In this paper the oscillation criterion was investigated for all solutions of the third-order half linear neutral differential equations. Some necessary and sufficient conditions are established for every solution of (a(t)[(x(t)±p(t)x(?(t) ) )^'' ]^? )^'+q(t) x^? (?(t) )=0, t?t_0, to be oscillatory. Examples are given to illustrate our main results.

A method for Approximated evaluation of linear functional differential equations is described. where a function approximation as a linear combination of a set of orthogonal basis functions which are chebyshev functions .The coefficients of the approximation are determined by (least square and Galerkin’s) methods. The property of chebyshev polynomials leads to good results , which are demonstrated with examples.

Abstract

            Rayleigh distribution is one of the important distributions used for analysis life time data, and has applications in reliability study and physical interpretations. This paper introduces four different methods to estimate the scale parameter, and also estimate reliability function; these methods are Maximum Likelihood, and Bayes and Modified Bayes, and Minimax estimator under squared error loss function, for the scale and reliability function of the generalized Rayleigh distribution are obtained. The comparison is done through simulation procedure, t

Abstract

The current research aims to identify the effect of using a model of generative learning in the achievement of first-middle students of chemical concepts in science. The researcher adopted the null hypothesis, which is there is no statistically significant difference at the level (0.05) between the mean scores of the experimental group who study using the generative learning model and the average scores of the control group who study using the traditional method in the chemical concepts achievement test. The research consisted of (200) students of the first intermediate at Al-Farqadin Intermediate School for Boys affiliated with the Directorate of General Education in Baghdad Governorate / Al-Karkh 3 wit

     We have presented the distribution of the exponentiated expanded power function (EEPF) with four parameters, where this distribution was created by the exponentiated expanded method created by the scientist Gupta to expand the exponential distribution by adding a new shape parameter to the cumulative function of the distribution, resulting in a new distribution, and this method is characterized by obtaining a distribution that belongs for the exponential family. We also obtained a function of survival rate and failure rate for this distribution, where some mathematical properties were derived, then we used the method of maximum likelihood (ML) and method least squares developed  (LSD)

In this research, we sought to identify the nature of the relationship between the exchange rate of the Chinese yuan and the value of Chinese exports, through the formulation of a standard model based on the model of common integration, and based on the data of the study and using the test "Angel-Granger" It reflects the relationship between the two research variables, through which the relationship between the RMB exchange rate and the value of Chinese exports was estimated during the period 1978-2017.

Average per capita GDP income is an important economic indicator. Economists use this term to determine the amount of progress or decline in the country's economy. It is also used to determine the order of countries and compare them with each other. Average per capita GDP income was first studied using the Time Series (Box Jenkins method), and the second is linear and non-linear regression; these methods are the most important and most commonly used statistical methods for forecasting because they are flexible and accurate in practice. The comparison is made to determine the best method between the two methods mentioned above using specific statistical criteria. The research found that the best approach is to build a model for predi

Protecting information sent through insecure internet channels is a significant challenge facing researchers. In this paper, we present a novel method for image data encryption that combines chaotic maps with linear feedback shift registers in two stages. In the first stage, the image is divided into two parts. Then, the locations of the pixels of each part are redistributed through the random numbers key, which is generated using linear feedback shift registers. The second stage includes segmenting the image into the three primary colors red, green, and blue (RGB); then, the data for each color is encrypted through one of three keys that are generated using three-dimensional chaotic maps. Many statistical tests (entropy, peak signa

A linear engine generator with a compact double-acting free piston mechanism allows for full integration of the combustion engine and generator, which provides an alternative chemical-to-electrical energy converter with a higher volumetric power density for the electrification of automobiles, trains, and ships. This paper aims to analyse the performance of the integrated engine with alternative permanent magnet linear tubular electrical machine topologies using a coupled dynamic model in Siemens Simcenter software. Two types of alternative generator configurations are compared, namely long translator-short stator and short translator-long stator linear machines. The dynamic models of the linear engine and linear generator, validated