no pictures or diagrams were allowed, and, much as i wanted to write "n n " to describe the dimensions of a matrix in my thesis, it had to be "n-by-n".

How would the previous sentence be correctly capitalized?
Answer: No pictures or diagrams were allowed, and, much as I wanted to write "n n " to describe the dimensions of a matrix in my thesis, it had to be "n-by-n".
the environmental quality of a product also depends on the quality of the parts and components purchased from other manufacturers.

How would the previous sentence be correctly capitalized?
Answer: The environmental quality of a product also depends on the quality of the parts and components purchased from other manufacturers.
the roman catholic idea that mary was not of ordinary human nature means that christ could not have been both "son of man" and "son of god".

How would the previous sentence be correctly capitalized?
Answer: The Roman Catholic idea that Mary was not of ordinary human nature means that Christ could not have been both "son of man" and "son of God".
such personal information will be used only to fulfill your request for registration on this site and capatarea quality.

How would the previous sentence be correctly capitalized?
Answer: Such personal information will be used only to fulfill your request for registration on this site and capatarea quality.