█████████

███████ █████████

In █████████ ███████ and ███████████, there is █████ ████████ in █████████████ the ██████ or ████████ ████████ in the ███████████ of a ████████. For ████████, if the ████████ were a ██████ ██████, the ██████ █████ be █████ by █████'s ███, which ████ that the █████ ███████████ by a ██████ is ████████████ to the ████████ █████████ from ███████████. ████████ which can be ██████████ to the ███████████ of a ████████ from some ████ █████ are ██████ ███████ ████████. In █████ █████████, ████████ are ███████ which can be ██████████ to the ███████████ ████ over ████. █████ are ██████ ███████ ████████. For ████████, in a █████ ████ as █████ the ████████ which █████ from ████████ the █████ do not ██████ on the ████████ the █████ has been ███████; ██████, they ██████ on ███ ███████ the ████████ ██████.

█████████ is the ████████ ████████ which ███████ the ███████ ████████ in a ████████ to the ████ of ██████ of a ███████████ (the ██████ ████). ████████ it ███████ to ███████ █████, it is ████ to █████████ and ██████ in a ██████ ████████ ████, ████ as a ██████ ███████ ████.

In the ███████ ████, a █████ is ███████ between ███ ██████████ █████ ██████, ███ █████ and ███ in ████████ ██████ at ████████ █████ ${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$ (███ ████████████ to the █████). If the █████ of the ███ █████ is ███ ██████ (to █████ ██████████), ████ in ██████ █████ the █████ █████████ ████ ████████ to it, and █████ █████ ██████ from ${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$ at the ██████ to ${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$ at the ███. ████ █████ of █████ █████ ██████ than the ███ ████ below it, and ████████ between ████ █████ ████ to a █████ █████████ █████ ████████ ██████. In ██████████, the █████ ███████ on the ███ █████ a █████ in the █████████ opposite to ███ ██████, and an █████ but opposite █████ on the ██████ █████. An ████████ █████ is █████████ ████████ in █████ to ████ the ███ █████ ██████ at ████████ █████.

In ████ ██████, the ████ ████████ is ████████ to ████ ████████ from ████ at the ██████ to ${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$ at the ███. ████████, the █████████ of the █████, ${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$, ██████ on the ███ █████ is █████ to be ████████████ to the █████ ${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$ and the ████ ${\displaystyle A}$ of ████ █████, and █████████ ████████████ to █████ ██████████ ${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$:

${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}=\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}A\frac{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}.}$

The ███████████████ ██████ is the ███████ █████████ of the █████, █████ ██████ ████████ to as the █████████. It is ███████ by the █████ ██████ ██ (█). The ███████ █████████ has the ██████████ ${\displaystyle (\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\mathrm{a}\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}/\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>})/\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$, █████████ █████████ in the ██ █████ and the ███████ █████:

${\displaystyle [\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}]=\frac{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\cdot \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}=\frac{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}{{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}^{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}}\cdot \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}=\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\mathrm{a}\cdot \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}=}$ ████████ ██████████ by ████ ${\displaystyle =}$ ██████ per ████ ██████ ██████████ by ████.

The ██████████████ █████ ${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}/\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$ is ██████ the ████ of █████ ███████████ or █████ ████████, and is the ██████████ of the █████ █████ in the █████████ ████████ to the ██████ ██████ of the ██████ (███ █████████████ to the █████). If the ████████ ████ not ████ ████████ with ${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$, ████ the ███████████ ██████████████ is:

${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}=\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\frac{\mathrm{\partial }\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}{\mathrm{\partial }\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}},}$

█████ ${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}=\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}/A}$, and ${\displaystyle \mathrm{\partial }\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}/\mathrm{\partial }\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$ is the █████ █████ ████████. This ██████████ is ████████ to as ██████'s ███ of █████████. In ████████ █████ with ██████ ████████, it is ████ ███████ ${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$. It is a ███████ ████ of the ███████ ██████████ of █████████ (███ below), which can be █████████ in ██████████-████ ████.

Use of the █████ ██████ ██ (${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$) for the ███████ █████████ (█████████ ████ ██████ the ████████ █████████) is ██████ among ██████████ and ████████ █████████, as ████ as ██████████████ and ██████████. ███████, the █████ ██████ ███ (${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$) is ████ used by ████████, ██████████, and the █████. The █████████ ${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$ is █████████ ████ ██████ the █████ █████████. ███████, at █████ ███ ██████ ███████████ the use of this ███████████, ██████ that ${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$ can ██████ in ███-████████ █████ in ████████ to ████████ █████.

█████████ █████████

In █████ ████████, it is █████████ ████ ███████████ to ████ in █████ of █████████ █████████ (█████████ ████ ██████ the ████████ ███████████), ███████ as the █████ of the ███████ █████████ (█) over the ███████ of the █████ (█). It is ███████ ███████ by the █████ ██████ ██ (█):

${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}=\frac{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}},}$

and has the ██████████ ${\displaystyle (\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}{)}^{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}/\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$, █████████ █████████ in the ██ █████ and the ███████ █████:

${\displaystyle [\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}]=\frac{{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}^{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}}{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}=\frac{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\cdot \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}\cdot \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}=\frac{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}\cdot \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}=}$ ████████ ██████ ██████████ by ████ ${\displaystyle =}$ ██████ per ████ ████ ██████████ by ████.

