The problem of Bi-level programming is to reduce or maximize the function of the target by having another target function within the constraints. This problem has received a great deal of attention in the programming community due to the proliferation of applications and the use of evolutionary algorithms in addressing this kind of problem. Two non-linear bi-level programming methods are used in this paper. The goal is to achieve the optimal solution through the simulation method using the Monte Carlo method using different small and large sample sizes. The research reached the Branch Bound algorithm was preferred in solving the problem of non-linear two-level programming this is because the results were better.

This research deals with unusual approach for analyzing the Simple Linear Regression via Linear Programming by Two - phase method, which is known in Operations Research: “O.R.”. The estimation here is found by solving optimization problem when adding artificial variables: Ri. Another method to analyze the Simple Linear Regression is introduced in this research, where the conditional Median of (y) was taken under consideration by minimizing the Sum of Absolute Residuals instead of finding the conditional Mean of (y) which depends on minimizing the Sum of Squared Residuals, that is called: “Median Regression”. Also, an Iterative Reweighted Least Squared based on the Absolute Residuals as weights is performed here as another method to

   In this work, a novel technique to obtain an accurate solutions to nonlinear form by multi-step combination with Laplace-variational approach (MSLVIM) is introduced. Compared with the  traditional approach for variational it overcome all difficulties and enable to provide us more an accurate solutions with extended of the convergence region as well as covering to larger intervals which providing us a continuous representation of approximate analytic solution and it give more better information of the solution over the whole time interval. This technique is more easier for obtaining the general Lagrange multiplier with reduces the time and calculations. It converges rapidly to exact formula with simply computable terms wit

The long – term behaviour of polyethylene products used out doors is affected by weathering. In the present work,
weathering test was carried out to find the effect of the environment conditions on the mechanical properties of
HDPE/LLDPE blends with different weight percents (0, 15, 30, and 45 %) relative to the LLDPE by increasing the
exposure times to (100, 150, 200, 250, 300) hr.
A series of tests (destructive), tensile, impact and hardness were carried out on the prepared samples, the results
obtained declare the changes on the material behaviour from ductile to brittle and the polymer shows a decline in the
mechanical properties with increasing the exposure times.
In the present work empirical equations were r

Background: This study was conducted to assess the effects of various beverages on the shear bond strength of light-cured orthodontic composite used to bond stainless steel orthodontic brackets on human teeth and to determine the site of bonding failure of this material. Materials and Methods: Fifty extracted human premolars were selected and randomly divided into five equal groups each with 10 teeth according to the beverage type (Control, One Tiger, Milk, Green tea and Coffee). After bonding, the teeth were immersed in specific beverages for 5 minutes twice daily with equal intervening intervals then washed and stored in distilled water at 37º C for the reminder of the day. The process was carried out for 30 days. The samples were then

ATTAPULGITE clay was modified in this study by the graphene oxide sheets and the clay was diagnosed before and after modification using several techniques (Fourier-transform infrared spectroscopy FT-IR, X-ray powder diffraction XRD, Scanning electron microscope SEM , energy dispersive spectroscopy EDX ) ,The surface of the attapulgite clay (before (Ata) after modification by graphene oxide (Ata-GO) ) was applied to adsorption of the Alizarin dye from its water solutions through the application of several kinetic models (pseudo first-order model , pseudo second -order model , intraparticle diffusion model ),It was found that the practical results follow pseudo second -order model. The process of modification on the surface of the mud has imp

Background: The aim of this in vitro study was to evaluate and compare the microleakage between Vertise Flow T M composite material and other conventional (Filtek Z250, riva light cure and SDR) composite materials when restoring CII mesial box only cavity at gingival margin through die penetration test Materials and methods: Forty maxillary first premolars were prepared with class II box design only cavities. Samples were divided into four groups of ten teeth according to material used: group I (FiltekZ250 only). Group II (SDR+FiltekZ250). Group III (Vertise Flow +FiltekZ250). Group IV (Riva light cure+ FiltekZ250). After 24 hrs. immersion in 2% in methylene blue, samples were sectioned and micro leakage was estimated. Results: None of the

This research deals with increasing the hardening and insulating the petroleum pipes against the conditions and erosion of different environments. So, basic material of epoxy has been mixed with Ceramic Nano Zirconia reinforcement material 35 nm with the percentages  (0,1,2,3,4,5) %, whereas the paint basis of broken petroleum pipes was used  to paint on it, then it was cut into dimensions (2 cm. × 2 cm.) and 0.3cm high. After the paint and percentages are completed, the samples were immersed into the paint. Then, the micro-hardness was checked according to Vickers method and thermal inspection of paint, which contained (Thermal conduction, thermal flux and Thermal diffusivity), the density of the painted samples was calculate