This study presents a practical method for solving fractional order delay variational problems. The fractional derivative is given in the Caputo sense. The suggested approach is based on the Laplace transform and the shifted Legendre polynomials by approximating the candidate function by the shifted Legendre series with unknown coefficients yet to be determined. The proposed method converts the fractional order delay variational problem into a set of (n ＋ 1) algebraic equations, where the solution to the resultant equation provides us the unknown coefficients of the terminated series that have been utilized to approximate the solution to the considered variational problem. Illustrative examples are given to show that the recommended appro

The variation of compression index C_c and swelling index C_s with the degree of saturation S was studied on unsaturated and fully saturated soils for different degrees of saturation (100%, 91%, 85%, 75%, 60%), several mathematical equations were found to describe these relationships, these equations can be used to predict settlement during the consolidation process in unsaturated and fully saturated soils.

        This paper concerns with openness concept in contemporary learning environment, which ranges from physical characters to its relation with learning efficiency and its output. Previous literatures differ to clear the effect of openness on the engagement between learner within themselves, and with this kind of spaces. Engagement means: active participation, the ability of making dialogue, self-reflection and the ability to explore and communicate with them and
within learning space. Research roblem was: The lack of knowledge about the effect of Openness on learner engagement with learning spaces. The two concepts were applied on three types of learning spaces in the Department of the Architectu

          The she/teacher is considered one of the basics of the educational process for its essential role in education and teaching the kindergarten child, thus  its lack to construct social relations in side the kindergarten environment working in it regarded one of the shortcoming factors she is suffering from which should be manipulated, because it could effect its enthusiasm to work in the kindergarten according to what has mentioned, the researcher presents the following objective:-

• Identifying level of social enhancement for the kindergarten teachers via the test of the following hypothesis:-

      In this work, a weighted H lder function that approximates a Jacobi polynomial which solves the second order singular Sturm-Liouville equation is discussed. This is generally equivalent to the Jacobean translations and the moduli of smoothness. This paper aims to focus on improving methods of approximation and finding the upper and lower estimates for the degree of approximation in weighted H lder spaces by modifying the modulus of continuity and smoothness. Moreover, some properties for the moduli of smoothness with direct and inverse results are considered.

The Adaptive Optics technique has been developed to obtain the correction of atmospheric seeing. The purpose of this study is to use the MATLAB program to investigate the performance of an AO system with the most recent AO simulation tools, Objected-Oriented Matlab Adaptive Optics (OOMAO). This was achieved by studying the variables that impact image quality correction, such as observation wavelength bands, atmospheric parameters, telescope parameters, deformable mirror parameters, wavefront sensor parameters, and noise parameters. The results presented a detailed analysis of the factors that influence the image correction process as well as the impact of the AO components on that process

This paper presents the application of nonlinear finite element models in the analysis of dappedends pre-stressed reinforced concrete girders under static loading by using ANSYS software. The girder dimensions are (4.90 m span, 0.40 m depth, 0.20 m width, 0.20 m nib depth, and 0.10 m nib length) and the parameters considered in this research are the pre-stress effect, and strand profile (straight and draped). The numerical results are compared with the experimental results of the same girders. The comparisons are carried out in terms of initial prestress effect, load- deflection curve, and failure load. Good agreement was obtained between the analytical and experimental results. Even that, the numerical model was stiffer than the experiment

This paper presents the application of nonlinear finite element models in the analysis of dapped-ends pre-stressed reinforced concrete girders under static loading by using ANSYS software. The girder dimensions are (4.90 m span, 0.40 m depth, 0.20 m width, 0.20 m nib depth, and 0.10 m nib length) and the parameters considered in this research are the pre-stress effect, and strand profile (straight and draped).

    The numerical results are compared with the experimental results of the same girders. The comparisons are carried out in terms of initial prestress effect, load- deflection curve, and failure load. Good agreement was obtained between the analytical and experimental results. Even that, the