{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,21]],"date-time":"2026-04-21T22:47:05Z","timestamp":1776811625646,"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>The synthesis of quasicrystals and observation of their unexpected 10-fold symmetric diffraction pattern by D. Shechtman and co-workers 1982\u20131984 provide a natural bridge for bringing solid state (condensed matter) physics within the purview of Santilli\u2019s 1967\u20132006 Lie-admissible generalization of quantum mechanics (QM) under the name \u201chadronic\u201d mechanics (HM) via our recent non-unitary scattering theory of HM for deep-inelastic [Formula: see text] and [Formula: see text] scattering processes. This is achieved in this paper by a re-formulation and elaboration of Bragg\u2019s law of diffraction for quasicrystals under the title Geno-Bragg\u2019s law which permits identification of the deformed quasicrystalline state with 10*x10 representation of SU(3) symmetry. Essentially, because only 1-,2-,3-,4- and 6-fold but not 5-fold point symmetry of perfectly periodic crystal lattice are allowed in 3-dimensional (3D) real or reciprocal lattice space, a (non-unitary) deformation of the allowed (cubic) 4-fold and (hexagonal) 6-fold symmetry axes into a common diffraction (square-hexagon) geno-plane having 10-fold point symmetry is achievable as envisaged in HM. As a result, the current icosahedron approximant structure is replaced by cube-hexagon genospace structure that permits determination of atomic distribution in quasicrystals as holographic (periodic) structure. Further elaboration of Geno-Bragg\u2019s law to high energy (relativistic) deep-inelastic scattering processes described by current-current interaction models of neutron synthesis\/decay is applied to the determination of the structure of the neutron and the implications for geno-renormalization of mass and the ratios of the masses of the elementary particles are discussed.<\/jats:p>","DOI":"10.3233\/jcm-120449","type":"journal-article","created":{"date-parts":[[2019,4,25]],"date-time":"2019-04-25T07:12:08Z","timestamp":1556176328000},"page":"1-17","update-policy":"https:\/\/doi.org\/10.1177\/sage-journals-update-policy","source":"Crossref","is-referenced-by-count":0,"title":["Geno-Bragg's law and 10*x10 representation of SU(3) symmetry for quasicrystal structures"],"prefix":"10.66113","volume":"13","author":[{"given":"Alexander O.E.","family":"Animalu","sequence":"first","affiliation":[{"name":"Department of Physics and Astronomy, University of Nigeria, Nsukka Enugu State, Nigeria and International Centre for Basic Research, 20 Limpopo Street, FHA, Maitama, Abuja, Nigeria."}]}],"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-120449","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/journals.sagepub.com\/doi\/pdf\/10.3233\/JCM-120449","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,4,21]],"date-time":"2026-04-21T22:06:45Z","timestamp":1776809205000},"score":1,"resource":{"primary":{"URL":"https:\/\/journals.sagepub.com\/doi\/10.3233\/JCM-120449"}},"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-120449"],"URL":"https:\/\/doi.org\/10.3233\/jcm-120449","relation":{},"ISSN":["1472-7978","1875-8983"],"issn-type":[{"value":"1472-7978","type":"print"},{"value":"1875-8983","type":"electronic"}],"subject":[],"published":{"date-parts":[[2013,1]]}}}