The aim of this paper is to derive a posteriori error estimates for semilinear parabolic interface problems. More specifically, optimal order a posteriori error analysis in the - norm for semidiscrete semilinear parabolic interface problems is derived by using elliptic reconstruction technique introduced by Makridakis and Nochetto in (2003). A key idea for this technique is the use of error estimators derived for elliptic interface problems to obtain parabolic estimators that are of optimal order in space and time.

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.

Abstract

The multiple linear regression model of the important regression models used in the analysis for different fields of science Such as business, economics, medicine and social sciences high in data has undesirable effects on analysis results . The multicollinearity is a major problem in multiple linear regression. In its simplest state, it leads to the departure of the model parameter that is capable of its scientific properties, Also there is an important problem in regression analysis is the presence of high leverage points in the data have undesirable effects on the results of the analysis , In this research , we present some of

Thank for Allah lord of worlds and peace be upon his messenger last one of them Muhammad
and his followers.
The honored thing which the searcher can present to serve the holly quran and all its sciences
in their searching and composing .
The straight is the order of Allah is great goal and elite target in this life and every Muslim
should follow and aim to get it and from the mercy of Allah to us he ordered us to follow it
and he showed to us how to and to obey him and showed the way to it as was mentioned in
the Quarn ( this is my straight way so you follow it and do not follow other ways ) and the importance of straight he ordered the prophet peace be upon him to catch the right and
straight and warned us f

The increasing population growth resulting in the tremendous increase in consumption of fuels, energy, and petrochemical products and coupled with the depletion in conventional crude oil reserves and production make it imperative for Nigeria to explore her bitumen reserves so as to meet her energy and petrochemicals needs. Samples of Agbabu bitumen were subjected to thermal cracking in a tubular steel reactor operated at 10 bar pressure to investigate the effect of temperature on the cracking reaction. The gas produced was analyzed in a Gas Chromatograph while the liquid products were subjected to Gas Chromatography-Mass Spectrometry (GC-MS) analysis. Heptane was the dominant gas produced in bitumen cracking at all temperatures and the r

  Weibull distribution is considered as one of the most widely  distribution applied in real life, Its similar to normal distribution in the way of applications, it's also considered as one of the distributions that can applied in many fields such as industrial engineering to represent replaced and manufacturing time ,weather forecasting, and other scientific uses in reliability studies and survival function in medical and communication engineering fields.

   In this paper, The scale parameter has been estimated for weibull distribution using Bayesian method based on Jeffery prior information as a first method , then enhanced by improving Jeffery prior information and then used as a se

This research deals with the study of top soil electrical conductive regions located within Baghdad City. The research included measuring the dissolved soil material extraction Electrical Conductivity (EC) with an aqueous solution for the top (0-30 cm) soil layer of the study area. As the electrical conductivity values increase by increasing the amount of dissolved salts in principle, we can consider that the aim of this research is to predict the amount and distribution of (soil contamination with salts) which is represented by the (Salt Index), this factor calculated for each soil representative sample taken from the region with a depth of (30 cm). Laboratory (EC) test values measured by the use of solutions (EC) digital meter for the ex

The work was carried out in two stages. The first stage concerned
with study of silicon carbide (SiC) ratio (1.5, 2.5, 3.5, and 4.5 wt%)
effect on the Thermal conductivity of polyvinyl chloride (PVC); and
the second stage concerned with the UV – weatherizing (25, 50, and
75 hr), thermal aging (40, 50, and 60 °C), and rain- weatherizing (1,
2.5, and 4 hr) effect on the samples involved. Thermal conductivity
results proved that there was slight increase in thermal conductivity
by (SiC) loading; it increased from 0.17 W/m.K for PVC to 0.19
W/m.K for 4.5% SiC/PVC; where as it was systematically decreased
by UV- weatherizing, thermal aging, and rain- weatherizing. This
property is in a good agreement with gene

      The effect of fiber volume fraction of the carbon fiber on the thermal conductivity of the polymer composite material was studied. Different percentages of carbon fibers were used (5%, 10%, 15%, 20%, and 25%). Specimens were made in two groups for unsaturated polyester as a matrix and carbon fibers, first group has parallel arrangement of fibers and the second group has perpendicular arrangement of fibers on the thermal flow, Lee's disk method was used for testing the specimens. This study showed that the values of the of thermal conductivity of the specimens when the fibers arranged in parallel direction was higher than that when the fibers arranged in the perpendicular direction  

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