. The equations are cast into a non-dimensional form, Scaling and translational symmetries of the equations are calculated for the cases of constant bottom friction coefficient and variable bottom friction coefficient. [...] Read more.

Long wave equations propagating along an open channel with bottom friction are considered. The equations are cast into a non-dimensional form, Scaling and translational symmetries of the equations are calculated for the cases of constant bottom friction coefficient and variable bottom friction coefficient. Using the symmetries, the partial differential equations are transformed into ordinary differential equations. Analytical and numerical solutions of the ordinary differential equations are found and solutions are contrasted with each other. Full article

481 KiB

Open AccessArticle

Chebyshev Collocation Method for Solving Linear Differential Equations

by İhsan Timuçin Dolapçi

Math. Comput. Appl. 2004, 9(1), 107-115; https://doi.org/10.3390/mca9010107 - 01 Apr 2004

Cited by 6 | Viewed by 3133

Abstract

A matrix method, which is called the Chebyshev-matrix method, for the approximate solution of linear differential equations in term of Chebyshev collocations is presented. The method is based on first taking the truncated Chebyshev series of the functions in equation and then substituting [...] Read more.

A matrix method, which is called the Chebyshev-matrix method, for the approximate solution of linear differential equations in term of Chebyshev collocations is presented. The method is based on first taking the truncated Chebyshev series of the functions in equation and then substituting their matrix forms into the given equation. Thereby the equation reduces to a matrix equation, which corresponds to a system of linear algebraic equations with unknown Chebyshev coefficients. To illustrate the method, it is applied to certain linear differential equation under the given conditions and the results are compared. Full article

244 KiB

Open AccessArticle

The GCD-Reciprocal LCM Matrices on GCD-Closed Sets

by Ayşe NaIII and Dursun Taşci

Math. Comput. Appl. 2004, 9(1), 101-106; https://doi.org/10.3390/mca9010101 - 01 Apr 2004

Viewed by 1191

Abstract

We have given a structure theorem for the GCD-Reciprocal LCM matrix and then we have calculated the value of the determinant of the GCD-Reciprocal LCM matrix. We have obtained formula for the determinant and the inverse of the GCD-Reciprocal LCM matrix defined on [...] Read more.

We have given a structure theorem for the GCD-Reciprocal LCM matrix and then we have calculated the value of the determinant of the GCD-Reciprocal LCM matrix. We have obtained formula for the determinant and the inverse of the GCD-Reciprocal LCM matrix defined on gcd-closed sets. Full article

626 KiB

Open AccessArticle

A Simple Method for Calculating the Number of Atoms in Ion Implanted Samples from the RBS Yield

by N. Can and H.G. Belik

Math. Comput. Appl. 2004, 9(1), 91-99; https://doi.org/10.3390/mca9010091 - 01 Apr 2004

Viewed by 1214

Abstract

A simple method that computes the number of atoms in implanted samples from the integral of the elastic backseattering yield, using a pocket calculator, is represented. The energy dependence E^-2, of the Rutherford law and the screening of the nuclear charge [...] Read more.

A simple method that computes the number of atoms in implanted samples from the integral of the elastic backseattering yield, using a pocket calculator, is represented. The energy dependence E^-2, of the Rutherford law and the screening of the nuclear charge by the electron cloud is considered. The method is based on the assumption that the stopping power is a linearly decreasing function of the energy in the range from 1.4 MeV to 2 MeV. The total yield can be integrated analytically, and the number of atoms in the sample can then be ascertained by an iteration procedure that can be accomplished with a scientific pocket calculator, The results obtained are compared with the values obtained using the computer simulation code for RBS spectra RUMP. Full article

686 KiB

Open AccessArticle

The Investigation of the log(ft) Values for the Allowed Gamow-Teller Transitions of Some Deformed Nuclei

by C. Selam, T. Babacan, H. A. Aygör, H. Bircan, A. Küçübursa and I. Maraş

Math. Comput. Appl. 2004, 9(1), 79-90; https://doi.org/10.3390/mca9010079 - 01 Apr 2004

Cited by 6 | Viewed by 1231

Abstract

The log(ft) values of allowed β^± decay between odd-A nuclei for 125 < A < 180 mass region are investigated. Single particle energies and wave functions are calculated by making use of a deformed Woods-Saxon potential. The calculations are performed in the [...] Read more.

