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).
A new modified differential evolution algorithm DE-BEA, is proposed to improve the reliability of the standard DE/current-to-rand/1/bin by implementing a new mutation scheme inspired by the bacterial evolutionary algorithm (BEA). The crossover and the selection schemes of the DE method are also modified to fit the new DE-BEA mechanism. The new scheme diversifies the population by applying to all the individuals a segment based scheme that generates multiple copies (clones) from each individual one-by-one and applies the BEA segment-wise mechanism. These new steps are embedded in the DE/current-to-rand/bin scheme. The performance of the new algorithm has been compared with several DE variants over eighteen benchmark functions including sever
... Show MoreHomomorphic encryption became popular and powerful cryptographic primitive for various cloud computing applications. In the recent decades several developments has been made. Few schemes based on coding theory have been proposed but none of them support unlimited operations with security. We propose a modified Reed-Muller Code based symmetric key fully homomorphic encryption to improve its security by using message expansion technique. Message expansion with prepended random fixed length string provides one-to-many mapping between message and codeword, thus one-to many mapping between plaintext and ciphertext. The proposed scheme supports both (MOD 2) additive and multiplication operations unlimitedly. We make an effort to prove
... Show Moreزاد الاهتمام بالأطفال ذوي اضطراب الانتباه المصحوب بالنشاط الزائد نظراً لانتشاره بين الأطفال في عمر المرحلة الابتدائية حيث تراوحت نسبته ما بين 3% إلى 20% ومعظمهم من الذكور ، وأن انتشاره يقع في مختلف الطبقات الاجتماعية بالنسبة لعوائل هؤلاء الأطفال كما أن المشكلات المتعلقة به لا تنتهي بانتهاء مرحلة الطفولة ، وغالباً ما تمتد إلى مرحلة المراهقة حيث توصل ويز و هتكمانWeiss&Hechtman,1989 إلى أن هناك علامات م
... Show MoreThe rotor dynamics generally deals with vibration of rotating structures. For designing rotors of a high speeds, basically its important to take into account the rotor dynamics characteristics. The modeling features for rotor and bearings support flexibility are described in this paper, by taking these characteristics of rotor dynamics features into standard Finite Element Approach (FEA) model. Transient and harmonic analysis procedures have been found by ANSYS, the idea has been presented to deal with critical speed calculation. This papers shows how elements BEAM188 and COMBI214 are used to represent the shaft and bearings, the dynamic stiffness and damping coefficients of journal bearings as a matrices have been found
... Show MoreThis study aims to identify the teaching problems that teachers of students with intellectual disabilities face, in addition to exploring the solutions suggested by them in order to overcome such problems or challenges. The researchers used a qualitative approach in order to understand the teachers' perceptions about these problems in a more in-depth way. The interview tools (in-depth and semi-structured interviews) were used to collect data from (3) female teachers from special education programs in the Asir region. The results revealed a number of themes including problems related to students, teachers and the teaching methods they use, curricula, school environment, and school administration. Moreover, the results indicated that famil
... Show MoreThe aim of this study is to identify the effectiveness of a rational, emotional, behavioral program in developing self-efficacy to reduce the level of Burnout in 20 teachers of students with autism disorder in Jazan, Saudi Arabia. The proposed program included 12 training sessions. The researcher found that the proposed program has contributed significantly to the development of self-efficacy and reduce the level of Burnout for the targeted subject in this study.