{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,2,21]],"date-time":"2025-02-21T10:42:40Z","timestamp":1740134560039,"version":"3.37.3"},"reference-count":16,"publisher":"Wiley","license":[{"start":{"date-parts":[[2014,1,1]],"date-time":"2014-01-01T00:00:00Z","timestamp":1388534400000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/3.0\/"}],"funder":[{"DOI":"10.13039\/501100004895","name":"European Social Fund","doi-asserted-by":"publisher","id":[{"id":"10.13039\/501100004895","id-type":"DOI","asserted-by":"publisher"}]},{"name":"National Resources"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Journal of Applied Mathematics"],"published-print":{"date-parts":[[2014]]},"abstract":"<jats:p>Albanese and Monk (2006) have shown that, it is impossible to recover the support of a three-dimensional current distribution within a conducting medium from the knowledge of the electric potential outside the conductor. On the other hand, it is possible to obtain the support of a current which lives in a subspace of dimension lower than three. In the present work, we actually demonstrate this possibility by assuming a one-dimensional current distribution supported on a small line segment having arbitrary location and orientation within a uniform spherical conductor. The immediate representation of this problem refers to the inverse problem of electroencephalography (EEG) with a linear current distribution and the spherical model of the brain-head system. It is shown that the support is identified through the solution of a nonlinear algebraic system which is investigated thoroughly. Numerical tests show that this system has exactly one real solution. Exact solutions are analytically obtained for a couple of special cases.<\/jats:p>","DOI":"10.1155\/2014\/715785","type":"journal-article","created":{"date-parts":[[2014,6,19]],"date-time":"2014-06-19T17:05:47Z","timestamp":1403197547000},"page":"1-11","source":"Crossref","is-referenced-by-count":2,"title":["On the Inverse EEG Problem for a 1D Current Distribution"],"prefix":"10.1155","volume":"2014","author":[{"given":"George","family":"Dassios","sequence":"first","affiliation":[{"name":"Department of Chemical Engineering, University of Patras and ICE\/HT-FORTH, Patras, Greece"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"George","family":"Fragoyiannis","sequence":"additional","affiliation":[{"name":"Department of Chemical Engineering, University of Patras and ICE\/HT-FORTH, Patras, Greece"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Konstantia","family":"Satrazemi","sequence":"additional","affiliation":[{"name":"Department of Chemical Engineering, University of Patras and ICE\/HT-FORTH, Patras, Greece"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","reference":[{"year":"1995","key":"13"},{"year":"1960","key":"12"},{"key":"16","doi-asserted-by":"publisher","DOI":"10.1007\/BF02476917"},{"issue":"1","key":"10","doi-asserted-by":"crossref","first-page":"25","DOI":"10.1016\/S0165-2125(97)00063-2","volume":"28","year":"1998","journal-title":"Wave Motion"},{"key":"4","series-title":"Mathematical Biosciences Subseries","first-page":"133","volume-title":"Electric and magnetic activity of the brain in spherical and ellipsoidal geometry","volume":"183","year":"2009"},{"key":"8","doi-asserted-by":"publisher","DOI":"10.1088\/0266-5611\/29\/6\/065012"},{"key":"11","first-page":"211\u2013233, 353","volume":"89","year":"1853","journal-title":"Annalen der Physik und Chemie"},{"key":"9","doi-asserted-by":"publisher","DOI":"10.1103\/RevModPhys.65.413"},{"key":"2","doi-asserted-by":"publisher","DOI":"10.1137\/S0036139900373927"},{"key":"1","doi-asserted-by":"publisher","DOI":"10.1088\/0266-5611\/22\/3\/018"},{"key":"7","doi-asserted-by":"publisher","DOI":"10.1088\/0266-5611\/25\/3\/035001"},{"key":"5","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9781139017749"},{"volume":"2","year":"1953","key":"14"},{"volume":"1","year":"1953","key":"15"},{"issue":"4","key":"6","doi-asserted-by":"crossref","first-page":"771","DOI":"10.1090\/S0033-569X-09-01144-7","volume":"67","year":"2009","journal-title":"Quarterly of Applied Mathematics"},{"year":"1947","key":"3"}],"container-title":["Journal of Applied Mathematics"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/downloads.hindawi.com\/journals\/jam\/2014\/715785.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/jam\/2014\/715785.xml","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/jam\/2014\/715785.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2017,6,22]],"date-time":"2017-06-22T11:15:00Z","timestamp":1498130100000},"score":1,"resource":{"primary":{"URL":"http:\/\/www.hindawi.com\/journals\/jam\/2014\/715785\/"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2014]]},"references-count":16,"alternative-id":["715785","715785"],"URL":"https:\/\/doi.org\/10.1155\/2014\/715785","relation":{},"ISSN":["1110-757X","1687-0042"],"issn-type":[{"type":"print","value":"1110-757X"},{"type":"electronic","value":"1687-0042"}],"subject":[],"published":{"date-parts":[[2014]]}}}