Please capitalize where necessary: a hectic period began.
A: A hectic period began.
Q: 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.
Q: these photographs should be different from those that were submitted for other awards.
A: These photographs should be different from those that were submitted for other awards.
Problem: projects that are affiliated with and receive support from spi are:
Can you repeat this sentence, but capitalize it?
Answer: Projects that are affiliated with and receive support from SPI are:
Text: before buying a vacuum cleaner hansa hvc-620c specify all your options, equipment, appearance and warranty from the seller. please note that we are not engaged in the sale and manufacture warranty.

Correct capitalization: Before buying a vacuum cleaner Hansa HVC-620C specify all your options, equipment, appearance and warranty from the seller. Please note that we are not engaged in the sale and manufacture warranty.
Q: you may have the chance to lead or influence others, so use that influence to help everyone concerned to grow with you.
A:
You may have the chance to lead or influence others, so use that influence to help everyone concerned to grow with you.