Bessel Function Model for Corneal Topography
Applied Mathematics and Computation 223 (2013), 436-443 In this paper we consider a new nonlinear mathematical model for corneal topography formulated as two-point boudary value problem. We derive it from first physical principles and provide some mathematical analysis. The existence and uniqeness t...
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| creator | Okrasiński, Wojciech Płociniczak, Łukasz |
| description | Applied Mathematics and Computation 223 (2013), 436-443 In this paper we consider a new nonlinear mathematical model for corneal
topography formulated as two-point boudary value problem. We derive it from
first physical principles and provide some mathematical analysis. The existence
and uniqeness theorems are proved as well as various estimates on exact
solution. At the end we fit the simplified model based on Modified Bessel
Function of the First Kind with the real corneal data consisting of matrix of
123x123 points and obtain an error of order of 1%. |
| doi_str_mv | 10.48550/arxiv.1111.6143 |
| format | Article |
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topography formulated as two-point boudary value problem. We derive it from
first physical principles and provide some mathematical analysis. The existence
and uniqeness theorems are proved as well as various estimates on exact
solution. At the end we fit the simplified model based on Modified Bessel
Function of the First Kind with the real corneal data consisting of matrix of
123x123 points and obtain an error of order of 1%.</description><identifier>DOI: 10.48550/arxiv.1111.6143</identifier><language>eng</language><subject>Mathematics - Analysis of PDEs</subject><creationdate>2011-11</creationdate><rights>http://arxiv.org/licenses/nonexclusive-distrib/1.0</rights><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>228,230,778,883</link.rule.ids><linktorsrc>$$Uhttps://arxiv.org/abs/1111.6143$$EView_record_in_Cornell_University$$FView_record_in_$$GCornell_University$$Hfree_for_read</linktorsrc><backlink>$$Uhttps://doi.org/10.48550/arXiv.1111.6143$$DView paper in arXiv$$Hfree_for_read</backlink></links><search><creatorcontrib>Okrasiński, Wojciech</creatorcontrib><creatorcontrib>Płociniczak, Łukasz</creatorcontrib><title>Bessel Function Model for Corneal Topography</title><description>Applied Mathematics and Computation 223 (2013), 436-443 In this paper we consider a new nonlinear mathematical model for corneal
topography formulated as two-point boudary value problem. We derive it from
first physical principles and provide some mathematical analysis. The existence
and uniqeness theorems are proved as well as various estimates on exact
solution. At the end we fit the simplified model based on Modified Bessel
Function of the First Kind with the real corneal data consisting of matrix of
123x123 points and obtain an error of order of 1%.</description><subject>Mathematics - Analysis of PDEs</subject><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2011</creationdate><recordtype>article</recordtype><sourceid>GOX</sourceid><recordid>eNotzjtvwjAUBWAvDBWwd6ryA5oQ9zqOPULES6Lqkj26dq5LpBBHDiD49zzPcnSWo4-xT54mQmVZOsNwac4JvyeRXMAH-17QMFAbrU6dPTa-i359fZ_Oh6jwoSNso9L3_j9gv79O2MhhO9D03WNWrpZlsYl3f-ttMd_FKDOITU4SciOs1gZ-asopM2iN1lxzq-tUObK1QuJaSXIShE25UQjoILdCGhizr9ftU1v1oTlguFYPdfVQww2yJDym</recordid><startdate>20111126</startdate><enddate>20111126</enddate><creator>Okrasiński, Wojciech</creator><creator>Płociniczak, Łukasz</creator><scope>AKZ</scope><scope>GOX</scope></search><sort><creationdate>20111126</creationdate><title>Bessel Function Model for Corneal Topography</title><author>Okrasiński, Wojciech ; Płociniczak, Łukasz</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-a653-b7e637b4c99b32de7e5bacb99191c9d08fecd8ae1986ef634c01b8a3af37c46b3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2011</creationdate><topic>Mathematics - Analysis of PDEs</topic><toplevel>online_resources</toplevel><creatorcontrib>Okrasiński, Wojciech</creatorcontrib><creatorcontrib>Płociniczak, Łukasz</creatorcontrib><collection>arXiv Mathematics</collection><collection>arXiv.org</collection></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext_linktorsrc</fulltext></delivery><addata><au>Okrasiński, Wojciech</au><au>Płociniczak, Łukasz</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Bessel Function Model for Corneal Topography</atitle><date>2011-11-26</date><risdate>2011</risdate><abstract>Applied Mathematics and Computation 223 (2013), 436-443 In this paper we consider a new nonlinear mathematical model for corneal
topography formulated as two-point boudary value problem. We derive it from
first physical principles and provide some mathematical analysis. The existence
and uniqeness theorems are proved as well as various estimates on exact
solution. At the end we fit the simplified model based on Modified Bessel
Function of the First Kind with the real corneal data consisting of matrix of
123x123 points and obtain an error of order of 1%.</abstract><doi>10.48550/arxiv.1111.6143</doi><oa>free_for_read</oa></addata></record> |
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| subjects | Mathematics - Analysis of PDEs |
| title | Bessel Function Model for Corneal Topography |
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