Sentence examples for bound of the function from inspiring English sources

However, the bound of the function (mathcal {Q}(x)) only accepts positive arguments.

After we introduce two examples, we will prove that, under the same assumptions of Proposition 1.1, we have a Hyers-Ulam constant K in (3) equal to (frac{1}{mu}), where μ is a lower bound of the function (|q(t)|).

Now we estimate the bound of the function.

An adaptive state-feedback stabilization is investigated for a class of high-order stochastic nonlinear systems in which the upper bound of the function fi depends on the state xi+1 besides the states x1, …, xi and z.

Let (T > 0), and (H = K e^{ K 'T}a real positive which is an upper bound of the function (varphi(t) = |X|_{X_{t}}^{2} ) ((0 leq t leq T)).

So we approximate I pos with the exponential function, which is a convex upper bound of the indicator function and will make optimization easier.

Next, we use the lower bound of the resonance function to recover the derivative on the nonlinear term (upartial_{x} u).

We prove a sharp upper bound of the counting function N r) modulo o(rn) in terms of the counting function of the reference operator in the smallest ball around the black box.

Since the proposed objective function is not convex, we further derive a lower bound of the objective function to make it convex which is different from the upper bound in [14].

There are three key steps in the proof of Theorem 12: (i) represent the density function of the product Z n in multiple integral form, (ii) estimate the lower bound of the density function by truncating the two tails of this integral, and (iii) apply Krein's criterion for the Stieltjes case.

An uncertainty bound of the approximation function is also produced by the scheme.