in the present study, a spectral finite element method is developed for free and forced transverse vibration of levy-type moderately thick rectangular orthotropic plates based on first-order shear deformation theory. levy solution assumption was used to convert the two-dimensional problem into a one-dimensional problem. in the first step, the governing out-of-plane differential equations are tr...

— In this note, we examine a particular quadratic program which arises in a variety of financial allocation problems and dérive a closed form solution for its first order Lagrangian conditions. Our technique bypasses the standard matrix inversion, thus reducing computational effort. As a conséquence, larger size portfolios can now be anaiyzed.