{"id":{"repo_id":"vt","oai_identifier":"oai:vtechworks.lib.vt.edu:10919/32191"},"canonical_url":"https://search.dev.ndltd.org/etd/vt/oai:vtechworks.lib.vt.edu:10919/32191","repository":{"repo_id":"vt","name":"Virginia Tech","base_url":"https://vtechworks.lib.vt.edu/oai/request"},"display":{"title":"Max-Plus Algebra","abstract":"In max-plus algebra we work with the max-plus semi-ring which is the set ℝ<sub>max</sub>=[-∞)∪ℝ together with operations 𝑎⊕𝑏 = max(𝑎,𝑏) and 𝑎⊗𝑏= 𝑎+𝑏. The additive and multiplicative identities are taken to be ε=-∞ and ε=0 respectively. Max-plus algebra is one of many idempotent semi-rings which have been considered in various fields of mathematics. Max-plus algebra is becoming more popular not only because its operations are associative, commutative and distributive as in conventional algebra but because it takes systems that are non-linear in conventional algebra and makes them linear. Max-plus algebra also arises as the algebra of asymptotic growth rates of functions in conventional algebra which will play a significant role in several aspects of this thesis. This thesis is a survey of max-plus algebra that will concentrate on max-plus linear algebra results. We will then consider from a max-plus perspective several results by Wentzell and Freidlin for finite state Markov chains with an asymptotic dependence.","abstract_html":"In max-plus algebra we work with the max-plus semi-ring which is the set ℝ&lt;sub&gt;max&lt;/sub&gt;=[-∞)∪ℝ together with operations 𝑎⊕𝑏 = max(𝑎,𝑏) and 𝑎⊗𝑏= 𝑎+𝑏. The additive and multiplicative identities are taken to be ε=-∞ and ε=0 respectively. Max-plus algebra is one of many idempotent semi-rings which have been considered in various fields of mathematics. Max-plus algebra is becoming more popular not only because its operations are associative, commutative and distributive as in conventional algebra but because it takes systems that are non-linear in conventional algebra and makes them linear. Max-plus algebra also arises as the algebra of asymptotic growth rates of functions in conventional algebra which will play a significant role in several aspects of this thesis. This thesis is a survey of max-plus algebra that will concentrate on max-plus linear algebra results. We will then consider from a max-plus perspective several results by Wentzell and Freidlin for finite state Markov chains with an asymptotic dependence.","abstract_has_math":false,"creators":["Farlow, Kasie Geralyn"],"institution":"Virginia Tech","degree_name":"Master of Science","degree_level":"masters","degree_discipline":"Mathematics","degree_department":"Mathematics","school":null,"contributors":[],"advisors":[],"committee_chairs":["Day, Martin V."],"committee_members":["Haskell, Peter E.","Wheeler, Robert L."],"year":2009,"date_issued":"2009-04-27","date_published":"2009-04-27","updated_at":"2026-07-22T22:20:32Z","subjects":["Markov Chains","Linear Algebra","Max-Plus"],"languages":[],"rights":["In Copyright"],"rights_urls":["http://rightsstatements.org/vocab/InC/1.0/"],"identifier_entries":[{"key":"dc:identifier.other","label":"Dc Identifier Other","values":["etd-05042009-152934"],"render_values":[{"text":"etd-05042009-152934","href":null,"code":true}]}]},"links":{"outbound_url":"http://hdl.handle.net/10919/32191","outbound_label":"Handle","outbound_source":"dc:identifier.uri"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor.committeechair","label":"Committee Chair","values":["Day, Martin V."]},{"key":"dc:contributor.committeemember","label":"Committee Member","values":["Haskell, Peter E.","Wheeler, Robert L."]