Mathematical and Computational Applications

168 KiB

Open AccessArticle

A Data Driven Parameter Estimation for the Three-Parameter Weibull Population from Censored Samples

by Ahmed M. M. Sultan

Math. Comput. Appl. 2008, 13(2), 129-136; https://doi.org/10.3390/mca13020129 - 01 Aug 2008

Cited by 1 | Viewed by 950

A method is described for the calculation of the three-parameter Weibull distribution function from censored samples. The method introduces a data driven technique based on an adapted Gaussian like kernel to match the censoring scheme. The method minimizes the Cramer von Mises distance

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A method is described for the calculation of the three-parameter Weibull distribution function from censored samples. The method introduces a data driven technique based on an adapted Gaussian like kernel to match the censoring scheme. The method minimizes the Cramer von Mises distance from a non-parametric density estimate and the parametric estimate at the order statistics. The maximum likelihood estimators are found and a comparison is made with the new estimator. A Monte Carlo experiment of size 1000 is conducted to test the performance of the new parameter estimation technique. The mean integrated square error is taken as a measure of the closeness of the estimated density and the true density.

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131 KiB

Open AccessArticle

A Root-Finding Algorithm with Fifth Order Derivatives

by M. Pakdemirli, H. Boyacı and H. A. Yurtsever

Math. Comput. Appl. 2008, 13(2), 123-128; https://doi.org/10.3390/mca13020123 - 01 Aug 2008

Cited by 18 | Viewed by 1106

Abstract

Perturbation theory is used to generate a root finding algorithm with fifth order derivatives. The algorithm is called Quintuple-Correction-Term algorithm. The new algorithm is contrasted with the previous Quadruple-Correction-Term and Triple-Correction-Term algorithms in the literature. It is found that adding a fifth correction

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Perturbation theory is used to generate a root finding algorithm with fifth order derivatives. The algorithm is called Quintuple-Correction-Term algorithm. The new algorithm is contrasted with the previous Quadruple-Correction-Term and Triple-Correction-Term algorithms in the literature. It is found that adding a fifth correction term in the algorithm does not improve the performance.

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151 KiB

Open AccessArticle

Differential Transform Technique for Solving Fifth-Order Boundary Value Problems

by Vedat Suat Ertürk and Shaher Momani

Math. Comput. Appl. 2008, 13(2), 113-121; https://doi.org/10.3390/mca13020113 - 01 Aug 2008

Cited by 2 | Viewed by 1091

Abstract

In this paper we apply the differential transform method for solving fifthorder boundary value problems. The analytical and numerical results of the equations have been obtained in terms of convergent series with easily computable components. Three examples are given to illustrate the efficiency

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In this paper we apply the differential transform method for solving fifthorder boundary value problems. The analytical and numerical results of the equations have been obtained in terms of convergent series with easily computable components. Three examples are given to illustrate the efficiency and implementation of the present method. Comparisons are made to confirm the reliability of the method. Differential transform technique may be considered as alternative and efficient for finding the approximate solutions of the boundary values problems.

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236 KiB

Open AccessArticle

Comparison of IBM-2 Calculations with X(5) Critical Point Symmetry for Low-Lying States in 144-154Nd

by Sait İnan, Nurettin Türkan, İlyas İnci and Davut Olgun

Math. Comput. Appl. 2008, 13(2), 101-112; https://doi.org/10.3390/mca13020101 - 01 Aug 2008

Cited by 2 | Viewed by 1062

Abstract

The X(5) would take place when moving continously from the pure U(5) symmetry to the SU(3) symmetry and it implies a definite relations among the level energies and among the E2 transition strengths. It was recently shown that a signature of phase transition

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The X(5) would take place when moving continously from the pure U(5) symmetry to the SU(3) symmetry and it implies a definite relations among the level energies and among the E2 transition strengths. It was recently shown that a signature of phase transition is observed in the chain of Sm, Mo and Nd isotopes, where ¹⁵²Sm,¹⁰⁴Mo and ¹⁵⁰Nd display the predicted features of the X(5) symmetry and mark therefore the critical point. However, more detailed studies and experiments are needed to get ideas about this signature. Without entering into detail we have firstly compared the results obtained in our previous study [15] of ^144-154Nd with that of the limits in X(5) symmetry and then given a clear descripton about the validity of the Hamiltonian parameters used in the study. At the end, we have concluded that some of Nd isotopes display X(5) symmetry features.

