Sentence examples for the proof requires from inspiring English sources
The proof requires a little time.
The proof requires a theory of the constant term for W-invariant functions satisfying the hypergeometric system.
In the latter case the proof requires some fine properties of BV functions in the Heisenberg group.
In the former case the proof requires a delicate analysis of minimizing geodesics of the group and of the differentiability properties of the squared distance function.
As in the previous work by the first author with Gigli and Savaré in the Sobolev case, the proof requires neither local compactness nor doubling and Poincaré.
The proof requires that the observability constant related to the control problem be uniform with respect to the support, property which is obtained by the control transmutation method.
Their primary argument relates to the proof required to convict a "tippee" of insider trading.
The proof required by Wells Fargo and approved by the court was "valid, accurate and true copies" of the front and back of the checks the borrowers sent in.
"The best thing we could find would be evidence of a moat," Dr. Deagan said, discussing the proof required to identify La Navidad.
In a note sent to a small group of researchers on Aug. 6, Dr. Deolalikar wrote: "The proof required the piecing together of principles from multiple areas within mathematics.
No one has quite figured out how to administer offset credits because the "proof" required is ultimately a matter of judgement, not fact, said Mr. Victor of the Laboratory on International Law and Regulation.
