In the context of normed space, Banach's fixed point theorem for mapping is studied in this paper. This idea is generalized in Banach's classical fixed-point theory. Fixed point theory explains many situations where maps provide great answers through an amazing combination of mathematical analysis. Picard- Lendell's theorem, Picard's theorem, implicit function theorem, and other results are created by other mathematicians later using this fixed-point theorem. We have come up with ideas that Banach's theorem can be used to easily deduce many well-known fixed-point theorems. Extending the Banach contraction principle to include metric space with modular spaces has been included in some recent research, the aim of study proves some properties of Banach space.
Background: Major depressive disorder (MDD) is mental disorder characterized by an all-encompassing low mood accompanied by low self-esteem, and by loss of interest or pleasure in normally enjoyable activities. The aims of the study: were to determine the prevalence of oral manifestation among patients with major depressive disorder receiving antidepressant drugs, and detect alkaline phosphatase (ALP), Total Salivary proteins (TSP), and Interleukin-6 (IL-6) in relation to MDD patients under treatment and to compare with healthy controls. Materials and method: (50) MDD patients; between the ages of 20 years and 60 years.The depression patients are divided into (25) patients under treatment with fluoxetine (Prozac), and (25) patients under tr
... Show MoreAbstract The wavelet shrink estimator is an attractive technique when estimating the nonparametric regression functions, but it is very sensitive in the case of a correlation in errors. In this research, a polynomial model of low degree was used for the purpose of addressing the boundary problem in the wavelet reduction in addition to using flexible threshold values in the case of Correlation in errors as it deals with those transactions at each level separately, unlike the comprehensive threshold values that deal with all levels simultaneously, as (Visushrink) methods, (False Discovery Rate) method, (Improvement Thresholding) and (Sureshrink method), as the study was conducted on real monthly data represented in the rates of theft crimes f
... Show MoreCarbonate-clastic succession which includes the Shu'aiba, Nahr Umr and Mauddud formations are representing a part of the Barremian-Aptian Sequence (Wasi'a Group). The present study includes three boreholes (Ba-1, 4 and 8) within the Balad Oil Field. The study area is located in central Iraq. This field represents a subsurface anticline with a northwest to southeast direction axis within the Mesopotamian Zone. Eight types of microfacies were recognized in the succession of the Mauddud and Shu’aiba formations. These microfacies represent shallow open marine, restricted and semi-restricted, reef - back reef, deep open marine and basinal depositional environments. While Nahr Umr Formation includes two successions, the first is the upp
... Show MoreThis paper develops a nonlinear transient three-dimensional heat transfer finite element model and a rate independent three-dimensional deformation model, developed for the CO2 laser welding simulations in Al-6061-T6 alloy. Simulations are performed using an indirect coupled thermal-structural method for the process of welding. Temperature-dependent thermal properties of Al-6061-T6, effect of latent heat of fusion, and the convective and radiative boundary conditions are included in the model. The heat input to the model is assumed to be a Gaussian heat source. The finite element code ANSYS12, along with a few FORTRAN subroutines, are employed to obtain the numerical results. The benefit of the proposed methodology is that it
... Show MoreBackground: To assess the alveolar bone crest level (ABCL) by Cone Beam Computed To-mography (CBCT) and to investigate several variables as predictors for the height of the alveolar bone in adolescents. Materials and methods: Age, sex, and ethnic groups were rec-orded for each patient. CBCT images were used to obtain measurements of the interproximal alveolar bone level from the cementoenamel junction (CEJ) to the alveolar crest. The highest measurement in each sextant was recorded along with any presence of a vertical bone defect or calculus. Results: Total of 720 measurements were recorded for 120 subjects. No vertical bony defects or calculus were observed radiographically. Statistically significant (P< 0.05) differences were observed be
... Show MoreThis study aimed at isolating uropathogenic Escherichia coli from urinary tract infections (UTIs) of human and cattle to examine the molecular diversity and phylogenetic relationship of the isolates. A total of 100 urine samples were collected from UTIs of human and cattle. The isolates identification was done using routine diagnostic methods and confirmed by Vitek2. Antimicrobial susceptibility was tested against 10 antimicrobials. Random amplified polymorphic DNA (RAPD)-polymerase chain reaction (PCR) was applied to identify the genetic diversity among E. coli isolates from human and animal origin by using five different octamer primers. The gelJ software for the phylogenetic analysis created Dendrograms. Out of 50 human urine samples, E.
... Show MoreThis study is a numerical investigation of the performance of reinforced concrete (RC) columns after fire exposure. This study aims to investigate the effect of introducing lateral ties and using the RC jacket on improving post-fire behavior of these columns, the effect of the duration of the fire on ultimate load of columns. The analysis was performed through ABAQUS, a 3D – non-linear finite element program. 4 m tall lengthening square RC column with a cross- section of 0.4 m × 0.4 m was used as a test specimen. The RC column was reinforced by 4Ø28 mm longitudinal bars bonded by steel tie bars of Ø10 mm spaced at 400 mm. The firing temperature was increased to 60