Tootfinder

Growth rates for the H\"older coefficients of the linear stochastic fractional heat equation with rough dependence in space
Chang Liu, Bin Qian, Ran Wang
https://arxiv.org/abs/2507.22379

Growth rates for the Hölder coefficients of the linear stochastic fractional heat equation with rough dependence in space
We study the linear stochastic fractional heat equation $$ \frac{\partial}{\partial t}u(t,x)=-(-Δ)^{\fracα{2}}u(t,x)+\dot{W}(t,x), \quad t>0, \quad x\in\mathbb{R}, $$ where $-(-Δ)^{\fracα{2}}$ denotes the fractional Laplacian with power $α\in (1,2)$, and the driving noise $\dot{W}$ is a centered Gaussian field that is white in time and has the covariance of a fractional Brownian motion with Hurst parameter $H\in\left(\frac{2-α}{2},\frac{1}{2}\right)$. We establish exact asymptotics for …

Designing Robots with, not for: A Co-Design Framework for Empowering Interactions in Forensic Psychiatry
Qiaoqiao Ren, Remko Proesmans, Arend Pissens, Lara Dehandschutter, William Denecker, Lotte Rouckhout, Joke Carrette, Peter Vanhopplinus, Tony Belpaeme, Francis wyffels
https://arxiv.org/abs/2507.14931

Designing Robots with, not for: A Co-Design Framework for Empowering Interactions in Forensic Psychiatry
Forensic mental health care involves the treatment of individuals with severe mental disorders who have committed violent offences. These settings are often characterized by high levels of bureaucracy, risk avoidance, and restricted autonomy. Patients frequently experience a profound loss of control over their lives, leading to heightened psychological stress-sometimes resulting in isolation as a safety measure. In this study, we explore how co-design can be used to collaboratively develop a co…

Uniqueness of diffeomorphic minimizers of $L^p$-mean distortion
Yizhe Zhu
https://arxiv.org/abs/2507.20597 https://arxiv.org/pdf/2507.20597

Uniqueness of diffeomorphic minimizers of $L^p$-mean distortion
We study the $L^p$-mean distortion functionals, \[{\cal E}_p[f] = \int_\mathbb Y K^p_f(z) \; dz, \] for Sobolev homeomorphisms $f: \overline{\mathbb Y}\xrightarrow{\rm onto} \overline{\mathbb X}$ where $\mathbb X$ and $\mathbb Y$ are bounded simply connected Lipschitz domains, and $f$ coincides with a given boundary map $f_0 \colon \partial \mathbb Y \to \partial \mathbb X$. Here, $K_f(z)$ denotes the pointwise distortion function of $f$. It is conjectured that for every $1 < p < \infty$, the f…

Taiwan has issued a land warning as Typhoon Danas approaches from the southwest, bringing the threat of heavy rain and strong winds. The storm is expected to peak from Sunday afternoon through Monday morning, affecting 18 counties and cities across the island.
https://youtu.be/DmtZ4TGKqN0

Analysis of three-body charmed $B$ meson decays $B \to {D}(V^* \to){V P}$
Jing Ou-Yang, Run-Hui Li, Si-Hong Zhou
https://arxiv.org/abs/2506.14675 https://

Analysis of three-body charmed $B$ meson decays $B \to {D}(V^* \to){V P}$
We systematically analyze the decays $B_{(s)} \to D_{(s)} (V^* \to)\, V\, P$, where $V^*$ represents a vector resonance ($ρ, \, ω$ or $K^*$), and $V P$ denotes the final-state meson pairs $ ω\, π$, $ ρ\, π$ and $ ρ\, K$. The intermediate subprocesses $B_{(s)} \to D_{(s)} V^*$ are calculated in the factorization-assisted topological-amplitude approach, while the intermediate resonant states $V^*$ are modeled using a relativistic Breit-Wigner distribution, subsequently decaying into $VP$ t…

A comparison of the regularity of certain classes of monomial ideals and their integral closures
Omkar Javadekar
https://arxiv.org/abs/2507.12178 https://

A comparison of the regularity of certain classes of monomial ideals and their integral closures
Let $S = \mathsf{k}[x_1, \ldots, x_n]$, $I$ be an ideal of $S$, and $\bar{I}$ denote its integral closure. A conjecture of Küronya and Pintye states that for any homogeneous ideal $I$ of $S$, the inequality $\operatorname{reg}(\bar{I}) \leq \operatorname{reg}(I)$ holds, where $\operatorname{reg}(\_)$ denotes the Castelnuovo-Mumford regularity. In this article, we prove the conjecture for certain classes of monomial ideals.

Mother-daughter duo transforms beach waste into stunning eco-friendly home, inspiring sustainable living and creativity. #climatechange #climatesolutions #climate

Mother-daughter duo turn beach waste into incredible seven-room home: 'So creative and so beautiful'
Brazilian builders Edna and Maria Gabrielly Dantas turned 8,000 discarded bottles from Itamaraca's beaches into the Salt House.