The method of operational matrices based on different types of polynomials such as Bernstein, shifted Legendre and Bernoulli polynomials will be presented and implemented to solve the nonlinear Blasius equations approximately. The nonlinear differential equation will be converted into a system of nonlinear algebraic equations that can be solved using Mathematica®12. The efficiency of these methods has been studied by calculating the maximum error remainder ( ), and it was found that their efficiency increases as the polynomial degree (n) increases, since the errors decrease. Moreover, the approximate solutions obtained by the proposed methods are compared with the solution of the 4th order Runge-Kutta method (RK4), which gives very

 تهدف هذه الدراسة إلى بحث ظاهرة الاغتراب في رواية " ديك الفداء " لايلي عامير ، لأن هذه الظاهرة تبدو أكثر وضوحا في هذه الرواية ، وتمثل تیارا مسيطرة على معطياتها واتجاهاتها الفكرية والفنية، خاصة أن الكاتب استطاع أن يجسد هذه الظاهرة المحورية تجسيدا فنيا متميزا ، وكشف عن طبيعة العلاقة بين عالم الواقع وعالم الحلم لدى الشخصيات، وعما تتسم به من تناقض و تعارض وتصادم و شعور بالإحباط والضياع والاغتراب. وقد اشتملت ال

Background: Colonization of soft denture liners by Candida albicans and other microorganisms continued to be a serious problem. The aim of this study was to evaluate the effect of incorporating silver nanoparticles into heat cured acrylic-based soft denture liner on the antifungal activity, and on water sorption, solubility, shear bond strength and color change of the soft lining material. Furthermore, evaluating the amount of silver released. Materials and methods: Silver nanoparticles were incorporated into soft denture liner in different percentages (0.05%, 0.1% and 0.2% by weight). Four hundred and twenty specimens were prepared and divided into five groups according to the test to be performed. The antifungal activity of the soft liner

The objective of the research is to identify the level of supervisory performance of the educational supervisor from the point of view of headmasters at secondary schools. The problem was the need to evaluate performance. A sample of (97) school headmasters was chosen to collect the needed data, they proportionated (38%) of the total community. the researcher designed a questionnaire consisted of (43) paragraphs with five areas. The results showed that there is a good level of performance among supervisors; there are no significant differences in the variable of the certificate, while there were significant differences in terms of gender for the benefit of males. The research concluded with a number of recommendations and suggestions.

Money matters exert a considerable influence on man’s life-style, social
rank and his relationship with other people. This paper aims at exploring the impact
of money matters on the characters’ inner feelings, social status, and personal
relationships in Muriel Spark’s modern novel The Ballad Of Peckham Rye. This
paper aspires to show that Spark’s subtle portrayal of characters reveals the
dominance of money matters over human and social relationships.
Muriel Spark ( 1918-2006) is a modern Scottish novelist whose wit and
detached sense of humour has brought her prolific body of both popular and critical
acclaim. Spark is interested not in building suspense but in exploring the moral
significance of the

During the 1970s, communicative view of language teaching began to be incorporated into syllabus design. The central question for the proponents of this view was: what does the learner want/need to do with the target language? This lead to the emergence of a teaching method (or approach) called communicative language teaching (CLT) during the late 1970s and early 1980s focusing on the functions that must be incorporated into a classroom. According to Brown (2001:43) CLT is a unified but broadly based, theoretically well informed set of tenets about the nature of language and of language learning and teaching. Harmer (2001:84) states that the communicative approach is the name which was given to a set of beliefs which included not only a

The Iraqi pharmaceutical sector faces significant challenges arising from the prevalence of substandard and falsified (S/F) medications, which pose a direct threat to public health safety. To strengthen regulatory oversight, health authorities have implemented national medicine track-and-trace system. However, the ultimate efficacy of these regulatory tools is heavily dependent on public awareness and the level of societal acceptance.

Tin oxide: titanium oxide: bismuth oxide (SnO2 )1–x(TiO 2 :Bi 2O3 ) x composites with different loading ratios (0, 0.1, 0.15, 0.2, 0.25 and 0.3) have numerous new application in microelectronics, sensors, and capacitors. This work concerned with the synthesis of (SnO 2 )1–x(TiO 2 :Bi 2O3 ) xcomposites as well as, thin films which were deposited on glass substrates as well as, silicon wafers by using pulsed laser deposition. The diffraction pattern confirms the anatase teteragonal phase of undoped tin oxide. It was observed some peaks related with titanium and bismuth oxides appeared at high loading ratios. Upon the transmission-spectra analysis, the undoped samples declared transmittance 60–67% in a visible spectrum, and the energy ga