In this study, simply supported reinforced concrete (RC) beams were analyzed using the Extended Finite Element Method (XFEM). This is a powerful method that is used for the treatment of discontinuities resulting from the fracture process and crack propagation in concrete. The mesoscale is used in modeling concrete as a two-phasic material of coarse aggregate and cement mortar. Air voids in the cement paste will also be modeled. The coarse aggregate used in the casting of these beams is a rounded aggregate consisting of different maximum sizes. The maximum size is 25 mm in the first model, and in the second model, the maximum size is 20 mm. The compressive strength used in these beams is equal to 26 MPa.

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          The present paper studies the generalized Φ-  recurrent of Kenmotsu type manifolds. This is done to determine the components of the covariant derivative of the Riemannian curvature tensor. Moreover, the conditions which make Kenmotsu type manifolds to be locally symmetric or generalized Φ- recurrent have been established. It is also concluded that the locally symmetric of Kenmotsu type manifolds are generalized recurrent under suitable condition and vice versa. Furthermore, the study establishes the relationship between the Einstein manifolds and locally symmetric of Kenmotsu type manifolds.

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  The current research aims to identify the effect of the learning mastery strategy using interactive learning as a therapeutic method on the achievement of secondary school students in mathematics. To achieve the research objective, the researcher selected second-grade middle school students at Al-Haybah Intermediate School for Boys and determined his research sample, which consisted of (77) students distributed into two sections: Section (A) the experimental group, with (38) students, and Section (B) the control group, with (39) students. The statistical equivalence of the two research sample groups was confirmed in the variables (intelligence test, previous achievement, and previous knowledge test). The researchers chose the par