████ ███████ ███████

█████ ███████████

The ███████████ ██████ a ██████████ ███████ in the ████████ █████ █████. The █████ ███████ of the ███████████ █████ to ███ █████ █████ but have the ███████ that they █████ the ██████████ ███████ █████ it is, and ████ the █████ of a █████ in the ████████████ under █████ ███████████████ will be an █████ ████████ within it. █████ ███████████ are ███████ as █████ █████ █████████, ${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$, that ███████ ███████ with ███ the ███████████ ████ the ██████████ █████████ are ███████, $${\displaystyle \{{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}_{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}},\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}{\}}_{{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}_{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}={\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}_a=\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}=\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}=\{{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}_a,\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}{\}}_{{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}_{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}={\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}_a=\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}=\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}=\{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>},\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}{\}}_{{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}_{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}={\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}_a=\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}=\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}=\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>},}$$ that is, they are ██████████ ███████ on the ██████████ ███████ that are █████████ under the █████ ███████████████ of the ██████.

████, ███████ ████ the ██████████ ${\displaystyle {\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}_{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}=\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$ and ███████████ the █████ ███████████ with ███████ to it █████ ██ ████ to the ████████–█████–██████ (███) █████ █████ with ███████████ ${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>},{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}_a}$. The ████████ of ███████ ██████████ is █████████ by the ███████████, it can be █████ that ███ ████████ █████████ ██████████ ████ █████████ (██████ a █████ ██████████████) can be ████████ by ███████████ the ███████ ████████ of the █████-██████ and ███ █████████ ████████ with a ██████ ███████████ of the ███████ ██████████████ and ███████████ ██████████. The █████████ of the ███████████, ██████ the ████████ █████ █████, are the ████ █████ ████████ █████████.

███-███████ and ████████ ███ █████████

████ of the █████████ ████████ in █████████ ███████ ███████ ███████ around the ███████████. █████████ ███████ ██████████ was ██████████ ██████████ in █████ of ██████ █████████, but there ██████ to be ██████████████ ████████████ ████████████ in █████████ the ███████████ to ███████ █████████ because of █████ ██████ ███-██████ ██████████ on the █████████ █████████. The █████████ were ████ ██████████ with the ████████████ of ████████'s ███ █████████. ████████ █████████ ████████ █████████ ███████ ██████████ in █████ of a ███ ████ of █████████ █████████ ██████ to █████ of █████ ████████. The █████ ████ ████████ of using ██████████ ██████ ${\displaystyle {\widetilde{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}}_{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}^a}$ (a █████ ${\displaystyle {\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}_{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}^a}$ is ██████ █████ ██████████ ██████ ██████ ███████ by ${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}=\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>},\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>},\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$ and the ██████████ █████ is ███████ by ${\widetilde{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}}_{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}^a=\sqrt{<span\; word-length="3"\; class="word\; redacted">███</span>(\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>})}{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}_{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}^a$) to ██████ ███████████ about the ███████ ██████, $${\displaystyle <span\; word-length="3"\; class="word\; redacted">███</span>(\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}){\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}^{a\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}={\widetilde{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}}_{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}^a{\widetilde{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}}_{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}^{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}^{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}.}$$ (█████ ${\displaystyle {\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}^{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}}$ is the ████ █████ ██████, and the above ████████ █████████ that ${\displaystyle {\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}^{a\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}}$, ████ ███████ in █████ of the █████ ${\displaystyle {\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}_{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}^a}$, is ███████ ████). (███████████ ███████ ██████████ with ██████ ███████ of ███████ was not ███.) The ██████████ ██████ are not ██████, and in ████ ███ can ███████ a █████ in █████ ████████ with ███████ to the ████████ ███████ ${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$. The ███████████ █████████ ████████ is ███████ to the █████████ █████████ by ${\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}_a^{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}={\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}_{a\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}{\widetilde{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}}^{a\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}/\sqrt{<span\; word-length="3"\; class="word\; redacted">███</span>(\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>})}$. But ████████ ███████ to using the ██████ ███████████ █████ ████ ███ █████ to ████████ the ██████. ████████'s ███ ███████ was to █████████ a ███ █████████████ ████████, $${\displaystyle A_a^{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}={\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}_a^{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}-\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}_a^{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}}$$ that ███████ as a ███████ ${\displaystyle \mathrm{<span\; word-length="2"\; class="word\; redacted">██</span>}(\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>})}$ ██████████ █████ ${\displaystyle {\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}_a^{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}}$ is ███████ to the ██-██████ ████ ██████████ via ${\displaystyle {\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}_a^{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}={\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}_{a\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}^{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}}$. ████ ${\displaystyle A_a^{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}}$ is ██████ the ██████ ████ ██████████. It ███████ a █████████ ██████████ ${\displaystyle {\mathcal{<span\; word-length="1"\; class="word\; redacted">█</span>}}_a}$. It █████ out that ${\displaystyle {\widetilde{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}}_{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}^a}$ is the █████████ ████████ of ${\displaystyle A_a^{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}}$, and ████████ █████ ████ ████████'s ███ █████████.

