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Legendre-Gauss-Lobatto Collocation Method for Optimal Control via Polynomial Approximations of Differential Equation Vector Fields
Gabriela Abadia-Doyle, William W. Hager, Anil V. Rao
https://arxiv.org/abs/2506.13938

Legendre-Gauss-Lobatto Collocation Method for Optimal Control via Polynomial Approximations of Differential Equation Vector Fields
A new method is described for solving optimal control problems using direct collocation at Legendre-Gauss-Lobatto points. The approach of this paper employs a polynomial approximation of the right-hand side vector field of the differential equations and leads to the following important outcomes. First, the first-order optimality conditions of the LGL integral form are derived, which lead to a full-rank transformed adjoint system and novel costate estimate. Next, a derivative-like form of the LG…

"When we say monumental, you had better believe it; the 500 pages of this volume, laid out with astonishing detail (and a very small font size) summarize the history and evolution of computers from 1945 to 1990. Throughout these pages, Waldrop reveals that the backbone, the axis, the arrow, the orientation, the mastermind of all that history was none other than Lick himself: he was the incarnation of the phrase “being at the right place at the right time”."

J. C. R. Licklider & M. Mitchell Waldrop
The writings of Jorge Luis Borges twist our perception of time and space. In between articles about Shaw, Chesterton, Wilde, and Coleridge, his 1952 book "Otras Inquisiciones" included an unexpected gem: a short story called "El Tiempo y J. W. Dunne". The question is, who was this John William Dunne and what does he have to do with time? Well, his name might be forgotten by contemporary audiences, but Dunne was the author of one of the biggest bestsellers of the first half of the twentieth cent…

The THESAN-ZOOM project: Mystery N/O more -- uncovering the origin of peculiar chemical abundances and a not-so-fundamental metallicity relation at $3<z<12$
William McClymont, Sandro Tacchella, Aaron Smith, Rahul Kannan, Enrico Garaldi, Ewald Puchwein, Yuki Isobe, Xihan Ji, Xuejian Shen, Zihao Wang, Vasily Belokurov, Josh Borrow, Francesco D'Eugenio, Laura Keating, Roberto Maiolino, Stephanie Monty, Mark Vogelsberger, Oliver Zier

The THESAN-ZOOM project: Mystery N/O more -- uncovering the origin of peculiar chemical abundances and a not-so-fundamental metallicity relation at $3
We present an analysis of metallicities and chemical abundances at $3