Sentence examples for then well defined from inspiring English sources

We experimentally put in evidence the appearance of photonic band gaps for N higher than 2, which are then well defined for N equal to 4, for the two structures.

end{aligned} (23)The quantity (R_{gamma, lambda }(Omega, x_0)) is then well defined and will be called the internal mass of (Omega ) at (x_0).

The coherence measure of this composite allele B x is then well defined by C x, and degrees of reproductive isolation from or coherence with other alleles or groups of alleles can be analyzed.

Given a potential ( V in L^infty _{mathrm{comp} } ( {mathbb {R}}; mathbb {C}) ) we further assume that begin{aligned} Gamma cap {mathbb {R}}supset [ - L, L ], mathrm{supp},V subset ( - L, L ). end{aligned} (2.68)The potential V is then a well defined function on (Gamma ), so that putting begin{aligned} P_{V, Gamma } := -partial _{z,Gamma }^2 + V z),, end{aligned} (2.69 makes sense.

To avoid this phenomenon, an ant stochastic decision based particle filter is proposed to encapsulate model switching information through dividing probabilistically particles into two model operations, and then a well defined re-sampling scheme is introduced to gain a better overlap with the true density function.

then, is well defined.

Then is well defined and the following are equivalent.

Moreover, if, then is well defined by (II).

for all Then is well defined and the following are equivalent.

then is well defined, takes values in, satisfies for all (for is smaller than any associated to ), and also satisfies (2.1), with replaced by, for all.

Then is well defined and the following hold: (1)   is single-valued; (2)   is firmly nonexpansive, that is, for any, (2.14).