},{"key":"dc:contributor.department","label":"Department","values":["Mathematics"]},{"key":"dc:creator","label":"Author","values":["Farlow, Kasie Geralyn"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.accessioned","label":"Dc Date Accessioned","values":["2014-03-14T20:35:01Z"]},{"key":"dc:date.available","label":"Dc Date Available","values":["2014-03-14T20:35:01Z","2009-05-26"]},{"key":"dc:date.issued","label":"Date","values":["2009-04-27"]},{"key":"dc:publisher","label":"Institution","values":["Virginia Tech"]},{"key":"dc:type","label":"Dc Type","values":["Thesis"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Mathematics"]},{"key":"thesis:degree_level","label":"Degree Level","values":["masters"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Master of Science"]},{"key":"thesis:institution_name","label":"Thesis Institution Name","values":["Virginia Polytechnic Institute and State University"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Markov Chains","Linear Algebra","Max-Plus"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:rights","label":"Dc Rights","values":["In Copyright"]},{"key":"dc:rights.uri","label":"Rights URI","values":["http://rightsstatements.org/vocab/InC/1.0/"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier.other","label":"Dc Identifier Other","values":["etd-05042009-152934"]},{"key":"dc:identifier.uri","label":"Identifier URI","values":["http://hdl.handle.net/10919/32191"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["In max-plus algebra we work with the max-plus semi-ring which is the set ℝ<sub>max</sub>=[-∞)∪ℝ together with operations 𝑎⊕𝑏 = max(𝑎,𝑏) and 𝑎⊗𝑏= 𝑎+𝑏. The additive and multiplicative identities are taken to be ε=-∞ and ε=0 respectively. Max-plus algebra is one of many idempotent semi-rings which have been considered in various fields of mathematics. Max-plus algebra is becoming more popular not only because its operations are associative, commutative and distributive as in conventional algebra but because it takes systems that are non-linear in conventional algebra and makes them linear. Max-plus algebra also arises as the algebra of asymptotic growth rates of functions in conventional algebra which will play a significant role in several aspects of this thesis. This thesis is a survey of max-plus algebra that will concentrate on max-plus linear algebra results. We will then consider from a max-plus perspective several results by Wentzell and Freidlin for finite state Markov chains with an asymptotic dependence."]},{"key":"dc:description.degree","label":"Dc Description Degree","values":["Master of Science"]},{"key":"dc:title","label":"Title","values":["Max-Plus Algebra"]}]}],"canonical_facts":{"dc:contributor.committeechair":["Day, Martin V."],"dc:contributor.committeemember":["Haskell, Peter E.","Wheeler, Robert L."],"dc:contributor.department":["Mathematics"],"dc:creator":["Farlow, Kasie Geralyn"],"dc:date.accessioned":["2014-03-14T20:35:01Z"],"dc:date.available":["2014-03-14T20:35:01Z","2009-05-26"],"dc:date.issued":["2009-04-27"],"dc:description.abstract":["In max-plus algebra we work with the max-plus semi-ring which is the set ℝ<sub>max</sub>=[-∞)∪ℝ together with operations 𝑎⊕𝑏 = max(𝑎,𝑏) and 𝑎⊗𝑏= 𝑎+𝑏. The additive and multiplicative identities are taken to be ε=-∞ and ε=0 respectively. Max-plus algebra is one of many idempotent semi-rings which have been considered in various fields of mathematics. Max-plus algebra is becoming more popular not only because its operations are associative, commutative and distributive as in conventional algebra but because it takes systems that are non-linear in conventional algebra and makes them linear. Max-plus algebra also arises as the algebra of asymptotic growth rates of functions in conventional algebra which will play a significant role in several aspects of this thesis. This thesis is a survey of max-plus algebra that will concentrate on max-plus linear algebra results. We will then consider from a max-plus perspective several results by Wentzell and Freidlin for finite state Markov chains with an asymptotic dependence."],"dc:description.degree":["Master of Science"],"dc:identifier.other":["etd-05042009-152934"],"dc:identifier.uri":["http://hdl.handle.net/10919/32191"],"dc:publisher":["Virginia Tech"],"dc:rights":["In Copyright"],"dc:rights.uri":["http://rightsstatements.org/vocab/InC/1.0/"],"dc:subject":["Markov Chains","Linear Algebra","Max-Plus"],"dc:title":["Max-Plus Algebra"],"dc:type":["Thesis"],"thesis:degree_discipline":["Mathematics"],"thesis:degree_level":["masters"],"thesis:degree_name":["Master of Science"],"thesis:institution_name":["Virginia Polytechnic Institute and State University"]},"updated_at":"2026-07-22T22:20:32Z"}