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.
The study aims to find out the effectiveness of using the Google classroom educational platform in teaching mathematics curricula from the viewpoint of teachers in the Governorate of Al Dhahirah, Sultanate of Oman. The researcher adopted the descriptive-analytical approach. To collect the needed data, a questionnaire of two dimensions was used. It includes (13) items to measure the effectiveness of using the Google classroom in teaching mathematics curricula from the teacher's point of view and includes (10) items to measure the difficulties of using the Google classroom in teaching mathematics curricula from the teachers' point of view. These tools were applied to (32) male and (31) female as the study sample. They represent mathematics
... Show MoreThe biosorption of lead (II) and chromium (III) onto dead anaerobic biomass (DAB) in single and binary systems has been studied using fixed bed adsorber. A general rate multi- component model (GRM) has been utilized to predict the fixed bed breakthrough curves for single and dual- component system. This model considers both external and internal mass transfer resistances as well as axial dispersion with non-liner multi-component isotherm (Langmuir model). The effects of important parameters, such as flow rate, initial concentration and bed height on the behavior of breakthrough curves have been studied. The equilibrium isotherm model parameters such as maximum uptake capacities for lead (II) and chromium (III) were found to be 35.12 and
... Show MoreMeta stable phase of SnO as stoichiometric compound is deposited utilizing thermal evaporation technique under high vacuum onto glass and p-type silicon. These films are subjected to thermal treatment under oxygen for different temperatures (150,350 and 550 °C ). The Sn metal transformed to SnO at 350 oC, which was clearly seen via XRD measurements, SnO was transformed to a nonstoichiometric phase at 550 oC. AFM was used to obtain topography of the deposited films. The grains are combined compactly to form ridges and clusters along the surface of the SnO and Sn3O3 films. Films were transparent in the visible area and the values of the optical band gap for (150,350 and 550 °C ) 3.1,
Silica-based mesoporous materials are a class of porous materials with unique characteristics such as ordered pore structure, large surface area, and large pore volume. This review covers the different types of porous material (zeolite and mesoporous) and the physical properties of mesoporous materials that make them valuable in industry. Mesoporous materials can be divided into two groups: silica-based mesoporous materials and non-silica-based mesoporous materials. The most well-known family of silica-based mesoporous materials is the Mesoporous Molecular Sieves family, which attracts attention because of its beneficial properties. The family includes three members that are differentiated based on their pore arrangement. In this review,
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The aim of the current research is to identify the level of administrative applications of expert systems in educational leadership departments in light of the systems approach. To achieve the objectives of the research, the descriptive-analytical and survey method was adopted. The results showed that the level of availability of the knowledge base for expert systems in educational leadership departments (as inputs) was low. The level of availability of resources and software for expert systems in educational leadership departments (as transformational processes) came to be low, as well as the level of availability of the user interface for expert systems in educational leadership departments (as outputs
... Show MoreIn this study, the effects of blending the un-branched acrylate polymer known as Poly (n-decyl acrylate), and the branched acrylate polymer known as Poly (iso-octyl acrylate), on the viscosity index (VI), and the pour point of the Iraqi base stocks 40, and 60 respectively, were investigated. Toluene was used as a carrier solvent for both polymer types. The improvement level of oils (VI, & pour point) gained by blending the oil with the acrylate derived polymers was compared with the values of (VI, and pour point) gained by blending the oil with a commercial viscosity index, and pour point improver. The commercial lubricant additive was purchased and used by Al-Daura Refineries. It consisted of an un-known olefin copolymer dissolved i
... Show MoreThe study aimed at identifying the level of administrative work quality of private Schools principals at Southern Governorates of Palestine from the teachers' point of view in their schools. To achieve the objectives of this research, a questionnaire was prepared by the researcher consisted of (28) items. It was applied to a sample of (350) teachers. The researcher adopted the descriptive-analytical approach. The results of the study showed that the degree to which principals of private schools in the southern governorates of Palestine practice Administrative Work Quality from the viewpoint of their teachers was very high, with relative weight (85.00%). The results also showed that there are statistically significant differences at the l
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