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1: 19.32 Conformal Map onto a Rectangle
then z ( p ) is a Schwartz–Christoffel mapping of the open upper-half p -plane onto the interior of the rectangle in the z -plane with vertices …
2: 30.14 Wave Equation in Oblate Spheroidal Coordinates
§30.14(v) The Interior Dirichlet Problem for Oblate Ellipsoids
3: 14.28 Sums
where 1 and 2 are ellipses with foci at ± 1 , 2 being properly interior to 1 . …
4: 30.13 Wave Equation in Prolate Spheroidal Coordinates
§30.13(v) The Interior Dirichlet Problem for Prolate Ellipsoids
5: 23.20 Mathematical Applications
The interior of R is mapped one-to-one onto the lower half-plane. … The interior of the rectangle with vertices 0 , ω 1 , 2 ω 3 , 2 ω 3 ω 1 is mapped two-to-one onto the lower half-plane. The interior of the rectangle with vertices 0 , ω 1 , 1 2 ω 1 + ω 3 , 1 2 ω 1 ω 3 is mapped one-to-one onto the lower half-plane with a cut from e 3 to ( 1 2 ω 1 + ω 3 ) ( = ( 1 2 ω 1 ω 3 ) ) . …
6: 2.4 Contour Integrals
We assume that in any closed sector with vertex t = 0 and properly interior to α 1 < ph t < α 2 , the expansion (2.3.7) holds as t 0 , and q ( t ) = O ( e σ | t | ) as t , where σ is a constant. Then (2.4.1) is valid in any closed sector with vertex z = 0 and properly interior to α 2 1 2 π < ph z < α 1 + 1 2 π . … Now suppose that in (2.4.10) the minimum of ( z p ( t ) ) on 𝒫 occurs at an interior point t 0 . … In the commonest case the interior minimum t 0 of ( z p ( t ) ) is a simple zero of p ( t ) . …
7: 1.9 Calculus of a Complex Variable
Points of a region that are not boundary points are called interior points. …
Jordan Curve Theorem
One of these domains is bounded and is called the interior domain of C ; the other is unbounded and is called the exterior domain of C . …
8: 33.22 Particle Scattering and Atomic and Molecular Spectra
For scattering problems, the interior solution is then matched to a linear combination of a pair of Coulomb functions, F ( η , ρ ) and G ( η , ρ ) , or f ( ϵ , ; r ) and h ( ϵ , ; r ) , to determine the scattering S -matrix and also the correct normalization of the interior wave solutions; see Bloch et al. (1951). …
9: 3.4 Differentiation
where C is a simple closed contour described in the positive rotational sense such that C and its interior lie in the domain of analyticity of f , and x 0 is interior to C . …
10: Bibliography
  • C. L. Adler, J. A. Lock, B. R. Stone, and C. J. Garcia (1997) High-order interior caustics produced in scattering of a diagonally incident plane wave by a circular cylinder. J. Opt. Soc. Amer. A 14 (6), pp. 1305–1315.