Sentence examples for congruence properties from inspiring English sources

We prove that Φ is a modified exponential, and deduce some remarkable congruence properties for the set of all numbers C, for fixed N. We prove a concise upper bound for C, which describes the asymptotic behaviour of the up down function C in the limit C⪡(N+1)!

The weakest requirement imposed on a necessity-like modal operator $\Box$ in systems of classical modal logic is the congruence property: \[\mathord{\vdash A \leftrightarrow B} \slashrel \mathord{\vdash \Box A \leftrightarrow \Box B}\] ("if $A \leftrightarrow B$ is provable, then so is $\Box A \leftrightarrow \Box B$").

(1.1) Sun studied congruence and divisibility properties of this kind of numbers in [1, 2] and posed the following conjecture.

Finally, we show that bisimilarity is a congruence, and this property holds also for the concurrent version of the π-calculus.

We show that bisimilarity for this semantics is a congruence, and this property holds also for the concurrent version of the π-calculus.

Then the perspective function (mathcal{P}_{F}) satisfies the property of congruence invariance: begin{aligned} mathcal{P}_{F}bigl(W^T_{1}W,ldots,W^T_{k+1} Wbigr)= W^mathcal{P}_{F}(T_{1},ldots, T_{k+1} W end{aligned} (4.1) for any invertible operator W on (mathcal{H}).

Your statement should read "XY = XY" or "Angle A = angle A" and the reason would be "Reflexive property of congruence".

Summing up, none of these three equivalences satisfies both properties: being decidable and a congruence.

We reduce the complexity of the encoding/decoding architecture of the optical line terminal reduced by exploiting arrayed waveguide gratings (AWGs) and the properties of the extended quadratic congruence codes (EQC codes).

Spectral and temporal modulation properties showed a relatively high congruence between more strongly connected neurons.

One of the applications of these properties yields general classes of congruences for generalized -Bernoulli polynomials, which are -extensions of the classes for generalized Bernoulli numbers and polynomials given by Fox (2000), Gunaratne (1995), and Young (1999, 2001).