The aim of this paper is to study the nonlinear delay second order eigenvalue problems which consists of delay ordinary differential equations, in fact one of the expansion methods that is called the least square method which will be developed to solve this kind of problems.

      In this paper, we introduce and study the notation of approximaitly quasi-primary submodules of a unitary left -module  over a commutative ring  with identity. This concept is a generalization of prime and primary submodules, where a proper submodule  of an -module  is called an approximaitly quasi-primary (for short App-qp) submodule of , if , for , , implies that either  or , for some . Many basic properties, examples and characterizations of this concept are introduced.

Shooting skill in basketball is one of the most important offensive skills and the final stage of the team's attack and the culmination of all skills in which points are scored, including the skill of peaceful shooting. The research aims to prepare competitive exercises and understand the impact of competitive exercises on developing coordination and balance for basketball players under 18 years old. The researcher used the experimental method with the single experimental group approach, including the research community of female athletes in the public directorates of education in Baghdad, totaling (6) directorates and (72) players. The research sample was selected intentionally, consisting of female athletes in the sports activity of the D

Theoretical and experimental investigations have been carried out on developing laminar
combined free and forced convection heat transfer in a vertical concentric annulus with uniformly
heated outer cylinder (constant heat flux) and adiabatic inner cylinder for both aiding and opposing
flows. The theoretical investigation involved a mathematical modeling and numerical solution for
two dimensional, symmetric, simultaneously developing laminar air flows was achieved. The
governing equations of motion (continuity, momentum and energy) are solved by using implicit
finite difference method and the Gauss elimination technique. The theoretical work covers heat flux
range from (200 to 1500) W/m2, Re range from 400 to 2000 an

  نقدم في هذا البحث تحليل لعملين أدبيين من منظور الحركات الطليعية ثبتت آثارها لدى بعض الكتاب العرب و أمريكا اللاتينية في فترة سنوات العشرينات والألفين.  كانت الحياة الخاصة للكاتب ميغيل انخل استورياس تلهمه أنتاج أعمال أدبية، اذ شغل منصب دبلوماسي وحصل على جائزة نوبل غواتيمالاكا. ولد وتوفى في مدينة غواتيملاكا   (1974- 1899)   يوجد تحول واضح في عمله ذات الشهرة السيد الرئيس(1948) الذي يكسر المعتاد، لأجل مست

The present work aims to study the effect of using an automatic thresholding technique to convert the features edges of the images to binary images in order to split the object from its background, where the features edges of the sampled images obtained from first-order edge detection operators (Roberts, Prewitt and Sobel) and second-order edge detection operators (Laplacian operators). The optimum automatic threshold are calculated using fast Otsu method. The study is applied on a personal image (Roben) and a satellite image to study the compatibility of this procedure with two different kinds of images. The obtained results are discussed.

Background: Avascular necrosis (AVN) is defined as cellular death of bone components due to interruption of the blood supply; the bone structures then collapse, resulting in bone destruction, pain, and loss of joint function. AVN is associated with numerous conditions and usually involves the epiphysis of long bones, such as the femoral head. In clinical practice, AVN is most commonly encountered in the hip. Early diagnosis and appropriate intervention can delay the need for joint replacement. However, most patients present late in the disease course. Without treatment, the process is almost always progressive, leading to joint destruction within 5 years.Treatment of a vascular necrosis depends mainly on early diagnosis which mainly base

Jordan  curve  theorem  is  one  of  the  classical  theorems  of  mathematics, it states  the  following :  If    is a graph of  a  simple  closed curve  in  the complex plane the complement  of   is the union of  two regions,  being the common  boundary of the two regions. One of  the region   is  bounded and the other is unbounded. We introduced in this paper one of Jordan's theorem generalizations. A new type of space is discussed with some properties and new examples. This new space called Contractible -space.

This study aims to enhance the RC5 algorithm to improve encryption and decryption speeds in devices with limited power and memory resources. These resource-constrained applications, which range in size from wearables and smart cards to microscopic sensors, frequently function in settings where traditional cryptographic techniques because of their high computational overhead and memory requirements are impracticable. The Enhanced RC5 (ERC5) algorithm integrates the PKCS#7 padding method to effectively adapt to various data sizes. Empirical investigation reveals significant improvements in encryption speed with ERC5, ranging from 50.90% to 64.18% for audio files and 46.97% to 56.84% for image files, depending on file size. A substanti