Proof that market equilibrium leads to maximum welfare of all participants in the trade

 Converting any reversible cycle operating between two points into a Carnot engine model and Finding efficiency in terms of operating temperatures of reversible paths

Derivation of lowering of boiling points ans increasing to melting points of dispersion medium in a colloidal solution

Eigenvalue interpretation of Hessian matrix and the determination of maxima minima or saddle points at gradient free points in domain by application of spectral theorem

A more generalized analysis of Spectral theorem in a general vector space and as a supplement to my article on Hessian Matrix Analysis