scholarly journals Observing 0D subwavelength-localized modes at ~100 THz protected by weak topology

2021 ◽  
Vol 7 (49) ◽  
Author(s):  
Jinlong Lu ◽  
Konstantin G. Wirth ◽  
Wenlong Gao ◽  
Andreas Heßler ◽  
Basudeb Sain ◽  
...  
Keyword(s):  
Weak Topology ◽  
Localized Modes

scholarly journals Localized modes on an Ablowitz–Ladik nonlinear impurity

2008 ◽  
Vol 372 (42) ◽  
pp. 6388-6391
Author(s):  
Mario I. Molina
Keyword(s):  
Localized Modes

scholarly journals Localized modes on a metasurface through multiwave interactions

2020 ◽  
Vol 4 (6) ◽  
Author(s):  
Martin Lott ◽  
Philippe Roux ◽  
Léonard Seydoux ◽  
Benoit Tallon ◽  
Adrien Pelat ◽  
...  
Keyword(s):  
Localized Modes

scholarly journals All adapted topologies are equal

2020 ◽  
Vol 178 (3-4) ◽  
pp. 1125-1172
Author(s):  
Julio Backhoff-Veraguas ◽  
Daniel Bartl ◽  
Mathias Beiglböck ◽  
Manu Eder
Keyword(s):  
Stochastic Processes ◽  
Weak Topology ◽  
Equilibrium Problems ◽  
Diffusion Processes ◽  
Temporal Structure ◽  
Wasserstein Distance ◽  
Optimal Stopping Problems ◽  
Reward Functions ◽  
Nested Distance ◽  
The Stability

Abstract A number of researchers have introduced topological structures on the set of laws of stochastic processes. A unifying goal of these authors is to strengthen the usual weak topology in order to adequately capture the temporal structure of stochastic processes. Aldous defines an extended weak topology based on the weak convergence of prediction processes. In the economic literature, Hellwig introduced the information topology to study the stability of equilibrium problems. Bion–Nadal and Talay introduce a version of the Wasserstein distance between the laws of diffusion processes. Pflug and Pichler consider the nested distance (and the weak nested topology) to obtain continuity of stochastic multistage programming problems. These distances can be seen as a symmetrization of Lassalle’s causal transport problem, but there are also further natural ways to derive a topology from causal transport. Our main result is that all of these seemingly independent approaches define the same topology in finite discrete time. Moreover we show that this ‘weak adapted topology’ is characterized as the coarsest topology that guarantees continuity of optimal stopping problems for continuous bounded reward functions.

Compactness in the Weak Topology

1955 ◽  
Vol 28 (3) ◽  
pp. 125 ◽  
Author(s):  
John Wells Brace
Keyword(s):  
Weak Topology
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