Optimization is essentially the art, science and mathematics of choosing the best among a given set of finite or infinite alternatives. Though currently optimization is an interdisciplinary subject cutting through the boundaries of mathematics, economics, engineering, natural sciences, and many other fields of human Endeavour it had its root in antiquity. In modern day language the problem mathematically is as follows - Among all closed curves of a given length find the one that closes maximum area. This is called the Isoperimetric problem. This problem is now mentioned in a regular fashion in any course in the Calculus of Variations. However, most problems of antiquity came from geometry and since there were no general methods to solve suc

This article examines and proposes a dietary chain model with a prey shelter and alternative food sources. It is anticipated that mid-predators' availability is positively correlated with the number of refuges. The solution's existence and exclusivity are examined. It is established that the solution is bounded. It is explored whether all potential equilibrium points exist and are locally stable. The Lyapunov approach is used to investigate the equilibrium points' worldwide stability. Utilizing a Sotomayor theorem application, local bifurcation is studied. Numerical simulation is used to better comprehend the dynamics of the model and define the control set of parameters.

   In this paper, a mathematical model for the oxidative desulfurization of kerosene had been developed. The mathematical model and simulation process is a very important process due to it provides a better understanding of a real process. The mathematical model in this study was based on experimental results which were taken from literature to calculate the optimal kinetic parameters where simulation and optimization were conducted using gPROMS software. The optimal kinetic parameters were Activation energy 18.63958 kJ/mol, Pre-exponential factor  2201.34 (wt)^-0.76636. min^-1  and the reaction order 1.76636. These optimal kinetic parameters were used to find the optimal reaction conditions which

Ajloun Governorate is considered the smallest governorate in Jordan in terms of area, and its population density rises to 472.2 people/ km² and is distributed among five municipalities. The Al-Shafa municipality is one of these municipalities. Al-Shafa is rich in its natural and human resources, and the first municipal council was established in it in 2001.

This study seeks to achieve the following general objective: inventory the natural and human resources that Al-Shafa enjoys, and highlight the role of Al-Shafa municipality in achieving and settling sustainable development for the local community. Certain content, which are: the comprehensive approach to geographical reality, the descriptive

Background: The aim of this study was to evaluate and compare the apical microleakage around retrograde cavities prepared with ultrasonic technique and filled with (Biodentineâ„¢) Materials and methods: 40 extracted single rooted human permanent maxillary teeth with mature apices were selected. The roots were prepared chemo-mechanically using k-files with crown-down technique and then obturated with lateral condensation gutta-percha technique. Teeth were divided into four main groups according to the cavity preparation method either manual or ultrasonic technique: Group A (n=10): A class I retrograde cavity at root end was prepared with traditional handpeice equipped and placement of Biodentine with manual condensation. Group B (n=10):

Background: The aim of this study was to evaluate and compare the apical microleakage around retrograde cavities prepared with ultrasonic technique and filled with (Biodentineâ„¢) Materials and methods: 40 extracted single rooted human permanent maxillary teeth with mature apices were selected. The roots were prepared chemo-mechanically using k-files with crown-down technique and then obturated with lateral condensation gutta-percha technique. Teeth were divided into four main groups according to the cavity preparation method either manual or ultrasonic technique: Group A (n=10): A class I retrograde cavity at root end was prepared with traditional handpeice equipped and placement of Biodentine with manual condensation. Group B (n=10):

We studied the relationship between DNA sequencing of interleukin-10 (IL-10) gene promoter for -1082 (A/G) and -592 (A/C) positions with the concentration of IL-10 in blood serum of Iraqi children with type 1 diabetes mellitus (T1D). Fifty blood serum samples collected from children with age ranged between 7-12 years. Thirty-five blood samples collected from patient children with T1D, and compared with 15 healthy children age matched as control sample. The results revealed decreasing in anti-inflammatory IL-10 concentration in T1D patient’s blood serum (0.068 Pg/ml) as compared with the control sample (0.111 Pg/ml). No significant differences were found in interleukin concentration between the studied samples when they analyzed with the M

Colorectal cancer (CRC), the second most fatal cancer and the 3rd most common cancer is expected to cause 0.9 million deaths globally in 2025. Carcinoembryonic antigen (CEA) is currently used in the follow-up of patients with colorectal cancer, and in this study, we are trying to find a better marker than CEA in following up on patients' health and knowing the effectiveness of the treatment used and as a diagnostic marker for colorectal cancer. To determine the significance of Cancer antigen 72-4 (CA72-4) as a prognosis predictor in patients with colorectal cancer, compare its prognostic validity to the CEA biomarker. this case-control study includes (150) participants, 100 patients (59 males and 41 females), and 50 healthy controls

This study focused on the synthesis of novel polymers incorporating the 1,3,4-oxadiazole ring. Four polymers were specifically prepared by blending polymers (6-9) with polyvinyl alcohol (PVA) in defined ratios, resulting in the formation of blended polymers (10-13). The synthesized polymers were characterized using Fourier Transform Infrared (FTIR) spectroscopy and proton nuclear magnetic resonance (1H-NMR). The results showed that the structure aligned with the proposed synthetic polymers. Furthermore, the physical and thermal properties were studied using scanning electron microscopy (SEM), thermogravimetric analysis (TGA) and Differential Scanning Calorimetry (DSC). Additionally, the biological activity was examined against two s

60 patients diagnosed as having urticaria were included in the study ; 30 patients were effected with acute urticaria and 30 patients were affected with chronic urticaria. In addition, 30 healthy adult volunteers were selected as control group .The patients and control groups sera were examined with enzyme linked immunosorbent assay ( ELISA) to detect total level IgE and radial immunodiffusion (RID) to detect levels of IgG , IgA and IgM . The total level of IgE in acute urticaria ( 1.45±0.13) IU/mL and chronic urticaria (2.12 ± 0.10) IU/mL patients were significantly higher than the control groups ( 0.85 ± 0.10)IU/mL (p<0.05). The level of IgG in acute urticaria ( 12.5± 0.42) g/L and chronic (13.16±0.40) g/L patients , IgA in acute (2.