The research aims to find approximate solutions for two dimensions Fredholm linear integral equation. Using the two-variables of the Bernstein polynomials we find a solution to the approximate linear integral equation of the type two dimensions. Two examples have been discussed in detail.

A new method based on the Touchard polynomials (TPs) was presented for the numerical solution of the linear Fredholm integro-differential equation (FIDE) of the first order and second kind with condition. The derivative and integration of the (TPs) were simply obtained. The convergence analysis of the presented method was given and the applicability was proved by some numerical examples. The results obtained in this method are compared with other known results.

one of the most important consequences of climate change is the rise in sea levels, which leads to the drowning of some low-lying island states, which leads to them losing the elements of statehood and thus affecting their status as a state, this resulted in several proposals made by the jurisprudence of international law to solve this issue, perhaps the most important of which is the idea of the government in exile, and the proposal to continue recognition of submerged countries, in a way that makes it possible to talk about a new concept of states represented by deterritorialized states, all of which are ultimately proposals that contain great difficulties that hinder their implementation in reality.

The article aims to study the crisis of political change  from three Phases . The first focuses on the crises of political legitimacy and democratic postponement, as fundamental issues in analyzing the phenomenon of power struggle through the dialectic between the concept of historical legitimacy and institutional fragility from the beginning of statehood in 1962 to the stage of multi-partyism and the cessation of the electoral process in the 1990s. While the second focuses on the question of the monopoly of power in the post-terrorism and national reconciliation according to considerations  Political, social and security measures to prolong the life of the regime and avoid the demands of political change brought about

The Aim of this paper is to investigate numerically the simulation of ice melting in one and two dimension using the cell-centered finite volume method. The mathematical model is based on the heat conduction equation associated with a fixed grid, latent heat source approach. The fully implicit time scheme is selected to represent the time discretization. The ice conductivity is chosen
to be the value of the approximated conductivity at the interface between adjacent ice and water control volumes. The predicted temperature distribution, percentage melt fraction, interface location and its velocity is compared with those obtained from the exact analytical solution. A good agreement is obtained when comparing the numerical results of one

Urban land uses of all kinds are the constituent elements of the urban spatial structure. Because of the influence of economic and social factors, cities in general are characterized by the dynamic state of their elements over time. Urban functions occur in a certain way with different spatial patterns. Hence, urban planners and the relevant urban management teams should understand the future spatial pattern of these changes by resorting to quantitative models in spatial planning. This is to ensure that future predictions are made with a high level of accuracy so that appropriate strategies can be used to address the problems arising from such changes. The Markov chain method is one of the quantitative models used in spatial planning to ana

This paper study two stratified quantile regression models of the marginal and the conditional varieties. We estimate the quantile functions of these models by using two nonparametric methods of smoothing spline (B-spline) and kernel regression (Nadaraya-Watson). The estimates can be obtained by solve nonparametric quantile regression problem which means minimizing the quantile regression objective functions and using the approach of varying coefficient models. The main goal is discussing the comparison between the estimators of the two nonparametric methods and adopting the best one between them

Direct contact membrane distillation is an effective method for production of fresh water from saline water. In this study two samples were used as feed solutions; the first one was RO waste from Al-Hilla Coca-Cola Factory (TDS= 2382 mg/l) and the other was Haji Ali drainage water (TDS= 4127 mg/l). Polytetrafluoroethylene (PTFE) hydrophobic membrane supported with polypropylene (PP) was used as flat sheet form with plate and frame cell. Results proved that membrane distillation is an effective technique to produce fresh water with high quality from brine with low salinity content. With membrane area of 8x8 cm², the volume of treated water decreased from 34.97 ml at first half hour to 33.02 ml after 180 min of

This paper describes a practical study on the impact of learning's partners, Bluetooth Broadcasting system, interactive board, Real – time response system, notepad, free internet access, computer based examination, and interaction classroom, etc, had on undergraduate student performance, achievement and involving with lectures. The goal of this study is to test the hypothesis that the use of such learning techniques, tools, and strategies to improve student learning especially among the poorest performing students. Also, it gives some kind of practical comparison between the traditional way and interactive way of learning in terms of lectures time, number of tests, types of tests, student's scores, and student's involving with lectures