• Some approximations for the null distribution of the test statistic for testing the homogeneity of normal means against simple order alternative when the common variance of the population is unknown have been developed.

• Comparing four test statistics, namely isotonic test based on arcsin transformation, isotonic test, likelihood ratio test and contrast test, which test the equality of binomial probabilities against ordered alternatives with respect to size and power by extensive simulations.

• Proposing some statistical test procedures that could be recommended as alternatives to the Likelihood Ratio test for testing the homogeneity of normal mean vectors against multivariate isotonic alternatives and investigating them through simulation.

• Investigating solutions of the two-body problem for inverse square potential classically and quantum mechanically

• Studying extensively a practically very successful quantum mechanical three-body model whose theoretical foundation was questionable.

• Studying axially symmetric solutions of Einstein and Einstein-Maxwell equations.

• Investigating rotating metrics representing dust and charged dust.

• Examining metrics representing certain kinds of charged matter and deflection of light and the precession of the orbit of test particles.

• Designed simple and short analytical proof of Fermat's last theorem for all exponents.

Fortran Programme for the calculation of Multivariate Isotonic Regression

Subroutine to Calculate Multivariate Isotonic Regression