Linear programming currently occupies a prominent position in various fields and has wide applications, as its importance lies in being a means of studying the behavior of a large number of systems as well. It is also the simplest and easiest type of models that can be created to address industrial, commercial, military and other dilemmas. Through which to obtain the optimal quantitative value. In this research, we dealt with the post optimality solution, or what is known as sensitivity analysis, using the principle of shadow prices. The scientific solution to any problem is not a complete solution once the optimal solution is reached. Any change in the values of the model constants or what is known as the inputs of the model that will chan

This research study Blur groups (Fuzzy Sets) which is the perception of the most modern in the application in various practical and theoretical areas and in various fields of life, was addressed to the fuzzy random variable whose value is not real, but the numbers Millbh because it expresses the mysterious phenomena or uncertain with measurements are not assertive. Fuzzy data were presented for binocular test and analysis of variance method of random Fuzzy variables , where this method depends on a number of assumptions, which is a problem that prevents the use of this method in the case of non-realized.

A numerical method is developed to obtain two-dimensional velocity and pressure distribution through a cylindrical pipe with cross jet flows. The method is based on solving partial differential equations for the conservation of mass and momentum by finite difference method to convert them into algebraic equations. This well-known problem is used to introduce the basic concepts of CFD including: the finite- difference mesh, the discrete nature of the numerical solution, and the dependence of the result on the mesh refinement. Staggered grid implementation of the numerical model is used. The set of algebraic equations is solved simultaneously by “SIMPLE” algorithm to obtain velocity and pressure distribution within a pipe. In order to

  The great scientific progress has led to widespread Information as information accumulates in large databases is important in trying to revise and compile this vast amount of data and, where its purpose to extract hidden information or classified data under their relations with each other in order to take advantage of them for technical purposes.

      And work with data mining (DM) is appropriate in this area because of the importance of research in the (K-Means) algorithm for clustering data in fact applied with effect can be observed in variables by changing the sample size (n) and the number of clusters (K)

This paper presents seven modified Adomian Decomposition Method (ADM) techniques for efficiently solving initial value problems, especially those involving non-homogeneous and nonlinear differential equations. While the classical ADM is effective for linear homogeneous cases, it has difficulties solving more complex problems. The proposed modifications—from MADM1 to MLADM—include Maclaurin and Taylor expansions, Laplace transforms, and single-step iterations.• These modifications enhance convergence, reduce complexity, and improve accuracy.• Each method offers specific advantages, such as accelerating convergence (MADM2, RADM4), simplifying computation (TSADM5), and achieving higher accuracy (MLADM).• Numerical examples confirm th

Reinforced concrete (RC) slabs strengthened with carbon fibre reinforced polymer (CFRP) and subjected to flexural actions may experience many types of failure, including FRP debonding, FRP rupture and concrete crushing. Of these different types of failure modes, FRP debonding stands out as the most predominant type of failure because of its dependence on the relatively weak bond interface between the soffit of the RC member and the FRP sheet attached to it. Many anchorage systems have been developed to enhance the performance of strengthened systems, one of which is the hybrid anchor, which combines the effects of patch anchors and spike anchors. Hybrid anchors have shown significant enhancement when used with RC members subjected to shear