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Cauchy Integral, Fractional Sobolev Spaces and Chord-Arc Curves
Huaying Wei, Michel Zinsmeister
https://arxiv.org/abs/2506.04564 https://

Cauchy Integral, Fractional Sobolev Spaces and Chord-Arc Curves
Let $Γ$ be a bounded Jordan curve and $Ω_i,Ω_e$ its two complementary components. For $s\in(0,1)$ we define $\mathcal{H}^s(Γ)$ as the set of functions $f:Γ\to \mathbb C$ having harmonic extension $u$ in $Ω_i\cup Ω_e$ such that $$ \iint_{Ω_i\cup Ω_e} |\nabla u(z)|^2 d(z,Γ)^{1-2s} dxdy<+\infty.$$ If $Γ$ is further assumed to be rectifiable we define $H^s(Γ)$ as the space of measurable functions $f:Γ\to \mathbb C$ such that $$\iint_{Γ\times Γ}\frac{|f(z)-f(ζ)|^2…

Supreme Court declines AR-15 ban appeal that Thomas, Alito and Gorsuch would've taken (Jordan Rubin/MSNBC)
https://www.msnbc.com/deadline-white-house/deadline-legal-blog/supreme-court-ar-15-ban-maryland-assault-weapons-rcna210358
http://www.memeorandum.com/250602/p67#a250602p67

Je viens d'écouter la dernière vidéo de @… « Comment parler intelligemment d'intelligence ? »
https://notes.sklein.xyz/2025-07-05_1538/

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A Practical Guide for Supporting Formative Assessment and Feedback Using Generative AI
Sapolnach Prompiengchai, Charith Narreddy, Steve Joordens
https://arxiv.org/abs/2505.23405

A Practical Guide for Supporting Formative Assessment and Feedback Using Generative AI
Formative assessment is a cornerstone of effective teaching and learning, providing students with feedback to guide their learning. While there has been an exponential growth in the application of generative AI in scaling various aspects of formative assessment, ranging from automatic question generation to intelligent tutoring systems and personalized feedback, few have directly addressed the core pedagogical principles of formative assessment. Here, we critically examined how generative AI, e…

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Je l'ai trouvé excellent ! Je pense avoir bien compris le message que tu as essayé de faire passer et je suis en accord avec tes…

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https://notes.sklein.xyz/2025-06-22_1502/

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This https://arxiv.org/abs/2506.04564 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Cauchy Integral, Fractional Sobolev Spaces and Chord-Arc Curves
Let $Γ$ be a bounded Jordan curve and $Ω_i,Ω_e$ its two complementary components. For $s\in(0,1)$ we define $\mathcal{H}^s(Γ)$ as the set of functions $f:Γ\to \mathbb C$ having harmonic extension $u$ in $Ω_i\cup Ω_e$ such that $$ \iint_{Ω_i\cup Ω_e} |\nabla u(z)|^2 d(z,Γ)^{1-2s} dxdy<+\infty.$$ If $Γ$ is further assumed to be rectifiable we define $H^s(Γ)$ as the space of measurable functions $f:Γ\to \mathbb C$ such that $$\iint_{Γ\times Γ}\frac{|f(z)-f(ζ)|^2…