{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,4,27]],"date-time":"2022-04-27T05:25:41Z","timestamp":1651037141494},"reference-count":4,"publisher":"Hindawi Limited","license":[{"start":{"date-parts":[[2012,1,1]],"date-time":"2012-01-01T00:00:00Z","timestamp":1325376000000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/3.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["International Journal of Mathematics and Mathematical Sciences"],"published-print":{"date-parts":[[2012]]},"abstract":"<jats:p>Carry Value Transformation (CVT) is a model of discrete deterministic dynamical system. In the present study, it has been proved that (1) the sum of any two nonnegative integers is the same as the sum of their CVT and XOR values. (2) the number of iterations leading to either<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mml:mrow><mml:mtext>CVT<\/mml:mtext><mml:mo>=<\/mml:mo><mml:mn>0<\/mml:mn><\/mml:mrow><\/mml:math>or<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mml:mrow><mml:mtext>XOR<\/mml:mtext><mml:mo>=<\/mml:mo><mml:mn>0<\/mml:mn><\/mml:mrow><\/mml:math>does not exceed the maximum of the lengths of the two addenda expressed as binary strings. A similar process of addition of modified Carry Value Transformation (MCVT) and XOR requires a maximum of two iterations for MCVT to be zero. (3) an equivalence relation is shown to exist on<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mml:mrow><mml:mi>Z<\/mml:mi><mml:mo>\u00d7<\/mml:mo><mml:mi>Z<\/mml:mi><\/mml:mrow><\/mml:math>which divides the CV table into disjoint equivalence classes.<\/jats:p>","DOI":"10.1155\/2012\/174372","type":"journal-article","created":{"date-parts":[[2012,4,1]],"date-time":"2012-04-01T17:00:23Z","timestamp":1333299623000},"page":"1-10","source":"Crossref","is-referenced-by-count":6,"title":["Properties of Carry Value Transformation"],"prefix":"10.1155","volume":"2012","author":[{"given":"Suryakanta","family":"Pal","sequence":"first","affiliation":[{"name":"Department of Basic Science and Humanities, Silicon Institute of Technology, Silicon Hills, Patia, Bhubaneswar 751024, India"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Sudhakar","family":"Sahoo","sequence":"additional","affiliation":[{"name":"Department of Computer Science, Institute of Mathematics and Applications, Andharua, Bhubaneswar 751003, India"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Birendra Kumar","family":"Nayak","sequence":"additional","affiliation":[{"name":"P.G. Department of Mathematics, Utkal University, Bhubaneswar 751004, India"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"98","reference":[{"issue":"1","key":"3","first-page":"1","volume":"9","year":"2011","journal-title":"International Journal of Computational Cognition"},{"key":"6"},{"issue":"2","key":"7","volume":"1","year":"2010","journal-title":"Alexandria Journal of Mathematics"},{"issue":"3","key":"5","first-page":"33","volume":"8","year":"2010","journal-title":"International Journal of Computational Cognition"}],"container-title":["International Journal of Mathematics and Mathematical Sciences"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/downloads.hindawi.com\/journals\/ijmms\/2012\/174372.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/ijmms\/2012\/174372.xml","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/ijmms\/2012\/174372.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2016,8,2]],"date-time":"2016-08-02T12:56:08Z","timestamp":1470142568000},"score":1,"resource":{"primary":{"URL":"http:\/\/www.hindawi.com\/journals\/ijmms\/2012\/174372\/"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2012]]},"references-count":4,"alternative-id":["174372","174372"],"URL":"https:\/\/doi.org\/10.1155\/2012\/174372","relation":{},"ISSN":["0161-1712","1687-0425"],"issn-type":[{"value":"0161-1712","type":"print"},{"value":"1687-0425","type":"electronic"}],"subject":[],"published":{"date-parts":[[2012]]}}}