Matches in SemOpenAlex for { <https://semopenalex.org/work/W806686435> ?p ?o ?g. }
Showing items 1 to 75 of
75
with 100 items per page.
- W806686435 abstract "In this thesis we consider the exponentially improved asymptotic solutions to unbounded multidimensional steepest descent type integrals in the case where the phase function has sets of non-isolated critical points. These sets are connected components of the critical set of the phase function and we consider the case where these sets have both general order of degeneracy and general dimension. We consider first the case of isolated critical points of general order of degeneracy as a lead-in to the general problem.In the isolated case, we justify the reduction of the study of the asymptotic behaviour of the general integral to the study of the asymptotic contribution to each individual critical point by appealing to the Morse lemma and results from the literature regarding the homology group of allowable integration surfaces. In the non-isolated case no such results exist, but we give a first step by appealing to the Morse-Bott lemma to suitably parameterise the integration surface. The analogous homological result does not yet exist and such a derivation is beyond the scope of this thesis, but we proceed to study individual contributions regardless, inspired by how readily the Morse-Bott lemma affords an analogous parameterisation of the integration surface in the non-isolated case.Once this justification is established we focus on individual critical connected components of the phase function. A full hyperasymptotic expansion representing the repeatedly exponentially improved asymptotic contribution to the integral for critical points of this type is derived for the first time, with examples provided to demonstrate this new theory. The case of a general bounded integration region is briefly considered, but we demonstrate that work still needs to be done to extend the theory to this case." @default.
- W806686435 created "2016-06-24" @default.
- W806686435 creator A5041629785 @default.
- W806686435 date "2015-04-01" @default.
- W806686435 modified "2023-09-23" @default.
- W806686435 title "Exponential asymptotics for integrals with degenerate and non-isolated critical points" @default.
- W806686435 hasPublicationYear "2015" @default.
- W806686435 type Work @default.
- W806686435 sameAs 806686435 @default.
- W806686435 citedByCount "2" @default.
- W806686435 countsByYear W8066864352015 @default.
- W806686435 countsByYear W8066864352020 @default.
- W806686435 crossrefType "dissertation" @default.
- W806686435 hasAuthorship W806686435A5041629785 @default.
- W806686435 hasConcept C121332964 @default.
- W806686435 hasConcept C134306372 @default.
- W806686435 hasConcept C14036430 @default.
- W806686435 hasConcept C151376022 @default.
- W806686435 hasConcept C18903297 @default.
- W806686435 hasConcept C202444582 @default.
- W806686435 hasConcept C2777727622 @default.
- W806686435 hasConcept C2777759810 @default.
- W806686435 hasConcept C28826006 @default.
- W806686435 hasConcept C33923547 @default.
- W806686435 hasConcept C46757340 @default.
- W806686435 hasConcept C60644358 @default.
- W806686435 hasConcept C62520636 @default.
- W806686435 hasConcept C72319582 @default.
- W806686435 hasConcept C75235859 @default.
- W806686435 hasConcept C78458016 @default.
- W806686435 hasConcept C86803240 @default.
- W806686435 hasConceptScore W806686435C121332964 @default.
- W806686435 hasConceptScore W806686435C134306372 @default.
- W806686435 hasConceptScore W806686435C14036430 @default.
- W806686435 hasConceptScore W806686435C151376022 @default.
- W806686435 hasConceptScore W806686435C18903297 @default.
- W806686435 hasConceptScore W806686435C202444582 @default.
- W806686435 hasConceptScore W806686435C2777727622 @default.
- W806686435 hasConceptScore W806686435C2777759810 @default.
- W806686435 hasConceptScore W806686435C28826006 @default.
- W806686435 hasConceptScore W806686435C33923547 @default.
- W806686435 hasConceptScore W806686435C46757340 @default.
- W806686435 hasConceptScore W806686435C60644358 @default.
- W806686435 hasConceptScore W806686435C62520636 @default.
- W806686435 hasConceptScore W806686435C72319582 @default.
- W806686435 hasConceptScore W806686435C75235859 @default.
- W806686435 hasConceptScore W806686435C78458016 @default.
- W806686435 hasConceptScore W806686435C86803240 @default.
- W806686435 hasLocation W8066864351 @default.
- W806686435 hasOpenAccess W806686435 @default.
- W806686435 hasPrimaryLocation W8066864351 @default.
- W806686435 hasRelatedWork W1545253388 @default.
- W806686435 hasRelatedWork W158349087 @default.
- W806686435 hasRelatedWork W1984638275 @default.
- W806686435 hasRelatedWork W2019458053 @default.
- W806686435 hasRelatedWork W2069815291 @default.
- W806686435 hasRelatedWork W2175313593 @default.
- W806686435 hasRelatedWork W2280922923 @default.
- W806686435 hasRelatedWork W2330399181 @default.
- W806686435 hasRelatedWork W2500769840 @default.
- W806686435 hasRelatedWork W2944527028 @default.
- W806686435 hasRelatedWork W2950225244 @default.
- W806686435 hasRelatedWork W2978819269 @default.
- W806686435 hasRelatedWork W3082605861 @default.
- W806686435 hasRelatedWork W3083369999 @default.
- W806686435 hasRelatedWork W3113198479 @default.
- W806686435 hasRelatedWork W3113778237 @default.
- W806686435 hasRelatedWork W98941348 @default.
- W806686435 hasRelatedWork W1457614870 @default.
- W806686435 hasRelatedWork W2336144428 @default.
- W806686435 hasRelatedWork W2340444998 @default.
- W806686435 isParatext "false" @default.
- W806686435 isRetracted "false" @default.
- W806686435 magId "806686435" @default.
- W806686435 workType "dissertation" @default.