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

Abstract-Industrial and urban development has resulted in the spread of plastic waste and the increase in the emissions of carbon dioxide resulting from the cement manufacturing process. The current research aims to produce green (environmentally friendly) concrete by using plastic waste as coarse aggregates in different proportions (10% and 20%) and nano silica sand powder as an alternative to cement in different proportions (5% and 10% by weight). The results showed that compressive strength decreased by 12.10% and 19.23% for 10% and 20% plastic waste replacement and increased by 12.89% and 20.39% for 5% and 10% silica sand replacement respectively at 28 days. Flexural strength decreased by 12.95% and 19.64% for 10% and 20% plastic waste

Industrial and urban development has resulted in the spread of plastic waste and the increase in the emissions of carbon dioxide resulting from the cement manufacturing process. The current research aims to produce green (environmentally friendly) concrete by using plastic waste as coarse aggregates in different proportions (10% and 20%) and nano silica sand powder as an alternative to cement in different proportions (5% and 10% by weight). The results showed that compressive strength decreased by 12.10% and 19.23% for 10% and 20% plastic waste replacement and increased by 12.89% and 20.39% for 5% and 10% silica sand replacement respectively at 28 days. Flexural strength decreased by 12.95% and 19.64% for 10% and 20% plastic waste r

Marketing plays a role in the transfer of consumer desires through research, studies and satisfy the needs process, and with the technical development has evolved and marketing departments in the world of commerce has made great strides since the expansion of the trade deal, especially in light of spread of the Internet and the culture of use where he became a lot as individuals or institutions are dealings via electronic shopping . In all cases, we find that the consumer is important party, and that the legal rules did not leave the shopping process or contracting E without protection and I've dealt with so many studies through the civil protection for the consumer in electronic contracts legally with an analytical study of the

            That analytical procedures are of analytical tools important because it gives assurance to the auditor-free financial statements of the economic units replace the audit of cases offraud and errors and distortions, and thereby to increase the effectiveness of the audit process and confirm the possibility oftrust and reliance on the financial statements that Adfgaha auditor.
Inspite of identify evidence of proof necessary to enhance the auditor's opinion the results reached in the audit p

The present study develops an artificial neural network (ANN) to model an analysis and a simulation of the correlation between the average corrosion rate carbon steel and the effective parameter Reynolds number (Re), water concentration (Wc) % temperature (T o) with constant of PH 7 . The water, produced fom oil in Kirkuk oil field in Iraq from well no. k184-Depth2200ft., has been used as a corrosive media and specimen area (400 mm2) for the materials that were used as low carbon steel pipe. The pipes are supplied by Doura Refinery . The used flow system is all made of Q.V.F glass, and the circulation of the two –phase (liquid – liquid ) is affected using a Q.V.F pump .The input parameters of the model consists of Reynolds number , w

The effect of micro-and nano silica particles (silica SiO2 (100 μm), Fused silica (12nm)) on some mechanical properties of epoxy resin was investigated (Young's modulus, Flexural strength). The micro-and nano composites were prepared by using three steps process with different volume fraction of micro-and nano particles (1, 2, 3, 4, 5, 7, 10, 15, and 20 vol. %). Flexural strength and Young's modulus of nano composites were increased at low volume fraction (max. enhancement at 4 vol.% ). However at higher volume fraction both Young's modulus and flexural strength decrease. Moreover, above, the mechanical properties are enhanced more than that of neat epoxy resin. The flexural strength decreases with increasing the volume fraction of micr

Bruggeman's symmetric effective-medium model of vanadium oxide is introduced, in which the transmittance was studied because of its importance in the subject of smart windows, it was studied from ( 5 nm-1000 nm) for each of the regions of the electromagnetic spectrum, the ultraviolet and visible region, and the near and medium sub-regions of the infrared and the results showed that the importance of studying the transmittance of vanadium oxide as a good candidate For this kind of industries. Our results showed that the small sizes of the material guarantee an almost constant and high transmittance to the visible region; this is due to the agreement of the direction of the dipoles in the material with the direction of the internal el

In this work, MWCNT in the epoxy can be prepared at room temperature and thickness (1mm) at different concentration of CNTs powder. Optical properties of multi-walled carbon nanotubes (CNTs) reinforced epoxy have been measured in the range of (300-800)nm. The electronic transition in pure epoxy and CNT/epoxy indicated direct allowed transition. Also, it is found that the energy gap of epoxy is 4.1eV and this value decreased within range of (4.1-3.5)eV when the concentration of CNT powder increased from (0.001-0.1)% respectively.
The optical constants which include (the refractive index (n), the extinction coefficient (k), real (ε1) and imaginarily (ε2) part of dielectric constant calculated in the of (300-800)nm at different concent