This paper suggest two method of recognition, these methods depend on the extraction of the feature of the principle component analysis when applied on the wavelet domain(multi-wavelet). First method, an idea of increasing the space of recognition, through calculating the eigenstructure of the diagonal sub-image details at five depths of wavelet transform is introduced. The effective eigen range selected here represent the base for image recognition. In second method, an idea of obtaining invariant wavelet space at all projections is presented. A new recursive from that represents invariant space of representing any image resolutions obtained from wavelet transform is adopted. In this way, all the major problems that effect the image and

This work describes two efficient and useful methods for solving fractional pantograph delay equations (FPDEs) with initial and boundary conditions. These two methods depend mainly on orthogonal polynomials, which are the method of the operational matrix of fractional derivative that depends on Bernstein polynomials and the operational matrix of the fractional derivative with Shifted Legendre polynomials. The basic procedure of this method is to convert the pantograph delay equation to a system of linear equations and by using, the operational matrices we get rid of the integration and differentiation operations, which makes solving the problem easier. The concept of Caputo has been used to describe fractional derivatives. Finally, some

       In this paper, the topic of forecasting the changes in the value of Iraqi crude oil exports for the period from 2019 to 2025, using the Markov transitional series based on the data of the time series for the period from January 2011 to November 2018, is real data obtained from the published data of the Central Agency Of the Iraqi statistics and the Iraqi Ministry of Oil that the results reached indicate stability in the value of crude oil exports according to the data analyzed and listed in the annex to the research.

Keywords: Using Markov chains

This investigation aimed to explain the mechanism of MFCA by applying this method on air-cooled engine factory which was suffering from high production cost. The results of this study revealed that MFCA is a useful tool to identify losses and inefficiencies of the production process. It is found that the factory is suffering from high losses due to material energy and system losses. In conclusion, it is calculated that system losses are the highest among all the losses due to inefficient use of available production capacity.

The 8 - mixing ratios of 7 - transitions from levels of 26 Mg populated in 23 Na (a, py)26Mg reaction are calculated using a2 — ratio method for the first time in the case of two mixed y - transitions from the same initial level. The results obtained have been compared with 8 - values determined by other methods. The comparison shows that the agreement is excellent. This confirms the validity of this method in calculating the 6 - values of such 7 - transitions.

Test anxiety for intermediate level The current study aims to measure the test anxiety of research’s sample and to identify the statistical differences of test anxiety, considering two variables gender and students classes level (first and third intermediate class). To do this, a stratified random sampling of (300) student from first and third intermediate classes had selected from both the karkh and Rusafa sides of Baghdad province for the academic year 2015-2016. The author tested the whole sample by using the test anxiety scale that had tested for its validity and reliability. The results revealed that the research’s sample as a whole was suffering from test anxiety, there were a statistical differences between male and female tha