This paper deals with the thirteenth order differential equations linear and nonlinear in boundary value problems by using the Modified Adomian Decomposition Method (MADM), the analytical results of the equations have been obtained in terms of convergent series with easily computable components. Two numerical examples results show that this method is a promising and powerful tool for solving this problems.

Due to its importance in physics and applied mathematics, the non-linear Sturm-Liouville problems
witnessed massive attention since 1960. A powerful Mathematical technique called the Newton-Kantorovich
method is applied in this work to one of the non-linear Sturm-Liouville problems. To the best of the authors’
knowledge, this technique of Newton-Kantorovich has never been applied before to solve the non-linear
Sturm-Liouville problems under consideration. Accordingly, the purpose of this work is to show that this
important specific kind of non-linear Sturm-Liouville differential equations problems can be solved by
applying the well-known Newton-Kantorovich method. Also, to show the efficiency of appl

The objective of this research is to know the economic feasibility of hydroponics technology by estimating the expected demand for green forage for the years 2021-2031 as well as Identify and analyze project data and information in a way that helps the investor make the appropriate investment decision in addition to preparing a detailed technical preliminary study for the cultivar barley project focusing on the commercial and financing aspects and the criteria that take into account the risks and uncertainties . that indicating the economic feasibility of the project to produce green forage using hydroponics technology. Cultured barley as a product falls within the blue ocean strategy. Accordingly, the research recommends the necess

In this research velocity of moving airplane from its recorded digital sound is introduced. The data of sound file is sliced into several frames using overlapping partitions. Then the array of each frame is transformed from time domain to frequency domain using Fourier Transform (FT). To determine the characteristic frequency of the sound, a moving window mechanics is used, the size of that window is made linearly proportional with the value of the tracked frequency. This proportionality is due to the existing linear relationship between the frequency and its Doppler shift. An algorithm was introduced to select the characteristic frequencies, this algorithm allocates the frequencies which satisfy the Doppler relation, beside that the tra

This  research aimes to expose the levels of geometrical thinking among the students of mathematic department in Basic Education College at AL-Mustansiriyah University throughout their respondes on the test of  geometrical thinking which consists (50) multi- choice items  distributed on the first four levels of Van Hiele ( recognition – analysis – ordering – deduction ).

The validity and the reliability of the test have been investigated. Besides, the difficulty and its discrimination have been measured. The activity of the wrong variables has been measured.

The test has been applied on (180) male and female students of the first, second and third grades.

Phonetics has close relevance with Musicology; in this study I decided explaining the interlinkages and harmony between Phonetics and Musicology. Linguists preceded philosophers in an attempt to link Phonetics with Musicology; the 1st serious attempt to link Phonetics with Musicology was done by Ibn Jeny (Dead 392 IC), but the real attempt is found with Farabi through his book under title Al Musiqa Al Kabeer, he defined music and link it with tune and relation between melody and tone, This is the same as pointed out by Ikhwan Al Safa who followed the doctrine of al-Farabi, their attention was with music and link it with phoneme, as they made music independent science, and they created special mathematics rules for it. Melody in music can

Hard water does not pose a threat to human health but may cause precipitation of soap or results stone in the boilers. These reactions are caused by the high concentrations of Ca and Mg. In the industry they are undesirable because of higher fuel consumption for industrial use .Electromagnetic polarization water treatment is a method which can be used for increasing the precipitation of Ca ²⁺ and CO₃ ^2- ions in hard water to form CaCO₃ which leads to decrease the water hardness is research has been conducted by changing the number of coil turns and voltage of the system. The spectroscopy electron microscope was used for imaging the produced crystals. Results of the investigation indicated that

The Enhanced Thematic Mapper Plus (ETM+) that loaded onboard the Landsat-7 satellite was launched on 15 April 1999. After 4 years, the image collected by this sensor was greatly impacted by the failure of the system’s Scan Line Corrector (SLC), a radiometry error.The median filter is one of the basic building blocks in many image processing situations. Digital images are often distorted by impulse noise due to errors generated by the noise sensor, errors that occur during the conversion of signals from analog-to-digital, as well as errors generated in communication channels. This error inevitably leads to a change in the intensity of some pixels, while some pixels remain unchanged. To remove impulse noise and improve the quality of the

Statistical studies are reported in this article for an active galactic nuclei sample of different type of active galaxies Seyferts 1, Seyferts 2, and Quasars. These sources have been selected from a Catalogue for bright X-ray galaxies. The name of this index is ROSAT Bright Source Catalogue (RBSC) and the NRAO VLA Sky Survey (NVSS). In this research, multi-wavelength observational bands Radio at 1.4 GHz, Optical at 4400 A0, and X-ray at energy 0.1-2.4 KeV have been adopted in this study. The behavior of flux density ratios has been studied ,  with respect to the absolute magnitude . Furthermore, the Seyfert1 and Seyfert 2 objects are combined in one group and the QSOs are collectest in another group. Also, it has been found that t