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.
In this work, a joint quadrature for numerical solution of the double integral is presented. This method is based on combining two rules of the same precision level to form a higher level of precision. Numerical results of the present method with a lower level of precision are presented and compared with those performed by the existing high-precision Gauss-Legendre five-point rule in two variables, which has the same functional evaluation. The efficiency of the proposed method is justified with numerical examples. From an application point of view, the determination of the center of gravity is a special consideration for the present scheme. Convergence analysis is demonstrated to validate the current method.
The topic of the research dealt with the image of Iraq in the British press based on a sample of the newspapers (The Guardian and the Daily Telegraph), which are among the most important and largest newspapers in the United Kingdom and the world, because of its active role in guiding local and international public opinion towards important issues and events, Since these two newspapers are interested in the accuracy of sensitive political topics, the message aimed at knowing the media image that these two newspapers painted about Iraq in the period that was limited to the first quarter of 2019, and also to know the nature of the contents promoted by these newspapers about the Iraqi reality, The method of content analysis was used as an ap
... Show MoreThe purpose of this paper is to solve the stochastic demand for the unbalanced transport problem using heuristic algorithms to obtain the optimum solution, by minimizing the costs of transporting the gasoline product for the Oil Products Distribution Company of the Iraqi Ministry of Oil. The most important conclusions that were reached are the results prove the possibility of solving the random transportation problem when the demand is uncertain by the stochastic programming model. The most obvious finding to emerge from this work is that the genetic algorithm was able to address the problems of unbalanced transport, And the possibility of applying the model approved by the oil products distribution company in the Iraqi Ministry of Oil to m
... Show MoreAmong a variety of approaches introduced in the literature to establish duality theory, Fenchel duality was of great importance in convex analysis and optimization. In this paper we establish some conditions to obtain classical strong Fenchel duality for evenly convex optimization problems defined in infinite dimensional spaces. The objective function of the primal problem is a family of (possible) infinite even convex functions. The strong duality conditions we present are based on the consideration of the epigraphs of the c-conjugate of the dual objective functions and the ε-c-subdifferential of the primal objective functions.
Background: Restoration of the gingival margin of Class II cavities with composite resin continues to be problematic, especially where no enamel exists for bonding to the gingival margin. The aim of study is to evaluate the marginal leakage at enamel and cementum margin of class II MOD cavities using amalgam restoration and modern composite restorations Filtek™ P90, Filtek™ Z250 XT (Nano Hybrid Universal Restorative) and SDR bulk fill with different restoratives techniques. Materials and method: Eighty sound maxillary first premolar teeth were collected and divided into two main groups, enamel group and cementum group (40 teeth) for each group. The enamel group was prepared with standardized Class II MOD cavity with gingival margin (1 m
... Show MoreIraqi EFL teachers face problems in teaching “English for Iraq Series” for primary public school pupils. In this paper, the researchers are going to identify the main problems faced by our teachers and try to find solutions to these problems. To achieve the aim of the study, list of questions asked and from teachers’ responses, the researchers have got an idea about the main problems which are related to textbook material, parents, learners, environment and technology. Therefore, the researchers adapted a questionnaire to achieve the purpose of the study with some changes and modifications. This questionnaire with five point scale (strongly agree, agree, undecided, disagree, strongly disagree). To achieve face validity, the
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