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. “Polyetheretherketone (PEEK)” is a biocompatible, high-strength polymer that is well-suited for use in dental applications due to its unique properties. However, achieving good adhesion between PEEK and hydrophilic materials such as dental adhesives or cement can be challenging. Also, this hydrophobicity may affect the use of PEEK as an implant material. Surface treatment or conditioning is often necessary to improve surface properties. The piranha solution is the treatment of choice to be explored for this purpose. Methods. PEEK disks of 10 mm diameter and 2 mm thickness were used in this study. Those samples were divided into five groups (each group has five samples). The first is the control group, in which no
... Show MoreDue to the great evolution in digital commercial cameras, several studies have addressed the using of such cameras in different civil and close-range applications such as 3D models generation. However, previous studies have not discussed a precise relationship between a camera resolution and the accuracy of the models generated based on images of this camera. Therefore the current study aims to evaluate the accuracy of the derived 3D buildings models captured by different resolution cameras. The digital photogrammetric methods were devoted to derive 3D models using the data of various resolution cameras and analyze their accuracies. This investigation involves selecting three different resolution cameras (low, medium and
... Show MoreThis study suggests using the recycled plastic waste to prepare the polymer matrix composite (PMCs) to use in different applications. Composite materials were prepared by mixing the polyester resin (UP) with plastic waste, two types of plastic waste were used in this work included polyethylene-terephthalate (PET) and Polyvinyl chloride (PVC) with varies weight fractions (0, 5, 10, 15, 20 and 25 %) added as a filler in flakes form. Charpy impact test was performed on the prepared samples to calculate the values of impact strength (I.S). Flexural and hardness tests were carried out to calculate the values of flexural strength and hardness. Acoustic insulation and optical microscope tests were carried out. In general, it is found that UP/PV
... Show MoreBackground: The synthesis and characterization of novel liquid crystalline compounds have garnered signi|cant attention due to their potential applications in biomedical sciences, including drug delivery systems, biosensing, and diagnostic tools. This study focuses on synthesizing and characterizing new thiazolothiadiazole-based liquid crystals and evaluating their mesophase properties. Methods: A series of novel compounds containing 5H-thiazolo[4,3−b][1,3,4] thiadiazole units were synthesized via multi-step chemical reactions. The synthesis involved the reaction of chloroethyl acetate with 4−hydroxybenzaldehyde to yield an aldehyde intermediate, followed by subsequent transformations using hydrazine hydrate, ethylacetoacetate, and 1,2
... Show MoreIn this paper, the concept of normalized duality mapping has introduced in real convex modular spaces. Then, some of its properties have shown which allow dealing with results related to the concept of uniformly smooth convex real modular spaces. For multivalued mappings defined on these spaces, the convergence of a two-step type iterative sequence to a fixed point is proved
Mixed-effects conditional logistic regression is evidently more effective in the study of qualitative differences in longitudinal pollution data as well as their implications on heterogeneous subgroups. This study seeks that conditional logistic regression is a robust evaluation method for environmental studies, thru the analysis of environment pollution as a function of oil production and environmental factors. Consequently, it has been established theoretically that the primary objective of model selection in this research is to identify the candidate model that is optimal for the conditional design. The candidate model should achieve generalizability, goodness-of-fit, parsimony and establish equilibrium between bias and variab
... Show MoreWater contamination is a pressing global concern, especially regarding the presence of nitrate ions. This research focuses on addressing this issue by developing an effective adsorbent for removing nitrate ions from aqueous solutions. two adsorbents Chitosan-Zeolite-Zirconium (Cs-Ze-Zr composite beads and Chitosan-Bentonite-Zirconium Cs-Bn-Zr composite beads were prepared. The study involved continuous experimentation using a fixed bed column with varying bed heights (1.5 and 3 cm) and inlet flow rates (1 and 3 ml/min). The results showed that the breakthrough time increased with higher bed heights for both Cs-Ze-Zr and Cs-Bn-Zr composite beads. Conversely, an increase in flow rate led to a decrease in breakthrough time. Notab
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