In this paper, there are two main objectives. The first objective is to study the relationship between the density property and some modules in detail, for instance; semisimple and divisible modules. The Addition complement has a good relationship with the density property of the modules as this importance is highlighted by any submodule N of M has an addition complement with Rad(M)=0. The second objective is to clarify the relationship between the density property and the essential submodules with some examples. As an example of this relationship, we studied the torsion-free module and its relationship with the essential submodules in module M.

Belgium is one of the countries that headed towards federalism through a peaceful transition, and over a few decades the country has witnessed deep transformations in its institutions, from a unified and central state in the early nineteenth century to a federal union, regional operations began since 1970 up and constitutionally established its diversity Linguistic and regional, the so -called "state reforms" have been implemented, which led to the emergence of political repercussions. The country has suffered about two decades ago, which caused many national governments that are considered to be among the Luxor in the modern political history of Belgium, However, institutional reforms to achieve the stability of the political system began,

Maxillofacial trauma in females is not widely reported. This study aimed to analyze the clinical characteristics and the patterns of maxillofacial injuries in females and to determine the differences in these patterns among different causes. This retrospective study analyzed several variables, including demographic, social, injury-related, and treatment-related variables, and compared these variables in relation to the main etiologies of maxillofacial trauma. The main etiologies of maxillofacial injuries involving females were assault, followed by road traffic accidents, and falls. There were significant differences in relation to the 3 etiologies in age groups (P= 0.002) and marital status (<

The research problem has crystallized and in light of these capabilities, the level of performance depends on the application of modern training methods based on actual experimentation, and those methods aim to develop the components of achievement in this competition, including the quantities of exerting the distinctive strength with speed for the arms and feet, which reflects on good skillful performance because the skill of shooting by jumping forward and high forms A major role in achieving goals during the competition that qualifies the team to win, and through the follow-up of the researcher in the field and academic field, I noticed that there is a weakness in some physical abilities, which affects performance and skill level

The research aims to identify the effect of the training program that is based on integrating futuristic thinking skills with classroom interaction patterns on mathematics teachers in order to provide their students with creative solution skills. The research sample consisted of 31teachers (15 teachers for the experimental group and 16 for the control groups). The researcher developed a measure for the academic self-efficacy consisting of (39) items. Its validity, reliability, coefficient of difficulty and discriminatory power were estimated. To analyze the findings, the researcher adopted the Mann-Whitney (U) test and the effect size, and the findings were as follows: There is a statistically significant difference at the significance leve

This study proposes a hybrid predictive maintenance framework that integrates the Kolmogorov-Arnold Network (KAN) with Short-Time Fourier Transform (STFT) for intelligent fault diagnosis in industrial rotating machinery. The method is designed to address challenges posed by non-linear and non-stationary vibration signals under varying operational conditions. Experimental validation using the FALEX multispecimen test bench demonstrated a high classification accuracy of 97.5%, outperforming traditional models such as SVM, Random Forest, and XGBoost. The approach maintained robust performance across dynamic load scenarios and noisy environments, with precision and recall exceeding 95%. Key contributions include a hardware-accelerated K