This paper deals with testing a numerical solution for the discrete classical optimal control problem governed by a linear hyperbolic boundary value problem with variable coefficients. When the discrete classical control is fixed, the proof of the existence and uniqueness theorem for the discrete solution of the discrete weak form is achieved. The existence theorem for the discrete classical optimal control and the necessary conditions for optimality of the problem are proved under suitable assumptions. The discrete classical optimal control problem (DCOCP) is solved by using the mixed Galerkin finite element method to find the solution of the discrete weak form (discrete state). Also, it is used to find the solution for the discrete adj

New polymer blend with enhanced properties was prepared from (80 %) epoxy resin (Ep), (20%) unsaturated polyester resin (UPE) as a matrix material. The as-obtained polymer blend was further reinforced by adding Sand particles of particle size (53 μm) with various weight fraction (5, 10, 15, 20 %). Thermal conductivity and sorption measurements are performed in order to determine diffusion coefficient in different chemical solutions (NaOH, HCl) with concentration (0.3N) after immersion for specific period of time (30 days). The obtained results demonstrate that the addition of sand powder to (80%EP/20%UPE) blend leads to an increase of thermal conductivity, with an optimum/minimum diffusion coefficient in (HCl)/(NaOH), respectively.

Numerical Investigation was done for steady state laminar mixed convection and thermally and hydrodynamic fully developed flow through horizontal rectangular duct including circular core with two cases of time periodic boundary condition, first case  on the rectangular wall while keeping core wall constant and other on both the rectangular duct and core walls. The used governing equations are continuity momentum and energy equations. These equations are normalized and solved using the Vorticity-Stream function and the Body Fitted Coordinates (B.F.C.) methods. The Finite Difference approach with the Line Successive Over Relaxation (LSOR) method is used to obtain all the computational results the (B.F.C.) method is used to generate th

Background: The PMMA polymer denture base materials are low in thermal and strength properties. The aim of the study was to investigate the change in glass transition temperature, E-Moudulus and coefficient of thermal expansion of acrylic denture base material by addition of Al2O3, TiO2 and SiO2nano-fillers in 5% by weight. Materials and methods: The type of polymerization is free radical bulk polymerization. one hundred twenty (120) specimens were prepared , the specimens were divided into four groups according to the material had been added (one control and three for Al2O3, TiO2 and SiO2nanocomposite) each group was subdivided in to three groups according to the test had been done on it, the degree of transition (Tg) was measured by The d

In this paper we introduce the definition of  Lie ideal on inverse semiring and we generalize some results of Herstein about Lie structure of an associative rings to inverse semirings.

Let S be a prime inverse semiring with center Z(S). The aim of this research is to prove some results on the prime inverse semiring with (α, β) – derivation that acts as a homomorphism or as an anti- homomorphism, where α, β are automorphisms on S.

In this study, a qualitative seismic velocity interpretation is made up through using 2D-seismic reflection data on Luhais oil field in southern of Iraq which is situated at about 105 Km to the east from the Basra city. Luhais oil field was chosen to study the type and nature of the distribution of the seismic velocities of Nahr Umr and Zubair Formations in order to show its explorational importance, where these formations contain abundant quantities of hydrocarbons. Picking of the tops of Nahr Umr and Zubair was carried out from the synthetic seismogram which is calculated from sonic-logs and check shot of well Lu-2. Velocity model was obtained via using an implementation of Petrel program version, 2013 and was corrected according to to

The first studies on shocks and vibrations were carried out at the beginning of the 1930s to improve the behavior of buildings during earthquakes. Vibration tests on aircraft were developed from 1940 to verify the resistance of parts and equipments prior to their first use. Flutter is a well-known example of dynamic aero elasticity, where when oscillation of structure interacted with unsteady aerodynamic forces the flutter will occur. Vibration on any structure without damping means that self-harmonic oscillation will occur, and in most cases the oscillation may start to increase until structural failure. This behavior is very similar to resonance phenomena if only the oscillation is being studied as a vibration case. In vibration suppre

      In this article, the boundary value problem of convection propagation through the permeable fin in a natural convection environment is solved by the Haar wavelet collocation method (HWCM). We also compare the solutions with the application of a semi-analytical method , namely the Temimi and Ansari (TAM), that is characterized by accuracy and efficiency.The proposed method is also characterized by simplicity and efficiency. The possibility of applying the proposed method to many types of  linear or nonlinear ordinary and partial differential equations.