In this paper Volterra Runge-Kutta methods which include: method of order two and four will be applied to general nonlinear Volterra integral equations of the second kind. Moreover we study the convergent of the algorithms of Volterra Runge-Kutta methods. Finally, programs for each method are written in MATLAB language and a comparison between the two types has been made depending on the least square errors.

       Canonical correlation analysis is one of the common methods for analyzing data and know the relationship between two sets of variables under study, as it depends on the process of analyzing the variance matrix or the correlation matrix. Researchers resort to the use of many methods to estimate canonical correlation (CC); some are biased for outliers, and others are resistant to those values; in addition, there are standards that check the efficiency of estimation methods.

In our research, we dealt with robust estimation methods that depend on the correlation matrix in the analysis process to obtain a robust canonical correlation coefficient, which is the method of Biwe

Lattakia city faces many problems related to the mismanagement of solid waste, as the disposal process is limited to the random Al-Bassa landfill without treatment. Therefore, solid waste management poses a special challenge to decision-makers by choosing the appropriate tool that supports strategic decisions in choosing municipal solid waste treatment methods and evaluating their management systems. As the human is primarily responsible for the formation of waste, this study aims to measure the degree of environmental awareness in the Lattakia Governorate from the point of view of the research sample members and to discuss the effect of the studied variables (place of residence, educational level, gender, age, and professional status) o

Nonlinear differential equation stability is a very important feature of applied mathematics, as it has a wide variety of applications in both practical and physical life problems. The major object of the manuscript is to discuss and apply several techniques using modify the Krasovskii's method and the modify variable gradient method which are used to check the stability for some kinds of linear or nonlinear differential equations. Lyapunov function is constructed using the variable gradient method and Krasovskii’s method to estimate the stability of nonlinear systems. If the function of Lyapunov is positive, it implies that the nonlinear system is asymptotically stable. For the nonlinear systems, stability is still difficult even though

Employing phase-change materials (PCM) is considered a very efficient and cost-effective option for addressing the mismatch between the energy supply and the demand. The high storage density, little temperature degradation, and ease of material processing register the PCM as a key candidate for the thermal energy storage system. However, the sluggish response rates during their melting and solidification processes limit their applications and consequently require the inclusion of heat transfer enhancers. This research aims to investigate the potential enhancement of circular fins on intensifying the PCM thermal response in a vertical triple-tube casing. Fin arrays of non-uniform dimensions and distinct distribution patterns were des

The research aims to measure, assess and evaluate the efficiency of the directorates of Anbar Municipalities by using the Data Envelopment Analysis method (DEA). This is because the municipality sector is consider an important sector and has a direct contact with the citizen’s life. Provides essential services to citizens. The researcher used a case study method, and the sources of information collection based on data were monthly reports, the research population is represented by the Directorate of Anbar Municipalities, and the research sample consists of 7 municipalities which are different in terms of category and size of different types. The most important conclusion reached by the research i

Coagulation - flocculation are basic chemical engineering method in the treatment of metal-bearing industrial wastewater because it removes colloidal particles, some soluble compounds and very fine solid suspensions initially present in the wastewater by destabilization and formation of flocs. This research was conducted to study the feasibility of using natural coagulant such as okra and mallow and chemical coagulant such as alum for removing Cu and increase the removal efficiency and reduce the turbidity of treated water. Fourier transform Infrared (FTIR) was carried out for okra and mallow before and after coagulant to determine their type of functional groups. Carbonyl and hydroxyl functional groups on the surface of

The aim of this research is to find out the influence of Daniel's model on the skills of the twenty-first century among the students of the scientific-fifth grade at the secondary and preparatory government morning schools for the academic year 2022- 2023. Two groups were chosen out of five groups for the fifth-scientific grade, one of which represents the experimental group that is taught by the Daniel model, and the other is the control group that is taught in the traditional method. The equivalence of the two research groups was verified with a set of variables. As for the research tool, a scale was developed by the researchers for the skills of the twenty-first century, in which they adopted the framework of the Partnership Organizat

Pragmatics of translation is mainly concerned with how social contexts have their own influence on both the source text (ST) initiator's linguistic choices and the translator's interpretation of the meanings intended in the target text (TT). In translation, socio-pragmatic failure(SPF), as part of cross-cultural failure, generally refers to a translator's misuse or misunderstanding of the social conditions placed on language in use. In addition, this paper aims to illustrate the importance of SPF in cross-cultural translation via identifying that such kind of failure most likely leads to cross-cultural communication breakdown. Besides, this paper attempts to answer the question of whether translators from English into Arabic or vice versa h