Text: many studies have shown the elderly people with high cholesterol levels live longer than elderly people with low cholesterol levels.

Correct capitalization: Many studies have shown the elderly people with high cholesterol levels live longer than elderly people with low cholesterol levels.

Text: they believed there was only only one particular equation for water waves and its solution was a sinusoidal function extending to infinity in both directions.

Correct capitalization: They believed there was only only one particular equation for water waves and its solution was a sinusoidal function extending to infinity in both directions.

Text: av installations for edutainment centers and museums - teletech

Correct capitalization: AV installations for edutainment centers and museums - Teletech

Text: cozy apartment with 10 m2 private terrace and 2 bedrooms

Correct capitalization:
Cozy apartment with 10 m2 private terrace and 2 bedrooms