The paper is concerned with the state and proof of the existence theorem of a unique solution (state vector) of couple nonlinear hyperbolic equations (CNLHEQS) via the Galerkin method (GM) with the Aubin theorem. When the continuous classical boundary control vector (CCBCV) is known, the theorem of existence a CCBOCV with equality and inequality state vector constraints (EIESVC) is stated and proved, the existence theorem of a unique solution of the adjoint couple equations (ADCEQS) associated with the state equations is studied. The Frcéhet derivative derivation of the "Hamiltonian" is obtained. Finally the necessary theorem (necessary conditions "NCs") and the sufficient theorem (sufficient conditions" SCs") for optimality of the stat

This paper aims to study the effect of circular Y-shaped fin arrangement to improve the low thermal response rates of a double-tube heat exchanger containing Paraffin phase change material (PCM). ANSYS software is employed to perform the computational fluid dynamic (CFD) simulations of the heat exchanger, including fluid flow, heat transfer, and the phase change process. The optimum state of the fin configuration is derived through sensitivity analysis by evaluating the geometrical parameters of the Y-shaped fin. For the same height of the fins (10 mm), the solidification time is reduced by almost 22%, and the discharging rate is enhanced by almost 26% using Y-shaped fins compared with the straight fins. The results demonstrate that the sol

It is important to note that Posaconazole (POCZ) is a newly developed extended-spectrum triazole that belongs to BCS class II and has a solubility of less than 1µg/ml. In patients with a weakened immune system, POCZ has been shown to be effective as an antifungal treatment for invasive infections caused by candida and aspergillus species. The nano-micelles technique can be used to increase POCZ solubility. In order to increase their apparent solubility in water, nano-micelles are made by combining macromolecules that self-assemble into ordered structures capable of entrapping hydrophobic drug molecules in the interior domain. Dispersed colloidal systems, of which nano-micelles are a subset, are a large and diverse group. Composed of a p

Reliability analysis methods are used to evaluate the safety of reinforced concrete structures by evaluating the limit state function 𝑔(𝑋𝑖). For implicit limit state function and nonlinear analysis , an advanced reliability analysis methods are needed. Monte Carlo simulation (MCS) can be used in this case however, as the number of input variables increases, the time required for MCS also increases, making it a time consuming method especially for complex problems with implicit performance functions. In such cases, MCS-based FORM (First Order Reliability Method) and Artificial Neural Network-based FORM (ANN FORM) have been proposed as alternatives. However, it is important to note that both MCS-FORM and ANN-FORM can also be time-con