| 31. | The section characterizations below states what necessary and sufficient conditions a quadrilateral must satisfy to have an incircle.
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| 32. | The converse does hold if ? is a Pisot number, although necessary and sufficient conditions are not known.
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| 33. | No necessary and sufficient conditions exist.
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| 34. | The von Neumann Morgenstern utility theorem provides necessary and sufficient conditions under which the expected utility hypothesis holds.
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| 35. | To me, that seems a necessary and sufficient condition for an article entitled " Kingdom of Mysore ".
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| 36. | Snow's being white is a necessary and sufficient condition for the truth of the proposition that snow is white.
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| 37. | Hiroshi Okamura obtained a necessary and sufficient condition for the solution of an initial value problem to be unique.
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| 38. | An indirect method works by analytically constructing the necessary and sufficient conditions for optimality, which are then solved numerically.
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| 39. | These background assumptions go up and beyond those necessary and sufficient conditions that correspond to a semantic feature account.
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| 40. | Another necessary and sufficient condition for a tetrahedron to be orthocentric is that its three bimedians have equal length.
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