Matches in SemOpenAlex for { <https://semopenalex.org/work/W9018946> ?p ?o ?g. }
Showing items 1 to 83 of
83
with 100 items per page.
- W9018946 abstract "Sensitivity analysis has long been an important technique in science: How sensitive is the international price equilibrium to the availability of oil? How does the strain on a bridge depend upon the weight carried? Or, how does the incidence of an infectious desease depend upon the fraction of the population that is checked daily? These questions can be answered by determining how solutions of systems of equations depend on a parameter. Does the solution continue as the parameter is varied? If it does, how far through the parameter range does it extend? Formally, let F: Rn+1 → Rn be a C1 map. (In practice, f is usually defined on a subset of Rn+1.) We denote by (x,α) a point in Rn+1 = Rn × R, where x ∈ Rn and α ∈ R (a scalar parameter), and let $${rm{C}},{rm{ = }},{rm{{ (X,}},{rm{alpha )}}, in ,{{rm{R}}^{{rm{r}},{rm{ + 1}}}}:,{rm{f}},{rm{(X,}},{rm{alpha )}}, = ,0} $$be the set of zeroes of f. When the implicit function theorem is applied at a point (x,ᾱ) ∈ C, one learns about the local structure of C near (x,ᾱ), and thus how small changes in the parameter α affect the set of zeroes. The conclusion of this theorem, however, says nothing about the set of zeroes globally (i.e., over the entire parameter range). Concentrating on the (connected) component of C that contains (x,ᾱ), we show that the hypotheses of the implicit function theorem imply certain global facts about this component." @default.
- W9018946 created "2016-06-24" @default.
- W9018946 creator A5022360238 @default.
- W9018946 creator A5048675723 @default.
- W9018946 date "1991-01-01" @default.
- W9018946 modified "2023-09-23" @default.
- W9018946 title "Global Implications of the Implicit Function Theorem" @default.
- W9018946 cites W1575154287 @default.
- W9018946 cites W1758764431 @default.
- W9018946 cites W1972657624 @default.
- W9018946 cites W1976231053 @default.
- W9018946 cites W2003529277 @default.
- W9018946 cites W2027828462 @default.
- W9018946 cites W2031636762 @default.
- W9018946 cites W2037032585 @default.
- W9018946 cites W2062780857 @default.
- W9018946 cites W2093957401 @default.
- W9018946 cites W2044360789 @default.
- W9018946 doi "https://doi.org/10.1007/978-1-4757-0172-2_11" @default.
- W9018946 hasPublicationYear "1991" @default.
- W9018946 type Work @default.
- W9018946 sameAs 9018946 @default.
- W9018946 citedByCount "0" @default.
- W9018946 crossrefType "book-chapter" @default.
- W9018946 hasAuthorship W9018946A5022360238 @default.
- W9018946 hasAuthorship W9018946A5048675723 @default.
- W9018946 hasConcept C114614502 @default.
- W9018946 hasConcept C127413603 @default.
- W9018946 hasConcept C134306372 @default.
- W9018946 hasConcept C138578839 @default.
- W9018946 hasConcept C14036430 @default.
- W9018946 hasConcept C144024400 @default.
- W9018946 hasConcept C149923435 @default.
- W9018946 hasConcept C21200559 @default.
- W9018946 hasConcept C24326235 @default.
- W9018946 hasConcept C2524010 @default.
- W9018946 hasConcept C2908647359 @default.
- W9018946 hasConcept C33923547 @default.
- W9018946 hasConcept C57691317 @default.
- W9018946 hasConcept C78458016 @default.
- W9018946 hasConcept C86803240 @default.
- W9018946 hasConceptScore W9018946C114614502 @default.
- W9018946 hasConceptScore W9018946C127413603 @default.
- W9018946 hasConceptScore W9018946C134306372 @default.
- W9018946 hasConceptScore W9018946C138578839 @default.
- W9018946 hasConceptScore W9018946C14036430 @default.
- W9018946 hasConceptScore W9018946C144024400 @default.
- W9018946 hasConceptScore W9018946C149923435 @default.
- W9018946 hasConceptScore W9018946C21200559 @default.
- W9018946 hasConceptScore W9018946C24326235 @default.
- W9018946 hasConceptScore W9018946C2524010 @default.
- W9018946 hasConceptScore W9018946C2908647359 @default.
- W9018946 hasConceptScore W9018946C33923547 @default.
- W9018946 hasConceptScore W9018946C57691317 @default.
- W9018946 hasConceptScore W9018946C78458016 @default.
- W9018946 hasConceptScore W9018946C86803240 @default.
- W9018946 hasLocation W90189461 @default.
- W9018946 hasOpenAccess W9018946 @default.
- W9018946 hasPrimaryLocation W90189461 @default.
- W9018946 hasRelatedWork W1563441177 @default.
- W9018946 hasRelatedWork W1656819531 @default.
- W9018946 hasRelatedWork W1976337900 @default.
- W9018946 hasRelatedWork W1978506534 @default.
- W9018946 hasRelatedWork W2006625376 @default.
- W9018946 hasRelatedWork W2022386131 @default.
- W9018946 hasRelatedWork W2032646515 @default.
- W9018946 hasRelatedWork W2048150856 @default.
- W9018946 hasRelatedWork W2067991545 @default.
- W9018946 hasRelatedWork W2079212116 @default.
- W9018946 hasRelatedWork W2085164356 @default.
- W9018946 hasRelatedWork W2113300884 @default.
- W9018946 hasRelatedWork W2230733683 @default.
- W9018946 hasRelatedWork W2230757501 @default.
- W9018946 hasRelatedWork W2333954654 @default.
- W9018946 hasRelatedWork W2807741636 @default.
- W9018946 hasRelatedWork W29062556 @default.
- W9018946 hasRelatedWork W7609366 @default.
- W9018946 hasRelatedWork W942957578 @default.
- W9018946 hasRelatedWork W1527065169 @default.
- W9018946 isParatext "false" @default.
- W9018946 isRetracted "false" @default.
- W9018946 magId "9018946" @default.
- W9018946 workType "book-chapter" @default.