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We can take the tracking distance into account as a function of a discounted effort-reward parameter in order to account for this uncertainty. We provide an analytical demonstration of the effects this parameter has on reducing the expected value of the first collision time between a nanosensor and the particle and confirming the existence of this technique.<\/jats:p>","DOI":"10.1142\/s1793005726500341","type":"journal-article","created":{"date-parts":[[2024,12,19]],"date-time":"2024-12-19T10:11:14Z","timestamp":1734603074000},"page":"699-712","source":"Crossref","is-referenced-by-count":3,"title":["Studying the Finiteness of a Tracking Technique with Random Distances and Velocities that Reduces the Collision Time Between a Brownian Particle and a Nanosensor in the Fluid"],"prefix":"10.1142","volume":"22","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-9407-9586","authenticated-orcid":false,"given":"Mohamed Abd","family":"Allah El-Hadidy","sequence":"first","affiliation":[{"name":"Mathematics Department, Faculty of Science, Tanta University, Tanta, Egypt"},{"name":"Mathematics and Statistics Department, College of Science, Taibah University, Yanbu, Saudi Arabia"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3742-8003","authenticated-orcid":false,"given":"Alaa A.","family":"Alzulaibani","sequence":"additional","affiliation":[{"name":"Mathematics and Statistics Department, College of Science, Taibah University, Yanbu, Saudi Arabia"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"219","published-online":{"date-parts":[[2024,12,19]]},"reference":[{"key":"S1793005726500341BIB001","doi-asserted-by":"publisher","DOI":"10.1137\/1007106"},{"key":"S1793005726500341BIB002","doi-asserted-by":"publisher","DOI":"10.1016\/0377-0427(83)90020-1"},{"key":"S1793005726500341BIB003","doi-asserted-by":"publisher","DOI":"10.1016\/S0377-2217(96)00314-1"},{"key":"S1793005726500341BIB004","doi-asserted-by":"publisher","DOI":"10.1057\/jors.1995.186"},{"key":"S1793005726500341BIB005","doi-asserted-by":"publisher","DOI":"10.1137\/0330008"},{"key":"S1793005726500341BIB006","doi-asserted-by":"publisher","DOI":"10.1051\/ro\/1989230100671"},{"key":"S1793005726500341BIB007","doi-asserted-by":"publisher","DOI":"10.15807\/jorsj.30.399"},{"key":"S1793005726500341BIB008","doi-asserted-by":"publisher","DOI":"10.2307\/3212585"},{"issue":"3","key":"S1793005726500341BIB009","first-page":"375","volume":"19","author":"Mohamed A. 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