Tootfinder

Universal Matrices for Counting Fibonomial and $C$-nomial Coefficients by their $p$-adic Valuations
Arav Chand
https://arxiv.org/abs/2508.18461 https://arx…

Universal Matrices for Counting Fibonomial and $C$-nomial Coefficients by their $p$-adic Valuations
Rowland found a matrix product formula for generating functions counting binomial coefficients by their $p$-adic valuations. A natural generalization of binomial coefficients was introduced by Knuth and Wilf defined by a sequence $C$. We obtain analogous matrix product formulas counting these $C$-nomial coefficients when $C$ is a strong divisibility sequence. Surprisingly, the matrices are universal in the sense that they are independent of $C$. We further extend this product to $C$-multinomial…

Shape optimization problems with random coefficients via the penalty method
Xiaowei Pang
https://arxiv.org/abs/2508.16961 https://arxiv.org/pdf/2508.16961

Shape optimization problems with random coefficients via the penalty method
For shape optimization problems, governed by elliptic equations with Dirichlet boundary condition and random coefficients, we utilize a penalization technique to get the approximate problem. We consider that uncertainties exists in the diffusion coefficients and minimize objective functions in mean value form. Finite element method, Monte Carlo method and accelerated version of the gradient descent method are applied to solve the corresponding discretized problem. The convergence analysis and n…

Full text of Illinois Gov. JB Pritkzer's speech at news conference on reported Trump military plan for Chicago - CBS Chicago
https://www.cbsnews.com/chicago/news/illinois-governor-jb-pritkzer-speech-news-conference-full-text-trump/

Police respond to possible active shooter in south Minneapolis (Aki Nace/CBS News)
https://www.cbsnews.com/minnesota/news/south-minneapolis-incident-august-27-2025/
http://www.memeorandum.com/250827/p62#a250827p62

Pentagon reportedly planning military deployment in Chicago; Pritzker accuses Trump of "attempting to manufacture a crisis" - CBS Chicago
https://www.cbsnews.com/chicago/news/brandon-johnson-donald-trump-threat-national-guard-crime-chicago/?intcid=CNR-01-0623

What's next for embattled Nicolšs Maduro as Trump pressures Venezuela (Sharyn Alfonsi/CBS News)
https://www.cbsnews.com/news/nicolas-maduro-venezuela-power-60-minutes/
http://www.memeorandum.com/251026/p60#a251026p60

Gavin Newsom says he will consider White House run after 2026 elections (Robert Costa/CBS News)
https://www.cbsnews.com/news/newsom-says-he-will-consider-white-house-run-after-2026-elections/
http://www.memeorandum.com/251026/p23#a251026p23

Billionaires pay a lower tax rate than the rest of America's taxpayers, new study finds (Aimee Picchi/CBS News)
https://www.cbsnews.com/news/income-taxes-billionaire-tax-rate-irs/
http://www.memeorandum.com/250827/p58#a250827p58

Transcript: Treasury Secretary Scott Bessent on "Face the Nation with Margaret Brennan," Oct. 26, 2025 (CBS News)
https://www.cbsnews.com/news/scott-bessent-treasury-secretary-face-the-nation-transcript-10-26-2025/
http://www.memeorandum.com/251026/p20#a251026p20

Transcript: Sen. Lindsey Graham on "Face the Nation with Margaret Brennan," Oct. 26, 2025 (CBS News)
https://www.cbsnews.com/news/lindsey-graham-south-carolina-republican-face-the-nation-transcript-10-26-2025/
http://www.memeorandum.com/251026/p45#a251026p45