If a i is not contained in a ring, no ring type is set.
If W u ( x i ) is not contained in W s ( x i + 1 ) then the heteroclinic cycle Σ cannot be asymptotically stable.
They might worry: 'Oh, I'm not containing my unhappiness and my personal difficulties – this is messing my child up.'" There's a lot written about how teenagers and young adults pull away from their parents, she says.
The fundamental problem with the relationship between a real ground and its consequent, therefore, is that the consequent is not identical with either the ground or a part of this concept i.e., it is not "contained in [the ground] by the analysis of concepts".
In terms of algebraic varieties this is equivalent to saying that the variety ∨ i = 1 h P V T i M is not contained in ∨ i = 1 h P V T i ′ M and vice versa.
Equation (14) means that our task is reduced to solving some countable system of linear algebraic equations; since, for every i which is not contained in the sample s from Eq. (15), we have α i, k = 0, the system of equations (14) coincides with the system (16) below.
While Algorithm 2 starts with the global index set I and reduces it sequentially as long as hypotheses are rejected, Algorithm 1 removes, for each J⊆ I, consecutively all indices from I that are not contained in J until the set J is obtained.
To allow for a fair scoring, only common nodes from silver standard networks and prediction lists were taken into consideration, i.e. if edge (i, j) is in the prediction list but node i or j is not contained in the silver standard, then the edge is not scored.
The point is that probabilistic reasoning, in quantum mechanics or in other disciplines, does not allow one to make inferences about matters which are outside the scope of discussion, i.e., which are not contained in the event algebra.
Given a database DB of workflow paths (task sequences), the problem of mining sequential patterns in workflows is to find the maximal paths (i.e., paths that are not contained in any other path) among all paths that have a minimum support.
