This paper deals with the modeling of a preventive maintenance strategy applied to a single-unit system subject to random failures.

According to this policy, the system is subjected to imperfect periodic preventive maintenance restoring it to ‘as good as new’ with probability

p and leaving it at state ‘as bad as old’ with probability q. Imperfect repairs are performed following failures occurring between consecutive

preventive maintenance actions, i.e the times between failures follow a decreasing quasi-renewal process with parameter a. Considering the

average durations of the preventive and corrective maintenance actions a

This paper is concerned with combining two different transforms to present a new joint transform FHET and its inverse transform IFHET. Also, the most important property of FHET was concluded and proved, which is called the finite Hankel – Elzaki transforms of the Bessel differential operator property, this property was discussed for two different boundary conditions, Dirichlet and Robin. Where the importance of this property is shown by solving axisymmetric partial differential equations and transitioning to an algebraic equation directly. Also, the joint Finite Hankel-Elzaki transform method was applied in solving a mathematical-physical problem, which is the Hotdog Problem. A steady state which does not depend on time was discussed f

In this paper we use Bernstein polynomials for deriving the modified Simpson's 3/8 , and the composite modified Simpson's 3/8 to solve one dimensional linear Volterra integral equations of the second kind , and we find that the solution computed by this procedure is very close to exact solution.

Background: Errors of horizontal condylar inclinations and Bennett angles had largely affected the articulation of teeth and the pathways of cusps. The aim of this study was to estimate and compare between the horizontal condylar (protrusive) angles and Bennett angles of full mouth rehabilitation patients using two different articulator systems. Materials and Methods: Protrusive angles and Bennett angles of 50 adult males and females Iraqi TMD-free full mouth rehabilitation patients were estimated by using two different articulator systems. Arbitrary hinge axis location followed by protrusive angles and Bennett angles, estimation was done by a semiadjustable articulator system. A fully adjustable articulator system was utilized to locate th

The presented study investigated the scheduling regarding  jobs on a single machine. Each  job will be processed with no interruptions and becomes available for the processing at time 0. The aim is finding a processing order with regard to jobs, minimizing total completion time , total late work , and maximal tardiness  which is an NP-hard problem. In the theoretical part of the present work, the mathematical formula for the examined problem will be presented, and a sub-problem of the original problem of minimizing the multi-objective functions  is introduced. Also, then the importance regarding the dominance rule (DR) that could be applied to the problem to improve good solutions will be shown. While in the practical part, two

This investigation aims to explore the potential of waterworks sludge (WS), low-cost byproduct of water treatment processes, as a sorbent for removing Congo Red (CR) dyes. This will be achieved by precipitating nano-sized (MgAl-LDH)-layered double hydroxide onto the surface of the sludge. The efficiency of utilizing MgAl-LDH to modify waterworks sludge (MWS) for use in permeable reactive barrier technology was confirmed through analysis with Fourier transform infrared and X-ray diffraction. The isotherm model was employed to elucidate the adsorption mechanisms involved in the process. Furthermore, the COMSOL model was utilized to establish a continuous testing model for the analysis of contaminant transport under diverse conditions.

In this work, an enhanced Photonic Crystal Fiber (PCF) based on Surface Plasmon Resonance (SPR) sensor using a sided polished structure for the detection of toxic ions Arsenic in water was designed and implemented. The SPR curve can be obtained by polishing the side of the PCF after coating the Au film on the side of the polished area, the SPR curve can be obtained. The proposed sensor has a clear SPR effect, according to the findings of the experiments. The estimated signal to Noise Ratio (SNR), sensitivity (S), resolution (R), and Figures of merit (FOM) are approaching; the SNR is 0.0125, S is 11.11 μm/RIU, the resolution is 1.8x〖10〗^(-4), and the FOM is 13.88 for Single-mode Fiber- Photonic Crystal Fiber- single mode Fiber (SMF-P

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