Tootfinder

In the field of public education, the dogma of "separate but free" has no place;
⭐️separate is inherently unfree.
As this Article uniquely clarifies, segregation deprives schoolchildren of freedom to become equal citizens and freedom to learn in democratic, integrated, and transformative settings.
We must name and reclaim these positive, social, emancipatory freedoms
—envisioned by the framers of state constitution education clauses,
developed by earl…

Radiative Transfer Modeling of Stripped-Envelope Supernovae. I: A Grid for Ejecta Parameter Inference
S. Karthik Yadavalli (Center for Astrophysics | Harvard and Smithsonian), V. Ashley Villar (Center for Astrophysics | Harvard and Smithsonian, The NSF AI Institute for Artificial Intelligence and Fundamental Interactions), Abigail Polin (Department of Physics and Astronomy, Purdue University), S. E. Woosley (Department of Astronomy and Astrophysics, University of California, Santa Cruz…

Radiative Transfer Modeling of Stripped-Envelope Supernovae. I: A Grid for Ejecta Parameter Inference
We present 1,800 multiwavelength Type Ib/c supernovae light curve models obtained by running the radiation transport code Sedona and varying the mass distribution, velocity profile, and abundance ejecta profiles of helium star progenitors. To create a flexible but physically-informed grid, we use autoencoders to construct a representation of ejecta profiles derived from stellar evolution models. We present simulated nearest-neighbor multiband light curves matches to SN 1994I, SN 2007gr, and iPT…

Perfect Matchings in Random Sparsifications of Dense Hypergraphs
Jie Han, Jingwen Zhao
https://arxiv.org/abs/2507.11359 https://arxiv…

Perfect Matchings in Random Sparsifications of Dense Hypergraphs
The decision problem of perfect matchings in uniform hypergraphs is famously an NP-complete problem. It has been shown by Keevash--Knox--Mycroft [STOC, 2013] that for every $\varepsilon>0$, such decision problem restricted to $k$-uniform hypergraphs $H$ satisfying that every $(k-1)$-set of vertices is in at least $(1/k+\varepsilon)|H|$ edges is tractable, and the quantity $1/k$ is best possible. In this paper we study the existence of perfect matchings in the random $p$-sparsification…

Initial traces and solvability of porous medium equation with power nonlinearity
Kazuhiro Ishige, Nobuhito Miyake, Ryuichi Sato
https://arxiv.org/abs/2507.11826

Initial traces and solvability of porous medium equation with power nonlinearity
In this paper we study qualitative properties of initial traces of solutions to the porous medium equation with power nonlinearity, and obtain necessary conditions for the existence of solutions to the corresponding Cauchy problem. Furthermore, we establish sharp sufficient conditions for the existence of solutions to the Cauchy problem using uniformly local Morrey spaces and their variations, and identify the optimal singularities of the initial data for the solvability of the Cauchy problem.

Boy Crisis of 2025, Meet the 'Boy Problem' of the 1900s (New York Times)
https://www.nytimes.com/2025/08/15/opinion/men-boys-crisis-progressive-era.html
http://www.memeorandum.com/250815/p55#a250815p55

Isometric-Universal Graphs for Trees
Edgar Baucher, Fran\c{c}ois Dross, Cyril Gavoille
https://arxiv.org/abs/2506.11704 https://arxiv…

Isometric-Universal Graphs for Trees
We consider the problem of finding the smallest graph that contains two input trees each with at most $n$ vertices preserving their distances. In other words, we look for an isometric-universal graph with the minimum number of vertices for two given trees. We prove that this problem can be solved in time $O(n^{5/2}\log{n})$. We extend this result to forests instead of trees, and propose an algorithm with running time $O(n^{7/2}\log{n})$. As a key ingredient, we show that a smallest isometric-un…

Feedback stabilization of a nanoparticle at the intensity minimum of an optical double-well potential
Vojt\v{e}ch Mlyn\'a\v{r} (Automation and Control Institute, TU Wien, Vienna, Austria), Salamb\^o Dago (University of Vienna, Faculty of Physics, Vienna Center for Quantum Science and Technology, Vienna, Austria), Jakob Rieser (University of Vienna, Faculty of Physics, Vienna Center for Quantum Science and Technology, Vienna, Austria), Mario A. Ciampini (University of Vienna, Facult…

Feedback stabilization of a nanoparticle at the intensity minimum of an optical double-well potential
In this work, we develop and analyze adaptive feedback control strategies to stabilize and confine a nanoparticle at the unstable intensity minimum of an optical double-well potential. The resulting stochastic optimal control problem for a noise-driven mechanical particle in a nonlinear optical potential must account for unavoidable experimental imperfections such as measurement nonlinearities and slow drifts of the optical setup. To address these issues, we simplify the model in the vicinity o…

The convergence proof of the sixth-order compact 9-point FDM for the 2D transport problem
Qiwei Feng
https://arxiv.org/abs/2506.12549 https://

The convergence proof of the sixth-order compact 9-point FDM for the 2D transport problem
It is widely acknowledged that the convergence proof of the error in the $l_{\infty}$ norm of the high-order finite difference method (FDM) and finite element method (FEM) in 2D is challenging. In this paper, we derive the sixth-order compact 9-point FDM with the explicit stencil for the 2D transport problem with the constant coefficient and the Dirichlet boundary condition in a unit square. The proposed sixth-order FDM forms an M-matrix for the any mesh size $h$ employing the uniform Cartesian…

The optical constants and grain sizes of interstellar dust measured directly using the dust scattered x-ray halo of GRB 221009A
Albert Sneppen, Darach Watson
https://arxiv.org/abs/2506.12125

The optical constants and grain sizes of interstellar dust measured directly using the dust scattered x-ray halo of GRB 221009A
X-ray scattering is a powerful probe of the optical constants and grain size distribution of interstellar dust. Bright, transient sources are excellent tools for this, since they fade rapidly, leaving only the expanding scattered x-ray halo. Here, we analyse the dust-scattered x-ray halo data of the unprecedentedly bright $γ$-ray burst, GRB 221009A, using anomalous diffraction theory to measure the grain size distribution of dust in the Galaxy as well as the complex refractive index, $m$, and …

Equivalent Characterizations and Their Applications of Solvability of $L^p$ Poisson--Robin(-Regularity) Problems on Rough Domains
Xuelian Fu, Dachun Yang, Sibei Yang
https://arxiv.org/abs/2507.11103

Equivalent Characterizations and Their Applications of Solvability of $L^p$ Poisson--Robin(-Regularity) Problems on Rough Domains
Let $n\ge2$, $Ω\subset\mathbb{R}^n$ be a bounded one-sided chord arc domain, and $p\in(1,\infty)$. In this article, we study the (weak) $L^p$ Poisson--Robin(-regularity) problem for a uniformly elliptic operator $L:=-\mathrm{div}(A\nabla\cdot)$ of divergence form on $Ω$, which considers weak solutions to the equation $Lu=h-\mathrm{div}\boldsymbol{F}$ in $Ω$ with the Robin boundary condition $A\nabla u\cdot\boldsymbolν+αu=\boldsymbol{F}\cdot\boldsymbolν$ on the boundary $\partialΩ$ for fu…