An efficient modification and a novel technique combining the homotopy concept with  Adomian decomposition method (ADM) to obtain an accurate analytical solution for Riccati matrix delay differential equation (RMDDE) is introduced  in this paper  . Both methods are very efficient and effective. The whole integral part of ADM is used instead of the integral part of homotopy technique. The major feature in current technique gives us a large convergence region of iterative approximate solutions .The results acquired by this technique give better approximations for a larger region as well as previously. Finally, the results conducted via suggesting an efficient and easy technique, and may be addressed to other non-linear problems.

Some researchers are interested in using the flexible and applicable properties of quadratic functions as activation functions for FNNs. We study the essential approximation rate of any Lebesgue-integrable monotone function by a neural network of quadratic activation functions. The simultaneous degree of essential approximation is also studied. Both estimates are proved to be within the second order of modulus of smoothness.

this paper presents a novel method for solving nonlinear optimal conrol problems of regular type via its equivalent two points boundary value problems using the non-classical

A 3D geological model for Mishrif Reservoir in Nasiriyah oil field had been invented "designed" "built". Twenty Five wells namely have been selected lying in Nasiriyah  Governorate in order to build Structural and petrophysical (porosity and water saturation) models represented by a 3D static geological model in three directions .Structural model showed that Nasiriyah oil field represents anticlinal fold its length about 30 km and the width about 10  km, its axis extends toward NW–SE  with structural closure about 65 km . After making zones for Mishrif reservoir, which was divided into 5 zones i.e. (MA zone, UmB 1zone,MmB1 zone ,L.mB1 zone and mB2zone) .Layers were built for each zone depending on petrophysical propertie

In this paper,the homtopy perturbation method (HPM) was applied to obtain the approximate solutions of the fractional order integro-differential equations . The fractional order derivatives and fractional order integral are described in the Caputo and Riemann-Liouville sense respectively. We can easily obtain the solution from convergent the infinite series of HPM . A theorem for convergence and error estimates of the HPM for solving fractional order integro-differential equations was given. Moreover, numerical results show that our theoretical analysis are accurate and the HPM can be considered as a powerful method for solving fractional order integro-diffrential equations.

The study aims to indicate the role of the agricultural initiative in building agricultural development, mediated by activation of the role of internal and external audit on agricultural initiative projects, for the purpose of meeting the challenges of abuses on agricultural land and lack of water used in agriculture and proportions of high poverty, which led to the rural people of the migration to the city and leave agriculture and livestock, and that of the main conclusions reached by the researcher. When comparing the work of the external auditing agencies (the Federal Office of Financial Supervision) on the initiative of agricultural projects with internal audit services in the Directorate of Agriculture and branches of the Agricultu