We prove a global implicit function theorem. In particular we show that any Lipschitz map ${f : \\mathbb{R}^{n} \\times \\mathbb{R}^{m} \\rightarrow \\mathbb{R}^{n}}$ (with n-dim. image) can be precomposed with a bi-Lipschitz map ${\\bar{g} : \\mathbb{R}^{n} \\...
Krantz, S., Parks, H.: The Implicit Function Theorem: History, Theory, and Applications Modern Birkhäuser Classics. Springer, New York (2012) Google Scholar Vietoris, L.: Über den höheren Zusammenhang kompakter Räume und eine Klasse von zusammenhangstreuen Abbildungen. Math. Ann. ...
Even carefully-designed formalisms that are sensitive to the implicit concerns of human agents are not guaranteed to learn the right preference structures in the right way without new forms of surveillance, control, and assigned roles for both humans and the systems themselves [90], [91]. Such...
Even before Heisen- berg, Max Born had shown in 1926 that in collisions of atomic particles we could only predict the probabilities for the atomic paths, confirming Boltzmann's requirement for microscopic ran- domness. So the original two cases for irreducible randomness, implicit in the work ...
How does the Maximizing or Rational decision-making model differ from the satisficing and implicit favorite model? A) It seeks to find the best solution to a problem. B) The Maximizing or Rational decision-making models predicts...
Hence, in the baseline scenario, refineries serve the country's large domestic demand at a loss and receive implicit compensation from the government budget. Refining activity decreases with the price reform, the refining sector is no longer loss making and becomes a source of revenue that can ...
“No, no, yes: a date with no time means midnight is implicit.” People who said this seem like they might naturally gravitate towards date-time semantics. It makes sense to me that programmers think this way; if you’re missing a piece of data, just fill in 0 and keep going. I’...
1 be any integer. The first player, a fugitive, starts on a marked vertexof a (di)graph G. The second player, an observer, marks at most k vertices, then the fugitivemoves along one edge/arc of G to a new vertex, then the observer marks at most k vertices,etc.The fugitive wins ...
Implicit function theoremReifenberg flatSard's TheoremUniform rectifiabilityWe prove a global implicit function theorem. In particular we show that any Lipschitz map f: ? ~n × ? ~m → ? ~n (with n-dim. image) can be precomposed with a bi-Lipschitz map ? ? ~n × ? ~m → ? ~n ...
For (implicit) oracle set\({\mathbb {H}} \), an oracle function\(f^{(\cdot )}\)(with domainDand rangeR), denoted\(f^{(\cdot )}:D \rightarrow R\), is a set of functions indexed by oracles\(h\in {\mathbb {H}} \)where each\(f^h\)maps\(D \rightarrow R\). ...