scholarly journals Smoke control in large scale spaces. Part 1: Analytic theories for simple smoke control problems.

1985 ◽  
Vol 5 (1) ◽  
pp. 31-40 ◽  
Author(s):  
Takeyoshi Tanaka ◽  
Toshio Yamana
Keyword(s):  
Large Scale ◽  
Control Problems ◽  
Smoke Control ◽  
Scale Spaces

scholarly journals Smoke Control in Large Scale Spaces

1985 ◽  
Vol 5 (1) ◽  
pp. 41-54 ◽  
Author(s):  
Toshio Yamana ◽  
Takeyoshi Tanaka
Keyword(s):  
Large Scale ◽  
Smoke Control ◽  
Scale Spaces

Retention of memory for large-scale spaces

Memory ◽  
2013 ◽  
Vol 21 (7) ◽  
pp. 807-817 ◽  
Author(s):  
Toru Ishikawa
Keyword(s):  
Large Scale ◽  
Scale Spaces

scholarly journals Coarse quotients by group actions and the maximal Roe algebra

2019 ◽  
Vol 11 (04) ◽  
pp. 875-907
Author(s):  
Logan Higginbotham ◽  
Thomas Weighill
Keyword(s):  
Automorphism Group ◽  
Metric Space ◽  
Large Scale ◽  
Countable Group ◽  
Crossed Product ◽  
Property A ◽  
Bounded Geometry ◽  
Roe Algebra ◽  
Scale Spaces ◽  
The Ideal

For a finitely generated group [Formula: see text] acting on a metric space [Formula: see text], Roe defined the warped space [Formula: see text], which one can view as a kind of large scale quotient of [Formula: see text] by the action of [Formula: see text]. In this paper, we generalize this notion to the setting of actions of arbitrary groups on large scale spaces. We then restrict our attention to what we call coarsely discontinuous actions by coarse equivalences and show that for such actions the group [Formula: see text] can be recovered as an appropriately defined automorphism group [Formula: see text] when [Formula: see text] satisfies a large scale connectedness condition. We show that for a coarsely discontinuous action of a countable group [Formula: see text] on a discrete bounded geometry metric space [Formula: see text] there is a relation between the maximal Roe algebras of [Formula: see text] and [Formula: see text], namely that there is a ∗-isomorphism [Formula: see text], where [Formula: see text] is the ideal of compact operators. If [Formula: see text] has Property A and [Formula: see text] is amenable, then [Formula: see text] has Property A, and thus the maximal Roe algebra and full crossed product can be replaced by the usual Roe algebra and reduced crossed product respectively in the above equation.

scholarly journals Superior properties of the PRESB preconditioner for operators on two-by-two block form with square blocks

2020 ◽  
Vol 146 (2) ◽  
pp. 335-368
Author(s):  
Owe Axelsson ◽  
János Karátson
Keyword(s):  
Optimal Control ◽  
Rate Of Convergence ◽  
Large Scale ◽  
Optimal Control Problems ◽  
Iterative Solution ◽  
Control Problems ◽  
Block Form ◽  
Solution Methods ◽  
Preconditioned Matrix ◽  
Iterative Solution Methods

Abstract Matrices or operators in two-by-two block form with square blocks arise in numerous important applications, such as in optimal control problems for PDEs. The problems are normally of very large scale so iterative solution methods must be used. Thereby the choice of an efficient and robust preconditioner is of crucial importance. Since some time a very efficient preconditioner, the preconditioned square block, PRESB method has been used by the authors and coauthors in various applications, in particular for optimal control problems for PDEs. It has been shown to have excellent properties, such as a very fast and robust rate of convergence that outperforms other methods. In this paper the fundamental and most important properties of the method are stressed and presented with new and extended proofs. Under certain conditions, the condition number of the preconditioned matrix is bounded by 2 or even smaller. Furthermore, under certain assumptions the rate of convergence is superlinear.

scholarly journals Decomposition of large-scale stochastic optimal control problems

2010 ◽  
Vol 44 (3) ◽  
pp. 167-183 ◽  
Author(s):  
Kengy Barty ◽  
Pierre Carpentier ◽  
Pierre Girardeau
Keyword(s):  
Optimal Control ◽  
Stochastic Optimal Control ◽  
Large Scale ◽  
Optimal Control Problems ◽  
Control Problems
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