Sentence examples for bound of the norm from inspiring English sources

We present a method for computing the upper bound and the lower bound of the norm of the sub-band operator based on the theory of circular matrix.

Instead of estimating the bounds in (1.2), we can try to obtain the upper bound and the lower bound of the norm of the sub-band operator.

A concept of the sub-band operator of multi-band wavelets is introduced, the theory of d-circular matrices is developed and the upper bound and the lower bound of the norm of the sub-band operator are obtained.

Rassias [3] attempted to weaken the condition for the bound of the norm of the Cauchy difference as follows: (1.1).

In particular, Rassias [4] relaxed the condition for the bound of the norm of Cauchy difference (f(x+y -f(x+y -f)).

In particular, Rassias [4] improved the condition for the bound of the norm of the Cauchy difference (f(x+y -f(x+y -f)).

Moreover, we will prove that a lower bound of the Euclidean norm, and indeed of any p-norm, of the design error for planar RRRR function-generating linkages exists and is attained with continuous approximate synthesis.

The error between the approximate and exact solutions is given, and an upper bound on the norm of the error in terms of a measure of the rate of change of the system matrix and the norm of the exact solution of the system is derived.

A sharp relation is obtained as a lower bound of the squared norm of second fundamental form in terms of the warping function and the slant angle.

In this paper we prove that the bound on the norm of the dyadic paraproduct in the weighted Lebesgue space L2(w) depends linearly on the Ad2 characteristic of the weight w using Bellman function techniques and extrapolate this result to the Lp(w) case.

Furthermore, using an Implicit function theorem, we get a bound on the norm of this gradient.