The log(ft) values of allowed β^± decay between odd-A nuclei for 125 < A < 180 mass region are investigated. Single particle energies and wave functions are calculated by making use of a deformed Woods-Saxon potential. The calculations are performed in the framework of proton-neutron quasi particle random phase approximation (QRPA) including the schematic residual spin-isospin interaction among the nucleons in the particle hole channel. The calculations indicated that the results obtained through using the χ_GT=5.2/A^0.7 are more in agreement with experimental observations. Full article

233 KiB

Open AccessArticle

Parametrization of Torsion Units in U1(ZS3)

by Tevfik Bilgin

Math. Comput. Appl. 2004, 9(1), 73-77; https://doi.org/10.3390/mca9010073 - 01 Apr 2004

Cited by 1 | Viewed by 1187

Abstract

In this study, a representation of the group ring ZS₃ is obtained by using a faithful irreducible representation of S₃ of degree 2. In ZS₃, all torsion units are expressed in terms of parameters by means of this representation. [...] Read more.

In this study, a representation of the group ring ZS₃ is obtained by using a faithful irreducible representation of S₃ of degree 2. In ZS₃, all torsion units are expressed in terms of parameters by means of this representation. It is shown that any torsion unit in U₁ (ZS₃) can be expressed in terms of two parameters. Full article

367 KiB

Open AccessArticle

A Note on Mellin Transform and Distributions

by Adem Kiliçman

Math. Comput. Appl. 2004, 9(1), 65-72; https://doi.org/10.3390/mca9010065 - 01 Apr 2004

Cited by 7 | Viewed by 1459

Abstract

Mellin Transform occurs in many branches of Applied Mathematics and Engineering. The Mellin transform is very much related to the Laplace and Fourier transforms and the theory for the ordinary functions is well established. In the distributional sense, first it was studied by [...] Read more.

Mellin Transform occurs in many branches of Applied Mathematics and Engineering. The Mellin transform is very much related to the Laplace and Fourier transforms and the theory for the ordinary functions is well established. In the distributional sense, first it was studied by Zemanian in [2]. In this work we try to extend to the wider class of distributions. Full article

910 KiB

Open AccessArticle

Elastic-Plastic Stress Analysis of Thermoplastic Matrix Laminated Composite Beams

by Hasan Çallioğlu, N. Sman Köksal, Necati Ataberk and İdris Kaynak

Math. Comput. Appl. 2004, 9(1), 49-64; https://doi.org/10.3390/mca9010049 - 01 Apr 2004

Viewed by 1175

Abstract

This study deals with an elastic-plastic behavior of woven steel fibers reinforced thermoplastic matrix laminated composite beam subjected to a bending moment. The beam consists of symmetric four orthotropic layers and its material is assumed to be strain hardening. The Tsai-Hill theory is [...] Read more.

This study deals with an elastic-plastic behavior of woven steel fibers reinforced thermoplastic matrix laminated composite beam subjected to a bending moment. The beam consists of symmetric four orthotropic layers and its material is assumed to be strain hardening. The Tsai-Hill theory is used as a yield criterion in the solution. The Bernoulli-Euler hypotheses are utilized for small plastic deformations. The beam lay-up sequences are chosen as [0°]₄, [15°/-15°]_s, [30°/-30°]_s and [45°/-45°]_s. The bending moment values that begin plastic flow at the upper and lower surfaces of the beam are carried out for various stacking sequences. The variations of the elastic, elastic-plastic and residual stress components versus increasing plastic region spread are given in tables and figures. The transverse displacement is obtained at the free end, numerically. Full article

280 KiB

Open AccessArticle

Upper Bounds for the Spectral and lp Norms of Cauchy-Toeplitz and Cauchy-Hankel Matrices

by Süleyman Solak, Ramazan Türkmen and Durmuş Bozkurt

Math. Comput. Appl. 2004, 9(1), 41-47; https://doi.org/10.3390/mca9010041 - 01 Apr 2004