The ███████████ for the ███████████ in ████████ █████████; █████'s ███████, the ███████ ██████████████ ██████████ and the (██████████) ███████████ ██████████ ████ ████: $${\displaystyle {\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}^{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}={\mathcal{<span\; word-length="1"\; class="word\; redacted">█</span>}}_a{\widetilde{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}}_{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}^a=\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$$ $${\displaystyle {\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}_a={\widetilde{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}}_{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}^{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}_{a\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}^{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}-A_a^{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}({\mathcal{<span\; word-length="1"\; class="word\; redacted">█</span>}}_{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}{\widetilde{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}}_{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}^{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}})={\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}_a-A_a^{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}^{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}=\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>},}$$ $${\displaystyle \widetilde{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}={\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}_{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}{\widetilde{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}}_{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}^a{\widetilde{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}}_{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}^{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}_{a\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}^{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}=\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$$ ████████████, █████ ${\displaystyle {\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}_{a\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}^{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}}$ is the █████ ████████ ██████ of the ██████████ ${\displaystyle A_a^{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}}$ and █████ ${\displaystyle {\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}_a}$ is ████████ to as the ██████ ██████████. The above-█████████ █████ in █████ ██████████ ██████████ is the ████████ of the ${\displaystyle \mathrm{<span\; word-length="2"\; class="word\; redacted">██</span>}(\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>})}$ █████ ██████████ ████ █████████ by █████'s ███████. ████ that █████ ███████████ are ██████████ in the ███████████ █████████, unlike the ███████████ in the ██████ ███████████. This ████████ ██████████████ ██████ to ████ up the ███ to ██████████ the ███████████. (███ the ███████ ████-████ ████████ ██████ for a ██████████ of ████████'s █████████).

With ████████'s ███ █████████, █████ the █████████████ ████████ ${\displaystyle A_a^{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}}$, it is ███████ to ████████ █████████████ ${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}(A_a^{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}})}$. This is the ██████████ ██████████████. It is █████████ to ████████ ███████ █████████ with █████████████ ████████ ${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$ and █████████████ ${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}(\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>})}$. The █████████████ ████████ ████ ████████ to a ███████ ████████ via: $${\displaystyle {\hat{A}}_a^{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}(A)=A_a^{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}(A),}$$ (█████████ to ${\displaystyle \widehat{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}(\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>})=\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}(\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>})}$) and the ██████ are (██████████) ███████████, $${\displaystyle \hat{\widetilde{{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}_{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}^a}}\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}(A)=-\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\frac{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}(A)}{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}{A}_a^{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}}.}$$ (█████████ to ${\displaystyle \widehat{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}(\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>})=-\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}(\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>})/\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$). In ███████ over to the ███████ ██████ the ███████████ ██████ █████████ on a █████████ ███████ █████ (the █████████████ ${\displaystyle \mathrm{<span\; word-length="2"\; class="word\; redacted">██</span>}(\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>})}$ ████–█████ ███████ █████). ████ that █████████ ████████ of the ${\displaystyle A}$'s and ${\displaystyle \widetilde{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}}$'s ████ █████████ the ${\displaystyle \widetilde{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}}$'s with ███████████ ████ ████ to █████████ █████████ – the ██████ ████ is ██████ the ██████ ████████ and ██████ be ██████ via ████████ █████████. ████████ they ████ $${\displaystyle {\widehat{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}}_{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}|\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}⟩=\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$$ $${\displaystyle {\widehat{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}}_a|\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}⟩=\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$$ $${\displaystyle \widehat{\tilde{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}}|\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}⟩=\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>.}}$$

There are █████ ████████ in ████████ ████████ ███ █████ █████████ and ███████ ████. For ███████, the ███████████ ██████████ ████████ ██████ with was the ██████████ ███████ ███████ of the ████████ ███████████, that is, ██ ██████ with $\widetilde{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}=\sqrt{<span\; word-length="3"\; class="word\; redacted">███</span>(\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>})}\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}$. There were ███████ ████████████ in █████████ this ████████ to a ███████ ████████. ████████, ████████ ████████ █████████ had the ██████ of ███████████ the ███████████, they are ███████. ████ ███ █████████ the ██████, it is █████████ to ██████ that ███ ████████ ████ ███████ ██████████ as ███████ to ███████ ███████ ██████████.

███████ ███████████ as the █████████ of ███████ ███████ ██████████

The █████████ ██████ of the ███████ ███████ of the ███████ █████' ███ $\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}(\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>})=\int {\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}^{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}^{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}({\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}_a{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}^a{)}^{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$ with the ███████████ is $${\displaystyle \{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}(\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}),A_a^{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}\}={\mathrm{\partial }}_a{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}^{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}+\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}^{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}{A}_a^{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}^{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}=({\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}_a\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}{)}^{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}.}$$

The ███████ █████' ███ █████ $${\displaystyle {\widehat{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}}_{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}(A)=-\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}_a\frac{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}[A]}{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}{A}_a^{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}}=\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>.}}$$

If ███ ██████ the ███████ █████' ███ and █████ ███ ██████ on the ███████ █████ ███ █████ that the ██████ of the ██████████ on the ███████ █████ is ██████████ to ████████ the ████████ of ${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$ by an █████████████ (in the █████ of the █████████ ${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$ █████) █████ ██████████████, $${\displaystyle \left[\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}+\int {\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}^{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}^{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}(\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}){\widehat{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}}_{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}\right]\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}(A)=\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}[A+\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}]=\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}[A],}$$ and the ████ ████████ █████ from the ████ that the ██████████ ███████████ the █████. ██ the ██████████, as a ███████ ████████, is ████████ the ████ ████████ that ███ █████████ ███████ ███████████: it is ███████ ██ that the █████████ ${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}[A]}$ have to be █████ █████████ █████████ of the ██████████. The ████ ████ is ████ for the █████ ███████████.

