Tootfinder

On the analytical approach to infinite-mode Boson-Gaussian states
Jorge R. Bola\~nos-Serv\'in, Roberto Quezada, Josu\'e I. Rios-Cangas
https://arxiv.org/abs/2506.04537

On the analytical approach to infinite-mode Boson-Gaussian states
We develop an analytical approach to quantum Gaussian states in infinite-mode representation of the Canonical Commutation Relations (CCR's), using Yosida approximations to define integrability of possibly unbounded observables with respect to a state $ρ$ ($ρ$-integrability). It turns out that all elements of the commutative $*$-algebra generated by a possibly unbounded $ρ$-integrable observable $A$, denoted by $\langle A\rangle$, are normal and $ρ\, $-integrable. Besides, $\langle A\rangle$…

The Hasse principle for homogeneous polynomials with random coefficients over thin sets II
Daniel Flores, Kiseok Yeon
https://arxiv.org/abs/2506.01291 http…

The Hasse principle for homogeneous polynomials with random coefficients over thin sets II
Let $d$ and $n$ be natural numbers. Let $ν_{d,n}: \mathbb{R}^n\rightarrow \mathbb{R}^{N}$ denote the Veronese embedding with $N=N_{n,d}:=\binom{n+d-1}{d}$, defined by listing all the monomials of degree $d$ in $n$ variables using the lexicographical ordering. Let $\langle \boldsymbol{a}, ν_{d,n}(\boldsymbol{x})\rangle\in \mathbb{Z}[\boldsymbol{x}]$ be a homogeneous polynomial in $n$ variables of degree $d$ with integer coefficients $\boldsymbol{a}$, where $\langle\cdot,\cdot\rangle$ denotes t…

🇺🇦 #NowPlaying on #KEXP's #PositiveVibrations
Ernest Ranglin:
🎵 Ranglin Satta
#ErnestRanglin
https://open.spotify.com/track/2K9OKYvp2VmzyhYEKCg0wn

Toukokuun keskilämpötila jäi alle pitkän ajan keskiarvon – koko kevät oli etelärannikolla poikkeuksellisen lämmin https://www.ilmatieteenlaitos.fi/tiedote/75WucvkvnucYQkCNjH4nrc

Toukokuun keskilämpötila jäi alle pitkän ajan keskiarvon – koko kevät
Toukokuu oli vertailukauden keskiarvoa koleampi, mikä rikkoi 12 kuukautta kestäneen keskiarvoa lämpimämpien kuukausien putken. Koko kevät eli maalis-toukokuu oli kuitenkin lähes koko maassa

This https://arxiv.org/abs/2505.15915 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

On spatial decay for coherent states of the Benjamin-Ono equation
We consider solutions to the Benjamin-Ono equation $$\partial_t u - H \partial_x^2 u = -\partial_x(u^2)$$ which are localized in a reference frame moving to the right with constant speed. We show that any such solution that decays at least like $\langle x\rangle^{-1-ε}$ for some $ε> 0$ in a comoving coordinate frame must in fact decay like $\langle x\rangle^{-2}$. In view of the explicit soliton solutions, this decay rate is sharp. Our proof has two main ingredients. The first is microloc…

Farlington Marshes, near #Portsmsouth UK. #silentsunday #photography #weather

Computing $H$-equations with 2-by-2 integral matrices
Gemma Bastardas, Enric Ventura
https://arxiv.org/abs/2506.05272 https://arxiv.o…

Computing $H$-equations with 2-by-2 integral matrices
We study the transference through finite index extensions of the notion of equational coherence, as well as its effective counterpart. We deduce an explicit algorithm for solving the following algorithmic problem about size two integral invertible matrices: ''given $h_1,\ldots, h_r; g\in \operatorname{PSL}_2(\mathbb{Z})$, decide whether $g$ is algebraic over the subgroup $H=\langle h_1,\ldots ,h_r\rangle \leqslant \operatorname{PSL}_2(\mathbb{Z})$ (i.e., whether there exist a non-trivial $H$-eq…

https://youtu.be/-2rNyUcl53g?si=x_5vVn3vP8H4R8D-
Ein MicroMacro-Spiel als App? Da bin ich gespannt. Wir hatten immer viel Spaß mit den Papier-Varianten.

Low Energy, lots of treats 🥲
#runcologne

On the heat kernel of a Cayley graph of $\operatorname{PSL}_2\mathbb{Z}$
Anders Karlsson, Kamila Kashaeva
https://arxiv.org/abs/2506.02340 https://

On the heat kernel of a Cayley graph of $\operatorname{PSL}_2\mathbb{Z}$
In this paper, we obtain an explicit formula for the heat kernel on the infinite Cayley graph of the modular group $\operatorname{PSL}_2\mathbb{Z}$, given by the presentation $\langle a,b\mid a^2=1, b^3=1\rangle$. Our approach extends the method of Chung--Yau in~\cite{MR1667452} by observing that the Cayley graph strongly and regularly covers a weighted infinite line. We solve the spectral problem on this line to obtain an integral expression for its heat kernel, and then lift this to the Cayle…