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Research Trends in Theoretical and Applied Sciences is a book based on the study of nonlinear structure in multicomponent plasma using various particle distributions, on the research of the analytical method to solve diffraction and radiation problem due wave interaction with a obstacle in water, as well as on studies on fractional quantum Hall effect without quasi-particle. Thus, chapter one chapter discusses how the plasma systems have been progressively developed with the inclusion of different particle distributions. Chapter two focuses on using the appropriate matching conditions along the virtual and physical boundaries between the regions, to obtain and then solve a system of linear equations for the unknown coefficients. Chapter three considers an alternate approach without any quasi-particle and interpret FQHE as a result of underlying physics involving strong Coulomb interactions and correlations among the normal electrons confined in an ultra thin layer. Further, a comparative analysis of the results is performed with the available experimental data as well as predictions by other strong analysis.