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21—30 of 60 matching pages
21: 36.5 Stokes Sets
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►In 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).
Red and blue numbers in each region correspond, respectively, to the numbers of real and complex critical points that contribute to the asymptotics of the canonical integral away from the bifurcation sets.
…The distribution of real and complex critical points in Figures 36.5.5 and 36.5.6 follows from consistency with Figure 36.5.1 and the fact that there are four real saddles in the inner regions.
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22: 1.6 Vectors and Vector-Valued Functions
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►and be the closed and bounded point set in the plane having a simple closed curve as boundary.
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1.6.44
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►Suppose is a piecewise smooth surface which forms the complete boundary of a bounded closed point set , and is oriented by its normal being outwards from .
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1.6.58
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1.6.59
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23: 1.5 Calculus of Two or More Variables
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►A function is continuous on a point set
if it is continuous at all points of .
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►For defined on a point set contained in a rectangle , let
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1.5.28
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1.5.29
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1.5.31
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24: 1.9 Calculus of a Complex Variable
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►A region is an open domain together with none, some, or all of its boundary points.
Points of a region that are not boundary points are called interior points.
►A function is continuous on a region
if for each point in and any given number () we can find a neighborhood of such that for all points in the intersection of the neighborhood with .
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25: Bibliography W
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Asymptotic behavior of stability regions for Hill’s equation.
SIAM J. Appl. Math. 47 (5), pp. 941–958.
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Spin-spin correlation functions for the two-dimensional Ising model: Exact theory in the scaling region.
Phys. Rev. B 13, pp. 316–374.
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26: 10.2 Definitions
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►Table 10.2.1 lists numerically satisfactory pairs of solutions (§2.7(iv)) of (10.2.1) for the stated intervals or regions in the case .
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27: 2.4 Contour Integrals
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►If is analytic in a sector containing , then the region of validity may be increased by rotation of the integration paths.
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►Additionally, it may be advantageous to arrange that is constant on the path: this will usually lead to greater regions of validity and sharper error bounds.
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►The problem of obtaining an asymptotic approximation to that is uniform with respect to in a region containing is similar to the problem of a coalescing endpoint and saddle point outlined in §2.3(v).
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28: 10.25 Definitions
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29: 19.33 Triaxial Ellipsoids
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►If a conducting ellipsoid with semiaxes bears an electric charge , then the equipotential surfaces in the exterior region are confocal ellipsoids:
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