Sentence examples for smallest fixed point from inspiring English sources

The above proof shows that the operator G = (G1, G2) defined by (6.8) satisfies the hypotheses of Lemma 2.1, whence G has the smallest fixed point x* = (u*, v*) and a greatest fixed point x* = (u*, v*).

Obviously, (sup W1, sup W2) is the supremum of W in P. Similarly one can show that each inversely well-ordered chain of the range of G has the infimum in P. The above proof shows that the operator G = (G1, G2) defined by (5.7) satisfies the hypotheses of Lemma 2.1, and therefore G has the smallest fixed point x* = (u*,v*) and the greatest fixed point x* = (u*, v*).

The problem of computing the smallest fixed point of an order-preserving map arises in the study of zero-sum positive stochastic games.

In fact, it is the smallest fixed point of f.

By transfinite induction, we have e ∗ ≤ e, concluding that e ∗ is the smallest fixed point.

By Theorem 1, there is a smallest fixed point; say e ∗ ∈ ε ( f ).

Recalling the arguments from Theorems 1 and 2, we know that the smallest fixed points e t ′ ∗ and e t ″ ∗ of the games Γ t ′ and Γ t ″ can be obtained by using g t ′ and g t ″ respectively.

Depending on our choice of large or small ECS the fixed point curve implies the presence/absence of a recovery threshold that defines the potassium clearance demand.

Then she moves the phone in a small circle around the fixed point for about 10 seconds.

Let E = ( x 1 ∗, x 2 ∗, x 3 ∗ ) be an equilibrium point of system (3.1) and x i = x i ∗ + η i, where η i is a small disturbance from a fixed point.

But when the coefficients of system satisfy the condition (cu_{ast}>1), for a small delay the positive fixed point of system is stable, the number of red blood cells reaches an equilibrium.