Tootfinder

Handlebar brackets are done… I’ll mount the board on it tomorrow.
#maker #diy #3DPrinting

My project that I completed yesterday. An old patio umbrella base, a fence post from a big box store, two old wall brackets for flower baskets, a couple of bird feeders that were on sale at CanTire, and a repurposed squirrel baffle. About $100 in total cost, not including the black oil seed. It's positioned right outside our sunroom for bifd watching, by us and our cat Casper.
#DIY #Birdwatching #Gardening

Double Poisson (vertex) algebra cohomology
Maxime Fairon, Daniele Valeri
https://arxiv.org/abs/2509.21232 https://arxiv.org/pdf/2509.21232

Double Poisson (vertex) algebra cohomology
A noncommutative (NC) version of Poisson geometry was initiated by Van den Bergh by introducing at the level of associative algebras the formalism of double Poisson brackets. Their key property is to induce (standard) Poisson brackets under each representation functor. Then, Pichereau and Van de Weyer developed and studied the corresponding cohomology theory under the assumption that there exists a NC bivector defining the double Poisson bracket. Our first main result is that one can remove thi…

Sometimes you forget to measure something precisely but it all still works out in the end.
#3DPrinting #DIY #maker

Generalization of the Fisher metric and Completely integrable system on Lie groups SO(2) and SO(3)
Prosper Rosaire Mama Assandje, Michel Bertrand Djiadeu Ngaha, Romain Nimpa Pefoukeu, Salomon Joseph Mbatakou
https://arxiv.org/abs/2509.20910

Generalization of the Fisher metric and Completely integrable system on Lie groups SO(2) and SO(3)
In this article, we propose a generalization of the Fisher metric within the framework of Souriau's Lie group thermodynamics, focusing on the rotation groups $SO(2)$ and $SO(3)$. We characterize the effect of central 2-cocycles on the information geometry and integrability of gradient systems on the Lie groups SO(2) and SO(3) using the geometry of Jean-Marie Souriau. We also show how a cocycle can locally modify the Fisher metric on a coadjoint orbit, in explicit terms of brackets and central e…

Found a @… repost on #Imgur.

Psyquandle Brackets
Sam Nelson, Natsumi Oyamaguchi
https://arxiv.org/abs/2508.13331 https://arxiv.org/pdf/2508.13331

Psyquandle Brackets
We extend the notion of biquandle brackets to the case of psyquandles, defining quantum enhancements of the psyquandle counting invariant for singular knots and pseudoknots. We provide examples to illustrate the computation of these invariants, establishing that the enhancement is proper. We compute a few toy examples, noting that the true power of this infinite family of invariants lies in more computationally expensive larger-cardinality psyquandles and infinite coefficient rings.

On the Poisson brackets of hybrid plasma models with kinetic ions and massless electrons
Yingzhe Li, Philip J. Morrison, Stefan Possanner, Eric Sonnendr\"ucker
https://arxiv.org/abs/2509.11160

On the Poisson brackets of hybrid plasma models with kinetic ions and massless electrons
We investigate the conditions under which the Jacobi identity holds for a class of recently introduced anti-symmetric brackets for the hybrid plasma models with kinetic ions and massless electrons. In particular, we establish the precise conditions under which the brackets for the vector-potential-based formulations satisfy the Jacobi identity, and demonstrate that these conditions are fulfilled by all physically relevant functionals. Moreover, for the magnetic-field-based formulation, we show …

After 20 years, bottom brackets can get a little stiff. M8x1mm holds the tool on.

how i remember markdown link syntax
it’s tidy to [put the link out of line][anchor]. the link text and anchor are both in []. the anchor is like a footnote reference so it goes after the link text
[anchor]: https://example•com
if the link text is the same as the [anchor][] the anchor can be abbreviated
if the url is not too unwieldy it can go inline in place of the anchor in ()
the change of brackets []-> () distinguishes anchors from relative URLs

Quantum Metric Corrections to Liouville's Theorem and Chiral Kinetic Theory
Kazuya Mameda, Naoki Yamamoto
https://arxiv.org/abs/2509.15731 https://arxi…

