And here's the lobby of the Best Western in Marlboro, MA which has that fountain: this space was packed with soccer fans out for the world cup the day before
#photo #photography #buildings
I have finished the outward architecture of #ProFed as a base for discussion. I've used AI to help me put my braindump into a more consistently readable text. be prepared to see a free AI-isms, though it isn't terrible, I think.
Civic Museums III - Relics🏛️
民间博物馆 III - 残垣 🏛️
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This week on #ProFed: I've documented the outward-facing architecture – ActivityPub extensions, federated search, and how other systems can integrate with ProFed.
This is aimed at developers of other projects who want to build on or cooperate with ProFed.
A Hadamard Formula for Equilibrium Envelopes under Parallel Deformation
Ziyu Li
https://arxiv.org/abs/2607.17187 https://arxiv.org/pdf/2607.17187 https://arxiv.org/html/2607.17187
arXiv:2607.17187v1 Announce Type: new
Abstract: Let $(X,\omega_0)$ be a compact K\"ahler manifold, and let $U\Subset X$ have $C^{3,1}$ uniformly strongly pseudoconvex boundary. For the equilibrium envelope $u_0$ associated with $X\setminus U$, the normalized Monge--Amp\`ere measure vanishes on $U$ and equals the background measure $V^{-1}\omega_0^n$ on $X\setminus\overline U$; its remaining component is a singular measure supported on $\partial U$, where $V=\int_X\omega_0^n$. We identify this boundary component as the negative outward Anzellotti trace of a divergence-measure flux current. We then prove a one-sided Hadamard formula for the normalized Monge--Amp\`ere energy along the outward parallel family $U_\varepsilon=\{\rho<\varepsilon\}$. The nonlinear telescoping identity gives the mixed Bedford--Taylor boundary traces that sum up to the trace of the current
\[
\mathcal J_{\mathrm{tot}}
=\frac1V\mathrm{d}^c u_0\wedge\sum_{p=0}^{n-1}(p 1)\omega_{u_0}^p\wedge\omega_0^{n-1-p},
\qquad \omega_{u_0}=\omega_0 \mathrm{d}\mathrm{d}^c u_0.
\]
These results provide a local weak formulation of boundary flux and normal variation for regular interface problems related to Darcy/Hele--Shaw type problems and Monge--Amp\`ere growth.
toXiv_bot_toot
It's been a hard days night and I've been sleeping like a Twig
#CatsOfMastodon
A Day Or Two At The Museum I🏛️
博物馆的一两天 I🏛️
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Same Place 🐲
同一個地方 🐲
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