Tootfinder

A big public thanks to @… for the Casual #emacs package (available on MELPA), which enables "casual" use of Emacs Calc.
In case you don't know, Emacs Calc is an advanced calculator and

I feel like I have lived in Excel land for so long this week. Excel at work, Excel in working on Smollish20.
Then my feed is like:
May I interest you to the best thing since sliced bread? Introducing Calc.

This https://arxiv.org/abs/2209.05564 has been replaced.
link: https://scholar.google.com/scholar?q=a

Deep Relaxation of Controlled Stochastic Gradient Descent via Singular Perturbations
We consider a singularly perturbed system of stochastic differential equations proposed by Chaudhari et al. (Res. Math. Sci. 2018) to approximate the Entropic Gradient Descent in the optimization of deep neural networks, via homogenisation. We embed it in a much larger class of two-scale stochastic control problems and rely on convergence results for Hamilton-Jacobi-Bellman equations with unbounded data proved recently by ourselves (ESAIM Control Optim. Calc. Var. 2023). We show that the limit …

I *still* would love to be able to strip the unit from a value by dividing by 1 unit in #CSS calc()… 🤔

On length-preserving and area-preserving inverse curvature flow of planar curves with singularities
Yunlong Yang, Yanwen Zhao, Jianbo Fang, Yanlong Zhang
https://arxiv.org/abs/2404.11872

On length-preserving and area-preserving inverse curvature flow of planar curves with singularities
This paper aims to investigate the evolution problem for planar curves with singularities. Motivated by the inverse curvature flow introduced by Li and Wang (Calc. Var. Partial Differ. Equ. 62 (2023), No. 135), we intend to consider the area-preserving and length-preserving inverse curvature flow with nonlocal term for $\ell$-convex Legendre curves. For the area-preserving flow, an $\ell$-convex Legendre curve %of with initial algebraic area $A_0>0$ evolves to a circle of radius $\sqrt{\frac{A_…

This https://arxiv.org/abs/2305.14505 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Nonuniqueness of generalised weak solutions to the primitive and Prandtl equations
We develop a convex integration scheme for constructing nonunique weak solutions to the hydrostatic Euler equations (also known as the inviscid primitive equations of oceanic and atmospheric dynamics) in both two and three dimensions. We also develop such a scheme for the construction of nonunique weak solutions to the three-dimensional viscous primitive equations, as well as the two-dimensional Prandtl equations. While in [D.W. Boutros, S. Markfelder and E.S. Titi, Calc. Var. Partial Differe…

This https://arxiv.org/abs/2305.14505 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Nonuniqueness of generalised weak solutions to the primitive and Prandtl equations
We develop a convex integration scheme for constructing nonunique weak solutions to the hydrostatic Euler equations (also known as the inviscid primitive equations of oceanic and atmospheric dynamics) in both two and three dimensions. We also develop such a scheme for the construction of nonunique weak solutions to the three-dimensional viscous primitive equations, as well as the two-dimensional Prandtl equations. While in [D.W. Boutros, S. Markfelder and E.S. Titi, Calc. Var. Partial Differe…

This https://arxiv.org/abs/2402.12206 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

On Li-Lin's open problem
In this paper, we give a first negative answer to a question proposed by Li and Lin (Arch Ration Mech Anal 203(3): 943-968, 2012). Meanwhile we also give a second positive answer to the Li-Lin's open problem. The first positive answer was given by G. Cerami, X. Zhong and W. Zou (Calc. Var. Partial Differential Equations, 54(2): 1793-1829, 2015).

This https://arxiv.org/abs/2402.12206 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

On Li-Lin's open problem
In this paper, we give a first negative answer to a question proposed by Li and Lin (Arch Ration Mech Anal 203(3): 943-968, 2012). Meanwhile we also give a second positive answer to the Li-Lin's open problem. The first positive answer was given by G. Cerami, X. Zhong and W. Zou (Calc. Var. Partial Differential Equations, 54(2): 1793-1829, 2015).