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

Aim: The current study was aimed to determine the relationship between the orthodontic force applied by monobloc and the salivary level of alkaline phosphatase (ALP) and lactate dehydrogenase (LDH) enzymes, considering the time factor after insertion of the appliance and whether there is a correlation between these enzymes. Materials and methods: A sample of 28 growing patients requiring orthodontic treatment with myofunctional appliance (Monoblock) was taken for the current study with an age range 9 to 12 years,all patients had Angle's class II division 1 malocclusion with no or mild crowding, the sample was selected using simple random sampling. Only 16 subjects (10 males and 6 females) were included who follow certain inclusion criteria.

Nanomaterials, including nanoparticles such as iron oxide nanoparticles, have received great attention from researchers due to their unique properties and applications. There are several diverse methods, including chemical, physical, and green biological methods, to prepare iron oxide nanoparticles. The green method was chosen because it is safer, purer, and less toxic compared to other methods. Therefore, the green method is a promising and environmentally friendly method in the near future. The aqueous extract of Iraqi orange leaves was used to prepare nano iron oxide, it was examined structurally and spectrally by several techniques (X-ray diffraction- XRD, Fourier transform infrared - FT-IR, field emission scanning electron micr

The study involved the synthesis of new complexes with tetradentate ligand (LH). The general formula of complexes was [M(LH)(H2O)2] with M of Ni2+, Co2+, Cu2+, and Zn+. The ligand was synthesized by treating the 2-hydroxybenzohydrazide with salicylaldehyde. The structural characteristics of ligands and complexes were analyzed using various techniques, including elemental analyses, magnetic susceptibility, molar conductivity, infrared, ultraviolet absorption, mass, and NMR spectroscopy studies. The physical measurements indicated that the prepared complexes are non-electrolyte and showed that the ligand is tetradentate when coordinated with metal ions through the nitrogen of azomethine (–C=N–), two oxygen atoms of O–H phenolic,