The stochastic Galerkin method involves representation of the solution through generalized polynomial chaos expansion and projection of the governing equations onto stochastic basis functions, resulting in an extended system of equations.
The proof, in J.M. Greene (preprint) [6], draws on most of the theorems in this paper together with a very different technique involving representations of noncommutative quadratic functions.
Memory may involve representations of the past, most modern representationists argue, without involving awareness of those representations themselves.
In addition, constructing mental models of some scientific phenomena may involve representation of the configuration of multiple components, the spatial relations between components, or information about the movements or causal interactions among the components (Gentner & Stevens, 1983; Hegarty & Just, 1993; Mayer, 1989).
In particular, the issue of how the content of memory representations is determined is barely mentioned: and the question of how memory traces could provide the right causal connections between past and present if they are not static and permanent inner items is postponed to section 3. Again, the key question here is whether memory does involve representation of the past.
ACC has been associated with alert states, self awareness and pain processing [12], whereas mPFC and PCC activations are frequently observed in conditions involving representation of the self and self values [13].
Dennett's chess program certainly involves explicit representations of the chess board, the pieces, etc. and perhaps some of the rules.
This involves mental representations of our goals for the future, even if it's the future in just a few seconds".
Both DNA fingerprints and brain images prominently involve visual representations of biological facts, but scientific representations can take many other forms, not all pictorial or graphic.
To date, most UV system designs for air treatment have been based on empirical approaches, often involving crude representations of dose delivery and dose response behavior.
