Sentence examples for a b p from inspiring English sources

Since { a k } k = 1 ∞ is an A B p t -zero set, there exists f ∈ A B p t such that f ( a k ) = 0 nowhere else.

The results of model (2) show five DMUs, A, B, P, C and D are efficient.

Proof Explicitly, we have to prove that A ( a, b ) P ( a, b ) < P ( a, b ) (5.6).

The Ea,b p-generalized trigonometric functions are defined as cos ( a,b p-generalizeds ϕ ) / a N a, b ; p and sin ( a, b ; p ) = ( sin ϕ ) / b N a, b ; p , ϕ ∈ [ 0, 2 π ). for positrigonometricand where Na,b;p=(|(cosϕ)/a| p +|(sinϕ)/b| p )1/p.

We remark here if the function p : I → ( 0, ∞ ) is twice continuously differentiable, then inequality (1.5) can be rewritten as follows: G p [ a, b ] ≜ ∫ a b p ∫ a b p ″ − ( ∫ a b p ′ ) 2 ⩽ 0, ∀ a, b ∈ I. (1.6).

Proof Let G p [ a, b ] ≜ ∫ a b p ∫ a b p ″ − ( ∫ a b p ′ ) 2. We just need to show that G p [ a, b ] ⩽ 0, ∀ a, b ∈.

According to the A-B-P maximum principle (see [20]), we have that (4.11).

The six surface loops (A-, B-, P-, S, T- and U-loops) are indicated.

The five surface loops (A-, B-, P-, S-, and T-loops) and U-loop are shown by rectangular frames.

The A-, B-, P-, S-, T- and U-loop regions (surface model) are indicated by different colors.

Applying the A-B-P maximum principle (see [20]), we have that in, which contradicts the definition of.