Quantum Metric Corrections to Liouville's Theorem and Chiral Kinetic Theory
Quasiparticles may possess not only Berry curvature but also a quantum metric in momentum space. We develop a canonical formalism for such quasiparticles based on the Dirac brackets, and demonstrate that quantum metric modifies the phase-space density of states at $\mathcal{O}(\hbar^2)$, leading to corrections to Liouville's theorem, kinetic theory, and related physical quantities. In particular, we show that, in the presence of an inhomogeneous electric field, quantum metric induces correction…

Local Rigidity of Quasi--Lie Brackets on Quaternionic Banach Modules and Applications to Nonlinear PDEs
Nassim Athmouni
https://arxiv.org/abs/2510.10124 https://

Local Rigidity of Quasi--Lie Brackets on Quaternionic Banach Modules and Applications to Nonlinear PDEs
We establish a local rigidity theorem for quasi--Lie brackets on quaternionic Banach right modules. Under quantitative control of antisymmetry and Jacobi defects, we construct an explicit bilinear correction that preserves right $\mathbb{H}$--linearity and restores the exact Lie property. The approach combines a radial homotopy operator, a controlled Neumann-series inversion, and a finite-rank adjustment, all with explicit operator estimates. This constructive framework bridges quaternionic fun…

this is my fave pic I took I think

Terminal users who use #accessibility tools, what is your take on emoji in console applications, especially compared to marker characters (eg. angular brackets for directions or hashes for comments) and to explicitly spelled out labels?
Does an "info" emoji render "ℹ️ Some information" (or a warning as in "⚠️ X went wrong") get across well for terminal assi…

On compatible linear and quadratic Poisson brackets on $gl(N)$
Andriy Panasyuk, Taras Skrypnyk
https://arxiv.org/abs/2509.24054 https://arxiv.org/pdf/2509.…

On compatible linear and quadratic Poisson brackets on $gl(N)$
In the present paper, using two constant tensors $c$ and $b$ on $sl(N)\otimes sl(N)$ satisfying certain linear-quadratic equation and a technique of Poisson bivectors and Schouten brackets, we explicitly construct quadratic Poisson bracket on the space $ (sl(N)+\mathbb{C})^*$ which is compatible with the standard Lie--Poisson bracket on $gl(N)^* \simeq (sl(N)\oplus \mathbb{C})^*$. The case of $N=3$ is considered in details. The relation of the proposed brackets with the generalized classical Sk…

#TIL Weibo's custom emoji shortcodes are in square brackets 🤔 https://emojipedia.org/sina-weibo

Once every few years I need to do some web development so I look at the state of html and javascript. Lo and behold, today is that day again.
I have now found out about web components, javascript modules, javascript template literals (like Python f-strings but you can pipe the string through a custom function that can rewrite the variables you put in curly brackets).

Unified Framework for Geodesic Dynamics with Conservative, Dissipative, and GUP Effects
Gaurav Bhandari, S. D. Pathak, Harjit Ghotra
https://arxiv.org/abs/2509.14663 https://

Unified Framework for Geodesic Dynamics with Conservative, Dissipative, and GUP Effects
We derive generalized geodesic equations in curved spacetime that include conservative forces, dissipative effects, and quantum-gravity-motivated minimal-length corrections. Conservative interactions are incorporated through external vector potentials, while dissipative dynamics arise from an exponential rescaling of the particle Lagrangian. Quantum-gravity effects are introduced via Generalized Uncertainty Principle (GUP) deformed Poisson brackets in the Hamiltonian framework. We show that fre…

It continues. STM32H750 flash wait state table.
You know left square brackets are a thing right?
#datasheetgore

"You know what? Let’s be crazy. Objective-C 3.0 would have removed the requirement for square brackets. Yes, I’ve said it. Extending the dot syntax for method calling. And since we’re at it, drop the @ sign for strings, arrays, and dictionaries. Seriously, just drop it."
https://akos.ma/blog/what-obje…

What Objective-C 3.0 Could Have Been
In a parallel universe, in a parallel WWDC 2014, instead of Swift, developers got Objective-C 3.0, and this is what it would have looked like. It’s the same parallel universe where Russia doesn’t annex Crimea, by the way.

