Text: many employers have been able to compensate for the shorter working time by means of increased tempo and flexibility while the effect on unemployment has been hard to see.

Correct capitalization: Many employers have been able to compensate for the shorter working time by means of increased tempo and flexibility while the effect on unemployment has been hard to see.

Text: to express an opinion about this book almost feels like a presumption.

Correct capitalization: To express an opinion about this book almost feels like a presumption.

Text: example 1: key-gym in a minor danish town

Correct capitalization: Example 1: Key-gym in a minor Danish town

Text: when tiny particles float in the air

Correct capitalization:
When tiny particles float in the air