# interior

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## 1—10 of 15 matching pages

##### 1: 19.32 Conformal Map onto a Rectangle

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►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
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##### 2: 30.14 Wave Equation in Oblate Spheroidal Coordinates

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###### §30.14(v) The Interior Dirichlet Problem for Oblate Ellipsoids

…##### 3: 14.28 Sums

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►where ${\mathcal{E}}_{1}$ and ${\mathcal{E}}_{2}$ are ellipses with foci at $\pm 1$, ${\mathcal{E}}_{2}$ being properly interior to ${\mathcal{E}}_{1}$.
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##### 4: 30.13 Wave Equation in Prolate Spheroidal Coordinates

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###### §30.13(v) The Interior Dirichlet Problem for Prolate Ellipsoids

…##### 5: 23.20 Mathematical Applications

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►The interior of $R$ is mapped one-to-one onto the lower half-plane.
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►The interior of the rectangle with vertices $0$, ${\omega}_{1}$, $2{\omega}_{3}$, $2{\omega}_{3}-{\omega}_{1}$ is mapped two-to-one onto the lower half-plane.
The interior of the rectangle with vertices $0$, ${\omega}_{1}$, $\frac{1}{2}{\omega}_{1}+{\omega}_{3}$, $\frac{1}{2}{\omega}_{1}-{\omega}_{3}$ is mapped one-to-one onto the lower half-plane with a cut from ${e}_{3}$ to $\mathrm{\wp}\left(\frac{1}{2}{\omega}_{1}+{\omega}_{3}\right)\phantom{\rule{0.3888888888888889em}{0ex}}(=\mathrm{\wp}\left(\frac{1}{2}{\omega}_{1}-{\omega}_{3}\right))$.
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##### 6: 2.4 Contour Integrals

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►We assume that in any closed sector with vertex $t=0$ and properly interior to $$, the expansion (2.3.7) holds as $t\to 0$, and $q(t)=O\left({\mathrm{e}}^{\sigma |t|}\right)$ as $t\to \mathrm{\infty}$, where $\sigma $ is a constant.
Then (2.4.1) is valid in any closed sector with vertex $z=0$ and properly interior to $$.
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►Now suppose that in (2.4.10) the minimum of $\mathrm{\Re}\left(zp(t)\right)$ on $\mathcal{P}$ occurs at an interior point ${t}_{0}$.
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►In the commonest case the interior minimum ${t}_{0}$ of $\mathrm{\Re}\left(zp(t)\right)$ is a simple zero of ${p}^{\prime}(t)$.
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##### 7: 1.9 Calculus of a Complex Variable

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►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

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►For scattering problems, the interior solution is then matched to a linear combination of a pair of Coulomb functions, ${F}_{\mathrm{\ell}}(\eta ,\rho )$ and ${G}_{\mathrm{\ell}}(\eta ,\rho )$, or $f(\u03f5,\mathrm{\ell};r)$ and $h(\u03f5,\mathrm{\ell};r)$, to determine the scattering $S$-matrix and also the correct normalization of the interior wave solutions; see Bloch et al. (1951).
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##### 9: 3.4 Differentiation

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►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 $C$.
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##### 10: Bibliography

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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.
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