Necessary and sufficient conditions for the operator equation I AXAX n  * , to have a real positive definite solution X are given. Based on these conditions, some properties of the operator A as well as relation between the solutions X andAare given.

In this paper, the main work is to minimize a function of three cost criteria for scheduling n jobs on a single machine. We proposed algorithms to solve the single machine scheduling multiobjective problem. In this problem, we consider minimizing the total completion times, total tardiness and maximum tardiness criteria. First a branch and bound (BAB) algorithm is applied for the 1//∑Ci+∑Ti+Tmax problem. Second we compare two multiobjective algorithms one of them based on (BAB) algorithm to find the set of efficient (non dominated) solutions for the 1//(∑Ci ,∑Ti ,Tmax) problem. The computational results show that the algorithm based on (BAB) algorithm is better than the other one for generated the total number of

     In this research, a type of gram negative bacteria was exposed to non-thermal plasma at a distance of (2 and 3 cm) from the plasma flow nozzle, with the use of an alternating power supply (5KHz), where exposure was made at two different voltages (4.9 and 8 kV). A negative gram of Pseudomonas aeruginosa bacteria was isolated and exposed to non-thermal plasma at different flow rates of argon gas whose value ranged from (1-5) liters/minute. The results showed that bacterial killing rate is directly proportional to distance while exposing the samples to non-thermal plasma, and the best factors by which a complete killing rate was obtained were at a distance of 2 cm with a voltage of 8 kV and a gas flow rate of 5 liters/min,

This paper discusses Ree–Eyring fluid’s peristaltic transport in a rotating frame and examines the impacts of Magnetohydrodynamics (MHD). The results deal with  systematically (analytically) applying each of the governing equations of Ree–Eyring fluid, the axial and secondary velocities, flow rate due to auxiliary stream, and bolus. The effects of some distinctive variables, such as Hartman number, heat source/sink, and amplitude ratio, are taken under consideration and illustrated through graphs.

     This article is devoted to presenting results on invariant approximations over a non-star-shsped weakly compact subset of a complete modular space by introduced a new notion called S-star-shaped with center f:  if   be a mapping and , . Then the existence of common invariant best approximation is proved for Banach operator pair of mappings by combined the hypotheses with Opial’s condition or demi-closeness condition

     In this work, plasma system that operates at vacuum was designed and built using a sheet of cobalt metal for the purpose of diagnosing plasma and measuring its parameters, as it is very important to know the processes that accompany plasma generation and are closely related to them, including the electron density in the plasma and its temperature. The spectroscopic diagnosis was done by optical emission spectroscopy (OES) which relies on the calculation of the optical radiation emitted by the plasma to describe plasma parameters in the chemical, molecular, and ionic radiator's near environment, and applied to cobalt metal at vacuum D.C high voltage power supply. The results showed the rise of spectral lines intensity with increa

In this research, the effect of electrode material on the parameters of the produced DBD plasma was investigated. First, a non-thermal plasma was created by applying a 15 kV AC voltage between two electrodes and using a glass plate as a dielectric barrier in the design Dielectric Barrier Discharge (DBD) plasma system. The obtained plasma spectrum was analyzed using optical emission spectroscopy to calculate plasma parameters by the Boltzmann plot method. Electrodes made of copper, aluminium, and stainless steel were employed in this research. Electron temperature ( ) for copper, aluminium, and stainless steel was found to be (1.398 eV), (1.093 eV) and (1.009 eV), respectively.

The approximate solution of a nonlinear parabolic boundary value problem with variable coefficients (NLPBVPVC) is found by using mixed Galekin finite element method (GFEM) in space variable with Crank Nicolson (C-N) scheme in time variable. The problem is reduced to solve a Galerkin nonlinear algebraic system (NLAS), which is solved by applying the predictor and the corrector method (PCM), which transforms the NLAS into a Galerkin linear algebraic system (LAS). This LAS is solved once using the Cholesky technique (CHT) as it appears in the MATLAB package and once again using the General Cholesky Reduction Order Technique (GCHROT), the GCHROT is employed here at first time to play an important role for saving a massive time. Illustrative

Objective of the research This study aimed to manufacture an innovative device that enables the player to walk after the operation and improves functional efficiency through improvement in the range of motion as well as improvement in the size of the muscles working on the knee joint Imposing research There are statistically significant differences between the pre and posttests of the experimental and control groups, there are Statistically significant differences between the post-tests between the experimental group and the control group in favor of the experimental group of the research sample. The researchers used the experimental approach by designing the control and experimental groups with a test (pre-post) for the suitabili