content_image/301316.jpg content_image/301315.jpg content_image/301314.jpg content_image/301313.jpg content_image/301312.jpg content_image/301311.jpg content_image/301310.jpg
is valid. Moreover, since α is an η − translation number for u ( t ) , one can confirm that 

and 

On the other hand, we have 

<img src='content_image/301316.jpg'>

<img src='content_image/301315.jpg'>

<img src='content_image/301314.jpg'>

For any p ∈ Z , if s ∈ ( θ$_{p}$ + η, θ$_{p}$$_{+1}$ − η ) , then one can show by using Lemma 5 . 1 , ( iii ) that the number s + α belongs to the interval ( θ$_{p}$$_{+}$$_{q}$, θ$_{p}$$_{+}$$_{q}$$_{+1}$ ) so that 

since | ( κ + ζ$_{p}$$_{+}$$_{q}$ ) − ( κ + ζ$_{p}$ + α ) | = ∣ ζ q p − α ∣ < ν by Lemma 5.1, ( ii ) . Besides, the inequality ∞ θ$_{p}$$_{−}$$_{λ}$ + η ∞ 

is valid. Therefore, (5.13) yields 

It can be verified by means of (5.12) that 

<img src='content_image/301313.jpg'>

<img src='content_image/301312.jpg'>

<img src='content_image/301311.jpg'>

<img src='content_image/301310.jpg'>

