Sentence examples for be any fixed from inspiring English sources

Let and be any fixed points.

Let s be any fixed nonnegative integer and v be any fixed vector with |v| < δ.

Let R be any fixed positive constant with (R<1).

Let (H_{1}) be any fixed self-adjoint subspace extension of (H_{0}) given by (2.12).

Let the real number p with β > p > 1 and p 2 > β be any fixed.

Let d be any positive nonsquare integer, and let N be any fixed integer.

where M is any fixed positive constant.

where p is any fixed positive number.

Suppose that (H_{1}) is any fixed self-adjoint subspace extension of (H_{0}).

Define a function G : X → P by G x) = p(x n, x), where n is any fixed positive integer.

Using Uchiyama's method and Furuta's Kantorovich-type inequality, we will point out that if and only if holds for any, where is any fixed positive number.