This study presents the multi criteria single-machine model. The machine scheduling problem (MSP) for ntasks on a single machine involves minimizing a function of three criteria: total completion time (C_j),maximum earliest (E_max), and tardiness (〖ΣT〗_j), This is an NP-hard issue. Within this work's theoretical section, we present the mathematical formulation of The presented topic thenhighlights the usefulness of the dominance rule (DR), which may be used to develop effective solutions. Whilein the practical part, one of the important exact methods; The proposed MSP tricriteria are solved by applyingthe Branch and Bound (BAB) method, which finds a set of efficient solutions for 1//F(ΣC_j ,ΣT_j ,E_max) upto n=100 jobs. The BAB appro

This paper presents a novel idea as it investigates the rescue effect of the prey with fluctuation effect for the first time to propose a modified predator-prey model that forms a non-autonomous model. However, the approximation method is utilized to convert the non-autonomous model to an autonomous one by simplifying the mathematical analysis and following the dynamical behaviors. Some theoretical properties of the proposed autonomous model like the boundedness, stability, and Kolmogorov conditions are studied. This paper's analytical results demonstrate that the dynamic behaviors are globally stable and that the rescue effect improves the likelihood of coexistence compared to when there is no rescue impact. Furthermore, numerical simul

The hydrodynamics of a co-current down flow bubble column has been investigated with air – water system. A Perspex bubble column of 5cm in diameter and 1.5m height is used as a test contactor using nozzles of 7, 8 and 9 mm diameter for air-water distributing. The column is provided with three electro-resistivity needle probes for bubble detection.
Experimental work is carried out with air flow rates from 0.09 to 0.45 m3/hr and liquid flow rates from 0.65 to 1.1m3/hr in order to study the effects of superficial gas velocity, nozzle diameter and liquid flow rate on the characteristics of hydrodynamic interactions viz. gas hold up, bubble diameter and bubble velocity by using two technical methods, direct height measurements for air-wa

Problem Statement: Despite the critical role of arm movement in freestyle swimming, many learners— specially female students at Baghdad University's College of Physical Education and Sport Sciences— face difficulties executing the pushing phase of the stroke correctly. This phase essential for generating propulsion and maintaining body coordination in water. Traditional teaching methods lack immediate feedback on the quality and force of arm movements, impeding effective motor learning and coordination. Approach: the researchers developed a custom-made device designed to measure the pressure force exerted by the palms during freestyle swimming. The device features pressure sensors attached both hands, a processor that analyzes the colle

The voice had a special place in the writting of the Andalusian poet (Ibn al-Abar ) , which aroused my attention because of the sonic capacity of the lettering inside the poetic at Ibn al-Abar poems . So Istudied the qualities of the lettering , structures and their exits . Scientists have not been able to determine the musical from the nonmusical sound , but we find the innate ability of Ibn al-Abar , which was able to determine this by using the lettering the right places and to revival the life to reflect the moments of his life , therefore came votes to express his purposes of praise and pride Etc. The poet Ibn al-Abar could exploit the lettering features in the effect of bilateral – static and moving and its ability to e

Transient mixed convection heat transfer in a confined porous medium heated at periodic sinusoidal heat flux is investigated numerically in the present paper. The Poisson-type pressure equation, resulted from the substituting of the momentum Darcy equation in the continuity equation, was discretized by using finite volume technique. The energy equation was solved by a fully implicit control volume-based finite difference formulation for the diffusion terms with the use of the quadratic upstream interpolation for convective kinetics scheme to discretize the convective terms and the temperature values at the control volume faces. The numerical study covers a range of the hydrostatic pressure head , , , , and ), sinusoidal amplitude range of

Violence occurs as a daily human action all over the world; it may cause so many kinds of damage to individuals as well as to society: physical, psychological, or both. Many literary authors of different genres have tried their best to portray violence by showing its negative effects, especially playwrights because they have the chance to show people the dangers of violence through performance on stage to warn them against such negatively affected action. It has been a human action since the beginning of human life on this planet when the first crime happened on earth when Cane killed his brother Abel. In our modern world, people are witnessing daily violent actions as a result of destructive wars that turned the humans into brutal beings.