the drawing of frequency-path (f-p) models of optical beams is an approach for nonlinearity analysis in nano-metrology systems and sensors based on the laser interferometers. in this paper, the frequency-path models of four nano-metrology laser interferometry systems are designed, analyzed and simulated, including conventional and modified two- and three-longitudinal-mode laser interferometers....

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...

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...

Chromium-vanadium (Cr-V) bimetallic catalysts are prepared by the introduction of vanadium into the Phillips catalyst which is one of the most significant industrial ethylene polymerization catalysts for tuning the Phillips catalyst performances and improving polyethylene properties. In the present work, titanium species were introduced into the fluorine-modified chromium-vanadium bimetallic ca...