Investigation regarding queue length dynamics have been explored using various kinds of models including ordinary differential equations (ODEs). ODEs possess the advantageous property of having a continuous-time representation of queue length dynamics, thus its adoption in this article in modelling various scenarios as system of first-order ODEs. Specifically, a multi-server queue is considered and a numerical approach for solving first-order ODEs using MATLAB is adopted to obtain approximate solutions of the resultant models. The results display the dynamics of the queue length in each scenario, thus showing the usefulness of ODEs in analysing the behaviour of queues using system of ODEs.
Piled raft is commonly used as foundation for high rise buildings. The design concept of piled raft foundation is to minimize the number of piles, and to utilize the entire bearing capacity. High axial stresses are therefore, concentrated at the region of connection between the piles and raft. Recently, an alternative technique is proposed to disconnect the piles from the raft in a so called unconnected piled raft (UCPR) foundation, in which a compacted soil layer (cushion) beneath the raft, is usually introduced. The piles of the new system are considered as reinforcement members for the subsoil rather than as structural members. In the current study, the behavior of unconnected piled rafts systems has been studie
... Show MoreIn this paper, a Sokol-Howell prey-predator model involving strong Allee effect is proposed and analyzed. The existence, uniqueness, and boundedness are studied. All the five possible equilibria have been are obtained and their local stability conditions are established. Using Sotomayor's theorem, the conditions of local saddle-node and transcritical and pitchfork bifurcation are derived and drawn. Numerical simulations are performed to clarify the analytical results
This study has contributed to understanding a delayed prey-predator system involving cannibalism. The system is assumed to use the Holling type II functional response to describe the consuming process and incorporates the predator’s refuge against the cannibalism process. The characteristics of the solution are discussed. All potential equilibrium points have been identified. All equilibrium points’ local stability analyses for all time delay values are investigated. The system exhibits a Hopf bifurcation at the coexistence equilibrium, which is further demonstrated. The center manifold and normal form theorems for functional differential equations are then used to establish the direction of Hopf bifurcation and the stability of the per
... Show MoreThe non static chain is always the problem of static analysis so that explained some of theoretical work, the properties of statistical regression analysis to lose when using strings in statistic and gives the slope of an imaginary relation under consideration. chain is not static can become static by adding variable time to the multivariate analysis the factors to remove the general trend as well as variable placebo seasons to remove the effect of seasonal .convert the data to form exponential or logarithmic , in addition to using the difference repeated d is said in this case it integrated class d. Where the research contained in the theoretical side in parts in the first part the research methodology ha
... Show MoreSince the beginning of mankind, the view of the sky was present through observations with the naked eye, then it developed with time, and the sciences and tools of astronomical observations developed, including photometric measurements, which reached a high degree of accuracy in describing various cosmic phenomena, including the study of galaxies, their composition, and the differences between them, and from here the importance of this study emerged, to determine the differences between two distinct types of classification of galaxies, which are normal and barred spiral galaxies, where two galaxies NGC 4662 and NGC 2649 were chosen that represented certain types of galaxies to study the morphological structure of the two galaxies, a
... Show MoreIn this study, aromatic polyamide reverse osmosis membranes were used to remove zinc ions from electroplating wastewater. Influence of different operating conditions such as time, zinc concentration and pressure on reverse osmosis process efficiency was studied. The experimental results showed, concentration of zinc in permeate increase with increases of time from 0 to 70 min, and flux of water through membrane decline with time. While, the concentrations of zinc in permeate increase with the increase in feed zinc concentration (10–300 mg/l), flux decrease with the increment of feed concentration. The raise of pressure from 1 to 4 bar, the zinc concentration decreases and the flux increase. The highest recovery percentage was found is 54.
... Show MoreIn this study, aromatic polyamide reverse osmosis membranes were used to remove zinc ions from electroplating wastewater. Influence of different operating conditions such as time, zinc concentration and pressure on reverse osmosis process efficiency was studied. The experimental results showed, concentration of zinc in permeate increase with increases of time from 0 to 70 min, and flux of water through membrane decline with time. While, the concentrations of zinc in permeate increase with the increase in feed zinc concentration (10–300 mg/l), flux decrease with the increment of feed concentration. The raise of pressure from 1 to 4 bar, the zinc concentration decreases and the flux increase. The highest recovery percentage was fou
... Show MoreThis work was conducted to study the extraction of pelletierine sulphate from Punica granatum L. roots by liquid membrane techniques. Pelletierine sulphate is used widely in medicine. The general behavior of extraction process indicates that pelletierine conversion increased with increasing the number of stages and the discs rotation speed but high rotation speed was not favored because of the increased risk of droplet formation during the operation. The pH of feed and acceptor solution was also important. The results exhibit that the highest pelletierine conversion was obtained when using two stages,(10 rpm) discs speed of stainless steel discs,(pH= 9.5) of feed solution and (pH= 2) of acceptor solution in n-decane. Assuming the existence
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