# components

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## 1—10 of 15 matching pages

##### 1: About Color Map
The following figure illustrates the piece-wise linear mapping of the height to each of the color components red, green and blue, written as $\left\langle R,\;G,\;B\right\rangle$. … Mathematically, we scale the height to $h$ lying in the interval $[0,4]$ and the components are computed as follows …
##### 2: 16.23 Mathematical Applications
In Janson et al. (1993) limiting distributions are discussed for the sparse connected components of these graphs, and the asymptotics of three ${{}_{2}F_{2}}$ functions are applied to compute the expected value of the excess. …
##### 3: 1.6 Vectors and Vector-Valued Functions
Much vector algebra involves summation over suffices of products of vector components. … The divergence of a differentiable vector-valued function $\mathbf{F}=F_{1}\mathbf{i}+F_{2}\mathbf{j}+F_{3}\mathbf{k}$ is
1.6.21 $\operatorname{div}\mathbf{F}=\nabla\cdot\mathbf{F}=\frac{\partial F_{1}}{% \partial x}+\frac{\partial F_{2}}{\partial y}+\frac{\partial F_{3}}{\partial z}.$
The line integral of a vector-valued function $\mathbf{F}=F_{1}\mathbf{i}+F_{2}\mathbf{j}+F_{3}\mathbf{k}$ along $\mathbf{c}$ is given by …
1.6.43 $\mathbf{F}(x,y)=F_{1}(x,y)\mathbf{i}+F_{2}(x,y)\mathbf{j}$
##### 4: 19.19 Taylor and Related Series
The number of terms in $T_{N}$ can be greatly reduced by using variables $\mathbf{Z}=\boldsymbol{{1}}-(\mathbf{z}/A)$ with $A$ chosen to make $E_{1}(\mathbf{Z})=0$. …
##### 5: 21.2 Definitions
21.2.1 $\theta\left(\mathbf{z}\middle|\boldsymbol{{\Omega}}\right)=\sum_{\mathbf{n}\in% {\mathbb{Z}}^{g}}e^{2\pi i\left(\frac{1}{2}\mathbf{n}\cdot\boldsymbol{{\Omega}% }\cdot\mathbf{n}+\mathbf{n}\cdot\mathbf{z}\right)}.$
$\theta\left(\mathbf{z}\middle|\boldsymbol{{\Omega}}\right)$ is also referred to as a theta function with $g$ components, a $g$-dimensional theta function or as a genus $g$ theta function. …
##### 6: 14.30 Spherical and Spheroidal Harmonics
14.30.11_5 $\mathrm{L}_{z}Y_{{l},{m}}=\hbar mY_{{l},{m}},$ $m=-l,-1+1,\dots,0,\dots,l-1,l$,
and $\mathrm{L}_{z}$ is the $z$ component of the angular momentum operator
14.30.13 $\mathrm{L}_{z}=-\mathrm{i}\hbar\frac{\partial}{\partial\phi};$
##### 7: 19.24 Inequalities
If $a$ ($\neq 0$) is real, all components of $\mathbf{b}$ and $\mathbf{z}$ are positive, and the components of $z$ are not all equal, then …
##### 8: Bibliography J
• S. Janson, D. E. Knuth, T. Łuczak, and B. Pittel (1993) The birth of the giant component. Random Structures Algorithms 4 (3), pp. 231–358.
• ##### 9: 21.7 Riemann Surfaces
where $P_{1}$ and $P_{2}$ are points on $\Gamma$, $\boldsymbol{{\omega}}=(\omega_{1},\omega_{2},\dots,\omega_{g})$, and the path of integration on $\Gamma$ from $P_{1}$ to $P_{2}$ is identical for all components. … where again all integration paths are identical for all components. …
##### 10: 19.28 Integrals of Elliptic Integrals
To replace a single component of $\mathbf{z}$ in $R_{-a}\left(\mathbf{b};\mathbf{z}\right)$ by several different variables (as in (19.28.6)), see Carlson (1963, (7.9)). …