In a series of two articles, we propose comprehensive mathematical framework for Coupled-Cluster-type methods. These methods aim at accurately solving the many-body Schrodinger equation. this first part, rigorously describe discretization schemes involved in Coupled-Cluster using graph-based concepts. This allows us to discuss different unified and more transparent manner, including multirefere...

This paper introduces a methodology for considering the uncertainties in stability analysis of gravity dams. For this purpose, a conceptual model based on the fuzzy set theory and Genetic Algorithm (GA) optimization is developed to be coupled to a gravity dam analysis model. The uncertainties are represented by the fuzzy numbers and the GA is used to estimate in what...

A coupled-line circuit structure is proposed in this paper to design a modified Schiffman phase shifter with short reference line. Based on the traditional transmission line theory and ABCD parameters, closed-form mathematical equations for electrical and scattering parameters are obtained. Obviously, this proposed coupled-line phase shifter has several advantages such as arbitrary phase differ...

A modified F-expansion method to find the exact traveling wave solutions of  two-component nonlinear partial differential equations (NLPDEs) is discussed. We use this method to construct many new solutions to the nonlinear Whitham-Broer-Kaup system (1+1)-dimensional. The solutions obtained include Jacobi elliptic periodic wave solutions which exactly degenerate to the soliton solutions, triangu...