Sentence examples for and not identical from inspiring English sources

In the above example, ψ is not the identity mapping and not identical with φ, and (theta(t) neq0), for all (t in [0, infty) ).

Next we show that, given any non-negative and not identical to zero initial data, ((u_{0}(x), v_{0}(x))), ((u x,t),v x,t))rightarrow tilde{u}, 0)) as (trightarrow+infty).

One can show that this can be described in an inconsistent theory in which the two boundaries are both identical and not identical, and it can be further argued that this is the most natural description of the practice.

It is in some sense a plurality and not identical with itself, and it can be broken up either in fact or at least in the understanding" (P 18).

Conversely, predicates such as "are identical", "is identical with itself", "is both identical and not identical with itself", etc., which are resolutely treated as logical in recent logic, are presumably categorematic.

The second one lies in that in JET mode, the ratio of the diagonal elements of D i is fixed; nevertheless, in BD-JET mode, the ratio of the diagonal elements of T i, as mentioned in the next remark, is block-equal and not identical between blocks in general.

All reactions rules are solutions of system of Eq. (2) and are not identical (see text and Fig. 2 for definition of identical rules).

Brothers certainly, but not necessarily twins, and definitely not identical.

A particular good by definition shares in and is not identical with goodness itself.

The first two are closely connected, since counting objects involves questions about which objects are and are not identical.

The mechanisms underlying this reciprocal cross-desensitization are complex, and likely not identical.