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167 KiB

Open AccessArticle

Dynamical Control of Accuracy Using the Stochastic Arithmetic to Estimate Double and Improper Integrals

by Mohammad Ali Fariborzi Araghi

Math. Comput. Appl. 2008, 13(2), 91-100; https://doi.org/10.3390/mca13020091 - 01 Aug 2008

Cited by 1 | Viewed by 922

Abstract

The CESTAC (Control et Estimation STochastique des Arrondis de Calculs) method is based on a probabilistic approach of the round-off error propagation which replaces the floating-point arithmetic by the stochastic arithmetic. This is an efficient method to estimate the accuracy of the results.

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The CESTAC (Control et Estimation STochastique des Arrondis de Calculs) method is based on a probabilistic approach of the round-off error propagation which replaces the floating-point arithmetic by the stochastic arithmetic. This is an efficient method to estimate the accuracy of the results. In this paper, we present the reliable schemes using the CESTAC method to estimate the definite double integral I = \({\int_a^b}{\int_c^d}\)f(x,y)dydx and the improper integral I = \(\int_a^\infty\)f(x)dx , where a, b, c, d ∈ R, by applying the trapezoidal or Simpson's rule. For each kind of integrals, we prove a theorem to show the accuracy of the results. According to these theorems, one can find an optimal value number of the points which we can find the best approximation of I from the computer point of view. Also, we observe that by using the stochastic arithmetic, we are able to validate the results.

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191 KiB

Open AccessArticle

Generalized Statistical Mechanics for Nucleus

by Halil Babacan, Ozhan Kayacan and Ramazan Atici

Math. Comput. Appl. 2008, 13(2), 81-90; https://doi.org/10.3390/mca13020081 - 01 Aug 2008

Viewed by 925

Abstract

In this study, we derived the grand partition function and some thermodynamical quantities of the nucleus in the high temperature limit by adopting the ideal Fermi gas partition function of generalized Tsallis thermostatistics. The behaviour of number of neutron and internal energy are

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In this study, we derived the grand partition function and some thermodynamical quantities of the nucleus in the high temperature limit by adopting the ideal Fermi gas partition function of generalized Tsallis thermostatistics. The behaviour of number of neutron and internal energy are depicted as a function of temperature. Sensitivity of q entropy index to the number neutron are also analyzed.

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163 KiB

Open AccessArticle

Long Term Energy Consumption Forecasting Using Genetic Programming

by Korhan Karabulut, Ahmet Alkan and Ahmet S. Yilmaz

Math. Comput. Appl. 2008, 13(2), 71-80; https://doi.org/10.3390/mca13020071 - 01 Aug 2008

Cited by 44 | Viewed by 1618

Abstract

Managing electrical energy supply is a complex task. The most important part of electric utility resource planning is forecasting of the future load demand in the regional or national service area. This is usually achieved by constructing models on relative information, such as

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Managing electrical energy supply is a complex task. The most important part of electric utility resource planning is forecasting of the future load demand in the regional or national service area. This is usually achieved by constructing models on relative information, such as climate and previous load demand data. In this paper, a genetic programming approach is proposed to forecast long term electrical power consumption in the area covered by a utility situated in the southeast of Turkey. The empirical results demonstrate successful load forecast with a low error rate.

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Math. Comput. Appl., Volume 13, Issue 2 (August 2008) – 7 articles , Pages 71-136

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