Text: uhlenbeck is a leading expert on partial differential equations and describes her mathematical interests as follows:

Correct capitalization: Uhlenbeck is a leading expert on partial differential equations and describes her mathematical interests as follows:

Text: deep sea fishing is also arranged.

Correct capitalization: Deep sea fishing is also arranged.

Text: in parallel with our traditional production, we run a number of trials in an attempt to identify the best dyeing method and the correct materials.

Correct capitalization: In parallel with our traditional production, we run a number of trials in an attempt to identify the best dyeing method and the correct materials.

Text: how should i take this medicine?

Correct capitalization:
How should I take this medicine?