Tootfinder

"Jim Coplien ends his talk with a simple call to action: at every conference where new technology is introduced, software engineers should strive to be skeptical; to ask whether it improves the quality of life of society as a whole, and to take it home only to increase the human value of our products and services.
Focus on the people. Again and again. Because that is what Agile and OOP were all about, to begin with."
https://deprogrammaticaipsum.com/james-coplien/

This https://arxiv.org/abs/2403.11479 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

A priori estimates for parabolic Monge-Ampère type equations
We prove the existence and regularity of convex solutions to the first initial-boundary value problem for the parabolic Monge-Ampère equationn $$ \left\{\begin{eqnarray} &&-u_t+\det D^2u= ψ(x,t) \quad\quad\ \text{ in } Q_T,\newline &&u=ϕ\quad\text{ on }\partial_pQ_T, \end{eqnarray}\right. $$ where $ψ,ϕ$ are given functions, $Q_T=Ω\times(0,T]$, $\partial_p Q_T$ is the parabolic boundary of $Q_T$, and $Ω\subset\mathbb{R}^n$ is a uniformly convex domain. Our approach can also be use…

Bifurcation from periodic solutions of central force problems in the three-dimensional space
Alberto Boscaggin, Guglielmo Feltrin, Duccio Papini
https://arxiv.org/abs/2506.05842

Bifurcation from periodic solutions of central force problems in the three-dimensional space
The paper deals with electromagnetic perturbations of a central force problem of the form \begin{equation*} \dfrac{\mathrm{d}}{\mathrm{d}t} \bigl( φ(\dot{x}) \bigr) = V'(|x|) \dfrac{x}{|x|} + E_{\varepsilon}(t,x)+\dot{x} \wedge B_{\varepsilon}(t,x), \qquad x \in \mathbb{R}^3 \setminus \{0\}, \end{equation*} where $V \colon (0,+\infty) \to \mathbb{R}$ is a smooth function, $E_\varepsilon$ and $B_\varepsilon$ are respectively the electric field and the magnetic field, smooth …

Toward Khintchine's theorem with a moving target: extra divergence or finitely centered target
Gilbert Michaud, Felipe A. Ram\'irez
https://arxiv.org/abs/2506.04187

Toward Khintchine's theorem with a moving target: extra divergence or finitely centered target
Sz{ü}sz's inhomogeneous version (1958) of Khintchine's theorem (1924) gives conditions on $ψ:\mathbb{N}\to\mathbb{R}_{\geq 0}$ under which for almost every real number $α$ there exist infinitely many rationals $p/q$ such that \begin{equation*} \lvertα- \frac{p+γ}{q}\rvert < \frac{ψ(q)}{q}, \end{equation*} where $γ\in\mathbb{R}$ is some fixed inhomogeneous parameter. It is often interpreted as a statement about visits of $qα\,(\bmod 1)$ to a shrinking target centered around $γ\,(\bmod…

This https://arxiv.org/abs/2503.21940 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Normalized vector solutions of nonlinear Schrödinger systems
Given $μ>0$ we look for solutions $ λ\in\mathbb{R}$ and $v_1,\dots,v_k\in H^1(\mathbb{R}^N)$ of the system \[ \begin{cases} \displaystyle -Δv_i+ λv_i+V_i(x)v_i = \sum_{\substack{j=1}}^kβ_{ij} v_iv_j^2 &\text{ in } \mathbb{R}^N, \text{ } i=1,\dots,k,\newline \displaystyle \int_{\mathbb{R}^N} \left(v_1^2+\dots+v_k^2 \right)\mathrm{d} x = μ, \end{cases}\] where $N=1,2,3$, $V_i:\mathbb R^N\to \mathbb R$ and $β_{ij}\in\mathbb{R}$ satisfy $β_{ij}=β_{ji}$ and $β_{ii}>0$. Under …

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Gaussian integrals on symmetric spaces (the complex case and beyond)
Salem Said
https://arxiv.org/abs/2505.22672 https://arxiv.org/pd…

Gaussian integrals on symmetric spaces (the complex case and beyond)
The present work is concerned with Gaussian integrals on simply-connected non-positively-curved Riemannian symmetric spaces. It is motivated by the aim of explicitly finding the high-rank limit of these integrals for each of the eleven families of classical Riemannian symmetric spaces. To begin, it deals with the easier complex case (where the isometry group admits a complex Lie group structure). To go beyond this case, it introduces a variational characterisation of the high-rank limit, as the…

Shape derivative approach to fractional overdetermined problems
Sidy M. Djitte, Ignace A. Minlend
https://arxiv.org/abs/2506.00268 https://

Shape derivative approach to fractional overdetermined problems
We use shape derivative approach to prove that balls are the only convex and $C^{1,1}$ regular domains in which the fractional overdetermined problem \begin{equation*} \left\{\begin{aligned} \Ds u&= λ_{s, p} u^{p-1}\quad\text{in}\quad\Om \\ u &= 0\quad \text{in}\quad\R^N\setminus \Om\\ u/d^s&=C_0\quad\text{on\;\; $\partialØ$} \end{aligned} \right. \end{equation*} admits a nontrivial solution for $p\in [1, 2]$ and where $λ_{s, p}= λ_{s, p}(Ø)$ is the best constant in the family of Subcritic…

This https://arxiv.org/abs/2504.05655 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Multi-bubble solutions for the Dirichlet problem of the $H$-system with higher degree
We consider a Dirichlet problem of the $H$-system \begin{equation*} \begin{cases} Δv = 2v_x\wedge v_y ~& \text{ in }\mathcal{D},\\ v=\varepsilon \tilde g ~& \text{ on }\partial{\mathcal{D}}, \end{cases} \end{equation*} where $\mathcal D\subset \mathbb{R}^2$ is the unit disk, $v:\mathcal D\to \mathbb{R}^3$, and $\tilde g:\partial \mathcal D\to \mathbb{R}^3$ is a given smooth map. As $\varepsilon\to 0^+$, we construct multi-bubble solutions concentrating at distinct points, taking around each po…

Solutions with large number of peaks for a slightly supercritical nonlinear equation in dimension three
Yixing Pu
https://arxiv.org/abs/2506.01652 https://…

Solutions with large number of peaks for a slightly supercritical nonlinear equation in dimension three
We investigate the existence of solutions to the semilinear equation with a slightly supercritical exponent in dimension three, \begin{align*} -Δu=K(x) u^{5+μ},\quad u>0 ~\text{in}~ \mathbf{B}, \quad u=0 ~\text{on}~ \partial \mathbf{B}, \end{align*} where $μ>0$, $\mathbf{B}$ is the unit ball in $\mathbb{R}^3$, $K(x)$ is a nonnegative radial function under suitable condition on $K$. We prove the existence of positive multi-peak solutions for $μ>0$ small enough. All peaks of our solut…