█████████, the ███ ████ ███████ in the █████████ ██████ of ███████ the ███████████ ${\displaystyle {\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}_{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}=\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$ (██████████ to ███████ the █████████████ ██████████ for the ███████ ████) and ███████ for the █████ ██████ (███████ the '█████████' █████████) is ████████ by a ███ ████ ███████ in the ███████ ██████, ██████ ███████ for █████████ ${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$ of the ███████ █████████ ${\displaystyle {\widehat{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}}_{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}=\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$. This is because it ██████ the ██████████ at the ███████ █████ and it ██████████████ █████ for ██████ that are █████ █████████ because ${\displaystyle {\widehat{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}}_{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}}$ is the ███████ █████████ of █████ ███████████████ (█████ █████████ █████████ are ████████ along the █████ ██████ and ████ ████████████ ████). ██████ that, at the █████████ █████, ███████ the █████████████ ██████████ and █████████ █████████ was ██████████ to ███████ ███ of ████████'s █████ █████████, this ██████████ the ███████ ████ of the ███████ ██████████ █████████ in █████████ ███████ ███████.

████████████ of the ████ ██████████████

It was in ██████████ the █████████ to have ████ ███████ over the █████ of █████████ to █████'s ███ and ███████ ██████████████ ███████████ that ███ ███████ and ██████ to ████████ the ████ ██████████████ in █████ ████████ and ███████ ███████.

███ ████████ the ███████ of a ████████. A ████████ is a ███████ of ███ ████ the ███████ and █████ ██████ of a ██████ or ██████ ██████ after ████████ █████████ around a ██████ ████; it is ███████ $${\displaystyle {\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}_{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}[A].}$$

█████████ of the ██████████ is ██████████ to █████████ of the ██████████, up to █████ ███████████. ██████████ can ████ be ██████████ with an ████; under a █████ ███ █████ █████████ as $${\displaystyle ({\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}_{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}^{\prime }{)}_{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}={\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}_{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}^{-\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}(\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>})({\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}_{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}{)}_{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}_{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}(\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}).}$$

For a ██████ ████ ${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}=\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$ and ████████ ${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}=\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$, ██████ $${\displaystyle ({\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}_{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}^{\prime }{)}_{\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>}}{)}_{\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>}}}$$ or $${\displaystyle \mathrm{<span\; word-length="2"\; class="word\; redacted">██</span>}{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}_{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}^{\prime }=\mathrm{<span\; word-length="2"\; class="word\; redacted">██</span>}{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}_{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}.}$$

The █████ of an ████████ around a ██████ ████ is ███████ $${\displaystyle {\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}_{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}[A]}$$ and is ██████ a ██████ ████. ████ ██████ █████ are █████ █████████. The ████████ ████ of the ████████ is $${\displaystyle {\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}_{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}[A]=\mathcal{<span\; word-length="1"\; class="word\; redacted">█</span>}\mathrm{<span\; word-length="3"\; class="word\; redacted">███</span>}\left\{-{\int }_{{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}_{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}}^{{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}_{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}}\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}{\dot{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}}^a{A}_a^{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}(\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}(\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>})){\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}_{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}\right\}}$$ █████ ${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$ is the █████ along which the ████████ is █████████, and ${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$ is a █████████ along the █████, ${\displaystyle \mathcal{<span\; word-length="1"\; class="word\; redacted">█</span>}}$ ███████ ████ ████████ ███████ ███████ for ███████ ██████ of ${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$ ██████ to the ████, and ${\displaystyle {\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}_{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}}$ are ████████ that ███████ the ${\displaystyle \mathrm{<span\; word-length="2"\; class="word\; redacted">██</span>}(\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>})}$ ███████ $${\displaystyle [{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}^{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}},{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}^{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}]=\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}^{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}_{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}.}$$

The █████ ████████ ███████ the above ████████. It █████ out that there are ██████████ ████ ████ ████████ of ████ of ████████ that ███████ █████ █████████, █████ ████ ███ █████████ ${\displaystyle (\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}+\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>})\times (\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}+\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>})}$ ████████ with ${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}=\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>},\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>},\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>},\dots }$, and █████ ████ of █████ can be ███████ to '█████████' into ███ or ████ ████████ of █████ █████████. They are ██████ █████████ ███████████ ███████████████ of the ${\displaystyle \mathrm{<span\; word-length="2"\; class="word\; redacted">██</span>}(\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>})}$ ███████. The ████ ███████████ ██████████████ being the █████ ████████. The ████████ is ████████ by a ████ ███████ ${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}/\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$ █████████ to the ███████████ ██████████████ used.