On The Road - To Xi’An ☁️
在路上 - 去西安 ☁️
📷 Pentax MX
🎞️Lucky SHD 400
#filmphotography #Photography #blackandwhite

Structure-preserving long-time simulations of turbulence in magnetized ideal fluids
Klas Modin, Michael Roop
https://arxiv.org/abs/2509.15425 https://arxiv…

Structure-preserving long-time simulations of turbulence in magnetized ideal fluids
We address three two-dimensional magnetohydrodynamics models: reduced magnetohydrodynamics (RMHD), Hazeltine's model, and the Charney-Hasegawa-Mima (CHM) equation. These models are derived to capture the basic features of magnetohydrodynamic turbulence and plasma behaviour. They all possess non-canonical Hamiltonian formulations in terms of Lie-Poisson brackets, which imply an infinite number of conservation laws along with symplecticity of the phase flow. This geometric structure in phase spac…

Supersymmetric M2-Brane Matrix Model with Restricted Volume-Preserving Deformations: Lorentz Covariance and BPS Spectrum
So Katagiri
https://arxiv.org/abs/2508.07259 https://

Supersymmetric M2-Brane Matrix Model with Restricted Volume-Preserving Deformations: Lorentz Covariance and BPS Spectrum
We present a novel supersymmetric Lorentz-covariant matrix model for M2-branes in M-theory, constructed via the framework of Restricted Volume-Preserving Deformations (RVPD) which is a residual symmetry from gauge-fixed volume-preserving diffeomorphisms. The model reformulates the supermembrane action entirely in terms of Nambu brackets, whose decomposition into Poisson brackets allows for a consistent matrix regularization that preserves both the Fundamental Identity and Lorentz covariance. Un…

Classical r-matrix structure for elliptic Ruijsenaars chain and 1 1 field analogue of Ruijsenaars-Schneider model
D. Murinov, A. Zotov
https://arxiv.org/abs/2508.12656 https://

Classical r-matrix structure for elliptic Ruijsenaars chain and 1+1 field analogue of Ruijsenaars-Schneider model
The classical dynamical $r$-matrix structure for the periodic elliptic Ruijsenaars chain is described. The Poisson brackets for the monodromy matrix are calculated as well, thus providing Liouville integrability of the model. Next, we study its continuous non-relativistic limit and reproduce the Maillet type non-ultralocal $r$-matrix structure for the field analogue of the elliptic Calogero-Moser model.

Wife and I improvised a wardrobe from scrap stuff we had laying around. 0€ spent, some 3D printed parts (designed in #SolveSpace) hold everything together. That's why I love #3DPrinting. 💪

An Intrinsic $L_{\infty}$-Algebra on the Khovanov-Sano Complex
Takahito Kuriya
https://arxiv.org/abs/2509.15018 https://arxiv.org/pdf/2509.15018

An Intrinsic $L_{\infty}$-Algebra on the Khovanov-Sano Complex
This paper reinterprets the symmetries of equivariant Khovanov homology, discovered by Khovanov and Sano, within the Batalin-Vilkovisky (BV) formalism. We identify the Shumakovitch operator $\hatν$ as a BV Laplacian whose nilpotency, a consequence of the algebra's defining relations, induces an $L_{\infty}$-algebra on homology. We prove this structure is non-trivial through explicit computations of higher brackets. Furthermore, we construct a dual $L_{\infty}$-structure, suggesting a unifying …

An $L^\infty$ Rashevskii-Chow Theorem
Ermal Feleqi, Rohit Gupta, Franco Rampazzo
https://arxiv.org/abs/2509.07572 https://arxiv.org/pdf/2509.07572

An $L^\infty$ Rashevskii-Chow Theorem
Consider a finite family $\{f_1,\dots,f_ν\}$ of $C^\infty$ vector fields on a $n$-dimensional ($n\in\mathbb{N}$), smooth manifold $\mathcal{M}$. The celebrated Rashevskii-Chow theorem states that, provided the vector fields $\{f_1,\dots,f_ν\}$, together with their iterated Lie brackets, span the whole tangent space at some $x_*\in\mathcal{M}$, then any $x$ in a neighborhood of $x_*$ can be connected to $x_*$ by means of a finite concatenation of integral curves of $\{\pm f_1,\dots,\pm f_ν\}$…

Mastering Cosmological Amplitudes Using Generalized Ramanujan's Theorem
Prashanth Raman, Qinglin Yang
https://arxiv.org/abs/2508.13126 https://arxiv.or…

