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 importance of vibrations in rotating rotors in engineering applications has been examined, as has the best approach to interpreting vibration data. The most extensively used analytical approaches for rotating shaft vibration analysis have been investigated. In this research, a detailed study was made of the Rayleigh and Dunkerley methods due to their importance in the special calculations to find the amplitude of vibrations in the rotation system. The multi-node method was used to calculate both Dunkerley's and Rayleigh's methods. An experimental platform was built to study the vibrations that occur in the rotating shafts, and the results were compared with theoretical calculations and with different distances of the bearings. It pro
... Show MoreThe middle Cenomanian – early Turonian Mishrif Formation, a major carbonate reservoir unit in southern Iraq, was studied using cuttings and core samples and wireline logs (gamma‐ray, density and sonic) from 66 wells at 15 oilfields. Depositional facies ranging from deep marine to tidal flat were recorded. Microfacies interpretations together with wireline log interpretations show that the formation is composed of transgressive and regressive hemicycles. The regressive hemicycles are interpreted to indicate the progradation of rudist lithosomes (highstand systems tract deposits) towards distal basinal locations such as the Kumait, Luhais and Abu Amood oilfield areas. Transgressive hemicycles (transgressive systems tract deposits)
... Show MoreBackground: Behçet’s disease (BD) is a disorder of systemic inflammatory condition. Its important features are represented by recurrent oral, genital ulcerations and eye lesions. Aims. The purpose of the current study was to evaluate and compare cytological changes using morphometric analysis of the exfoliated buccal mucosal cells in Behçet’s disease patients and healthy controls, and to evaluate the clinical characteristics of Behçet’s disease. Methods. Twenty five Behçet’s disease patients have been compared to 25 healthy volunteers as a control group. Papanicolaou stain was used for staining the smears taken from buccal epithelial cells to be analyzed cytomorphometrically. The image analysis software has been used to
... Show MoreFor the most reliable and reproducible results for calibration or general testing purposes of two immiscible liquids, such as water in engine oil, good emulsification is vital. This study explores the impact of emulsion quality on the Fourier transform infrared (FT-IR) spectroscopy calibration standards for measuring water contamination in used or in-service engine oil, in an attempt to strengthen the specific guidelines of ASTM International standards for sample preparation. By using different emulsification techniques and readily available laboratory equipment, this work is an attempt to establish the ideal sample preparation technique for reliability, repeatability, and reproducibility for FT-IR analysis while still considering t
... Show MoreGiven that the Crimean and Congo hemorrhagic fever is one of the deadly viral diseases that occur seasonally due to the activity of the carrier “tick,” studying and developing a mathematical model simulating this illness are crucial. Due to the delay in the disease’s incubation time in the sick individual, the paper involved the development of a mathematical model modeling the transmission of the disease from the carrier to humans and its spread among them. The major objective is to comprehend the dynamics of illness transmission so that it may be controlled, as well as how time delay affects this. The discussion of every one of the solution’s qualitative attributes is included. According to the established basic reproductio
... Show MoreIn this work, a joint quadrature for numerical solution of the double integral is presented. This method is based on combining two rules of the same precision level to form a higher level of precision. Numerical results of the present method with a lower level of precision are presented and compared with those performed by the existing high-precision Gauss-Legendre five-point rule in two variables, which has the same functional evaluation. The efficiency of the proposed method is justified with numerical examples. From an application point of view, the determination of the center of gravity is a special consideration for the present scheme. Convergence analysis is demonstrated to validate the current method.
Under-reamed piles are piles with enlarged bases, which may be single bulb or multi bulbs. Such piles are suitable for resisting considerable soil movement of filed up ground, soft clay, and loose sand and have the advantages of increasing the soil strength and decreasing the displacement. In the present study, the finite element method was used to analyse the performance of a single pile with under-reamed bulbs of different shapes, that is, single cone, double cone, and half and full sphere, embedded in homogeneous, poorly graded sandy soil. The model of under-reamed pile was made of reinforced concrete and the bulb located at the middle of the embedded length of the pile. The dynami
The major cause of destruction during vertical vibration is the failure of the soil structure. The soil may fail due to loss of strength during continues vibration. The saturated sandy soil losses strength due to an increase in pore pressure, this phenomenon is called "liquefaction". Piled foundations are usually adopted as a foundation solution in potentially liquefiable soil under dynamic loading. In this research, 3D finite element model using PLAXIS Software was employed for pile foundation in saturated sandy soil. The results show the acceleration mobilization and velocity on the footing increases with increasing the intensity of dynamic loads and it becomes zero at maximum value of vertical settlement which indicates the end of the ti
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