The use of ██████ █████ ██████████ ██████ the █████ █████ ██████████. ████ ██████████████ is ████████ to ██████ the ███████ ██████████████ ██████████. With ██████ █████ as a █████, ███ █████ █████ █████████ ████████ ███████ as, $${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}[A]=\sum _{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}[\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}]{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}_{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}[A].}$$

This is ██████ the ████ █████████ and is █████████ to the ████████ ██████████████ in ███████ █████████ (███ ████████ and ████████ █████). The ██ ██████████████ has a █████ of ██████ ${\displaystyle \mathrm{<span\; word-length="3"\; class="word\; redacted">███</span>}(\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>})}$ ████████ by a ██████ ${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$ and ███████ as $${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}[\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}]=\int \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}(\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>})\mathrm{<span\; word-length="3"\; class="word\; redacted">███</span>}(\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}).}$$ and █████ with the ████████████ of the █████████ ${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}(\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}).}$

The ███████ ████ █████████ is ███████ by $${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}[\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}]=\int [\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}A]\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}[A]{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}_{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}[A].}$$

This ███████ the ████ ██████████████. █████ an ████████ ${\displaystyle \widehat{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}}$ in the ██████████ ██████████████, $${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}[A]=\widehat{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}[A]\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>},}$$ ███ ██████ ██████ the █████████████ ████████ ${\displaystyle {\widehat{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}}^{\prime }}$ on ${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}[\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}]}$ in the ████ ██████████████ via, $${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}[\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}]={\widehat{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}}^{\prime }\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}[\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}]\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>},}$$ █████ ${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}[\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}]}$ is ███████ by the █████ ███████ ████ █████████, $${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}[\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}]=\int [\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}A]\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}[A]{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}_{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}[A]\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>.}}$$

A ██████████████ ███████ ██████ the ██████ of the ████████ ${\displaystyle {\widehat{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}}^{\prime }}$ on ${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}[\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}]}$ in █████ of the ██████ of the ████████ ${\displaystyle \widehat{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}}$ on ${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}[A]}$ is ████ ████████ by ████████ the █.█.█. of ${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$ with the █.█.█. of ${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$ with ${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$ ███████████ into ${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$, ██████ $${\displaystyle {\widehat{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}}^{\prime }\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}[\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}]=\int [\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}A]{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}_{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}[A]\widehat{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}[A],}$$ or $${\displaystyle {\widehat{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}}^{\prime }\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}[\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}]=\int [\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}A]({\widehat{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}}^{†}{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}_{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}[A])\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}[A],}$$ █████ ${\displaystyle {\widehat{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}}^{†}}$ █████ the ████████ ${\displaystyle \widehat{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}}$ but with the ███████ ██████ ████████ (████████ from ██████ ███████ █████████ █████ the ███████ of █████████ is ████████ under ███████████). The ██████ of this ████████ on the ██████ ████ is █████████ as a ███████████ in the ██████████ ██████████████ and the ██████ is ██████████ ██████ as a ████████████ in █████ of █████ (with ██████ to the ██████ on the ██████ ████, the ██████ ███████████ ████████ is the ███ with the opposite ██████ ████████ ████████ to the ███ used for ███ ██████ on █████████████ ${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}[A]}$). This █████ the ████████ ███████ of the ████████ ${\displaystyle {\widehat{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}}^{\prime }}$. For ███████, if ${\displaystyle {\widehat{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}}^{†}}$ ████████████ to a ███████ ██████████████, ████ this can be ███████ of as ███████ the ██████████ █████ ${\displaystyle A}$ of ${\displaystyle {\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}_{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}[A]}$ █████ it is █████ ██████████ a ███████ ██████████████ on ${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$ ███████. █████████, the ███████ of ${\displaystyle {\widehat{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}}^{\prime }}$ is a ███████ ██████████████ on ${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$, the ████████ of ${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}[\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}]}$.

In the ████ ██████████████, the ███████ ██████████████ ██████████ is ██████ by considering █████████ of █████ ${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}[\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}]}$ that are █████████ under ███████ ███████████████ of the ████ ${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$. That is, ████ ██████████ are used. This █████ up an ██████████ ██████████ between ████ ██████ and ███████ ███████.

███ ██████████ of ███-████████████ ██████ █████ ███████ ████████'s ███████ ███████████ ██████████. Using a ██████████ ████████ of █████ and █████████ ${\displaystyle {\widetilde{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}}_{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}^a}$ by a ██████████, the ██████ of the ███████ ███████████ ██████████ on a ██████ ████ is $${\displaystyle {\widehat{\tilde{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}}}^{†}{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}_{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}[A]=-{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}_{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}{\widehat{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}}_{a\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}^{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}\frac{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}{A}_a^{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}}\frac{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}{A}_{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}^{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}}{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}_{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}[A].}$$

████ a ██████████ is █████ it ██████ down the ███████ ██████, ${\displaystyle {\dot{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}}^a}$, of the ████, ${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$. ██, $${\displaystyle {\widehat{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}}_{a\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}^{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}{\dot{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}}^a{\dot{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}}^{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}.}$$

███████, as ${\displaystyle {\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}_{a\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}^{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}}$ is ████-█████████ in the ███████ ${\displaystyle a}$ and ${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$ this ████████ (this ███████ that ${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$ is not █████████████ ████████ and ██ the ███████ ██████ is ██████).

