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Generalized to stochastic versions (stochastic transitivity), the study of transitivity finds applications of in decision theory, psychometrics and utility models. [19] A quasitransitive relation is another generalization; [5] it is required to be transitive only on its non-symmetric part. Such relations are used in social choice theory or ...
If a group G acts on a space V, then a surface S ⊂ V is a surface of transitivity if S is invariant under G (i.e., ∀g ∈ G, ∀s ∈ S: gs ∈ S) and for any two points s 1, s 2 ∈ S there is a g ∈ G such that gs 1 = s 2. By definition of the Lorentz group, it preserves the quadratic form
In quantum mechanics, the Schrödinger equation describes how a system changes with time. It does this by relating changes in the state of the system to the energy in the system (given by an operator called the Hamiltonian). Therefore, once the Hamiltonian is known, the time dynamics are in principle known.
Transitivity (grammar), a property regarding whether a lexical item denotes a transitive object; Transitive verb, a verb which takes an object; Transitive case, a grammatical case to mark arguments of a transitive verb
A change of basis is sometimes called a change of coordinates, although it excludes many coordinate transformations. For applications in physics and specially in mechanics, a change of basis often involves the transformation of an orthonormal basis, understood as a rotation in physical space, thus excluding translations. This article deals ...
In introductory physics, momentum is usually defined as mass times velocity. However, there is a more fundamental way to define momentum, in terms of translation operators. This is more specifically called canonical momentum , and it is usually but not always equal to mass times velocity.
The mathematical definition of ergodicity aims to capture ordinary every-day ideas about randomness.This includes ideas about systems that move in such a way as to (eventually) fill up all of space, such as diffusion and Brownian motion, as well as common-sense notions of mixing, such as mixing paints, drinks, cooking ingredients, industrial process mixing, smoke in a smoke-filled room, the ...
Transitivity: if < and < then <. A transitive relation is asymmetric if and only if it is irreflexive. [3] So the definition is the same if it omits either irreflexivity or asymmetry (but not both). A strict partial order is also known as an asymmetric strict preorder.