| 单词 | saddle point |
| 释义 | > as lemmassaddle point saddle point n. Mathematics (a) a point at which a curved surface is locally level but at which its curvature in two directions differs in sign, i.e. for a surface defined by a function f of x and y, a point at which ∂f/∂x = ∂f/∂y = 0 and (∂2f/∂x2)(∂2f/∂y2) < 0; (b) (in a zero-sum game) the joint outcome of the two parties following their unmixed optimal strategies, where these exist. ΘΚΠ the world > relative properties > number > geometry > point > [noun] > on a surface or plane conical point1812 umbilicus1841 stigma1863 binode1869 branch-point1878 saddle point1907 saddle1952 the world > relative properties > number > mathematics > [noun] > mathematical enquiry > result of > in specific case saddle point1907 Poincaré cycle1943 1907 Amer. Jrnl. Math. 29 371 The intersection of the surface with any plane Z = c is a quartic curve which, when Z = 0, degenerates into two parabolæ, Y4 + 2Y2X − X2 = 0, tangents to each other at the origin, which thus becomes a saddle-point. 1946 H. Jeffreys & B. S. Jeffreys Methods Math. Physics xvii. 472 Through any saddle-point it will be possible to draw at least two curves such that ϕ is constant along them. 1960 A. Rapoport Fights, Games, & Debates vii. 136 A saddle point is an entry in the game matrix which is the smallest in its row and the largest in its column. 1966 S. Beer Decision & Control xviii. 467 In the inadequate game-theoretic model, neither side can exploit information about the other, because the game has a fixed saddle point. 2004 K. Nakamura & T. Harayama Quantum Chaos & Quantum Dots v. 70 This divergence occurs when saddle points (periodic orbits) become degenerate. Examples are (i) systems that have continuous symmetry and (ii) those showing orbit bifurcations. < as lemmas |
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