it will be appreciated that the developer of this theme has realized that the future was also shopping sociel also integrating buddypress.

How would the previous sentence be correctly capitalized?
Answer: It will be appreciated that the developer of this theme has realized that the future was also shopping Sociel also integrating BuddyPress.
as the energy of the quantum harmonic oscillator increases fluctuations in probability density become more dense and hence no matter how short the interval over which they are averaged there will be some energy level at which the average is equal to the classical time-spent probability density function.

How would the previous sentence be correctly capitalized?
Answer: As the energy of the quantum harmonic oscillator increases fluctuations in probability density become more dense and hence no matter how short the interval over which they are averaged there will be some energy level at which the average is equal to the classical time-spent probability density function.
first work the squares they are gradually worked tog.

How would the previous sentence be correctly capitalized?
Answer: First work the squares they are gradually worked tog.
he is a big, beautiful bronze statue made by his owner, the sculpturer, joop hekman, who from the window in his studio has been able to enjoy his lovely dog after he had to say the last farewell.

How would the previous sentence be correctly capitalized?
Answer: He is a big, beautiful bronze statue made by his owner, the sculpturer, Joop Hekman, who from the window in his studio has been able to enjoy his lovely dog after he had to say the last farewell.