the costs of these initiatives have been estimated:

How would the previous sentence be correctly capitalized?
Answer: The costs of these initiatives have been estimated:
the relationship between the average particle size and the green density as well as the compressive strength of compacts is shown in fig. 5.31 for a const ant pressure.

How would the previous sentence be correctly capitalized?
Answer: The relationship between the average particle size and the green density as well as the compressive strength of compacts is shown in Fig. 5.31 for a const ant pressure.
some may call it "the new world order". others may call it schizophrenic paranoia".

How would the previous sentence be correctly capitalized?
Answer: Some may call it "The New World Order". Others may call it schizophrenic paranoia".
a heart symbolizes passion.

How would the previous sentence be correctly capitalized?
Answer: A heart symbolizes passion.