Viewed by 1294

Abstract

In this study we have given some upper bounds for the spectral and l_p norms of Cauchy-Toeplitz and Cauchy-Hankel matrices of the forms T = [1/(1/2 + |i + j|]_n×n and H= [1/(1/2 + (i + j))]_n×n respectively. Full article

1057 KiB

Open AccessArticle

Numerical Simulations of Flow Distribution in Unpacked and Partially Packed Vessels

by Habib D. Zughbi and Saiffudin Sheikh

Math. Comput. Appl. 2004, 9(1), 25-39; https://doi.org/10.3390/mca9010025 - 01 Apr 2004

Cited by 2 | Viewed by 1310

Abstract

In this study, flow in an unpacked and a partially packed vessels is investigated using numerical simulations. The effects of various factors including the number of inlets and outlets, and throttling the jets by inserting orifice plates above them on the flow fields [...] Read more.

In this study, flow in an unpacked and a partially packed vessels is investigated using numerical simulations. The effects of various factors including the number of inlets and outlets, and throttling the jets by inserting orifice plates above them on the flow fields are investigated. Other factors investigated include fluid flow rate and turbulence model. ft was found that for a given number and location inlets and outlets, the injection velocity does not have a very significant impact on the flow distribution, This distribution could be improved with a careful choice of the number and location of inlets and outlets. For partially packed vessels, the packing may behave like a good distributor depending on the resistance to flow offered by the bed. Full article

291 KiB

Open AccessArticle

Transport Coefficients of Nuclear Matter at High Temperatures

by K. Manisa and R Oğul

Math. Comput. Appl. 2004, 9(1), 19-24; https://doi.org/10.3390/mca9010019 - 01 Apr 2004

Viewed by 1186

Abstract

High temperature coefficients of viscosity and heat conductivity of nuclear matter are calculated on the basis of Chapman-Enskong approximation in the dilute gas limit. It is observed that increasing temperatures produce significant changes in coefficients. Full article

379 KiB

Open AccessArticle

Flow of a Third Grade Fluid between Concentric Circular Cylinders

by M. Yürüsoy

Math. Comput. Appl. 2004, 9(1), 11-17; https://doi.org/10.3390/mca9010011 - 01 Apr 2004

Cited by 8 | Viewed by 1255

Abstract

The steady-state flow of a third grade fluid between concentric circular cylinders with heat transfer is examined. The temperature of pipes is assumed to be higher than the temperature of the fluid. Reynold's model viscosity case is treated. Approximate analytical solutions are presented [...] Read more.

The steady-state flow of a third grade fluid between concentric circular cylinders with heat transfer is examined. The temperature of pipes is assumed to be higher than the temperature of the fluid. Reynold's model viscosity case is treated. Approximate analytical solutions are presented using perturbation technique. Full article

606 KiB

Open AccessArticle

Active Suspension Control of Eight Degrees of Freedom Vehicle Model

by Rahmi Guclu

Math. Comput. Appl. 2004, 9(1), 1-10; https://doi.org/10.3390/mca9010001 - 01 Apr 2004

Cited by 4 | Viewed by 1532

Abstract

In this study, the dynamic behavior of eight degrees of freedom vehicle model having active suspensions and a PID controlled passenger seat is examined. The suspensions considered are Mc Pherson strut type of independent suspensions. Three cases of control strategies are taken into [...] Read more.

In this study, the dynamic behavior of eight degrees of freedom vehicle model having active suspensions and a PID controlled passenger seat is examined. The suspensions considered are Mc Pherson strut type of independent suspensions. Three cases of control strategies are taken into account. First, only the passenger seat is controlled. Second, only the vehicle body is controlled. Third, both the vehicle body and the passenger seat are controlled at the same time. PID controller is applied as a conventional method. Since this control method can be applied easily and is widely well known, it has an important place in control applications. The time and frequency responses of the vehicle model due to road disturbance are obtained for each control strategy. At the end of the study, performances of these strategies have been compared and discussed. Full article

Journal Menu

Journal Browser

Math. Comput. Appl., Volume 9, Issue 1 (April 2004) – 13 articles , Pages 1-123

Further Information

Guidelines

MDPI Initiatives

Follow MDPI