Text: all of the settlements are believed to have been the homes of single families or small groups during the summer period.

Correct capitalization: All of the settlements are believed to have been the homes of single families or small groups during the summer period.

Text: "so why did lavrentev credit you with it?" ahlfors said "he probably thought i must know it and was too lazy to look it up in the literature".

Correct capitalization: "So why did Lavrentev credit you with it?" Ahlfors said "He probably thought I must know it and was too lazy to look it up in the literature".

Text: this report reports on the sinking of the hms curacoa.

Correct capitalization: This report reports on the sinking of the HMS Curacoa.

Text: enjoy the comfort of our comfortable rooms and the pleasant ambience of the hotel's various facilities.

Correct capitalization:
Enjoy the comfort of our comfortable rooms and the pleasant ambience of the hotel's various facilities.