Sentence examples for equivalence condition for from inspiring English sources

Next, we present an equivalence condition for singular tensors.

We obtain the equivalence conditions for an on-diagonal upper bound of heat kernels on self-similar measure energy spaces.

(Equivalence conditions).

Similarly, we can obtain other equivalence conditions.

Next, we give some equivalence conditions.

From a detailed reaction mechanism for n-alkanes covering n-octane to n-hexadecane with 2115 species and 8157 reactions, two skeletal mechanisms for n-decane generated using DRGEPSA, one covering a comprehensive range of temperature, pressure, and equivalence ratio conditions for autoignition and the other limited to high temperatures, are presented and validated.

It is not clear that the above equation is a sufficient condition for constructing equivalence classes.

Approximate equivalence for representations of C∗-algebras is shown to be determined by a trace condition, analogous to the trace condition for unitary equivalence of representations of finite groups.

So we have our necessary and sufficient condition for elementary equivalence, and a bit more besides.

(b) Let R i ∈ B ( X ), i = 1, 2, be Riesz operators such that R = R 1 ⊕ R 2 commutes with M C. A sufficient condition for the equivalence M C + R satisfies Wt ⟺ M 0 + R satisfies Wt is that M 0 is finitely polaroid.  .

Let R i ∈ B ( X ), i = 1, 2, be Riesz operators such that R = R 1 ⊕ R 2 commutes with M C. If σ a ( M 0 ) = σ a ( M 0 + R ), then a sufficient condition for the equivalence M C + R satisfies a - Wt ⟺ M 0 + R satisfies a-Wt is that M 0 is finitely a-polaroid.