for girls it's an interesting possibility, and real entertainment in the world of computer games.

How would the previous sentence be correctly capitalized?
Answer: For girls it's an interesting possibility, and real entertainment in the world of computer games.
46 bce: cleopatra gives birth to caesar's child, a boy who is named ptolemy caesar and called caesarion.

How would the previous sentence be correctly capitalized?
Answer: 46 BCE: Cleopatra gives birth to Caesar's child, a boy who is named Ptolemy Caesar and called Caesarion.
we have to analyze this matter carefully because it has a tremendous significance not only from the historical, but especially from the political, educational and practical points of view.

How would the previous sentence be correctly capitalized?
Answer: We have to analyze this matter carefully because it has a tremendous significance not only from the historical, but especially from the political, educational and practical points of view.
mesons are required to have quarks of two different colors.

How would the previous sentence be correctly capitalized?
Answer: Mesons are required to have quarks of two different colors.