KKM in an arbitrary product of simplices

1996 ◽  
Vol 170 (1) ◽  
pp. 13-21 ◽  
Author(s):  
J. Cesco ◽  
E. Marchi
2013 ◽  
Vol 60 (6) ◽  
pp. 667-672 ◽  
Author(s):  
Sheng-Fang Wang ◽  
Yi-Min Liu ◽  
Guo-Feng Li ◽  
Xian-Song Liu ◽  
Zhan-Jun Zhang

2015 ◽  
Vol DMTCS Proceedings, 27th... (Proceedings) ◽  
Author(s):  
Suho Oh ◽  
Hwanchul Yoo

International audience We introduce an axiom system for a collection of matchings that describes the triangulation of product of simplices. Nous introduisons un système d’axiomes pour une collection de couplages qui décrit la triangulation de produit de simplexes.


2001 ◽  
Vol 03 (01) ◽  
pp. 57-65
Author(s):  
JUAN C. CESCO ◽  
EZIO MARCHI

In the first part of this note, we present a generalisation of a lemma due to Gale (1984) to a product of simplices. Then, we use it to derive a permutation-based extension of Browder Fixed Point Theorem proved by Bapat (1989). In the last part, we propose a model of an economy with regional sub-economies in the line of Gale's work (1984) and prove existence equilibrium results under different set of hypothesis.


1999 ◽  
Vol 566 ◽  
Author(s):  
D. Boning ◽  
B. Lee ◽  
C. Oji ◽  
D. Ouma ◽  
T. Park ◽  
...  

In previous work, we have formalized the notions of “planarization length” and “planarization response function” as key parameters that characterize a given CMP consumable set and process. Once extracted through experiments using carefully designed characterization mask sets, these parameters can be used to predict polish performance in CMP for arbitrary product layouts. The methodology has proven effective at predicting oxide interlevel dielectric planarization results.In this work, we discuss extensions of layout pattern dependent CMP modeling. These improvements include integrated up and down area polish modeling; this is needed to account for both density dependent effects, and step height limits or step height perturbations on the density model. Second, we discuss applications of the model to process optimization, process control (e.g. feedback compensation of equipment drifts), and shallow trench isolation (STI) polish. Third, we propose a framework for the modeling of pattern dependent effects in copper CMP. The framework includes “removal rate diagrams” which concisely capture dishing height and step height dependencies in dual material polish processes.


Author(s):  
NEIL LYALL ◽  
ÁKOS MAGYAR

AbstractWe establish that any subset of ℝd of positive upper Banach density necessarily contains an isometric copy of all sufficiently large dilates of any fixed two-dimensional rectangle provided d ⩾ 4.We further present an extension of this result to configurations that are the product of two non-degenerate simplices; specifically we show that if Δk1 and Δk2 are two fixed non-degenerate simplices of k1 + 1 and k2 + 1 points respectively, then any subset of ℝd of positive upper Banach density with d ⩾ k1 + k2 + 6 will necessarily contain an isometric copy of all sufficiently large dilates of Δk1 × Δk2.A new direct proof of the fact that any subset of ℝd of positive upper Banach density necessarily contains an isometric copy of all sufficiently large dilates of any fixed non-degenerate simplex of k + 1 points provided d ⩾ k + 1, a result originally due to Bourgain, is also presented.


2019 ◽  
Vol 95 (1) ◽  
pp. 1-5
Author(s):  
Murat Altunbulak ◽  
Aslı Güçlükan İlhan
Keyword(s):  

10.37236/8114 ◽  
2019 ◽  
Vol 26 (1) ◽  
Author(s):  
Karola Mészáros ◽  
Connor Simpson ◽  
Zoe Wellner

Recent progress on flow polytopes indicates many interesting families with product formulas for their volume. These product formulas are all proved using analytic techniques. Our work breaks from this pattern. We define a family of closely related flow polytopes $F_{(\lambda, {\bf a})}$ for each partition shape $\lambda$ and netflow vector ${\bf a}\in Z^n_{> 0}$. In each such family, we prove that there is a polytope (the limiting one in a sense) which is a product of scaled simplices, explaining their product volumes. We also show that the combinatorial type of all polytopes in a fixed family $F_{(\lambda, {\bf a})}$ is the same. When $\lambda$ is a staircase shape and ${\bf a}$ is the all ones vector the latter results specializes to a theorem of the first author with Morales and Rhoades, which shows that the combinatorial type of the Tesler polytope is a product of simplices.


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