Tootfinder

B05 - Pressure Point
BLAKE: [V.O.] Avon, give me a rundown check on what you're going to do.
AVON: We teleport directly into the Forbidden Zone, we make an analysis of the defence systems, and then we teleport directly to your location. [Inside the church]
https://blake.torpidity.net/m/205/288

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Companion site to the Blakes7Bot Twitter, Mastodon, and Bluesky accounts. Automated lines of Blakes 7 dialog. Includes a script search facility.

Hyperbinary partitions and q-deformed rationals
Thomas McConville (Kennesaw State University), James Propp (University of Massachusetts Lowell), Bruce E. Sagan (Michigan State University)
https://arxiv.org/abs/2508.20026

Hyperbinary partitions and q-deformed rationals
A hyperbinary partition of the nonnegative integer n is a partition where every part is a power of 2 and every part appears at most twice. We give three applications of the length generating function for such partitions, denoted by h_q(n). Morier-Genoud and Ovsienko defined the q-analogue of a rational number [r/s]_q in various ways, most of which depend directly or indirectly on the continued fraction expansion of r/s. As our first application we show that [r/s]_q = q h_q(n-1)/h_q(n) where r/s…

Big-Stop Semantics: A Simple Way to Get the Benefits of Small-Step Semantics in a Big-Step Judgment
David M Kahn, Jan Hoffmann, Runming Li
https://arxiv.org/abs/2508.15157 https…

Big-Stop Semantics: A Simple Way to Get the Benefits of Small-Step Semantics in a Big-Step Judgment
As evident in the programming language literature, many practitioners favor specifying dynamic program behavior using big-step over small-step semantics. Unlike small-step semantics, which must dwell on every intermediate program state, big-step semantics conveniently jump directly to the ever-important result of the computation. Big-step semantics also typically involve fewer inference rules than their small-step counterparts. However, in exchange for ergonomics, big-step semantics give up pow…

A direct PinT algorithm for higher-order nonlinear equations
Shun-Zhi Zhong, Yong-Liang Zhao
https://arxiv.org/abs/2507.05743 https://

A direct PinT algorithm for higher-order nonlinear equations
This paper mainly studies a direct time-parallel algorithm for solving time-dependent differential equations of order 1 to 3. Different from the traditional time-stepping approach, we directly solve the all-at-once system from higher-order evolution equations by diagonalization the time discretization matrix $B$. Based on the connection between the characteristic equation and Chebyshev polynomials, we give explicit formulas for the eigenvector matrix $V$ of $B$ and its inverse $V^{-1}$ , and pr…