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.

In this study, we set up and analyze a cancer growth model that integrates a chemotherapy drug with the impact of vitamins in boosting and strengthening the immune system. The aim of this study is to determine the minimal amount of treatment required to eliminate cancer, which will help to reduce harm to patients. It is assumed that vitamins come from organic foods and beverages. The chemotherapy drug is added to delay and eliminate tumor cell growth and division. To that end, we suggest the tumor-immune model, composed of the interaction of tumor and immune cells, which is composed of two ordinary differential equations. The model’s fundamental mathematical properties, such as positivity, boundedness, and equilibrium existence, are exami

God saw his servants with truth and light, and made him easy for them, and he commanded those who help them, including a counselor, guide and preacher, so if a Muslim sees deficiencies or defects, he must help him to reform and refine it. That it was in the hands of the prophets, God Almighty created the human being together straight, then melted on those scholars and researchers in all religions on psychological counseling and religious sychotherapy, stressing the importance of religious values in the process of understanding man in the process of psychotherapy and in controlling human behavior. A lot of research and studies have been published. I dealt with the religious approach in the process of treating mental disorders and the aim of

Energy efficiency is a significant aspect in designing robust routing protocols for wireless sensor networks (WSNs). A reliable routing protocol has to be energy efficient and adaptive to the network size. To achieve high energy conservation and data aggregation, there are two major techniques, clusters and chains. In clustering technique, sensor networks are often divided into non-overlapping subsets called clusters. In chain technique, sensor nodes will be connected with the closest two neighbors, starting with the farthest node from the base station till the closest node to the base station. Each technique has its own advantages and disadvantages which motivate some researchers to come up with a hybrid routing algorit

Background: left ventricular hypertrophy is independent risk factor for cardiovascular morbidity and mortality. The presence of diabetic complications such as autonomic neuropathy and retinopathy may predict cardiac structural changes in diabetic patients. Objective: To explore the chance of occurrence of left ventricular hypertrophy in diabetic patients and whether it is related to the presence of other diabetic complications. Methods: ninty seven (97) normotensive diabetic patients (57) type II with mean duration of diabetes of (12±6 y) and forty (40) type I with mean duration of (8±6 y) were studied by echocardiography and compared with 41 patients as control. Results: The LVMI was significantly higher in type II diabetics compared

The current study introduces a novel technique to handle electrochemical localized corrosion in certain limited regions rather than applying comprehensive cathodic protection (CP) treatment. An impressed current cathodic protection cell (ICCPC) was fabricated and firmly installed on the middle of a steel structure surface to deter localized corrosion in fixed or mobile steel structures. The designed ICCPC comprises three essential parts: an anode, a cathode, and an artificial electrolyte. The latter was developed to mimic the function of the natural electrolyte in CP. A proportional-integrated-derivative (PID) controller was designed to stabilize this potential below the ICCPC at a cathodic potential of −850 mV, which is crucial for prote

It is proposed and studied a prey-predator system with a Holling type II functional response that merges predation fear with a predator-dependent prey's refuge. Understanding the impact of fear and refuge on the system's dynamic behavior is one of the objectives. All conceivable steady-states are investigated for their stability. The persistence condition of the system has been established. Local bifurcation analysis is performed in the Sotomayor sense. Extensive numerical simulation with varied parameters was used to explore the system's global dynamics. A limit cycle and a point attractor are the two types of attractors in the system. It's also interesting to note that the system exhibits bi-stability between these 2 types of attractors.