Sentence examples for and satisfy the same from inspiring English sources

Suppose that and satisfy the same conditions as in Theorem 3.2.

(3.6) It is clear (1.1) and (3.3) are the same for (1 < x < infty) and satisfy the same condition (3.4).

For instance, on simple inspection, it is easy to convince oneself that the two LTSs depicted above have the same behavior, and satisfy the same PDL formulas.

Moreover, and satisfy the same relation: (A.20)The uniqueness of the solutions for the initial value problems implies that for, and hence.

where and It is easy to show that is continuous for all and satisfy the same condition (Hb) with possibly different constants if satisfies (Hb).

Then, in a neighborhood of ( λ 0, μ 0 ), the solution is unique and satisfies the same Hölder condition as in Corollary  4.2.

This paper is devoted to deducing some basic integral inequalities based on the β-difference operator, when β has one fixed point (s_{0}in I) and satisfies the same condition.

The authors further show that the Riesz transform ∇L−1/2 maps Hω,L(Rn) into the classical Orlicz–Hardy space Hω(Rn) for pω∈(nn+1,1] and the corresponding fractional integral L−γ for certain γ>0 maps Hω,L(Rn) continuously into H˜ω,L(Rn), where ˜ω is determined by ω and γ, and satisfies the same property as ω.

The noise reduction subsystems of the used hearing instruments were equivalent and thus satisfy the same requirements and design.

Let the linear mappings T and F satisfy the same conditions as in Lemma  4.2.

Our algorithms can construct n DNA words of shorter length (e.g., 2.1logn+6.28k) and can satisfy the same sets of constraints as the words constructed by the algorithms of Kao et al.. Furthermore, we extend these new algorithms to construct words that satisfy a larger set of constraints for which the algorithms of Kao et al.