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The (F/G)-expansion method is firstly proposed, where F=F(ξ) and G = G(ξ) satisfies a first order ordinary differential equation systems (ODEs). We give the exact travelling wave solutions of the variant Boussinesq equations and the KdV equation and by using (F/G)-expansion method. When some parameters of present method are taken as special values, results of the -expansion method are also derived. Hence, -expansion method is sub method of the proposed method. The travelling wave solutions are expressed by three types of functions, which are called the trigonometric functions, the rational functions, and the hyperbolic functions. The present method is direct, short, elementary and effective, and is used for many other nonlinear evolution equations.
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Raeed Salim Ahmed Al-Nuamman (2016). Mathematical & Spatial Relationship between Dome and Al- Mousala in Congregational Mosques (An Analytical Study of Basic Dimension of Central Dome Pattern). International Journal of Mathematical Research, 5(1): 1-24. DOI: 10.18488/journal.24/2016.5.1/18.104.22.168
Islamic architecture has a clear impact for systems and the relationships of Mathematical and Geometrical proportions , which reflected in their buildings. The research will deal with an important aspect that linked in two mains elements in the Congregational Mosques. The first is a house of prayer (Al-mousala) as the main and most importantly space in the mosque, and the second is a dome as structural and decorative element, who was significantly associated with Congregational Mosques later. This study is one of very few studies which have investigated the kind of the Mathematical& Geometrical proportions relationship, also the spatial linking of these two elements with each other's. Through the statistical analysis that links the relationship between their different dimensions and the positioning kind of the main dome on a house of prayer (Al-mousala). For this purpose the resaerch has been selected two sets of samples. The first models include a different regions of Islamic Congregational Mosques represent different patterns of Congregational Mosques as a sample of general Islamic architecture while the second comprises a number of Congregational Mosques in Mosul city, a representative of the local architecture.