102,365 research outputs found

    The complex plank problem

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    It is shown that if (vj)(v_{j}) is a sequence of norm 11 in a complex Hilbert space and (tj)(t_{j}) is a sequence of nonnegative numbers satisfying tj2=1\sum t_{j}^{2}=1 then there is a unit vector z for which $|\langle v_{j}, z \rangle|\geq t_{j} for every j. The result is a strong, complex analogue of the author's real plank theorem

    plank stick; plank sticks

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    stick nI mean to say out there in the cemetery now they cut _ they used to cut plank sticks.My grandfather cut plank sticks where the cemetery is now,see. (trees cut for making planks ?)YesJ. D. A. WIDDOWSON JUL 1973Used I and SupUsed INot used~fenc

    plank (v)

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    plank...there's so many bars in the set, they used to call it, and... an' they'd... they'd go right to it - plank it right down, sir!YesJ.D.A.WIDDOWSONNot usedNot usedWithdraw

    plank stick; plank sticks

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    stick nAn' of course there ;d be a flake room to keep up,there'd be a stage to repair,or boats to repair,an' then you'd have to cut your plank sticks.... (trees for cutting into planks ?)YesJ. D. A. WIDDOWSON JUL 1973Used I and SupUsed INot used~fenc

    David Plank and Joy Plank interview, 2022 February 15

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    Oral history interview documenting McCoy Farm and Gardens located on Walden's Ridge on Signal Mountain in Tennessee

    David Plank and Joy Plank interview, 2022 February 15

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    Oral history interview documenting McCoy Farm and Gardens located on Walden's Ridge on Signal Mountain in Tennessee

    plank out (v)

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    plank outAn' the same way you lay it on _ you lay it on a wharf stick, see, if you was goin' to plank out a wharf. You lay birch rine over _ over your stick, see, would preserve it from _ from the water seepin' into it an' makin' it rotten quicker than what 'twould.... if there was nothing there. (put planks over framework of wharf?)YesJ.D.A.WIDDOWSON JUL 1973Not usedNot usedWithdraw

    plank (v); planked

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    plankShe just was _ she plank _ planked one of her _ one of her feet on top of it...YesJ.D.A.WIDDOWSONNot usedNot usedWithdraw

    America’s Toll Roads Heritage: The Achievements of Private Initiative in the 19th Century

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    Private toll roads shaped and accommodated trade and migration routes, leaving social and political imprints on the communities that debated and supported them. Private road building came and went in waves throughout the 19th century and across the country. All told, between 2,500 and 3,200 companies successfully financed, built, and operated their toll road. Although most of these roads operated for only a fraction of the 100+ period, the combined mileage of private toll roads that operated at any point in time would be in range of 30,000 to 52,000 miles. The paper explores the character, methods, and purposes of the private toll roads, and draws lessons for the privatization of highways today.toll roads; turnpikes; plank roads; privatization; free riding; regulation
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