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George Lakoff and Mark Turner originated the idea under the name invariance hypothesis, later revising and renaming it. Lakoff (1993: 215) defines the invariance principle as: "Metaphorical mappings preserve the cognitive topology (that is, the image-schema structure) of the source domain, in a way consistent with the inherent structure of the ...
Springer, T. A. (1977), Invariant Theory, New York: Springer, ISBN 0-387-08242-5 An older but still useful survey. Sturmfels, Bernd (1993), Algorithms in Invariant Theory, New York: Springer, ISBN 0-387-82445-6 A beautiful introduction to the theory of invariants of finite groups and techniques for computing them using Gröbner bases.
Gibson was interested in the structures of the ambient optic array that are invariant, or structures that remain static regardless of the actions of the observer. For example, Gibson noted that the upper hemisphere of the array (the sky) tends to be much less structured and brighter than the lower hemisphere (the cluttered earth).
An ordinary invariant means a relative invariant, in other words something transforming according to a character of a group, as opposed to an absolute invariant. osculant Main article: osculant
In algebra, the first and second fundamental theorems of invariant theory concern the generators and relations of the ring of invariants in the ring of polynomial functions for classical groups (roughly, the first concerns the generators and the second the relations). [1] The theorems are among the most important results of invariant theory.
Predicate transformer semantics were introduced by Edsger Dijkstra in his seminal paper "Guarded commands, nondeterminacy and formal derivation of programs".They define the semantics of an imperative programming paradigm by assigning to each statement in this language a corresponding predicate transformer: a total function between two predicates on the state space of the statement.
For example, measurement invariance can be used to study whether a given measure is interpreted in a conceptually similar manner by respondents representing different genders or cultural backgrounds. Violations of measurement invariance may preclude meaningful interpretation of measurement data.
(The expression "a mathematical function of person and item parameters" is analogous to Lewin's equation, B = f(P, E), which asserts that behavior is a function of the person in their environment.) The person parameter is construed as (usually) a single latent trait or dimension. Examples include general intelligence or