With ██████ to ████ ██████████████, the █████████████ ${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}[\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}]}$ ██████ ████ the ████ has ███████████████ and are ████ ██████████. ████ █████████ █████ the █████ ███, the ███████ ██████████████ ██████████ and (████████) the ███████████ ██████████. This ██████ an ████████ ███ of █████ (if ████ ██████) █████████ to ███ the █████████ of ███████ ███████ ██████████! This █████████ a ███ of ████████ in the ████████ and ██████████ ███ to ███.

█████████ █████████, the ████ for ████████████ ██████ █████ and ████ ███████ ██████

The ███████ █████████ ████████ is the ████. ███ ██ ██████ ███████████ ██ that the ███████ ${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$ is █████████████ by ${\displaystyle {\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}^{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}=\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$. The ████ of █████ █████████████ of the ███████ ${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$ is the ███████ of ██████ of ████ ████ █████ ${\displaystyle \mathrm{<span\; word-length="3"\; class="word\; redacted">███</span>}\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$ █████ ${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$ is the █████ between the █████. ███ ███ ████ is █████ by the ██████ ${\displaystyle \overrightarrow{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}}$ and the █████ by ${\displaystyle \overrightarrow{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}}$ ████, $${\displaystyle A=\Vert \overrightarrow{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}\Vert \Vert \overrightarrow{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}\Vert \mathrm{<span\; word-length="3"\; class="word\; redacted">███</span>}\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}=\sqrt{\Vert \overrightarrow{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}{\Vert }^{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}\Vert \overrightarrow{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}{\Vert }^{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}(\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}-{\mathrm{<span\; word-length="3"\; class="word\; redacted">███</span>}}^{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>})}=\sqrt{\Vert \overrightarrow{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}{\Vert }^{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}\Vert \overrightarrow{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}{\Vert }^{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}-(\overrightarrow{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}\cdot \overrightarrow{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}{)}^{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}}}$$

In the █████ ███████ by ${\displaystyle {\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}^{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}}$ and ${\displaystyle {\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}^{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}}$ there is an █████████████ █████████████ █████████ by ${\displaystyle \overrightarrow{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}={\overrightarrow{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}}_{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}^{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}}$ and ${\displaystyle \overrightarrow{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}={\overrightarrow{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}}_{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}^{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}}$. Using ${\displaystyle {\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}_{A\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}^{(\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>})}={\overrightarrow{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}}_A\cdot {\overrightarrow{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}}_{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}}$ (█████ the ███████ ${\displaystyle A}$ and ${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$ ███ from █ to █), ██████ the ████ of the ███████ ${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$ █████ by $${\displaystyle A_{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}={\int }_{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}^{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}^{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}\sqrt{<span\; word-length="3"\; class="word\; redacted">███</span>\left({\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}^{(\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>})}\right)}}$$ █████ ${\displaystyle <span\; word-length="3"\; class="word\; redacted">███</span>({\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}^{(\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>})})={\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}_{\mathrm{<span\; word-length="2"\; class="word\; redacted">██</span>}}{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}_{\mathrm{<span\; word-length="2"\; class="word\; redacted">██</span>}}-{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}_{\mathrm{<span\; word-length="2"\; class="word\; redacted">██</span>}}^{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}}$ and is the ███████████ of the ██████ ███████ on ${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$. The ██████ can be █████████ ${\displaystyle <span\; word-length="3"\; class="word\; redacted">███</span>({\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}^{(\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>})})={\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}^{A\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}^{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}_{A\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}_{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}/\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$ █████ the ███████ ${\displaystyle A\dots \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$ ██ from █ to █. This can be ███████ █████████ as $${\displaystyle <span\; word-length="3"\; class="word\; redacted">███</span>({\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}^{(\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>})})=\frac{{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}^{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}a\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}^{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}_{a\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}_{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}}{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}.}$$

The ████████ ███████ for an ███████ ██████ is $${\displaystyle {\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}^{a\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}=\frac{{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}^{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}^{a\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}_{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}_{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}}{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}!<span\; word-length="3"\; class="word\; redacted">███</span>(\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>})}.}$$

There is a ██████████ between this and the ██████████ for ${\displaystyle <span\; word-length="3"\; class="word\; redacted">███</span>({\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}^{(\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>})})}$. But in ████████ █████████, ${\displaystyle {\widetilde{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}}_{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}^a{\widetilde{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}}^{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}=<span\; word-length="3"\; class="word\; redacted">███</span>(\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}){\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}^{a\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}}$. █████████, $${\displaystyle A_{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}={\int }_{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}^{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}^{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}\sqrt{{\widetilde{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}}_{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}^{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}{\widetilde{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}}^{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}}.}$$

