The necessary optimality conditions with Lagrange multipliers  are studied and derived for a new class that includes the system of Caputo–Katugampola fractional derivatives to the optimal control problems with considering the end time free. The formula for the integral by parts has been proven for the left Caputo–Katugampola fractional derivative that contributes to the finding and deriving the necessary optimality conditions. Also, three special cases are obtained, including the study of the necessary optimality conditions when both the final time  and the final state  are fixed. According to convexity assumptions prove that necessary optimality conditions are sufficient optimality conditions.

Airlift reactors are widely used in the chemical and biochemical applications as effective contactors for mass and heat transfer. The main advantages of airlift contactor compared with simple bubble column are ease of construction, low shear rate, high capacity, good mixing and liquid circulation without mechanical agitators and circulating pumps.

In this work, growth characteristics of Chlorella vulgaris microalgae were studied in an internal loop airlift photobioreactor for biomass production. The bioreactor operated under batch and semi-continuous culture mode using commercially available 20:20:20+TE NPK fertilizer as nutrients. The experiments were conducted to evaluate the growth rate and biomass productivity of

As a well-known oral and intravenous antifungal, voriconazole (VRN) has an extensive history of usage in the medical field. Solid lipid nanoparticles (SLNs) have been produced to treat ocular fungal keratitis in the eye. A 32Box-behnken design was used to produce a variety of new formulas for hot-melt extrusion. The SLNs were evaluated by entrapment efficiency (EE percent), particle size (PS), polydispersity index (PDI), and zeta potential (ZP). A series of in-vitro and in-vivo studies were carried out on the new formula. The produced vesicles’ EE, PS, PDI, and ZP values were all good. SLNs eye drops were numerically adjusted to include carbopol, a stabilizer, lipids, and a surfactant, among other substances. ZP of -36.5 ± 0.20 m

In the knowledge society, artificial intelligence (AI) forms a cornerstone of global education. This quasi-experimental study examines the impact of an Intelligent Adaptive Learning Strategy (IALS) on flexible thinking (FT) and academic achievement among 60 3rd-year undergraduate students at the College of Education/University of Baghdad (experimental n = 30; control n = 30). The IALS was implemented via an AI-supported educational platform, while the control group received conventional instruction. Post-test intervention assessments included an FT test (10 items, content validity = 0.89, Cronbach’s α = 0.87) and an achievement test (10 objective items, α = 0.85). Results revealed statistically significant superiority of the exp

The subject of dumping is considering today one of the subjects in which form an obstruction arise in front of the cycle of growth for some countries , such as the study of dumping is capturing a large attention by the competent because either a big  role and effect in growing the economies of nations then the subject of dumping became a field turn around its sides many measures and laws … and may be done resorting to by many states of the world to anti-dumping as approach of determent weapon delimit  the impact of dumping and gives the national agriculture sector the opportunity for rising and growing so this section of international economics is capturing a special importance and represent in same time an important

In most manufacturing processes, and in spite of statistical control, several process capability indices refer to non conformance of the true mean (µc ) from the target mean ( µT ), and the variation is also high. In this paper, data have been analyzed and studied for a blow molded plastic product (Zahi Bottle) (ZB). WinQSB software was used to facilitate the statistical process control, and process capability analysis and some of capability indices. The relationship between different process capability indices and the true mean of the process were represented, and then with the standard deviation (σ ), of achievement of process capability value that can reduce the standard deviation value and improve production out of theoretical con