Sentence examples for classification conjecture from inspiring English sources
As a corollary, we confirm Elliott's classification conjecture under reasonably general hypotheses which, notably, do not require any inductive limit structure.
We establish six equivalent characterisations of the proper subclass which satisfies the strong form of Elliott's classification conjecture: two C∗-algebraic (Z-stability and approximate divisibility), one K-theoretic (strict comparison of positive elements), and three topological (finite decomposition rank, slow dimension growth, and bounded dimension growth).
(In the case of simple suchC*-algebras, it has been proved that the above invariant is the complete invariant by George Elliott and the author.) These examples prove that the classification conjecture of Elliott for the case of non simple real rank zeroC*-algebras should be revised one needs extra invariants.
Mathematical standards have a good track record when it comes to questions such as whether 1 + 2 is equal to 3, or what the series 1 + 1/4 + 1/9 + 1/16 + … converges to, or whether the Poincaré Conjecture (concerning the classification of 3-manifolds) is true; but they do not have a proven track record when it comes to questions such as whether these truths are platonist or structuralist.
Commenting on the six-month postponement between classification and release, Thunderbirds historian Chris Bentley conjectures that United Artists had lost faith in distributing the Thunderbirds franchise in light of the disappointing box office returns for Thunderbirds Are Go, and therefore intentionally shelved the sequel between January and July.
The proof of the Lawson conjecture can be extended to give a classification of all Alexandrov immersed minimal tori in (S^3): (Brendle [10]) Let (F: Sigma rightarrow S^3) be an immersed minimal surface in (S^3) of genus (1).
And though the exhibition is roughly divided into categories — animals as muses, symbols, companions, talking creatures and moral teachers — notice is served from the start by a quote from Jorge Luis Borges: There is "no classification of the Universe that is not arbitrary and full of conjectures".
(Church 1936a, 1936b) and (Turing 1936) imply the existence of theorems whose shortest proof is very large, and the proof of the Four Color Theorem in (Appel and Haken 1977), the Classification of Simple Groups in (Gorenstein 1982), and the proof of the Kepler Conjecture in (Hales 2005a) may well be just samples of what is yet to come.
This seems to reinforce the the conjecture that redundancy removal from the top PCAIMs does not significantly affect classification performance, while considerably reducing the number of markers.