█████████ to the █████ of █████████ ████████████ the ██████ ${\displaystyle {\widetilde{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}}_{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}^{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}}$ ██████ be ████████ to ███████ █████████, $${\displaystyle {\widehat{\tilde{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}}}_{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}^{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}\sim \frac{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}{A}_{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}^{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}}.}$$

The ████ ${\displaystyle A_{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}}$ can be ████████ to a ████ ███████ ███████ ████████ despite the ████ that it ████████ a ███████ of ███ ██████████ ███████████ and a ██████-████. ███████ ${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}=\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$ (${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$-██ ██████████████), $${\displaystyle \sum _{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}^{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}^{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}=\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}(\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}+\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>})\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>.}}$$

This ████████ is █████████ in the █████ ███████ for the ████ ████████. The ██████ is $${\displaystyle {\hat{A}}_{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}_{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}[A]=\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}_{\text{<span word-length="6" class="word redacted">██████</span>}}^{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\sum _{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}\sqrt{{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}_{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}({\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}_{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}+\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>})}{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}_{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}[A]}$$ █████ the ███ is over ███ █████ ${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$ of the ██████ ████ that ██████ the ███████ ${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$.

The ███████ for the ██████ of a ██████ ${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$ is █████ by $${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}={\int }_{\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>}\sqrt{<span\; word-length="3"\; class="word\; redacted">███</span>(\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>})}={\int }_{\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>}}\sqrt{\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>}}_{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>}}{\widetilde{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}}_{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}^a{\widetilde{\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>}}{\widetilde{\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>}}}.}$$

The ████████████ of the ██████ ████████ the ████ ███ as with the ████. ████ ████ the ██████████ is █████, it ██████ down the ███████ ██████ ${\displaystyle {\dot{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}}^a}$, and ████ the ██████ ████████ ████ on ███-████████████ ██████ █████ the ██████ ████████. ███████ ██████ with ███-████ ██████ ████ █████████ ███████ █████████████. █████ that the ████-█████████ █████████ is █████ over in the ███████ for the ██████, it █████ █████████████ with at █████ █████ ███-████████ █████. At █████ ████-██████ ████████ are ██████ for the ██████ ████████ to be ███-█████████.

████████ the ████ ██████████████ █████ the █████ █████ is ${\displaystyle \mathrm{<span\; word-length="2"\; class="word\; redacted">██</span>}(\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>})}$, ██████ █████ are an over ████████ █████ as there are ██████████ ████████ █████████ ██████ █████. █████ █████ because ██████ █████ are █████ on ████████ (the ████████) and █████ ████████ ███████ ██████████. █████ ███ ███ ${\displaystyle \mathrm{<span\; word-length="2"\; class="word\; redacted">██</span>}(\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>})}$ ████████ ${\displaystyle \mathbb{A}}$ and ${\displaystyle \mathbb{<span\; word-length="1"\; class="word\; redacted">█</span>}}$, $${\displaystyle \mathrm{<span\; word-length="2"\; class="word\; redacted">██</span>}(\mathbb{A})\mathrm{<span\; word-length="2"\; class="word\; redacted">██</span>}(\mathbb{<span\; word-length="1"\; class="word\; redacted">█</span>})=\mathrm{<span\; word-length="2"\; class="word\; redacted">██</span>}(\mathbb{A}\mathbb{<span\; word-length="1"\; class="word\; redacted">█</span>})+\mathrm{<span\; word-length="2"\; class="word\; redacted">██</span>}(\mathbb{A}{\mathbb{<span\; word-length="1"\; class="word\; redacted">█</span>}}^{-\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}).}$$

This ███████ that █████ ███ █████ ${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$ and ${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$ that █████████, $${\displaystyle {\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}_{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}[A]{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}_{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}[A]={\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}_{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\circ \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}[A]+{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}_{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\circ {\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}^{-\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}}[A]}$$ █████ by ${\displaystyle {\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}^{-\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}}$ ██ ████ the ████ ${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$ █████████ in the opposite █████████ and ${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\circ \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$ █████ the ████ ████████ by █████ around the ████ ${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$ and ████ along ${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$. ███ ██████ below. █████ that the ████████ are ███████ ███ has that ${\displaystyle {\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}_{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}[A]={\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}_{{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}^{-\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}}[A]}$. ████ █████ the ██████ ████████ of the ██████ ██████ (█.█. ${\displaystyle \mathrm{<span\; word-length="2"\; class="word\; redacted">██</span>}(\mathbb{A}\mathbb{<span\; word-length="1"\; class="word\; redacted">█</span>})=\mathrm{<span\; word-length="2"\; class="word\; redacted">██</span>}(\mathbb{<span\; word-length="1"\; class="word\; redacted">█</span>}\mathbb{A})}$) ███ has that ${\displaystyle {\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}_{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\circ \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}[A]={\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}_{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\circ \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}[A]}$. █████ ██████████ can be ████████ with ████ █████ into ███████ ██████████ of ██████████ ██████████ ██████ ████ █████. █████ ██████████ are the ██-██████ ██████████ ██████████. ████ ████████ ███████ are ██████ ████████████ of ████████████ ██████ █████ ████████ to ███████ the over-████████████ ██████████ by the ██████████ ██████████ (for █████████ █████████████ they █████████ the over-████████████ ████████) and ████████ ██████████ a █████ for ███ █████ █████████ █████████.

