Can I patent part of my work presented that in my own research paper?
There are caveats to the grace period but the U.S. you have a one year grace period to file. 
35 U.S.C. 102 Conditions for patentability; novelty.

(a) NOVELTY; PRIOR ART.—A person shall be entitled to a patent unless—
    (1) the claimed invention was patented, described in a printed publication, or in public use, on sale, or otherwise available to the public before the effective filing date of the claimed invention; or
    (2) the claimed invention was described in a patent issued under section 151, or in an application for patent published or deemed published under section 122(b), in which the patent or application, as the case may be, names another inventor and was effectively filed before the effective filing date of the claimed invention.
(b) EXCEPTIONS.—
    (1) DISCLOSURES MADE 1 YEAR OR LESS BEFORE THE EFFECTIVE FILING DATE OF THE CLAIMED INVENTION.—A disclosure made 1 year or less before the effective filing date of a claimed invention shall not be prior art to the claimed invention under subsection (a)(1) if—
        (A) the disclosure was made by the inventor or joint inventor or by another who obtained the subject matter disclosed directly or indirectly from the inventor or a joint inventor; or 


For most all of the rest of the world, the day something is published it is no longer patentable, at least to the extent of what was disclosed. Nor is anything patentable that is obvious from what was published.