Sentence examples for i e for from inspiring English sources

Here, the subscript s denotes the particle species, and i, e, for ions and electrons, respectively.

Hence, further investigation is needed to derive an appropriate expression for I e for concrete/CFS composite beams.

(a) The union of these soft sets is the soft set G C, where g C ( e ) = ∪ i ∈ I ( f A ) i ( e ) for each e ∈ E. We write ⊔ i ∈ I ( F A ) i = G C.   (b) The intersection of these soft sets is the soft set H D, where h D ( e ) = ∩ i ∈ I ( f A ) i ( e ) for all e ∈ E. We write ⊓ i ∈ I ( F A ) i = H D.  .

When the observed signals in each frequency bin are centered and whitened (x ← x - E x) so that E x) = 0, then x ← Vx so that E xx H) = I, E for expectation, V is the whitening matrix), the demixing matrices W [f] become orthonormal, so the term ∑ f = 1 F log det W f becomes zero.

If either ( 1 − α i + β i ) 2 < 4 β i e − 2 ν i. or β i e ν i 4 + β i ( 1 − α i ) < 1, where ν i = β i α i e for i = 1, 2, then there exists n 0 ≥ 0 such that ( x n, y n ) ∈ ( 0, 1 ] 2 for all n ≥ n 0. Proof Assume that γ 1, δ 1 and the function K ( x n ) are defined as in the previous proof.

B E) is expected to vary smoothly as a function of energy and can be approximated as a polynomial function of the X-ray energy, E. A series of equations (eq 10) will be expressed, with different values of I i (E), for each incident energy used.

M = q I - E, for q I ≥ E 0, otherwise (4a4b).

This shows that when the resolution R is sufficiently large, the total number of neurons N is minimized when r i ≈ e for all i.

An operator A : E → E is called m-accretive if it is an accretive operator and the range R λA + I) = E for all λ > 0, where I is the identity of E. If A is an m-accretive operator then it is a demiclosed operator, i.e., if the sequence {x n } ⊂ D(A) satisfies x n ⇀ x and A(x n ) → f, then A x) = f[10, 11].

We split the interface ∂ Ω i into four open edges ℰ, and define a restriction operator I E 0 : V h ( ∂ Ω i ) → V h ( ∂ Ω i ) ( V h ( ∂ Ω i ) = V h ( Ω i ) | ∂ Ω i ) as: for any v ∈ V h ( ∂ Ω i ) I E 0 v = { v, on  E, 0, on  ∂ Ω i ∖ E. For the operator I E 0, we have the following result.

Also, no synergistic enhancement was observed with I + E for either TEAB or sucrose.