Bézier curves
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11: 27.19 Methods of Computation: Factorization
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βΊType I probabilistic algorithms include the Brent–Pollard rho algorithm (also called Monte Carlo method), the Pollard algorithm, and the Elliptic Curve Method (ecm).
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12: 31.8 Solutions via Quadratures
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βΊThe variables and are two coordinates of the associated hyperelliptic (spectral) curve
.
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βΊThe curve
reflects the finite-gap property of Equation (31.2.1) when the exponent parameters satisfy (31.8.1) for .
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13: 28.32 Mathematical Applications
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βΊAlso let be a curve (possibly improper) such that the quantity
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βΊ
28.32.6
βΊdefines a solution of Mathieu’s equation, provided that (in the case of an improper curve) the integral converges with respect to uniformly on compact subsets of .
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14: 1.6 Vectors and Vector-Valued Functions
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βΊThe geometrical image of a path is called a simple
closed curve if is one-to-one, with the exception .
The curve
is piecewise differentiable if is piecewise differentiable.
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βΊand be the closed and bounded point set in the plane having a simple closed curve
as boundary.
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βΊ
1.6.44
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15: 32.3 Graphics
16: 36.5 Stokes Sets
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βΊThe Stokes set is itself a cusped curve, connected to the cusp of the bifurcation set:
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βΊFor , the set consists of the two curves
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βΊIn Figures 36.5.1–36.5.6 the plane is divided into regions by the dashed curves (Stokes sets) and the continuous curves (bifurcation sets).
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17: Philip J. Davis
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βΊMoreover, a cutting plane feature allows users to track curves of intersection produced as a moving plane cuts through the function surface.
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18: 21.4 Graphics
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βΊThis Riemann matrix originates from the Riemann surface represented by the algebraic curve
; compare §21.7(i).
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βΊ
19: 36.7 Zeros
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βΊInside the cusp, that is, for , the zeros form pairs lying in curved rows.
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βΊThe zeros of these functions are curves in space; see Nye (2007) for and Nye (2006) for .
20: Preface
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βΊSaunders was responsible for mesh generation for curves and surfaces, data computation and validation, graphics production, and interactive Web visualization.
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