As █████████ above the ████████ █████ ███ ███ to █████████ ████ ████ ████ █████████. A ████ ███████ █████ ███████ an █████████ to a ███ of ████ ████ █████████ ███████ out a ████ in █████, ███████ and █████████. █████ are █████████ by ████ ████████ ${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$: the █████ are ████████ by █████ ████████ with '████████████' at the ████████ which are ████████████ for ███ to ███ over █████████ ████ the █████ are ████████. The ███ over █████████ are ██████ as ████ to ████ the ████ of the ███████████ █████████ under █████ █████ ███████████████.

███████████ ██████████ of ███

In the ████ ███████ of █████████ ███████ ███████ ███████████ the ███████████ ██████████ as a ███████ ████████ (███████–██████ ████████) in a ██████████████ ████████ ██████ has been a ██████████ ███████. It was in the ████ ██████████████ that a ██████████████ ████ ███████ ███████████ ██████████ was ███████ ██████████ in ████. ██ █████ ████ ███████ of ███ ████████████ to the ███████ ███████████ ██████████ of ███. This ████████ with the ███████ ████████ of the █████ ███ and ███████ ██████████████ ██████████ ███████ in the ████ ██████████████ are the ███████ █████████ of ███ (██████ █████████ ███████ ███████ ██████████).

███████ the ██████ that are ███████████ by █████ ███████████ (the ████████ ██████), and ███████ the █████████████ ████████ █████ ███████, and ███████████ is the ████ ████ of the █████████ ████ of ███.

An █████████ ██████ of the ███████████ ████████ is that it ████ ████ at ████████ (a ███████████ of this is that ████████'s ███████████ ████████, like ████████'s ████████, ███████████ ███-████████████ █████ except ███ it is not ████ ██████ and has ████████ ████████████ ███████). ████ █████████, ███ ██████ is ███-████ on at █████ ████████ of ███████ █████ and ███████ and ███████ in a ██████ ███████████ of ███ ████ ████████ █████ the ████████ █████ has been ████████ by the ████████ of █████ at ████ ██████ ████████ and a ██████ in the ██████ of the ████████ █████ of the ██████.

██████ ████████ and the ███████ ████████ ███████

A ███████████ █████████ in ███████████ ███████ ████ in ████████ ███, a ██████ of ███████ █████████, with the ████████ █████ of ████████ ███████, which █████████ ███████████ ██████ and █████████. A █████ ████████ in this ████████ is the ███████ ████████ ███████, which ██████ ████ █████████████ ██████ ████████ into the ███ █████████.

██████ ████████, ████ as █████████ and ██████, are ███████████ █████████ █████████████ by █████ "██████████" or █████████. This ████████ ████████ that a ████████ and ███ ██████ █████ ██████ ███████████ under ████ ████████████. This █████████ is ███████████ to the ████████ █████'s ███████ in ██████████ ████████ ████████ █████████.

███████, ████████ to █████████ ██████ ████████ into ███ █████ ██████ in the ██████████ of ████████, ██████-█████ █████████. ███████ of a ██████ ████-██████ ███████, for ████████, the ██████ ████████ the █████████ of ████ a ████-██████ and a █████-██████ ███████. This "████████" ███████████ the ████████ █████████ of the ████████ █████ and ████████ ███ ██████████ █████.

The ███████ ████████ ███████ █████ a ███████████ ██████ in ████████████ a ██████████ ██████ of ███████ ███████. The ████████ █████'s ████████ in ██████████ the ████████ at the ████████ ██████ ██████ ███████ on the ██████ ██████████ of ██████ ████████. Without a ████████ to this ███████, █████████████ ██████ and ███ ████████████ into a ███████ █████████ of ███████ ███████ ███████ a ███████████ █████████.

█████████, █████████ the ███████ ████████ ███████ is ███████ for █████████ ███ █████████████ of the ████████ at ███ ████ ███████████ █████ and ██████████ a ████████ ██████ that ██████ ███████ with the ███████ █████.

████ ████ ███████ from the ███████████ ██████████ ████████

The ███████████ ██████████ █████████ '████' █████████. ███████ the ███████████ ██████████ ██████ ████ ██ ███ ███████ ██████ ██████ in '████' from an ███████ ████ ███████ █████ to a █████ ████ ███████ █████. ███ ████████ to ███████ the ███████████ ██████████ ██████ with ████ is ██████ the █████ █████ ████████. The █████████ of which over █████████ █████████ of ███████ can be ██████████ as a █████████ over █████████ █████████ of '███████████ ████████' in the '████' █████████ ███████ the ███████ ████ ███████ to the █████ ████ ███████. ████ ████ a ███████████ ████████ ████ it ████ ██ by ██████ a ███ ████ at the ██████.

