his 1948 papers are on somewhat different topics, being on topological spaces and linkages.

How would the previous sentence be correctly capitalized?
Answer: His 1948 papers are on somewhat different topics, being on topological spaces and linkages.
the background and subject of the oil painting work is mainly black in large, but artist chen yifei applied with the contrast of light and colors smartly, challenge the peak of techniques of realistic painting. he uses classical and ultra-realism combined techniques, and integrated delicate and nuanced eastern exoticism, thus to perform the elegant moods of the female flute player naturally and vividly.

How would the previous sentence be correctly capitalized?
Answer: The background and subject of the oil painting work is mainly black in large, but artist Chen Yifei applied with the contrast of light and colors smartly, challenge the peak of techniques of realistic painting. he uses classical and ultra-realism combined techniques, and integrated delicate and nuanced eastern exoticism, thus to perform the elegant moods of the female flute player naturally and vividly.
homoeopathic remedies should not be taken together with food and drinks or directly before or after teeth brushing.

How would the previous sentence be correctly capitalized?
Answer: Homoeopathic remedies should not be taken together with food and drinks or directly before or after teeth brushing.
now subtract the original number from 100x.

How would the previous sentence be correctly capitalized?
Answer: Now subtract the original number from 100x.