Sentence examples for and thus e from inspiring English sources

The functional J : X → R is sequentially weakly lower semi-continuous, Φ : X → R is sequentially weakly continuous, and thus E is sequentially weakly lower semi-continuous.

(35) Hence E is the sum of 'an absolutely function' and 'a nonincreasing function', and thus, E is a continuous function except a countable set of points in which (29) holds.

Lemma 3.3 (1) The functional J : X → R is sequentially weakly lower semi-continuous, Φ : X → R is sequentially weakly continuous, and thus E is sequentially weakly lower semi-continuous.

The average number of slots required for a packet waiting for transmission in the j stage is (CWj+1)/2, and thus E i [Tdrop] can be expressed as: (18).

Thus u ∈ X{0} is a (weak) solution of (P) if and only if u is a critical point of E. (3) The functional J : X → R is sequentially weakly lower semi-continuous, Φ, Ψ: X → R are sequentially weakly continuous, and thus E is sequentially weakly lower semi-continuous.

Both the value for |u NO| and |v rel| (and thus E coll) are readily obtained from the analysis described above, provided that the calibration of the detector is accurately known, i.e., the conversion from pixel units to meter per second units must be accurately determined.

But battery prices, and thus E-bike prices, are coming down swiftly, as battery technology advances and competition in the E-bike manufacturing space continues.

High E-cadherin levels inhibit shedding of tumor cells from the primary tumor, and thus E-cadherin is considered a metastasis-suppressor [ 26, 61, 62, 63, 64].

+ ⋯ ] = e − U L + U L / 2 (5)and is thus e − U L / 2. A plot of surviving infectious particles (parent genomes producing at least some viable progeny) would be log-linear with slope − U, but the number of viable progeny from mutagenized parents would have slope −1.5 U.

Assuming that the NA is at the center of the ITO, this equation can be obtained by substituting the expressions for y and A into the expressions for t and w; thus, E b t b + t I 2 t b w + E I 0 t b w − E 0 t 0 + t I 2 t 0 w = 0 (5).

Nevertheless, genomic comparison by GISH and retrotransposon analysis found obvious differences between D- and E-genomes, and thus suspected E as the direct donor [ 28, 63].