Sentence examples for the relation implies from inspiring English sources

Indeed, if, then the relation implies that.

First note that the relation implies that ∩ n F(T n ) is a singleton.

According to the theory, this relation implies that after cell 3jumps down, cell 2 jumps up and down, and then cell 3 does the same again before cell1 jumps up, as observed in the simulation.

Since the second relation implies the first one, we also consider the universal C⁎-algebra T⁎ϑT generated by two isometries u and v with the weaker relation uv= e2πiϑvu.

The above relation implies that the Mellin transform of the last integral is equal to the function e λ n s n, that is, e λ n s n = 1 π M { ∫ 0 ∞ e λ n r n cos ( n π 2 ) cos ( r ln ( t ) − λ n r n sin ( n π 2 ) ) d r ; s } = 1 π ∫ 0 ∞ t s − 1 ∫ 0 ∞ e λ n r n cos ( n π 2 ) cos ( r ln ( t ) − λ n r n sin ( n π 2 ) ) d r d t.

Note that the equivalence relation implies that the weighted sum-rate can be replaced with a optimization form with some additional auxiliary variables, see (14).

The first condition in (12) means that P m is dense enough in ℕ (every segment of ℕ of length m contains a point of P m ); the second relation implies that the set E = { m − d m : m ∈ N }, E ⊆ N (13). is infinite.

The curvilinearity of the P F relation implies that microvascular resistance does not remain constant during one cardiac cycle.

The symbolic relation implies an openness for exploring and naming the multiplicity that characterizes the subject-dimensions or subject positions [ 26].

The proportionality relation implies that all nodes have the same probability of being intruded when subjected to the same IAE for the same amount of time, even though an attacker could still choose to attack different nodes with different variations of effort.

Since and are linearly independent on, the above relation implies that by Hölder's inequality, which proves the first conclusion.