Sentence examples for i a k from inspiring English sources

We have that if i(A, K ∩ Ω, K) ≠0, then A has a fixed point in K ∩ Ω.

She has already written "The Six Wives of Henry VIII" (Anne was the second); "Henry VIII: The King and His Court" (Anne played an active role in court intrigue); "Children of Henry VIII" (Anne bore him one, a daughter); and "The Life of Elizabeth I" (that daughter grew up to be Elizabeth I, a k a the Virgin Queen).

Thus, we have the following conclusions: (i) If ∥ y ∥ ≤ ∥ A y ∥ for y ∈ ∂ K r, then i ( A, K r, K ) = 0.   (ii) If ∥ y ∥ ≥ ∥ A y ∥ for y ∈ ∂ K r, then i ( A, K r, K ) = 1.  .

As for the average power of the interference-plus-noise term, we have I k, a k = σ 2 E ∥ h k, a k ∥ 2 + ∑ i ≠ k p i tr E h i, a k h i, a k H h k, a k h k, a k H = σ 2 tr ( R k, a k + ∑ i ≠ k p i tr R i, a k R k, a k , (4).

If A u ≠ u for any u ∈ K ∩ ∂ Ω, then the fixed point index i ( A, K ∩ Ω, K ) has a definition.

This means that A satisfies the condition of Lemma 2.5 in K ∩ ∂ Ω 2. By Lemma 2.5, i ( A, K ∩ Ω 2, K ) = 0. (23).

"Yes," Szczerbiak said, straight-faced, "and I've tried for years to have my father change the spelling of our name to 'S-e-r-b-i-a-k,' but I haven't succeeded".

The activity of ADAMTS-4 was monitored using the QF peptide substrate carboxyfluorescein-A-E↓L-N-G-R-P-I-S-I-A-K N, N, N′, N′-tetramethyl-6-carboxyrhodamine [Fam-AE↓LQGRPISIAK-Tamra (custom synthesized by Bachem) at a final concentration of 0.5 μM with an excitation wavelength of 485 nm and an emission wavelength of 538 nm (495 nm cut-off) [ 15].

A d-th degree WD kernel of two sequences, a and b, of length L is defined as (1) k (a, b ) = ∑ k = 1 d β k ∑ i = 1 L - k + 1 I [ a k (i ) = b k (i ) ], where β k are weights for different k-mers and I is an indicator function such that it is 1 when the condition inside the bracket is true and 0 otherwise.

Proof Since A is an irreducible M-matrix and A − 1 is a doubly stochastic matrix by Lemma 2.4, we have a i i = ∑ k ≠ i | a i k | + 1 = ∑ k ≠ i | a k i | + 1, i ∈ N. Without loss of generality, for i ≠ j, assume that a i i β i i − T i ∑ k ≠ i | a k i | β i i ≤ a j j β j j − T j ∑ k ≠ j | a k j | β j j. (2.5).

More precisely, a one-dimensional arithmetic CNN is realized as the form d d t x i ( t ) = − x i ( t ) + z i ¯ + ∑ k ∈ N i ¯ a k ; i ¯ f ( x i ⋅ ℓ k ( t ) ), i ∈ N, (27).