شماره راهنما :
1235 دكتري
پديد آورنده :
كاظمي، مهسا
عنوان :
نظريه و پياده سازي آناليز انشعابات موضعي تكين ها براي توابع هموار
محل تحصيل :
اصفهان: دانشگاه صنعتي اصفهان، دانشكده علوم رياضي
صفحه شمار :
يازده، [۱۵۴]ص.: مصور، جدول، نمودار
يادداشت :
داورها: رضا خوش سير قاضياني از دانشگاه شهركرد و مليحه يوسف زاده از دانشگاه اصفهان هستند.
واژه نامه :
انگليسي به فارسي ; فارسي به انگليسي
توصيفگر ها :
ساختارهاي جبري , پايه هاي گربنر , انشعاب مقاوم , انشعابات موضعي
استاد داور :
رضا خوش سيرقاضياني، مليحه يوسف زاده، رسول عاشقي
تاريخ ورود اطلاعات :
1397/07/17
كد ايرانداك :
ID1235 دكتري
چكيده انگليسي :
Theory and implimentation for local bifurcation analysis of smooth maps Mahsa Kazemi Nooreddinvand mahsa kazemi@math iut ac ir June 17 2018 Doctor of Philosophy Thesis Department of Mathematical Sciences Isfahan University of Technology Isfahan 84156 83111 Iran Supervisor Dr Majid Gazor mgazor@cc iut ac ir Advisor Dr Amir Hashemi amir hashemi@cc iut ac ir Department of Mathematical Sciences Isfahan University of Technology Isfahan 84156 83111 IranAbstractMany mathematical models of real life problems are described by real zeros of smooth maps The local zero structure of a singular smooth map may qualitatively change when the map issubjected to small perturbations The changes include births and or deaths of zeros Thesematerialize as the occurrence of a new solution type to the singular real life problem Hence the inevitable imperfections are the actual factors to determine the real world solution typeto occur A qualitative change in the zero structures is called a bifurcation and the map isnamed a singularity Singularity theory is designed for appropriate modeling re nement thelocal bifurcation analysis and control of singular phenomena However there does not existany symbolic computer library for this purpose We suitably generalize some powerful toolsfrom algebraic geometry for correct implementation of the results from singularity theory We have accordingly developed a Maple end user friendly library named Singularity for an e cient and complete local bifurcation analysis of real zeros of scalar smooth maps 3 8 Key Words Singularity and bifurcation theory Persistent bifurcation diagram classi cation Transition sets Ideal membership problem Standard and Gr bner bases Equiv oariant bifurcation theory Submodule membership problem Z2 equivariant Standard basis Z2 equivariant normal form Comprehensive standard systems Geometric theorem discovery Determinacy Milnor number MSC 2010 37G10 13P10 58K50 58K60 37G40 68W30 58K40 IntroductionSingularities frequently occur in real life problems and their proper managements are essentialto achieve a desired outcome Roughly speaking we refer to a phenomenon as singular whensmall smooth changes into certain parameters of the problem would lead to a qualitativelydi erent result In other words a qualitative change starts at a singularity For instance 1
استاد داور :
رضا خوش سيرقاضياني، مليحه يوسف زاده، رسول عاشقي