Mastering Cosmological Amplitudes Using Generalized Ramanujan's Theorem
We present a systematic method for computing cosmological amplitudes, including in-in correlators and wavefunction coefficients, in FRW spacetime. Specializing to cases with conformally-coupled external scalars and massive scalar exchanges, we introduce a decomposition into massive family trees, which capture the nested time structure common to these observables. We then evaluate these building blocks using the Method of Brackets (MoB), a multivariate extension of Ramanujan's master theorem tha…

Wronskians as $N$-ary brackets in finite-dimensional analogues of $sl(2)$
Arthemy V. Kiselev
https://arxiv.org/abs/2510.02145 https://arxiv.org/pdf/2510.02…

Wronskians as $N$-ary brackets in finite-dimensional analogues of $sl(2)$
The Wronskian determinants (for coefficients of higher-order differential operators on the affine real line or circle) satisfy the table of Jacobi-type quadratic identities for strong homotopy Lie algebras -- i.e. for a particular case of $L_\infty$-deformations -- for the Lie algebra of vector fields on that one-dimensional affine manifold. We show that the standard realisation of $\mathfrak{sl}(2)$ by quadratic-coefficient vector fields is the bottom structure in a sequence of finite-dimensio…

(Quasi) Hamiltonian Systems and Non-Decomposable Poisson Geometry
C. Sard\'on, X. Zhao
https://arxiv.org/abs/2510.08307 https://arxiv.org/pdf/2510.0830…

(Quasi) Hamiltonian Systems and Non-Decomposable Poisson Geometry
In this work, we conduct a systematic study of Hamiltonian and quasi-Hamiltonian systems within the framework of nondecomposable generalized Poisson geometry. Our focus lies on the interplay between the algebraic structure of nondecomposable generalized Poisson brackets and the dynamical behavior of systems exhibiting specific symmetry properties. In particular, we demonstrate that if a dynamical system admits suitable invariance conditions -- such as those arising from Lie symmetries or conser…

Constrained Dynamics on Eccentric Conic Orbits: Dirac-Bergmann and Hamilton-Jacobi Approaches
Alejandro G. Andarcia-Caballero, Jaime Manuel-Cabrera, Luis G. Romero-Hern\'andez, Jorge M. Paulin-Fuentes
https://arxiv.org/abs/2507.23271

Constrained Dynamics on Eccentric Conic Orbits: Dirac-Bergmann and Hamilton-Jacobi Approaches
In this work, we investigate a Lagrangian model describing a particle constrained to move along non-degenerate conic sections, parameterized by the orbital eccentricity \( e \). In the non-relativistic regime, we apply the Dirac--Bergmann algorithm to identify a set of four second-class constraints, compute the corresponding Dirac brackets, and isolate the true physical degrees of freedom. This procedure yields a unified Hamiltonian treatment of circular (\( e = 0 \)), elliptical (\( 0 < e < 1 …

Imposing quasineutrality on electrostatic plasmas via the Dirac theory of constraints
D. A. Kaltsas, J. W. Burby, P. J. Morrison, E. Tassi, G. N. Throumoulopoulos
https://arxiv.org/abs/2508.02389

Imposing quasineutrality on electrostatic plasmas via the Dirac theory of constraints
We present a method for imposing quasineutrality and, more generally, charge density conservation in the Vlasov-Poisson (VP) and Vlasov-Ampère (VA) systems, which describe electrostatic plasma dynamics, by applying the Dirac theory of constraints. Leveraging the Hamiltonian field formulations of the VP and VA models, we construct generalized Dirac brackets using the Dirac algorithm. The resulting constrained systems enforce charge density conservation, and consequently quasineutrality, through…

Faddeev-Jackiw Quantization of Classical Constrained Systems
Shaza Abdul Majid, Ansha S Nair, Saurabh Gupta
https://arxiv.org/abs/2507.22505 https://arxiv.…

Faddeev-Jackiw Quantization of Classical Constrained Systems
We accomplish the quantization of a few classical constrained systems à la (modified) Faddeev-Jackiw formalism. We analyze the constraint structure and obtain basic brackets of the theory. In addition, we disclose the gauge symmetries within the symplectic framework. We also provide new interpretation for Lagrange multipliers and outline a MATLAB implementation algorithm for symplectic formulation.