Do you put periods after Asian characters in a sentence?

Quick answer from Wikipedia regarding Japanese kanji:

“The full stop (句点 kuten?) is a small circle, called the “Ideographic Full Stop” by the Unicode consortium. (A Unicode character name does not always reflect usual terminology.) In horizontal writing, the full stop is placed in the same position as it would be in English, that is, at the bottom right of the preceding character. In vertical writing, it is placed immediately below and to the right of the last character, in a separate square if using genkō yōshi. (Note the difference in placement with the Chinese full stop, which is always placed in the centre of the square.)

Unlike the Western full stop, it is often used to separate consecutive sentences, rather than to finish every sentence; it is frequently left out where a sentence stands alone, or where text is terminated by a quotation mark instead. No extra space is left after a full stop.

In manuscripts that contain a mixture of Japanese and Western characters, the English full stop may be incorporated as well.”

Very helpful. Thanks, thorninmud.

What are “Asian characters”? And do you mean an English sentence?