Early algebra ideas about binomial expansion, Stephanie's interview seven of seven, Clip 5 of 7: Developing numerical representations for each case for the number of Unifix-cube towers 5-tall and 6-tall selecting from red and yellow cubes. [PDF]
, 1996 In the fifth clip in a series of seven from the seventh of seven interviews, 8th grader Stephanie and researcher Carolyn Maher extend their earlier investigation of how to represent the number of Unifix cube towers for cases from no red cubes to four red
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Invariant Measure and Universality of the 2D Yang–Mills Langevin Dynamic
Communications on Pure and Applied Mathematics, Volume 79, Issue 8, Page 1973-2102, August 2026.ABSTRACT We prove that the Yang–Mills (YM) measure for the trivial principal bundle over the two‐dimensional torus, with any connected, compact structure group, is invariant for the associated renormalised Langevin dynamic. Our argument relies on a combination of regularity structures, lattice gauge‐fixing and Bourgain's method for invariant measures ...
Ilya Chevyrev, Hao Shen
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Engineering Reports, Volume 8, Issue 8, August 2026.This graphical abstract presents a lightweight and automated BiLSTM‐based Multi‐Cycle GAN framework for retinal blood vessel and optic disc segmentation in fundus images. Initially, fundus images undergo preprocessing, including green channel extraction, denoising, resizing, and dataset splitting.
Rasmita Kumari Mohanty +7 more
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Numerical Linear Algebra with Applications, Volume 33, Issue 4, August 2026.ABSTRACT We derive eigenvalue bounds for symmetric block‐tridiagonal multiple saddle‐point systems preconditioned with block‐diagonal Schur complement matrices. This analysis applies to an arbitrary number of blocks and accounts for the case where the Schur complements are approximated, generalizing the findings in [11, Bergamaschi et al., Linear ...
Marco Pilotto +2 more
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The Legacy of Policy Inaction in Climate‐Growth Models
International Economic Review, Volume 67, Issue 3, Page 915-935, August 2026.ABSTRACT To better understand the structure and core mechanisms of a broad class of climate‐growth models, we study a simplified version of the dynamic integrated model of climate and the economy (DICE) through the lens of growth theory. We analytically show that this model features a continuum of saddle‐point stable steady states.
Thomas Steger, Timo Trimborn
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Early algebra ideas about binomial expansion, Stephanie's interview four of seven, Clip 5 of 9: Building (a+b) cubed and identifying the pieces. [PDF]
, 1996 In the fifth clip in a series of nine from the fourth of seven interviews in which 8th grader Stephanie explores Early Algebraic Ideas about Binomial Expansion, Stephanie uses the small and large cube and 6 rectangular prisms provided to construct a cube
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On Aubin's Veto Mechanism: A Survey
Journal of Public Economic Theory, Volume 28, Issue 4, August 2026.ABSTRACT We revisit Aubin's veto mechanism—known as the fuzzy veto—in which agents may participate in a blocking coalition with only a fraction of their endowments, and show that its Core‐Walras equivalence stems directly from the classical Debreu‐Scarf and Aumann theorems.
Carlos Hervés‐Beloso +2 more
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Resolutions over symmetric algebras with radical cube zero
Journal of Algebra, 2008 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Universal C *-Algebra of Real Rank zero [PDF]
, 2000 It is well-known that every commutative separable unital C *-algebra of real rank zero is a quotient of the C *-algebra of all compex continous functions defined on the Cantor cube.
Chigogidze, A. "Alex" +1 more
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Early algebra ideas about binomial expansion, Stephanie's interview six of seven, Clip 11 of 11: Extending ideas about generating towers 4-cubes tall selecting from green and blue cubes to towers 5-cubes tall with exactly 1 green cube and connecting to Fermat and Pascal [PDF]
, 1996 In the final clip in a series of eleven from the sixth of seven interviews, 8th grader Stephanie is challenged by researchers Carolyn Maher and Robert Speiser to extend her ideas about how to build the Unifix-cube towers across cases for towers 4-cubes ...
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