Tootfinder

Global Calder\'on-Zygmund estimates for asymptotically convex fully nonlinear Grad-Mercier type equations
Yao Zhang, Xiaofeng Jin, Lingwei Ma, Zhenqiu Zhang
https://arxiv.org/abs/2506.23216

Global Calderón-Zygmund estimates for asymptotically convex fully nonlinear Grad-Mercier type equations
In this paper, we consider the following Dirichlet problem for the fully nonlinear elliptic equation of Grad-Mercier type under asymptotic convexity conditions \begin{equation*} \left\{ \begin{array}{ll} F(D^2u(x),Du(x),u(x),x)=g(|\{y\in Ω:u(y)\ge u(x)\}|)+f(x) & \text{in } Ω, u=ψ&\text{on } \partial Ω. \end{array} \right. \end{equation*} In order to overcome the non-convexity of the operator $F$ and the nonlocality of the nonhomogeneous term $g$, we apply the compactn…

This https://arxiv.org/abs/2405.03536 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_csLO_…

Extensional and Non-extensional Functions as Processes
Following Milner's seminal paper, the representation of functions as processes has received considerable attention. For pure $λ$-calculus, the process representations yield (at best) non-extensional $λ$-theories (i.e., $β$ rule holds, whereas $η$ does not). In the paper, we study how to obtain extensional representations, and how to move between extensional and non-extensional representations. Using Internal $π$, $\mathrm{I}π$ (a subset of the $π$-calculus in which all outputs are boun…

The Center Is Not Holding -- The institutionalists are all but extinct. The moderates are fleeing. (The Bulwark)
https://www.thebulwark.com/p/the-center-is-not-holding-bacon-tillis-republicans-big-beautiful-bill-trump-supreme-court-congress
http://www.memeorandum.com/250630/p151#a250630p151

Characterizing Small Circuit Classes from FAC^0 to FAC^1 via Discrete Ordinary Differential Equations
Melissa Antonelli, Arnaud Durand, Juha Kontinen
https://arxiv.org/abs/2506.23404

Characterizing Small Circuit Classes from FAC^0 to FAC^1 via Discrete Ordinary Differential Equations
In this paper, we provide a uniform framework for investigating small circuit classes and bounds through the lens of ordinary differential equations (ODEs). Following an approach recently introduced to capture the class of polynomial-time computable functions via ODE-based recursion schemas and later applied to the context of functions computed by unbounded fan-in circuits of constant depth (FAC^0), we study multiple relevant small circuit classes. In particular, we show that natural restrictio…

A Practical Approach to Power Saving in Hearables Using Sub-Nyquist Sampling with Bandwidth Extension
Tarikul Islam Tamiti, Anomadarshi Barua
https://arxiv.org/abs/2506.22321

A Practical Approach to Power Saving in Hearables Using Sub-Nyquist Sampling with Bandwidth Extension
Hearables are wearable computers that are worn on the ear. Bone conduction microphones (BCMs) are used with air conduction microphones (ACMs) in hearables as a supporting modality for multimodal speech enhancement (SE) in noisy conditions. However, existing works don't consider the following practical aspects for low-power implementations on hearables: (i) They do not explore how lowering the sampling frequencies and bit resolutions in analog-to-digital converters (ADCs) of hearables jointly im…

A Comparison of Relativistic Coupled Cluster and Equation of Motion Coupled Cluster Quadratic Response Theory
Xiang Yuan, Lo\"ic Halbert, Lucas Visscher, Andr\'e Severo Pereira Gomes
https://arxiv.org/abs/2506.22905

A Comparison of Relativistic Coupled Cluster and Equation of Motion Coupled Cluster Quadratic Response Theory
We present the implementation of relativistic coupled cluster quadratic response theory (QR-CC), following our development of relativistic equation of motion coupled cluster quadratic response theory (QR-EOMCC) [X. Yuan et al., J. Chem. Theory Comput. 2023, 19, 9248]. These codes, which can be used in combination with relativistic (2- and 4-component based) as well as non-relativistic Hamiltonians, are capable of treating both static and dynamic perturbations for electric and magnetic operators…

Pullback dynamics for a semilinear heat equation with homogeneous Neumann boundary conditions on time-varying domains
Gleiciane S. Arag\~ao, Flank D. M. Bezerra, Lucas G. Mendon\c{c}a
https://arxiv.org/abs/2506.22585

Pullback dynamics for a semilinear heat equation with homogeneous Neumann boundary conditions on time-varying domains
We are interested in studying a non-autonomous semilinear heat equation with homogeneous Neumann boundary conditions on time-varying domains. Using a differential geometry approach with coordinate transformations technique, we will show that the non-autonomous problem on a time-varying domain is equivalent, in some sense, to a non-autonomous problem on a fixed domain. Furthermore, we intend to show the local existence and uniqueness of solutions to this problem, as well as, to extend these solu…

A New Experimental Method for Determining the Pinning Energy of an Abrikosov Vortex
Elmeri O. Rivasto
https://arxiv.org/abs/2506.21706 https://

A New Experimental Method for Determining the Pinning Energy of an Abrikosov Vortex
We demonstrate a novel method of experimentally addressing the pinning energy of an Abrikosov vortex in high-temperature superconducting thin films. The method is based on our previously published theoretical framework considering the optimization of heterostructural bilayer films. To demonstrate our method, we have estimated the pinning energy of a typical BaZrO$_3$-nanocolumn within YBa$_2$Cu$_3$O$_{6+x}$ lattice using the experimental data from our previous study. Our calculations result in …

Decay estimates for discrete bi-Laplace operators with potentials on the lattice $\mathbb{Z}$
Sisi Huang, Xiaohua Yao
https://arxiv.org/abs/2506.23119 http…

Decay estimates for discrete bi-Laplace operators with potentials on the lattice $\mathbb{Z}$
It is known that the discrete Laplace operator $Δ$ on the lattice $\mathbb{Z}$ satisfies the following sharp time decay estimate: $$\big\|e^{itΔ}\big\|_{\ell^1\rightarrow\ell^{\infty}}\lesssim|t|^{-\frac{1}{3}},\quad t\neq0,$$ which is slower than the usual $ O(|t|^{-\frac{1}{2}})$ decay in the continuous case on $\mathbb{R}$. However, this paper shows that the discrete bi-Laplacian $Δ^2$ on $\mathbb{Z}$ actually exhibits the same sharp decay estimate $|t&#…

Evolution models with time-dependent coefficients in friction and viscoelastic damping terms
Halit Sevki Aslan
https://arxiv.org/abs/2506.24058 https://

Evolution models with time-dependent coefficients in friction and viscoelastic damping terms
We study the following Cauchy problem for the linear wave equation with both time-dependent friction and time-dependent viscoelastic damping: \begin{equation} \label{EqAbstract}\tag{$\ast$} \begin{cases} u_{tt}- Δu + b(t)u_t - g(t)Δu_t=0, &(t,x) \in (0,\infty) \times \mathbb{R}^n, \\ u(0,x)= u_0(x),\quad u_t(0,x)= u_1(x), &x \in \mathbb{R}^n. \end{cases} \end{equation} Our goal is to derive decay estimates for higher order energy norms of solutions to this problem. We focus on the interplay b…