Sentence examples for an invariant distribution from inspiring English sources

We study the possibility of factoring a covariant distribution on reductive Lie algebras as finite sum of products of an invariant distribution by a covariant polynomial.

D is an invariant distribution.

In the case of persistence, we prove that there exists an invariant distribution which is ergodic.

In the case of persistence, they proved that there exists an invariant distribution which is ergodic.

end{aligned}It is easy to verify that ({mathcal {D}}=mathrm {Span}{X_3,,X_4}) is an invariant distribution and ({mathcal {D}}^theta =mathrm {Span}{X_1,,X_2}) is a slant distribution of M with slant angle (theta =cos ^{-1}left( frac{3}{17}right) ) such that (X_5=xi =frac{partial }{partial z}) is tangent to M. Thus, M is a proper semi-slant submanifold of ({mathbb {R}^9}).

Suppose further that X converges weakly to an invariant distribution π as t → ∞.

The solutions were typically observed at a time long enough ("steady-state") for all the variables at each spatial point to reach an approximately invariant distribution.

As a result, there is a relatively invariant distribution of pattern occurrence that changes modestly with increasing population size.

The process has a unique invariant distribution which arises as the decomposing measure in a natural problem of harmonic analysis on U posed in Olshanski (2003) [44].

The result of a temperature invariant distribution of relaxation times observed previously in isothermal experiments allows a direct translation of M T, t) data into the variation of a characteristic relaxation time τ(T) or of a fictive temperature Tf(T) as a function of the actual temperature.

A submanifold M of M ̄ is said to be semi-invariant submanifold if there exist on M, a differentiable invariant distribution D such that its orthogonal complementary distribution D⊥ is anti-invariant, i.e., ϕD x ∈ T x M and ϕ D x ⊥ ⊂ T x ⊥ M for each x ∈ M. For a semi-invariant submanifold of an almost contact metric manifold M ̄, we have T M = D ⊕ D ⊥ ⊕ ⟨ ξ ⟩. (2.17).