Sentence examples for be a modulus and from inspiring English sources

Let f be a modulus and (beta geqalpha>0).

Let f be a modulus and let (0 < delta<1).

Let f be a modulus and α be a positive real number.

Let ((M,rho)) be a metric space, f be a modulus and (theta= (k_{r})) be a lacunary sequence.

To show that the strict inclusion may occur, let f be a modulus and consider the sequence (x =(x_{k})) defined by x_{k}= textstylebegin{cases} 1 &mbox{if }k = n^{2}, 0 &mbox{if }k neq n^{2}, end{cases}displaystyle quad n = 1,2,3, ldots.

Let be a modulus function and the sequence be bounded; then (2.2). and the inclusions are strict.

Proof (a) Let f be a modulus function, and let ε be a positive number.

Let f be a modulus function and α̃ be a positive real number.

Theorem 3.3 Let f be a modulus function and ( X, g ) be a paranormed space.

[10, 25] Let f be a modulus function and let 0 < δ <1.

(b) If the φ-function φ ( u ) and the matrix A are given, and if the modulus function f is bounded, then S θ 0 ( A, φ ) ⊂ N θ 0 ( A, φ, f, p ). Proof (a) Let f be a modulus function and let ε be a positive numbers.