An efficient combination of Adomian Decomposition iterative technique coupled with Laplace transformation to solve non-linear Random Integro differential equation (NRIDE) is introduced in a novel way to get an accurate analytical solution. This technique is an elegant combination of theLaplace transform, and the Adomian polynomial. The suggested method will convert differential equations into iterative algebraic equations, thus reducing processing and analytical work. The technique solves the problem of calculating the Adomian polynomials. The method’s efficiency was investigated using some numerical instances, and the findings demonstrate that it is easier to use than many other numerical procedures. It has also been established that (LTADM) is a trustworthy technique for solving differential equations. Using the Mathematica 13.3 programme, the graphs of the approximate solutions and consecutive error are presented. Two applications are presented as examples of how the proposed technique can be utilised to obtain analytical or numerical solutions for certain kinds of Random Integro Differential Equations (RIDEs) in order to demonstrate its efficacy and potential.
This paper proposed a new method to study functional non-parametric regression data analysis with conditional expectation in the case that the covariates are functional and the Principal Component Analysis was utilized to de-correlate the multivariate response variables. It utilized the formula of the Nadaraya Watson estimator (K-Nearest Neighbour (KNN)) for prediction with different types of the semi-metrics, (which are based on Second Derivative and Functional Principal Component Analysis (FPCA)) for measureing the closeness between curves. Root Mean Square Errors is used for the implementation of this model which is then compared to the independent response method. R program is used for analysing data. Then, when the cov
... Show MoreThe differential protection of power transformers appears to be more difficult than any type of protection for any other part or element in a power system. Such difficulties arise from the existence of the magnetizing inrush phenomenon. Therefore, it is necessary to recognize between inrush current and the current arise from internal faults. In this paper, two approaches based on wavelet packet transform (WPT) and S-transform (ST) are applied to recognize different types of currents following in the transformer. In WPT approach, the selection of optimal mother wavelet and the optimal number of resolution is carried out using minimum description length (MDL) criteria before taking the decision for the extraction features from the WPT tree
... Show Morein this paper sufficient conditions of oscillation of all of nonlinear second order neutral differential eqiation and sifficient conditions for nonoscillatory soloitions to onverage to zero are obtained
Aims to find out the (Extent of mathematics teachers' appreciation of the mathematical problem `multiple solutions) Research sample consisted of (100) mathematics teachers distributed on the General Directorates of Education in Baghdad (Rusafa 1/2/3) and (Karkh 1/2/ 3) There was two research approach which are: The first - two different answers of students to the same issue where teachers must assess each answer and explain which one the teacher will accept and why? The second - Different solutions of students' to the same issue, including wrong answers , Teachers should correct the answers and give them final grades (0-10). Descriptive and analytical Approch was used in this research methodology And zero hypotheses, which are as f
... Show MoreMany production companies suffers from big losses because of high production cost and low profits for several reasons, including raw materials high prices and no taxes impose on imported goods also consumer protection law deactivation and national product and customs law, so most of consumers buy imported goods because it is characterized by modern specifications and low prices.
The production company also suffers from uncertainty in the cost, volume of production, sales, and availability of raw materials and workers number because they vary according to the seasons of the year.
I had adopted in this research fuzzy linear program model with fuzzy figures
... Show MoreThe use of Bayesian approach has the promise of features indicative of regression analysis model classification tree to take advantage of the above information by, and ensemble trees for explanatory variables are all together and at every stage on the other. In addition to obtaining the subsequent information at each node in the construction of these classification tree. Although bayesian estimates is generally accurate, but it seems that the logistic model is still a good competitor in the field of binary responses through its flexibility and mathematical representation. So is the use of three research methods data processing is carried out, namely: logistic model, and model classification regression tree, and bayesian regression tree mode
... Show MoreIn today's digital era, the importance of securing information has reached critical levels. Steganography is one of the methods used for this purpose by hiding sensitive data within other files. This study introduces an approach utilizing a chaotic dynamic system as a random key generator, governing both the selection of hiding locations within an image and the amount of data concealed in each location. The security of the steganography approach is considerably improved by using this random procedure. A 3D dynamic system with nine parameters influencing its behavior was carefully chosen. For each parameter, suitable interval values were determined to guarantee the system's chaotic behavior. Analysis of chaotic performance is given using the
... Show MoreIn this work, the dyes Rhodamine B and Coumarin 102 containing titanium dioxide nanoparticles were used as scattering centers to fabricate a random gain medium. The laser dye was dissolved in hexanol and methanol solvent respectively. The titanium dioxide nanoparticles were synthesized by DC reaction magnetron spraying technique. The random-gain medium was made by adding 2.5 mg of titanium dioxide nanoparticles to Rhodamine and coumarin 102 dyes by coating the glass cell with two-sided titanium dioxide with high spectral efficiency and low production cost. A narrow line optical emission was detected at 565 nm for Rhodamine B and 534 nm for coumarin 102, where it was found that rhodamine B dye has FWHM 8 nm and coumarin dye 102 has FWHM 9 nm
... Show More