Of is an emphatically defining word when it follows and restricts a relational singular noun. With singular relational nouns (N1), abstract or concrete, the N1 of N2 is a standard construction, N2 being definite or indefinite, countable or uncountable. When N1 is plural, you can test for the need of your fronting the and replace it with an unstressed "some." If unstressed "some" works tolerably well for you, you can dispose of the (and "some," if no some was originally intended.)
Back to singulars.
(i)…whenever the appointment of a new judge is due…
(ii)… a restaurant is located at the corner of a busy intersection…
No particular appointment is meant in (i), and no particular corner is meant in (ii).
In a similar vein, "the use of available resources," "the integration of parts," and "the implementation of group work" neither entail nor imply particular instances of use, integration, or implementation.
In all of the examples above, N2s are indefinite. There could be many judge appointments, street intersections usually have more than two corners, resources and parts can be numerous and grouped in many ways; group work is also indefinite. Why the definite article then?
Just think: the post nominal of-phrase must provide some specification of the concept denoted by N1. Since reference to an individual instance is not available, only kind reference is left. That sort of definiteness is know as weak: the condition of presupposed existence still holds, but token uniqueness is not satisfied and no (anaphoric) familiarity is required.
But… It so happens that the definie
the is often omitted in structures like yours. The problem is that for some people "history of science" means the same as "the history of science," "performance of a/the play" means the same as "the performance of a/the play," and "production at a/the factory" means the same as "the production at a/the factory." Those speakers apparently think it more convincing to strike out the marking
the, because either they have lost their sense of definiteness or their desire to sound abstractly scientific overwhelms them. Or they have lost their sense of definiteness.
I have to go now.