The objective of this paper is, firstly, we study a new concept noted by algebra and discuss the properties of this concept. Secondly, we introduce a new concept related to the algebra such as smallest algebra. Thirdly, we introduce the notion of the restriction of algebra on a nonempty subset  of and investigate some of its basic properties. Furthermore, we present the relationships between field, monotone class, field and algebra. Finally, we introduce the concept of measure relative to the algebra and prove that every measure relative to the   is complete.

OBJECTIVE: Synthetic vertebral body replacement has been widely used recently to treat different spinal conditions affecting the anterior column. They arrange from trauma, infections, and even tumor conditions. In this study, we assess the functional outcome of this modality in different spinal conditions. PATIENTS AND METHODS: Thirty-six cases operated from October 2010 to December 2017. Twelve patients had spinal type A3 fractures, 11 cases with spinal tuberculosis (TB), and 13 cases with spinal tumors. They were followed clinically for a mean period of 2.4 years. RESULTS: All the cases were approached anteriorly. Seven cases had a post-operative infection. No neurological worsening reported. We had dramatic neurologic

Background: Poly cystic ovary syndrome is a common disorder in women of reproductive age, it is associated with disturbance of reproductive, endocrine and metabolic functions. The pathophysiology of PCOS appears to be multifactorial and polygenic. Leptin seems to play an important role in pathophysiology of PCOS especially in women with BMI ≥25kg/m2. Objectives: To assess leptin level in both PCOS and healthy women and explore the relation to their body weight and body mass index. Patient and Methods: A total of 120 women were enrolled in this study, 60 women (50%) had PCOS (study group) and the reminder 60 women (50%) were healthy women and considered as control group. BMI was calculated first. Both groups were further sub

Retained soft tissue foreign bodies following injuries are frequently seen in the Emergency and Plastic Surgery practice. The patients with such presentations require a watchful and detailed clinical as- sessment to overcome the anticipant possibility of missing them. However, the diagnosis based on the clinical evaluation is usually challenging and needs to be supported by imaging modalities that are suboptimal and may fail in identifying some types of foreign bodies. Owing to that, serious complications such as chronic pain, infection, and delayed wound healing can be faced that necessitate a prompt intervention to halt those detrimental consequences. The classical method of removal is a surgical exploration which is not free of risks.

Background: Body image is one of the most important psychological factors that affects adolescents’ personality and behavior. Body image can be defined as the person’s perceptions, thoughts, and feelings about his or her body.

Objectives: to identify the prevalence of body image concerns among secondary school students and its relation to different factors.

Subjects and methods: A cross-sectional study conducted in which 796 secondary school students participated and body shape concerns was investigated using the body shape questionnaire (BSQ-34).

Results: The prevalence of moderate/marked concern was (21.6%). Moderate/ marked body shape concern was significantly associated

In this research, we find the Bayesian formulas and the estimation of Bayesian expectation for product system of Atlas Company.  The units of the system have been examined by helping the technical staff at the company and by providing a real data the company which manufacturer the system.  This real data include the failed units for each drawn sample, which represents the total number of the manufacturer units by the company system.  We calculate the range for each estimator by using the Maximum Likelihood estimator.  We obtain that the expectation-Bayesian estimation is better than the Bayesian estimator of the different partially samples which were drawn from the product system after  it checked by the

This research deals with a shrinking method concernes with the principal components similar to that one which used in the multiple regression “Least Absolute Shrinkage and Selection: LASS”. The goal here is to make an uncorrelated linear combinations from only a subset of explanatory variables that may have a multicollinearity problem instead taking the whole number say, (K) of them. This shrinkage will force some coefficients to equal zero, after making some restriction on them by some "tuning parameter" say, (t) which balances the bias and variance amount from side, and doesn't exceed the acceptable percent explained variance of these components. This had been shown by MSE criterion in the regression case and the percent explained v

The researcher [1-10] proposed a method for computing the numerical solution to quasi-linear parabolic p.d.e.s using a Chebyshev method. The purpose of this paper is to extend the method to problems with mixed boundary conditions. An error analysis for the linear problem is given and a global element Chebyshev method is described. A comparison of various chebyshev methods is made by applying them to two-point eigenproblems. It is shown by analysis and numerical examples that the approach used to derive the generalized Chebyshev method is comparable, in terms of the accuracy obtained, with existing Chebyshev methods.

This paper sheds the light on the vital role that fractional ordinary differential equations(FrODEs) play in the mathematical modeling and in real life, particularly in the physical conditions. Furthermore, if the problem is handled directly by using numerical method, it is a far more powerful and efficient numerical method in terms of computational time, number of function evaluations, and precision. In this paper, we concentrate on the derivation of the direct numerical methods for solving fifth-order FrODEs  in one, two, and three stages. Additionally, it is important to note that the RKM-numerical methods with two- and three-stages for solving fifth-order ODEs are convenient, for solving class's fifth-order FrODEs. Numerical exa