In this paper, the continuous classical boundary optimal control problem (CCBOCP) for triple linear partial differential equations of parabolic type (TLPDEPAR) with initial and boundary conditions (ICs & BCs) is studied. The Galerkin method (GM) is used to prove the existence and uniqueness theorem of the state vector solution (SVS) for given continuous classical boundary control vector (CCBCV). The proof of the existence theorem of a continuous classical boundary optimal control vector (CCBOCV) associated with the TLPDEPAR is proved. The derivation of the Fréchet derivative (FrD) for the cost function (CoF) is obtained. At the end, the theorem of the necessary conditions for optimality (NCsThOP) of this problem is stated and prov

Contracting cancer typically induces a state of terror among the individuals who are affected. Exploring how chemotherapy and anxiety work together to affect the speed at which cancer cells multiply and the immune system’s response model is necessary to come up with ways to stop the spread of cancer. This paper proposes a mathematical model to investigate the impact of psychological scare and chemotherapy on the interaction of cancer and immunity. The proposed model is accurately described. The focus of the model’s dynamic analysis is to identify the potential equilibrium locations. According to the analysis, it is possible to establish three equilibrium positions. The stability analysis reveals that all equilibrium points consi

Owing to the energy crisis and pollution problems of today, investigations have concentrated on
decreasing fuel consumption and on lowering the concentration of toxic components in combustion
products by using non-petroleum, renewable, sustainable and non-polluting fuels. While conventional energy sources such as natural gas, oil and coal are non-renewable, alcohol can be coupled to renewable and sustainable energy sources.
In this study, the combustion characteristics of diesel fuel and methanol blends were compared.
The tests were performed at steady state conditions in a four-cylinder DI diesel engine at full load at
1500-rpm engine speed. The experimental results showed that diesel methanol blends provided
12.7% inc

In this study, stabilization of expansive soils using waste materials namely; Cement Kiln Dust (CKD), and waste plastic bottles (WPB) was experimentally investigated. Using CKD and WPB are exponentially increasing day by day, due to their capability to solve both environmental and geotechnical problems successfully. Expansive soils were collected from locations with a wide range of plasticity index (PI) (15 - 27) and liquid limit (LL) (35% - 64%). Stabilizer percentages were varied from 0% to 20%, and curing durations for CKD cases were 7 and 28 days. Results showed the best percentages of CKD and WPB are 12% of each one respectively. LL, plastic limit (PL), and swelling percent (SP) loss were observed, which are 46%, 55%, and 96% respec

In the last few years, the use of artificial neural network analysis has increased, particularly, in geotechnical engineering problems and has demonstrated some success. In this research, artificial neural network analysis endeavors to predict the relationship between physical and mechanical properties of Baghdad soil by making different trials between standard penetration test, liquid limit, plastic limit, plasticity index, cohesion, angle of internal friction, and bearing capacity. The analysis revealed that the changes in natural water content and plastic limit have a great effect on the cohesion of soil and the angle of internal friction, respectively. . On the other hand, the liquid limit has a great impact on the bearing capacity and

      Background: Polycystic ovary syndrome (PCOS) is common heterogeneous disorder syndrome in females, characterized by chronic oligoovulation, polycystic ovary, and hyperandrogenism. This study aimed to the association of ferritin and transforming growth factor- β1 (TGF-β1) levels with insulin resistance, cardiovascular and type 2 diabetes risks. Patients and methods: (61) Iraqi women with PCOS patients diagnosed according to the Rotterdam criteria, were subdivided according to their Body Mass Index (BMI) to: (20) lean women with normal BMI: (18-24), (17) overweight women with BMI: (25-29) and (25) obese women with BMI >30. For the the purpose of comparison, (20) healthy Iraqi women were enrolled as controls ma