The Wang-Ball polynomials operational matrices of the derivatives are used in this study to solve singular perturbed second-order differential equations (SPSODEs) with boundary conditions. Using the matrix of Wang-Ball polynomials, the main singular perturbation problem is converted into linear algebraic equation systems. The coefficients of the required approximate solution are obtained from the solution of this system. The residual correction approach was also used to improve an error, and the results were compared to other reported numerical methods. Several examples are used to illustrate both the reliability and usefulness of the Wang-Ball operational matrices. The Wang Ball approach has the ability to improve the outcomes by minimizing the degree of error between approximate and exact solutions. The Wang-Ball series has shown its usefulness in solving any real-life scenario model as first- or second-order differential equations (DEs).
Reducing the drag force has become one of the most important concerns in the automotive industry. This study concentrated on reducing drag through use of some external modifications of passive flow control, such as vortex generators, rear under body diffuser slices and a rear wing spoiler. The study was performed at inlet velocity (V=10,20,30,40 m/s) which correspond to an incompressible car model length Reynolds numbers (Re=2.62×105, 5.23×105, 7.85×105 and 10.46×105), respectively and we studied their effect on the drag force. We also present a theoretical study finite volume method (FVM) of solvi
This study aimed at identity baying the difficulties which face public basic school
principals in jar ash governorate in editing formal letters and correspondence and means of
debating with these problems to collect data the researchers developed a question air were
established the population of the study which represents its sample consisted of 129 principals
65 males and 64 females
The results of the study revealed that the principals face difficulties in office and file
management in preparing plans and reports and writing formal letters and answering them
saved recommendations were presented among which were organizing training sessions and
workshops to train the principals on how to dead with there problems.<
Research Summary
First: the problem of research and its importance
The teacher's success in facilitating the students' learning and growth according to the educational and educational goals set out, he must identify the problems of discipline of students in the classroom in terms of sources and reasons and types and methods of prevention and treatment and the teacher to remember that success in his teaching and instruction is not completed more fully once he has the information And knowledge of the subject of the lesson, but must understand the dynamics of the group (class group) and master the skills of classroom management, su
... Show MoreIn this investigation, Rayleigh–Ritz method is used to calculate the natural frequencies of rectangular isotropic and laminated symmetric and anti-symmetric cross and angle ply composite plate with general elastic supports along its edges. Each of the admissible functions here is composed of a trigonometric function and an arbitrary continuous function that is introduced to ensure the sufficient smoothness of the so-called residual displacement function at the edges. Perhaps more importantly, this study has developed a general approach for deriving a complete set of admissible functions that can be applied to various boundary conditions. Several numerical examples are studied to demonstrate the accuracy and convergence of the current s
... Show MoreIn this study, the modified Rayleigh-Ritz method and Fourier series are used to determine the thermal buckling behavior of laminated composite thin plates with a general elastic boundary condition applied to in-plane uniform temperature distribution depending upon classical laminated plate theory(CLPT). A generalized procedure solution is developed for the Rayleigh-Ritz method combined with the synthetic spring technique. The transverse displacement of the orthotropic rectangular plates is not a different term as a new shape expansion of trigonometric series. In this solution approach, the plate transverse deflection and rotation due to bending are developed into principle Fourier series with a sufficient smoothness auxi
... Show Moreان الغرض من هذا البحث هو المزج بين القيود الضبابية والاحتمالية. كما يهدف الى مناقشة اكثر حالات مشكلات البرمجة الضبابية شيوعا وهي عندما تكون المشكلة الضبابية تتبع دالة الانتماء مرة دالة الاتنماء المثلثية مرة اخرى، من خلال التطبيق العملي والتجريبي. فضلا عن توظيف البرمجة الخطية الضبابية في معالجة مشكلات تخطيط وجدولة الإنتاج لشركة العراق لصناعة الأثاث، وكذلك تم استخدام الطرائق الكمية للتنبؤ بالطلب واعتماده
... Show MoreThis paper is dealing with an experimental study to show the influence of the geometric characteristics of the vortex generators VG son the thickness of the boundary layer (∂) and drag coefficients (CD) of the flat plate. Vortex generators work effectively on medium and high angles of attack, since they are "hidden" under the boundary layer and practically ineffective at low angles.
The height of VGs relative to the thickness of the boundary layer enables us to study the efficacy of VGs in delaying boundary layer separation. The distance between two VGs also has an effect on the boundary layer if we take into
... Show MoreSteady natural convection in a square enclosure with wall length (L= 20 cm) partially filled by saturated porous medium with same fluid (lower layer) and air (upper layer) is investigated. The conceptual study of the achievements of the heat transfer is performed under effects of bottom heating by constant heat flux (q=150,300,450,600W/m2 ) for three heaters size (0.2,0.14,0.07)m with symmetrically cooling with constant temperature on two vertical walls and adiabatic top wall. The relevant filled studied parameters are four different porous medium heights (Hp=0.25L,0.5L, 0.75L, L), Darcey number (Da1) 3.025×10-8 and (Da2) 8.852×10-4 ) and Rayleigh number range (60.354 - 241.41), (1.304×106 – 5.2166×106 ) for Da1 and Da2 cases respecti
... Show MoreThe contractual imbalance is perceived today by the majority of the doctrine as being one of the pitfalls to the execution of the contracts. As a result, most legislations grant judges the power to intervene to restore it. Granting the judge the power to complete the contract raises the question of the extent to which the judge can obtain such power. Is it an absolute authority that is not limited? If so, is it a broad discretion in which the judge operates in his conscience, or is it a power of limited scope by specific legal texts and conventions? This is what we will try to answer in this research.