In this paper, we discuss the difference between classical and nonclassical symmetries. In addition, we found the non-classical symmetry of the Benjamin Bona Mahony Equation (BBM). Finally, we found a new exact solution to a Benjamin Bona Mahony Equation (BBM) using nonclassical symmetry.

Abstract

The research aims to examine the effect of Hawkins' strategy on students in the fourth grade of primary school in the General Directorate of Education in Baghdad / Karkh 3 for the academic year (2020-2021). The research was limited to the topics of the Arabic language grammar book for the fourth grade of primary school. The researcher developed the research hypothesis, which is: that there is no statistically significant difference at the significance level (0.05) between the average scores of the experimental group students who study using the Hawkins strategy and the average scores of the control group students who study in the traditional method in the achievement test. The researcher set a number of

The researcher attempts to examine Barman model in acquiring the historical concepts among fourth-grade students at literary classrooms. To this end, the researcher held the null hypothesis, there is no significant difference between the experimental groups who was taught based on Barman model and the control group that taught based on the traditional method in acquiring the historical concepts on the post-test. To testify the effectiveness of Barman model, the researcher administered a questionnaire included (60) items on bunch of female-students who were selected from al-khamaeal preparatory school in al-hurriyah district in Baghdad. The author utilized different statistical tools to analyze the collected data.    &

    In this article, we introduce and study two new families of analytic functions by using strong differential subordinations and superordinations associated with Wanas differential operator/. We also give and establish some important properties of these families.

This study is dedicated to investigate the effects of initial laser intensity on the nonlinear optical properties of the laser dye DQOCI dissolved in methanol with a concentration of 10 ^-5 M and doped with PMMA film. The properties were studied by using open and closed aperture Z-scan technique, with different levels of initial intensity (I₀), excited by continuous diode solid-state laser at a wavelength of 532 nm. Three lenses of different focal lengths were employed to change the radius of the Gaussian laser beam and then change the initial intensity. For I₀= 6.83 and 27.304 kWatt/cm², the Z-scan curves show a saturation of absorption (SA) known as the negative type of nonlinearity, in which

This is a survey study that presents recent researches concerning factional controllers. It presents several types of fractional order controllers, which are extensions to their integer order counterparts. The fractional order PID controller has a dominant importance, so thirty-one paper are presented for this controller. The remaining types of controllers are presented according to the number of papers that handle them; they are fractional order sliding mode controller (nine papers), fuzzy fractional order sliding mode controller (five papers), fractional order lag-lead compensator (three papers), fractional order state feedback controller (three papers), fractional order fuzzy logic controller (three papers). Finally, several conclusions

Recently, the financial mathematics has been emerged to interpret and predict the underlying mechanism that generates an incident of concern. A system of differential equations can reveal a dynamical development of financial mechanism across time. Multivariate wiener process represents the stochastic term in a system of stochastic differential equations (SDE). The standard wiener process follows a Markov chain, and hence it is a martingale (kind of Markov chain), which is a good integrator. Though, the fractional Wiener process does not follow a Markov chain, hence it is not a good integrator. This problem will produce an Arbitrage (non-equilibrium in the market) in the predicted series. It is undesired property that leads to erroneous conc

Abstract

The current research aims to identify the impact of triangular bridging strategy in the acquisition of sociology of fourth-stage students. To achieve the research objective, the following null hypotheses were adopted: there are no statistically significant differences at a significance level (0, 05) between the average grades of the experimental group students who studied the triangular bridging strategy in acquiring concepts of sociology and average grades of the control group. The researcher has selected the fourth-stage students from Alexandronah School for girls that s related to the Directorate General of Baghdad the sample consisted of (87) students at litera