> He arrived in New York last January.其中的last January
"Last" is a commonly confused word. Technically, it means "immediately past" (see dict.org, where an example is "last Thursday"), "most recent; next before the present" (see dictionary.com, where an example is "last Friday"). So if today is Friday, "last Thursday" as the "immediately past" or "most recent" Thursday would technically be yesterday. Similarly, if it's any month after January now, "last January" would be January this year.
But as Gary B. Larson in his Style Manual points out,
The word last can also be confusing to mean "most recent" when using the name of a month or day; does last April mean April this year or April last year? Preferred: It happened in April. It happened Wednesday. Or: It happened last week. It happened last month. Redundant: It happened last Wednesday.
I think Mr. Larson has a good point (although I don't have the feeling of redundancy in the last sentence).Use "last" only when it's not ambiguous; e.g., if it's February now, "last May" means May last year. But say "last Month" or "in January" to refer to the January of this year, and "in January last year" to refer to that in the last year.