In this paper, the continuous classical boundary optimal control problem (CCBOCP) for triple linear partial differential equations of parabolic type (TLPDEPAR) with initial and boundary conditions (ICs & BCs) is studied. The Galerkin method (GM) is used to prove the existence and uniqueness theorem of the state vector solution (SVS) for given continuous classical boundary control vector (CCBCV). The proof of the existence theorem of a continuous classical boundary optimal control vector (CCBOCV) associated with the TLPDEPAR is proved. The derivation of the Fréchet derivative (FrD) for the cost function (CoF) is obtained. At the end, the theorem of the necessary conditions for optimality (NCsThOP) of this problem is stated and prov

This survey investigates the thermal evaporation of Ag2Se on glass substrates at various thermal
annealing temperatures (300, 348, 398, and 448) °K. To ascertain the effect of annealing
temperature on the structural, surface morphology, and optical properties of Ag2Se films,
investigations and research were carried out. The crystal structure of the film was described by Xray diffraction and other methods.The physical structure and characteristics of the Ag2Se thin films
were examined using X-ray and atomic force microscopy (AFM) based techniques. The Ag2Se
films surface morphology was examined by AFM techniques; the investigation gave average
diameter, surface roughness, and grain size mutation value

Background: Bone density is a major factor that affect mini implant primarily stability; no Iraqi studies have evaluated bone density related to mini-implant placement for orthodontic anchorage at age 13 -15 years. The present research aims to evaluate gender, side and site differences in the bone density at various orthodontic implant sites for the maxillary alveolar bone. Materials and methods: Twenty nine individuals (16 males and 13 females) had subjected to clinical examination, then 64-multislice computed tomography scan data were evaluated and bone density was measured in Hounsfield unit at 21 points (9 points for each side and 3 points between the right and left central incisors) . Results: The results obtained showed that there ar

  In this paper, we use the repeated corrected Simpson's 3/8 quadrature method for obtaining the numerical solutions of Fredholm linear integral equations of the second kind. This method is more accurately than the repeated corrected Trapezoidal method and the repeated Simpson's 3/8 method. To illustrate the accuracy of this method, we give a numerical example

     One hundred samples of root canal bacteria were isolated  from patients teeth with primary and secondary infected root canal from all the ages . Biochemical and microscopial tests were done for identification of these isolates. Twenty four isolates were confirmed as       E. faecalis species by using these tests. Genetic diagnosis for the all isolates was also done by using polymerase chain reaction ( PCR ). Thirty two isolates were confirmed to  belong to E. faecalis species by using this test.

Bearing capacity of soil is an important factor in designing shallow foundations. It is directly related to foundation dimensions and consequently its performance. The calculations for obtaining the bearing capacity of a soil needs many varying parameters, for example soil type, depth of foundation, unit weight of soil, etc. which makes these calculation very variable–parameter dependent. This paper presents the results of comparison between the theoretical equation stated by Terzaghi and the Artificial Neural Networks (ANN) technique to estimate the ultimate bearing capacity of the strip shallow footing on sandy soils. The results show a very good agreement between the theoretical solution and the ANN technique. Results revealed that us