███████ ██████████

In ████ ███████ █████, the ███████ ████████ in a █████ are ███████ as █████ █████████ from the ████████ ████████ of █████████ █████ █████████. As ████, the ███████ ████████ ████ ██████ on ███████ █████████ of the ████ ████████. If the ████████ █████████ are █████, ████ to a █████ █████████████ the ███████ ████████ ██████ ████ on the █████ ███████████ of the ████████. (For █████████ ██████, this is ████ a ██████ ██████████.) In █████████ ███████████, the ███████ ████████████ can ████ be ███████ as

${\displaystyle {\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}_{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}=\sum _{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}\sum _{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}_{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}\frac{\mathrm{\partial }{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}_{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}}{\mathrm{\partial }{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}_{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}},}$

█████ ${\displaystyle {\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}_{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}}$ is a █████████ ██████ that ████ the ████████ ████████ ██████ ${\displaystyle \mathrm{\partial }{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}_{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}/\mathrm{\partial }{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}_{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}}$ onto the ███████ ██████ ██████ ${\displaystyle {\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}_{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}}$. Since the ███████ in this ██████████ can ████ from █ to █, there are ██ "█████████ ████████████" ${\displaystyle {\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}_{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}}$ in █████. ███████, ████████ that the █████████ ████-█ ██████ is █████████ ███████ █████ ██ ████████████ to █████ ███████████ ██████████ ${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$, ${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$, ${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$:

${\displaystyle {\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}_{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}=\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}_{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}_{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}+\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}_{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}_{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}+\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}_{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}_{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}},}$

and ███████████, it is ███████ that ██ ███████ ██████ ███ █████ ████ the █████ is ██████████ ██████ █████-████ ████████, ████ ${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}=\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$, ███████ ████ ███ ███████████ ██████████. The ████ █████ █████████████ is in █████ of the ████████ (██████) █████████ ${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$ and the ████ █████████ ${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$ ████ that ${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}=\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}-\frac{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$ and ${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}=\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}=\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$. In ██████ ████████ this ███████ as:

${\displaystyle \mathit{<span\; word-length="1"\; class="word\; redacted">█</span>}=\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\left[\mathrm{\nabla }\mathbf{<span\; word-length="1"\; class="word\; redacted">█</span>}+(\mathrm{\nabla }\mathbf{<span\; word-length="1"\; class="word\; redacted">█</span>}{)}^{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}\right]-\left(\frac{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}-\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\right)(\mathrm{\nabla }\cdot \mathbf{<span\; word-length="1"\; class="word\; redacted">█</span>})\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>},}$

█████ ${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$ is the ████ ██████. This ████████ can be ███████ of as a ███████████ ████ of ██████'s ███ of █████████.

The ████ █████████ (████ ██████ ██████ █████████) █████████ a ████ of ████████ ████████ that ███████ the █████████ ███████████ or █████████ of a █████. █████████ of ${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$ is ██████████ not █████████ in █████ ████████ ████████. For ███████, an ██████████████ █████ █████████ ${\displaystyle \mathrm{\nabla }\cdot \mathbf{<span\; word-length="1"\; class="word\; redacted">█</span>}=\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$ and ██ the ████ ██████████ ${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$ █████ out. ████████, ${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$ is █████ ███████ to be ██████████ for █████ since it is ${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$ in a █████████ █████ ███. ███ █████████ in which ${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$ can be █████████ is the ███████████ of ██████ ████ in █████ and █████ █████, █████████ by ██████' ███ of █████ ███████████, since █████ █████████ ███████ █████ ██████████ and ████████████.

The ████████ █████████ for █████████ are not ███████████ ████ of ██████, ██ █████ ██████████, as ████ as ███████ for █████████ or ███████████ the █████████, ████ be ███████████ using ████████ █████. A █████████ █████ is that █████████ ███████, in █████████, on the ████ ███████████ █████ of the █████, which ███████████ the █████████ and ███████ of █████ ████████ in the ██████. ████ ██████ ████████ ███████████ is █████████ not █████████ in █████████ ███████. ███████, under ███████ ██████████ ████ of this ███████████ can be █████ to be ██████████. In ██████████, for █████████ ██████ near ███████████ and ███ from ██████████ (████ █████), the █████████ ███████ ████ █████- and ████-█████████ ███████████ ██████ (████ as ███████████ and ███████) ████████ █████ ███████████.

████████████, █████████ ███ █████ █████ a ███-██████████ ██████████ on ███████ ██████ ██████████, ████ as ███████████, ████████, and the █████████ and █████████ of ███ ████████ ███████. █████████, █████████ ████████████ of █████████ are ████ ███████ with ███████ to a ████████ █████ █████. To ███████████ ███████████ among ███████████ and ███████████ ██████, █████████ ████ is █████████ ████████████ to █████ ████████ █████, ████ as the ████ █████ █████, or (for █████) the ████ ███████ █████.