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

Summary
This research is included in the study of one of the most important rules of jurisprudence, which is (necessity descends the status of necessity, controls and applications) branching from the major rule (hardship brings facilitation) and since the jurisprudential rule is defined as knowledge of a total or majority rule that applies to all its parts. He has to know all the branches that fall under him, which leads to understanding Sharia, controlling jurisprudential issues and linking them to its rules, so that no contradiction occurs, and he has the jurisprudential faculty that he promotes in consideration and diligence. And what is meant by need: is what is lacking in terms of expansion and raising the distress that often lea

The musical templates are the fundamental reason for admiration and interest among a lot of cultural and societal medias because of the beauty of it's melodic value, where a lot of Iraqi singing and music specialists and composers try to consolidate daily life idea and translate it into music in a manner that preserve the template and rhythm horizontally and vertically, through the involvement of the scientific and philosophical concepts and theories of modern thought to reach the recipient,, as is the theory of form (Gestalt), one of the most important theories that stretched to their interpretations to the field in general art and in music science, especially, as an area that can be manifested as partial components template music, conn

Media and communication's research are varied in accordance to research approaches' variety which seeks to reach convergent social, psycholo

Cerium (III), Neodymium (III) and Samarium (III) Complexes existent a wide range of implementation that stretch from their play in the medicinal and pharmaceutical area because of their major significant pharmacological characteristic such as antifungal, anti-cancer, anti-bacterial ,anti-human immunodeficiency virus ,antineoplastic, anti-inflammation,inhibition corrosion,in some industrial (polymers, Azo dye).It is likely to open avenuesto research among various disciplines such as physics, electronics, chemistry and materials science by these complexes that contain exquisitely designed organic molecules.This paper reviews the definition, importance and various applications of Cerium (III), Neodymium (III) and Samarium (III) Complexes anddi

The human kidney is one of the most important organs in the human body; it performs many functions
and has a great impact on the work of the rest of the organs. Among the most important possible treatments is
dialysis, which works as an external artificial kidney, and several studies have worked to enhance the
mechanism of dialysate flow and improve the permeability of its membrane. This study introduces a new
numerical model based on previous research discussing the variations in the concentrations of sodium,
potassium, and urea in the extracellular area in the blood during hemodialysis. We simulated the differential
equations related to mass transfer diffusion and we developed the model in MATLAB Simu

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

The aim of this book is to present a method for solving high order ordinary differential equations with two point boundary condition of the different kind, we propose semi-analytic technique using two-point osculatory interpolation to construct polynomial solution. The original problem is concerned using two-points osculatory interpolation with the fit equal numbers of derivatives at the end points of an interval [0 , 1] . Also, we discussion the existence and uniqueness of solutions and many examples are presented to demonstrate the applicability, accuracy and efficiency of the methods by compared with conventional method .i.e. VIDM , Septic B-Spline , , NIM , HPM, Haar wavelets on one hand and to confirm the order convergence on the other

In this research, we have added nano anatase TiO₂ as a partial replacement of Portland cement by a weight percentage of (0.25 to 1%) for the development of properties for protection against bacteria. The control mix was made by using "the cement to sand" proportion about (1: 2.75) with the "water to cement" proportion of (0.5) to study the structure, porosity, water absorption, density, mechanical properties, as well as anti-bacterial behavior. Inspections have been done such as scanning electron microscopy (SEM), and atomic force microscope (AFM) for mortar. Experimental results showed that after the addition of Nano powders in cement mortar, the structural properties improved significantly with the development of hydration o