{Java$\Omega$: Higher Order Programming in Java -- The Technical Complements

The paper contains the technical complements of the paper, of the same authors, published in the book "Java in Academia and Research", iConcept Press Ltd, 2011, that describes the extensions of Java 1.5 with Higher Order (H.O. for short) mechanisms. The present complements contain the complete tables of (i) The translation semantics of a form of closure for Java; (ii) The translation semantics of H.O. methods with mc\_parameters as arguments; (iii) The translation semantics of Java extended with the above mechanisms put together; (iv) Theorems, lemmas and proofs of all the properties of the mechanisms and of the semantics discussed in the paper.