The Taylor series is defined by the f and g series. The solution to the satellite's equation of motion is expanding to generate Taylor series through the coefficients f and g. In this study, the orbit equation in a perifocal system is solved using the Taylor series, which is based on time changing. A program in matlab is designed to apply the results for a geocentric satellite in low orbit (height from perigee, hp= 622 km). The input parameters were the initial distance from perigee, the initial time, eccentricity, true anomaly, position, and finally the velocity. The output parameters were the final distance from perigee and the final time values. The results of radial distance as opposed to time were plotted for dissimilar times in seconds and their comparison with the exact solution, with the aim of selecting an optimized reference orbit at a height of 622 km. The results indicated that the two series diverged excessively as the time increased from the exact solution, excluding the time of 850 sec. The f and g series had a little shift. Besides, the root mean square error (rmse) is computed for 750 sec. It was about 5 for the two series before diverging at about 180 sec and rapidly growing with time. For 850 sec, the (rmse) is approaching 10 for the two series and increasing quickly over time. So, the (rmse) is directly proportional to time, which means that as time increases, the diverging behavior and the value of the (rmse) will also increase. If more terms (Δt) are used for the two series and more time is included, the two series will deviate from the exact solution. The program's results are compared to other published studies in this field; they demonstrated high convergence.
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The method of operational matrices is based on the Bernoulli and Shifted Legendre polynomials which is used to solve the Falkner-Skan equation. The nonlinear differential equation converting to a system of nonlinear equations is solved using Mathematica®12, and the approximate solutions are obtained. The efficiency of these methods was studied by calculating the maximum error remainder ( ), and it was found that their efficiency increases as increases. Moreover, the obtained approximate solutions are compared with the numerical solution obtained by the fourth-order Runge-Kutta method (RK4), which gives a good agreement.
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In this paper, we investigate the behavior of the bayes estimators, for the scale parameter of the Gompertz distribution under two different loss functions such as, the squared error loss function, the exponential loss function (proposed), based different double prior distributions represented as erlang with inverse levy prior, erlang with non-informative prior, inverse levy with non-informative prior and erlang with chi-square prior.
The simulation method was fulfilled to obtain the results, including the estimated values and the mean square error (MSE) for the scale parameter of the Gompertz distribution, for different cases for the scale parameter of the Gompertz distr
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For any group G, we define G/H (read” G mod H”) to be the set of left cosets of H in G and this set forms a group under the operation (a)(bH) = abH. The character table of rational representations study to gain the K( SL(2,81)) and K( SL(2, 729)) in this work.
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A factor group is a mathematical group obtained by aggregating similar elements of a larger group using an equivalence relation that preserves some of the group structure. In this paper, the factor groups K(SL(2,121)) and K(SL(2,169)) computed for each group from the character table of rational representations.
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