# interior

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## 1—10 of 15 matching pages

##### 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 …
##### 3: 14.28 Sums
where $\mathcal{E}_{1}$ and $\mathcal{E}_{2}$ are ellipses with foci at $\pm 1$, $\mathcal{E}_{2}$ being properly interior to $\mathcal{E}_{1}$. …
##### 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 $0$, $\omega_{1}$, $2\omega_{3}$, $2\omega_{3}-\omega_{1}$ 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 $\wp\left(\frac{1}{2}\omega_{1}+\omega_{3}\right)\>(=\wp\left(\frac{1}{2}\omega% _{1}-\omega_{3}\right))$. …
##### 6: 2.4 Contour Integrals
We assume that in any closed sector with vertex $t=0$ and properly interior to $\alpha_{1}<\operatorname{ph}t<\alpha_{2}$, the expansion (2.3.7) holds as $t\to 0$, and $q(t)=O\left(e^{\sigma|t|}\right)$ as $t\to\infty$, where $\sigma$ is a constant. Then (2.4.1) is valid in any closed sector with vertex $z=0$ and properly interior to $-\alpha_{2}-\frac{1}{2}\pi<\operatorname{ph}z<-\alpha_{1}+\frac{1}{2}\pi$. … Now suppose that in (2.4.10) the minimum of $\Re\left(zp(t)\right)$ on $\mathscr{P}$ occurs at an interior point $t_{0}$. … In the commonest case the interior minimum $t_{0}$ of $\Re\left(zp(t)\right)$ is a simple zero of $p^{\prime}(t)$. …
##### 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, $F_{\ell}\left(\eta,\rho\right)$ and $G_{\ell}\left(\eta,\rho\right)$, or $f\left(\epsilon,\ell;r\right)$ and $h\left(\epsilon,\ell;r\right)$, 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.