This ████ █████████ █████ ████ to the ███-███████ (a █████████████ ███ of █████ that ████ along █████, which in ████ ████ on ████████) ██████████ the ████ ████ ███████████; ██ ██████ ███████ an ███████ ████ ███████ ████████ out a ███████, the ██████ of the ███████████ ██████████ ████████ is to ███████ a ███ ██████ ███████ ████████ at the ██████. ██ are ████ to use the ██████ of the ███████████ ██████████ on the ██████ of a ████ ███████ █████ to █████████ an █████████ to ████ "███████████" (in ███████ to ███████ ████████). ███ ██████ below. This █████ a ███ of ██████ to ████████ ████ █████████ ███ to a ████ ████████ ███████████. ████ as a ████ ████████ ████████ ███████ █████, ████ █████████████ ████████████ to █████ ████ █████████, or ████ over ███████, ████████ '███████ █████████'. Because of █████ ███████████ to ████ █████ and the ███ they are ███████ ████ ████ ████ █████ '███████ ██████████' the ████ '████ █████'.

There are ███████ ██████ ████████████ with this ██████████ ████████, for ███████ the ███████████ ████████ is not ████-███████, in ████ it is not ████ a ██████ ████████ (█.█. the ████████ ████ not ███████ with ███ ███████) and ██ the ████████ ███████ ██████ be used to ██████ the ███████████ in ███████. The ████ ███████ ███████ is that the ${\displaystyle \widehat{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}(\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>})}$'s are not ████████ █████████, it can ████ be █████ the ██████ ████████ $\int [\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}]{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}^{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\int {\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}^{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}(\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>})\widehat{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}(\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>})}$ ██████ ████ ██████ a (███████████) █████████. The ██████ ██████████ (███ below) ████ not ██████ from █████ ████████ and as ████ ██████ a ███ of ██████████ the █████████ ██████ to the ████ ████████ ███████████.

████ █████ from ██ ██████

It █████ out there are ███████████ ██████ to ███████████ the ████ ████████, ███████ █████ ██████████ to the ███████████ █████████ is ████ █████. ███ ███ is to █████ with the ██ ██████. This is a ███████ ██████ than ███████ ██████████, it has ██ █████ ███████ of ███████ and as ████ ███████ ████ on ███████████ ███████ of the ██████. ██ ██████ is ████ is █████ as a ███████████ █████ ██████. ████████████, it █████ out that ███████ ██████████ can be ████████ from ██ ██████ by ████████ a ██████████, ██ ██████ ████████ a █████ ${\displaystyle {\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}_{a\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}^{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}}$ and if ███ ███████ the █████ ${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$ to be the (████-█████████) ███████ of ███ ███████ $${\displaystyle {\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}_{a\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}^{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}=\frac{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}\left({\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}_a^{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}_{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}^{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}-{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}_{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}^{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}_a^{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}\right)}$$ (███████ are like ██████ but in ████ █████████ ██████████), ███ ████████ ███████ ██████████. The █████████ that the ${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$ █████ be █████ by the ███████ of ███ ███████ is ██████ the ██████████ ██████████. The ████ ████ ████████ of the ███████████ █████ ██████ is ████ ██████████. █████ the ████ ████ '███████████' ██████████ for this ██████ ██████, ███ ████ █████ to █████████ the ██████████ ██████████ to ██████ a ████ ████████ for ███████ ██████████. The ███-███████ ████ of ████████████ a ████ ████ █████ is ████ ███████ to the ████████ of ███ this ██████████ ██████████ ██████ be ███████ in the ███████ ██████. The █████ ███████ at this was the ██████ ███████–█████ █████. ███████ this █████ was █████ to be ███████████, for ███████ there ███ not ████ to be ██████ ███████ of ███████ to ██████ the ███████ █████████ █████. It has been ██████ that the ██████████ ██████████ was ███████ ███ ████████ at the ███████ █████ and ██████ ████ be ███████ in the █████ of ███████████ ██████ ████ as with the ██████ █████ █████████ ${\displaystyle {\mathrm{\partial }}_{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}{\hat{A}}^{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}}$ in the █████–███████ █████████ of ███████ ███████████████. ███ ██████ have ███ been ███ ███████, █████████ █████████ by ████████ the ██████████ ██████████ in a ██████ █████.

███████ ██████████ ████ is that ████ █████ are ███████ on a ██████████████ of █████████. █████ this ████████ ██ ████████ for a ███████████ █████ ██████ as it has ██ █████ ███████ of ███████, it ████████ ████████ for ██. This is █████ as the ███████ █████████████████ ██████████.

██████ ███████████ of ████ █████

████ as ████████ the █████████ ██████████ ██████████ ████████ ███████ ██████████ from ██ ██████, it is ████████ that an ███████████ ███████ ██████████ ██████████ will ███████ ███████ ███████ from ███████ ██ ██████.

████████ has been ████ with ██████ to this █████ by █████, ███████, and ███████, ███████ and ███████ and ██████ and ████████ in ████████ ████ ████ ███████████ ██████████ with ██████ █████████.

An ███████ to ████ ███████ between ████-██ ████ ████ and the █████████ ███████████ of ███ has been ████.

████ ████ ███████ from the ██████ ██████████ ████████

███ below.