Please capitalize where necessary: the aim of the resumed excavation, planned for the early spring of 2011, is to expose parts of the old excavation areas and re-find some of the recorded archaeological features.
A: The aim of the resumed excavation, planned for the early spring of 2011, is to expose parts of the old excavation areas and re-find some of the recorded archaeological features.

Q: fertilising conifers/deciduous trees - may, spring, trees and hedges, tree and shrub care, fertilising

A: Fertilising conifers/deciduous trees - May, Spring, Trees And Hedges, Tree And Shrub Care, Fertilising

Q: composed of a 3u rack-mountable unit and a dedicated wooden head-cabinet
A: Composed of a 3U rack-mountable unit and a dedicated wooden head-cabinet

Problem: a minute is 60 seconds.
Can you repeat this sentence, but capitalize it?
Answer: A minute is 60 seconds.

Text: he held the two posts, one at the moscow state teachers training institute and the other at the steklov institute, until he retired in 1972 and 1973 respectively.

Correct capitalization: He held the two posts, one at the Moscow State Teachers Training Institute and the other at the Steklov Institute, until he retired in 1972 and 1973 respectively.

Please capitalize where necessary: 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.
A:
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.