{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,21]],"date-time":"2026-04-21T22:47:24Z","timestamp":1776811644443,"version":"3.51.2"},"reference-count":0,"publisher":"European Society of Computational Methods in Sciences and Engineering","issue":"1-2","license":[{"start":{"date-parts":[[2013,1,1]],"date-time":"2013-01-01T00:00:00Z","timestamp":1356998400000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/journals.sagepub.com\/page\/policies\/text-and-data-mining-license"}],"content-domain":{"domain":["journals.sagepub.com"],"crossmark-restriction":true},"short-container-title":["Journal of Computational Methods in Sciences and Engineering"],"published-print":{"date-parts":[[2013,1]]},"abstract":"<jats:p>A matrix theory of n-dimensional mathematical field and the motion of mathematical points in n-dimensional metric space is developed. Two spaces are considered: the n-dimensional space of an integrable coordinate vector [Formula: see text] with the integrable metric [Formula: see text] and the n-dimensional space of a non-integrable but differentiable coordinate vector [Formula: see text], where [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text]. We call the coordinate space of the vector Q as the absolute space.<\/jats:p>\n                  <jats:p>The derivatives of the non-integrable but differentiable matrix e are expressed through the elements of the Christoffel symbols and the elements of the Ricci and Riemann curvature matrices. The absolute velocity vector [Formula: see text] and the absolute mathematical field matrix [Formula: see text] are introduced. We obtain two groups of the matrix field equations, the first of which is written in the two following forms: [Formula: see text], [Formula: see text], where [Formula: see text] the trace of the matrix P, K is is the absolute Ricci matrix function, [Formula: see text] is the n-dimensional absolute velocity vector, \u03c1 is a scalar function, which is the eigenvalue of K with the corresponding eigenvector [Formula: see text]. The interpretation of this pure mathematical theory in 4-dimensional space is the theory of the electromagnetic and gravitational fields and the motion of charged and neutral particles in the electromagnetic-gravitational field.<\/jats:p>","DOI":"10.3233\/jcm-120454","type":"journal-article","created":{"date-parts":[[2019,4,25]],"date-time":"2019-04-25T07:12:49Z","timestamp":1556176369000},"page":"59-109","update-policy":"https:\/\/doi.org\/10.1177\/sage-journals-update-policy","source":"Crossref","is-referenced-by-count":3,"title":["The matrix theory of mathematical field and the motion of mathematical points in n-dimensional metric space"],"prefix":"10.66113","volume":"13","author":[{"given":"Alexander D.","family":"Dymnikov","sequence":"first","affiliation":[{"name":"Louisiana Accelerator Center, Physics Department, Louisiana University at Lafayette, Lafayette, LA, USA"}]}],"member":"55691","published-online":{"date-parts":[[2013,1,1]]},"container-title":["Journal of Computational Methods in Sciences and Engineering"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/journals.sagepub.com\/doi\/pdf\/10.3233\/JCM-120454","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/journals.sagepub.com\/doi\/pdf\/10.3233\/JCM-120454","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,4,21]],"date-time":"2026-04-21T22:06:48Z","timestamp":1776809208000},"score":1,"resource":{"primary":{"URL":"https:\/\/journals.sagepub.com\/doi\/10.3233\/JCM-120454"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2013,1]]},"references-count":0,"journal-issue":{"issue":"1-2","published-print":{"date-parts":[[2013,1]]}},"alternative-id":["10.3233\/JCM-120454"],"URL":"https:\/\/doi.org\/10.3233\/jcm-120454","relation":{},"ISSN":["1472-7978","1875-8983"],"issn-type":[{"value":"1472-7978","type":"print"},{"value":"1875-8983","type":"electronic"}],"subject":[],"published":{"date-parts":[[2013,1]]}}}